Spatial Distribution of Fast Ion Loss Detectors in the ASDEX Upgrade Tokamak

UNIVERSITY OF SEVILLE DOCTORAL THESIS Spatial Distribution of Fast Ion Loss Detectors in the ASDEX Upgrade Tokamak Author: Javier GONZALEZ MARTIN Supervisors: Prof. Dr. Jaime DOMINGUEZ ABASCAL Prof. Dr. Manuel GARCIA MUÑOZ A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mechanical Engineering and Manufacturing April, 2021 iii UNIVERSITY OF SEVILLE Abstract Higher Technical School of Engineering Department of Mechanical Engineering and Manufacturing Doctor of Philosophy Spatial Distribution of Fast Ion Loss Detectors in the ASDEX Upgrade Tokamak by Javier GONZALEZ MARTIN To ensure heating efficiency and device integrity in future fusion reactors, suprathermal (fast) ions need to be confined for a sufficient time so that their energy is transferred to the bulk plasma via Coulomb collisions. In order to understand the mechanisms responsible for the loss of fast-ion confinement, fast-ion loss detectors (FILD) provide velocity-space measurements at the reactor wall. These measurements are nevertheless spatially localized and do not provide enough information to characterize the spatial distribution of the losses required to fully understand (and therefore mitigate) the loss mechanism induced by MHD instabilities and externally applied 3D magnetic perturbations. In order to characterize the spatial distribution of the fast-ion losses, in the frame of this thesis, the FILD suite of the ASDEX Upgrade (AUG) tokamak is upgraded with two new fast-ion loss detectors, being both located below the tokamak midplane. One of these diagnostics, labelled FILD5, is installed right above the lower divertor, between two saddle coils. The other new detector, known as FILD4, is an in-situ probe consisting of an in-vessel coil that, when externally energized, creates a magnetic dipole that tries to align with the existing tokamak toroidal magnetic field, generating the torque required to move the probe head back an forth. The equations governing the coil dynamics and motion of the probe head are derived and linearized to optimize the coil parameters for fast-retraction. A multibody model is applied to estimate the induced stresses on the more sensitive components and the effect of friction on the diagnostic trajectory. The mechanical stresses induced by thermal expansion on the probe head under convective heat loads is analyzed to optimize the measurement cycle. A programmable power supply is employed to energize the magnetic coil, enabling real-time retraction when overheating is detected on the probe head. These new detectors enabled simultaneous measurements of multiple FILDs in quiescent plasmas and in the presence of MHD instabilities such as toroidicity induced Alfvén eigenmodes (TAEs) and magnetic islands. Moreover, the insertion of iv the magnetically-driven FILD4 is rapidly scanned during plasma discharges, enabling unprecedented radially-resolved velocity-space measurements of escaping ions generated by ICRH and NBI. The light-ion beam probe technique is employed to these scans to radially resolve the internal structure of MHD instabilities. The impact of the poloidal spectrum of the applied 3D magnetic perturbations on fast-ion losses and TAEs amplitude is investigated experimentally. The hybrid kinetic-MHD MEGA code is employed to model these experiments. The plasma response to the externally applied 3D perturbations is modelled using the MEGA code for the first time. The observed TAEs are reproduced in both axisymetric and 3D equilibriums, finding a phase-space overlap of the TAE fast-ion drive and the edge resonant transport layer induced by the 3D fields. v Contents Abstract iii 1 Introduction 1 1.1 Introduction and objectives ......................... 1 1.2 Basics of tokamak reactors .......................... 2 1.2.1 Thermonuclear fusion ........................ 2 1.2.2 What is a plasma? .......................... 4 1.2.3 Tokamaks: ITER and AUG ..................... 5 1.2.4 Fast-ions in tokamak plasmas .................... 10 1.3 Structure of this thesis ............................ 13 2 Theoretical Background 15 2.1 Fast-ion orbits in tokamaks ......................... 15 2.1.1 Motion in homogeneous magnetic field .............. 15 2.1.2 Orbit drifts ............................... 17 2.1.3 Adiabatic invariants ......................... 20 2.1.4 Orbit topology ............................ 21 2.2 MHD waves in tokamaks .......................... 22 2.2.1 Fluid description of the plasma ................... 22 2.2.2 Wave dispersion relations ...................... 24 2.2.3 Alfvén Eigenmodes .......................... 26 2.2.4 Other instabilities ........................... 28 2.3 Heat loads on plasma facing components ................. 30 2.4 Finite elements analysis ........................... 31 3 Scintillator-based FILDs in AUG 33 3.1 Working principle ............................... 33 3.1.1 Brief history of fast-ion loss diagnostics .............. 33 3.1.2 Main components of AUG FILD heads .............. 34 3.1.3 Types of light acquisition systems ................. 35 3.1.4 Strike map calculation ........................ 35 3.2 Importance of simultaneous FILD measurements ............. 36 3.3 FILD5 set up .................................. 40 3.3.1 Detector head design and location ................. 40 3.3.2 Reciprocating system ......................... 41 3.3.3 Optics relay and light acquisition systems ............. 42 vi 3.3.4 First measurements .......................... 44 3.4 FILD4 set up .................................. 45 3.4.1 Detector head design and location ................. 46 3.4.2 Reciprocating system ......................... 49 3.4.3 Optics relay and light acquisition systems ............. 51 3.4.4 First measurements .......................... 53 4 Smart FILD 57 4.1 Magnetically-driven actuator ........................ 57 4.1.1 Analytical characterization ..................... 57 4.1.2 Selecting number of windings ................... 59 4.1.3 Multibody modelling ........................ 60 4.2 Thermomechanical assessment ....................... 64 4.2.1 Estimated heat load on the probe head .............. 64 4.2.2 Simulated temperature evolution .................. 65 4.2.3 Induced stress ............................. 68 4.3 Real-time control ............................... 70 4.3.1 Energizing the in-vessel coil ..................... 70 4.3.2 Video real-time protection of FILDs ................ 73 4.3.3 Expanding the FILD operational limit ............... 75 5 Experimental Results 77 5.1 Validation of the magnetically-driven actuator .............. 77 5.2 Simultaneous measurements of multiple FILDs .............. 79 5.3 Radially resolved fast-ion loss measurements ............... 80 5.3.1 (E, Pitch, R) measurements of fast-ion losses ........... 81 5.3.2 Radial measurements of NBI and ICRH ions ........... 83 5.3.3 Radial profiles from different NBI sources ............. 85 5.3.4 Radially-resolved perturbations .................. 86 5.4 FILD measurements during TAE control experiments using externally applied 3D fields ............................... 91 5.4.1 Saddle coils in AUG ......................... 92 5.4.2 TAE control using n=2 fields .................... 92 5.4.3 TAE control using n=4 fields .................... 94 5.4.4 TAE control using mixed spectrum n=2+4 ............. 98 6 Modelling 101 6.1 The hybrid kinetic-MHD model of the MEGA code ...........102 6.2 Simulation set up ...............................104 6.2.1 Equilibrium, kinetic profiles and fast-ion population ......104 6.2.2 Convergence on discretization and diffusive parameters . . . . 105 6.2.3 Imposed 3D fields ..........................106 6.3 Results .....................................107 vii 6.3.1 Plasma response to externally applied 3D fields .........107 6.3.2 TAEs destabilized in axisymetric and 3D equilibriums . . . . . 110 6.3.3 TAE-MPs interaction via fast-ion phase-space ..........115 7 Summary and conclusions 119 7.1 Outlook .....................................120 A Manufacturing Drawings 121 B Publication Record 133 Acknowledgements 135 List of Figures 144 Bibliography 145 1 Chapter 1 Introduction 1.1 Introduction and objectives The global energy consumption has been dramatically increasing since the Industrial Revolution. Up to now, fossil fuels and nuclear fission were enough to satisfy this demand, however, it is well-known that their supplies are scarce to satisfy the energy needs in the near future. On the other hand, renewable sources of energy have made a significant progress during the last decades. Nonetheless, their somewhat inefficient energy storage, dependence on weather and rather low power density still impedes self-sufficiently meeting the world energy needs and securing the energy supply for the next generations. In that circumstance, thermonuclear fusion is considered as a promising source of virtually unlimited energy. It is based on the nuclear reactions of light ions that, having sufficient energy to overcome the Coulomb potential barrier, collide, merging into a heavier ion and releasing a large amount of energy. This thesis is framed within the context of tokamak1fusion reactors, which are torus shaped chambers where ions are confined by means of magnetic fields. In tokamaks, the so-called fast (energetic) ions have energies well above the rest of the fusion fuel. These fast-ions are born during fusion reactions or externally generated to heat up the fusion fuel. The success of tokamaks for energy production still relies on our ability to confine these fast-ions so they can thermalize transferring their energy to the plasma fuel via Coulomb collisions. Different diagnostics techniques are combined with modelling to investigate (and mitigate) the mechanisms responsible of fast-ion losses. One of them, the fast-ion loss detector (FILD), is an outstanding diagnostic used to provide accurate velocityspace measurements2of escaping ions at very high temporal resolution. Despite its unique capabilities, the fact that FILD provides local measurements, requires multiple probes to obtain the spatial measurements of fast-ion losses in the presence of magneto-hydrodynamic (MHD)3fluctuations that are needed to understand the loss mechanisms and optimise plasma conditions. 1See section 1.2 for more details. 2The velocity-space is the fast-ion distribution at a given spatial location. It can be expressed as a function of particle energy (E) and pitch angle (α=arccos vk/v). 3See section 2.2 for more details. 8Chapter 1. Introduction FIGURE 1.3: Poloidal plot of a tokamak magnetic equilibrium. Extracted from [4]. along magnetic field lines on a gyromotion governed by Lorentz law, while they are transported across flux surfaces only by collisions. As a result, the flux surfaces have also uniform temperatures and densities. Each magnetic flux surface can be labelled with the poloidal magnetic flux lying within each magnetic surface (ψ). Together with φand θ,ψis the third coordinate needed to describe the system. Sometimes it is more intuitive to define an alternative radial coordinate (ρpol) ranging from 0 to 1 and defined as ρpol =ψ−ψa ψs−ψa1 2, (1.10) where ψsand ψaare the poloidal magnetic flux at the separatrix and magnetic axis respectively. As described on [5], in equilibrium state, each magnetic flux surface has the same field line helicity (q), q(ρpol) = 1 2πZ2π 0rBφ RBθdθ. (1.11) Since the field line helicity plays an important role on determining equilibrium stability, it can is also called safety factor. One can interpret the definition in 1.11 as the number of toroidal turns that a field line needs to close on itself, leading to a more 1.2. Basics of tokamak reactors 9 intuitive definition of q, q(ρpol) = ∆φ 2π. (1.12) To reach ignition in a tokamak and maintain it, the plasma needs to be heated up to several keV, which can be done with different methods5: •Ohmic heating (OH): The current circulating in a plasma (with a Spitzer resistivity ηs) produces heat by the Joule effect. As mentioned on section 1.2.4 this method is not efficient at large electron temperatures and can only produce a limited temperature increase, not sufficient to reach the ignition point. •αparticle heating: The D-T reaction produces 4He ions (so called αparticles) with 3.5 MeV of energy that can be transferred to the rest of the plasma via Coulomb collisions if they are confined for a sufficient time. This method is crucial to maintain ignition but cannot be used to ignite the plasma. •Radio frequency (RF) heating: Electromagnetic waves are launched into the plasma, which resonate with the gyromotion of electrons or ions. The different gyro-frequencies imply different technologies: the ion cyclotron resonance heating (IRCH) requires in-vessel antennas, while the electron cyclotron resonance heating (ECRH) is generated by gyrotrons located outside the torus hall and injected into the plasma using wave guides and mirrors. •Neutral Beam Injection (NBI): Electric fields accelerate ions that are neutralized before being injected into the plasma. These high energy neutrals penetrate the plasma and are eventually ionized by charge exchange and electron impact excitation. These energetic ions thermalize transferring their energy to the rest of the plasma. ITER and AUG The largest tokamak project that is being build is called ITER. It is located in Provence (France) and belongs to a consortium comprised of United States, Europe, China, India, Russia, South Korea and Japan. It is expected to demonstrate the scientific and technological feasibility of a fusion reactor, reaching ignition and producing ten times more power than the employed in externally heating the plasma. Its large size to maximize the particle confinement time, low-temperature superconductors to produce a large magnetic field and the high energy neutron flux produced by D-T reactions implies an unprecedented degree of complexity. In order to design ITER and predict its behaviour, many other smaller experimental reactors were and are run around the world. These devices, with lower magnetic field and lower neutron flux are used to develop and test the different 5RF, NBI and αparticle heating are a source of fast-ions, whose implications will be discussed in section 1.2.3. 10 Chapter 1. Introduction models and theories on which ITER is based. Normally, these tokamaks consist of deuterium plasmas to avoid (radioactive) tritium handling and high neutron flux. The ASDEX Upgrade tokamak (AUG) is a remarkable experimental device, which has been operational since 1991 at the Max-Planck Institute of Plasmaphysics in Garching (Germany). Its predecessor, the AxiSymetric Divertor EXperiment (ASDEX) discovered the H-mode [6] in 1982. AUG is a tokamak of R0=1.65 m and BT=2.8 T equipped with a flexible heating system and a complete suit of diagnostics. Its medium size enables easy development of novel diagnostic techniques and plasma scenarios while using ITER-relevant parameters. Typical values of ITER and AUG are compared in table 1.2. Parameter ITER AUG units Major radius (R0) 6.2 1.65 m Minor radius (a) 2.0 0.5 m Toroidal magnetic field (BT)5.3 2.8 T Maximum heating power (Pheat) 50 30 MW Plasma current (Ip) 15.0 1.2 MA Gas D, T D, H, He TABLE 1.2: Comparison of typical ITER and AUG parameters 1.2.4 Fast-ions in tokamak plasmas In a tokamak plasma, one can distinguish between ions at thermal temperatures and the so called fast-ions, with energies much larger than the thermal plasma. These fast-ions have longer collisional times (due to their higher temperature) and therefore larger mean path. Consequently, the fast-ion distribution is often considered collisionless and requires special treatment. The fast-ions are produced by different mechanisms: •Fusion reactions: D-T reactions generate αparticles at 3.5 MeV. This population is isotropic and core localized because density and temperature (therefore D-T cross section) is more elevated at the plasma core. •ICRH heating: Ion cyclotron waves resonate with thermal (or already fast) ions accelerating them up to several MeV. These fast-ions are accelerated across the so-called absorption layer, whose radial location is determined by the injected wave frequency and the profile of the magnetic field modulus. By changing the ICRH frequency, one can create an absorption layer for deuterium, tritium but also hydrogen or helium [7]. •NBI heating: Injected beam neutral atoms travel in straight lines, becoming fast-ions held by the magnetic field when ionized. These fast-ions will follow different trajectories depending on the injection energy and angle and the deposition point. The ionization profile depends on the plasma density, the larger 1.2. Basics of tokamak reactors 11 the density, the more localized at the edge. On the other hand, if the density is too low, the neutrals might cross the whole plasma and hit the inner side of the wall [8]. These fast-ions are slowed down through collisions with electrons and ions, transferring its energy to the bulk plasma, unless a lost of confinement is induced by any of the following process: •Coulomb collisions: While transferring its energy to the thermal plasma, the fast-ion can suffer variations on its pitch angle, especially when colliding with another ion. These pitch angle variations can eventually transform a confined orbit into a non-confined ion. •Prompt losses: A fraction of the neutral injected by the NBI are directly born in an unconfined orbit. On their trajectories, they escape the plasma and reach the wall without colliding with another particle after a few poloidal bounces. NBI fast-ions ionized at the plasma edge due to large densities are a good example. •3D fields: In reality, tokamaks are not strictly axisymetric. A small (but not always negligible) 3D magnetic field component is generated by the finite number of toroidal coils. This component produces geometrical resonances with the fast-ion orbits, which leads to radial transport and eventual losses of the ions. A clearer example are the externally applied 3D fields, which are routinely used for ELM mitigation [9,10], can induce fast-ion losses [11]. •MHD instabilities: Magneto-hydrodynamic (MHD) perturbations6are present in a plasma. These perturbations propagate around the plasma with an associated electromagnetic field component that produce convective and diffusive fast-ion losses [12]. To ensure a self-maintained ignition in ITER, the mechanisms leading to a loss of confinement need to be well understood and mitigated. Moreover, the ions generated by auxiliary heating systems need to be confined to reach the ignition point. If the ions are lost at a localized position at the wall, the reactor integrity might be jeopardized. Up to now, the JET [13] and TFTR [14] tokamaks were capable of producing an αparticle distribution that could be similar to the one expected in ITER. On the other hand, the fast-ion populations generated by NBI and ICRH in medium size tokamaks, such as AUG, are being used as a test-bed to predict the behaviour of the αparticle distribution in ITER and its consequences to the overall plasma performance. In AUG, and other medium size tokamaks, modelling is combined with experimental measurements to characterize the fast-ion distribution. Some remarkable fast-ion diagnostics installed in AUG are: 6MHD perturbations will be described in more detail in section 2.2 12 Chapter 1. Introduction •Fast-ion Dαlight (FIDA): Fast-ions passing through the NBI line of sight might eventually collide with a neutral atom. A neutralization reaction takes place, in which a photon is emitted with a wavelength λ=656.1 nm [15]. This light is analyzed using spectroscopic techniques, allowing to infer the confined fastion content at different points along the beam. The averaged velocity of the fast-ion population can be obtained by analyzing the Doppler-shifted emitted light. •Neutral Particle Analyzer (NPA): After a neutralization reaction, the fast-ions become neutrals and escape the plasma on a straight line with unmodified energy. These escaping neutrals allow to infer the velocity distribution of the confined ions [16]. Very recently, in-vessel collimators and ionization foils were combined with scintillator plates to develop imaging neutral particle analyzers (INPA), which can deliver information of the fast-ion energy along the plasma radius [17]. •Neutrons: The content of energetic ions can be measured by the neutrons emitted during the beam-plasma reactions [18]. Gamma rays produced in many nuclear reactions can also be employed [19]. •Collective Thomsom Scattering (CTS): The ECRH mirrors are used to inject a electromagnetic probe beam into the plasma. Information of the fast-ion velocity distribution can be inferred from the received scattered-off radiation [20]. •Ion Cyclotron Emission (ICE): Electromagnetic waves are radiated by the ions on their gyromotion. The frequency and intensity of the measured signal determines the fast-ion content and at the emission radial location [21,22,23]. •Fast-Ion Loss Detector (FILD): Escaping fast-ion reaching the wall are collimated onto a scintillator plate. The emitted light pattern determines the gyroradious and pitch angle of these ions. The fast decay time (490 µs) of the scintillating material allows us to identify the MHD phenomena responsible for fast-ion radial transport [24,25]. The main diagnostic used in this thesis is the FILD diagnostic. FILD prototypes can be tested in the AUG tokamak, which is a less restrictive environment when compared to ITER. Furthermore, the FILD systems installed on different locations on the wall provide measurements at different phase-space7regions of the fast-ion population generated by NBI and ICRH. These measurements are needed to help predicting the αparticle dynamics in ITER. 7The phase-space is the 6D space given by the particle position (R,Z,φ) and particle velocity (E,α,ξ), where ξis the particle gyrophase. 1.3. Structure of this thesis 13 1.3 Structure of this thesis After a brief introduction and a description of the objectives of this thesis, subsection 1.2.1 discusses the relevance of D-T fusion reactions as a virtually unlimited source of energy. The main properties of its fuel (the plasma) are described in subsection 1.2.2 and the basis of the tokamak as a fusion reactor on subsection 1.2.3. The source of fast-ions and loss mechanisms are introduced on subsection 1.2.4. The rest of the document is organized as follows: Chapter 2contains the theoretical background needed to understand the rest of the thesis. Section 2.1 starts by describing the gyromotion of a charged particle embedded on a static and uniform magnetic field and finishes by describing the topology of fast-ion orbits in tokamak plasmas. In section 2.2 wave dispersion relations are obtained from the linearized ideal MHD treatment of the plasma. The main plasma instabilities responsible of fast-ion losses are introduced. The technique employed to measure the heat fluxes on plasma facing components (and therefore on the FILD probe head) is discussed in section 2.3, while section 2.4 explains the finite elements analysis employed to resolve the evolution of the temperature fields on the FILD probe head. In chapter 3, the array of FILD detectors installed in the AUG tokamak is described along with the two new detectors developed in the frame of this thesis. Section 3.1 describes the main components and working principle of the FILD detectors. The applications of multiple FILD detectors on different locations of the tokamak wall are discussed on section 3.2. The FILD5 diagnostic, installed right above the lower divertor of the AUG tokamak is described on section 3.3, including its mechanical design, light acquisition systems and validation measurements. Section 3.4 describes the conceptual and mechanical design of the magnetically-driven FILD4 diagnostic along its light acquisition systems and validation measurements. Chapter 4describes in more detail the design of the FILD4 probe. Section 4.1 focuses on the dynamical characterization of its magnetically driven actuator. The equations of motion are derived an linearized to optimize the design of the in-vessel coil while multibody modelling is employed to assess the impact of friction and the induced mechanical stresses on the manipulator. On the other hand, section 4.2 discusses the thermal behaviour of the FILD probe head under convective heat loads and the mechanical stresses associated with thermal expansion. The operational limits of the FILD probe head are defined. Section 4.3 describes the power supply employed by the Discharge Control System to energize the in-vessel coil in real-time and the safety cameras that monitor the temperature of the FILD probe head in realtime. Strategies to expand the FILD operational window are discussed. Chapter 5contains the main experimental observations obtained with the two new detectors. Section 5.1 discusses validation experiments of the FILD4 magneticallydriven actuator. Section 5.2 presents unprecedented FILD measurements at different locations on the AUG wall. The radial location of the FILD4 diagnostic is rapidly 14 Chapter 1. Introduction scanned during plasma discharges to obtain radially-resolved measurements of the fast-ion velocity-space. In section 5.3, this new technique is employed to ICRH and NBI ions in quiescent plasmas and in the presence of MHD instabilities. Section 5.4 discusses the control of TAE instabilities by modifying the poloidal spectrum of externally applied 3D magnetic perturbations and the associated FILD signals. Chapter 6is devoted to the modelling of the destabilized TAEs and the FILD signal in the presence of externally applied 3D magnetic fields. The hybrid kinetic- MHD MEGA code is described in section 6.1. The employed simulation set-up, including convergence tests, is described in section 6.2. Section 6.3 contains the main results of these modelling activities: plasma response to the externally applied 3D fields, destabilized TAEs in axisymetric and 3D equilibriums and the interaction of TAEs and magnetic perturbations through fast-ion phase-space. Chapter 7concludes the thesis summarizing the main results and proposing future applications. 15 Chapter 2 Theoretical Background This chapter starts by describing the motion of a charged particle in a tokamak plasma, which is fundamental to understand the process whereby fast-ions escape the plasma and hit the wall or a FILD detector. Then, MHD waves and their implication to measurable fast-ion losses are introduced. The chapter concludes with a brief overview of the heat loads sources on the plasma facing components (such as the FILD head) and the finite analysis method employed to model their thermomechanical behaviour. 2.1 Fast-ion orbits in tokamaks The subsections 2.1.1,2.1.2 are a summary of the fast-ion motion, which are described on reference [1] among many others. 2.1.1 Motion in homogeneous magnetic field The Lorentz’s law governs the motion of a charged particle in arbitrary magnetic (B) and electric (E) fields, mdv dt =q(E+v×B), (2.1) where qis the particle charge, mthe particle mass, and vthe particle velocity. A constant and uniform magnetic field would be the simplest case to particularize equation 2.1. To tackle this case, it is convenient to start by projecting equation 2.1 along the magnetic field and on the perpendicular plane. The following expressions are obtained: dvk dt =0, (2.2a) mdv⊥ dt =q(v⊥×B). (2.2b) One can deduce from equation 2.2a that the particle moves at constant velocity along the magnetic field lines. The perpendicular motion described on equation 2.2b is 16 Chapter 2. Theoretical Background projected on the Xand Yaxes, obtaining: dvx dt =qB mvy, (2.3a) dvy dt =−qB mvx, (2.3b) the solutions of this sytem can be found to be vx=v⊥sin ωct, (2.4a) vy=v⊥cos ωct. (2.4b) One can clearly deduce that this corresponds to a circular trajectory characterized by a radius (so called Larmor radius) rLand a constant angular frequency (so called cyclotron frequency) ωc: ωc=qB m(2.5a) rL=v⊥ ωc =v⊥m qB . (2.5b) For a given magnetic field vector, the sign of the charge qwill determine the rotation direction of the particle. Therefore electrons rotate following the right-hand rule with respect to the magnetic field and ions rotate on the opposite direction. One can notice that the Larmor radius depends on the particle perpendicular energy, but the cyclotron frequency depends only on the magnetic field an on the charge to mass ratio, being independent on the particle energy. The circular motion on the perpendicular plane combined with the constant velocity along the magnetic field produces a helical trajectory as depicted on figure 2.1. On this figure, one can observe how the particle location (r) with respect to a fixed observer (O) is the sum of the position of the gyro-center (rc) moving at constant speed (vk) and the Larmor radius vector (rL). FIGURE 2.1: Helical trajectory of a particle with parallel vkand perpendicular velocity v⊥with respect to the magnetic field. 2.1. Fast-ion orbits in tokamaks 17 2.1.2 Orbit drifts If a parallel electric field Ekis applied or if the magnetic field is not constant along its field line, the particle velocity along the magnetic field will be perturbed: •∇kBacceleration: It can be shown that a parallel gradient ∇kBproduces a force on the gyrocenter of a particle producing a acceleration given by dvk dt =− 1 2v2 ⊥ B∇kB. (2.6) The particle will not suffer this acceleration in case it moves strictly parallel to the magnetic field (i.e. v⊥=0). This acceleration can even reverse the parallel motion of the particle (an effect known as magnetic mirror) when the magnetic field gradient and perpendicular velocity are sufficiently large. •Ekacceleration: The equation of motion is given by dvk dt =q mEk(2.7) The gyromotion of the charged particles around their guiding centre takes place at the cyclotron frequencies. The guiding centre of a particle can drift perpendicularly on a larger timescale when the particle is not embedded on a strictly uniform and constant magnetic field. In tokamak plasmas, the main perpendicular drifts suffered by the ions guiding centers are: •E×Bdrift: When there is an electric field perpendicular to the magnetic field, the equation of motion becomes: mdv dt =q(E+v×B). (2.8) Aligning the Yaxis along the electric field and following a similar procedure as the one described in the previous section, one can obtain the following equations of motion, dvx dt =qB mvy, (2.9a) dvy dt =q mE−qB mvx, (2.9b) whose solution are vx=v⊥sin ωct+E B, (2.10a) vy=v⊥cos ωct. (2.10b) 24 Chapter 2. Theoretical Background linearized set of equations is, ∂ρ1 ∂t+ρ0∇·u1=0, (2.43a) ρ0du1 dt =−∇p1+1 µ0(∇×B1)×B0, (2.43b) p1=p0 ρ0γρ1=c2 sρ1, (2.43c) ∂B1 ∂t=∇×(u1×B0), (2.43d) where the sound velocity cs=pγp0/ρ0is introduced. The Fourier transform in space and time is applied to the linearized equations, obtaining: −ω˜ ρ1+ρ0¯ k·˜u1=0, (2.44a) −ωρ0˜u1=−¯ kc2 s˜ ρ11 µ0¯ kט B1ׯ B0, (2.44b) ω˜ B1+¯ k×(˜u1ׯ B0)=0. (2.44c) 2.2.2 Wave dispersion relations Once the Fourier transformed linear set of ideal MHD equations is derived, the dispersion relation of a wave propagating in the plasma can be obtained. The simplest case would be an equilibrium magnetic field along the Zaxis, ¯ B0= (0,0, B0), (2.45) and a wave propagating on the XZ plane, ¯ k= (kx, 0, kz). (2.46) There are two types of waves that will be treated separately. The transverse waves have their associated perturbation in a plane perpendicular to the magnetic field and the longitudinal waves have their perturbation along the magnetic field. •Transverse waves: These waves are also known as shear Alfvén waves. The perturbation of the fluid velocity is perpendicular to both ¯ kand ¯ B0, ˜u1= (0, u1y, 0). (2.47) This definition of the transverse waves implies that the fluid velocity and propagation are perpendicular, ¯ k·˜u1=0, which can be included into the mass conservation equation (2.44a), −ωρ1+ρ0¯ k·˜u1=0→ρ1=0, (2.48) 2.2. MHD waves in tokamaks 25 implying that these waves are non-compressible. Moreover, the momentum conservation (2.49a) and induction (2.49b) equations can be particularized, obtaining ωρ0vy+1 µ0B0kzB1y=0, (2.49a) kzB0uy+ωB1y=0, (2.49b) which can be expressed on matrix form, "kzB0ω ωρ0B0kz/µ0#"uy(ω,kz) B1y(ω,kz)#=0. (2.50) Non-trivial solutions (u1y6=0 and kz6=0) are obtained when the matrix is singular, allowing to define the values of ωand kzof the dispersion relation, which is, k2 zB2 0/µ0−ω2ρ0=0. (2.51) The Alfvén speed can be defined as vA=B0/√µ0ρ0and θas the angle between ¯ kand ¯ B0. The dispersion relation of the transverse wave can be rewritten as ω2=v2 Ak2cos θ2. (2.52) Shear Alfvén waves are transverse polarized waves. A parallelism can be draw with transverse waves on a guitar: the tension is provided by the magnetic field and the mass density by the plasma ions. •Longitudinal waves: In this case, the fluid velocity perturbation has a component aligned with the equilibrium magnetic field, ˜u1= (u1x, 0, u1z). (2.53) This perturbation on the fluid velocity ˜u1can be substituted on equation 2.44a to obtain the perturbation of the density as ρ1=ρ0 ω(kxux+kzuz), (2.54) and from the induction equation (2.44c), Bx=−kzB0 ωu1x, (2.55a) Bz=kxB0 ωu1x. (2.55b) 26 Chapter 2. Theoretical Background These expressions are included into the momentum equation to obtain the following in matrix form, "ω2−c2 sk2 x−v2 Ak2 x+k2 z−c2 skxkz −c2 skxkzω2−c2 sk2 z#"uy uz#=0, (2.56) from whose determinant one can obtain the dispersion relation ω4−ω2k2(c2 s+v2 A)−c2 sv2 Ak2k2 z=0. (2.57) In a typical tokamak plasma, the Alfvén speed is much larger than the sound speed, γp0 B2 0/µ<< 1→c2 s/v2 A<< 1, (2.58) so the dispersion relation can be expressed as ω2≃1 2k2v2 A1+c2 s v2 A1±1−2k2 zc2 s k2v2 A. (2.59) This dispersion relation 2.57 is a quadratic equation, and therefore has two possible solutions. First, by considering the positive sign in 2.59, the dispersion relation of the fast compressional wave is obtained, ω2≃k2v2 A1+c2 s v2 A sin θ2. (2.60) The negative sign in 2.59 results in the dispersion relation of the slow magnetosonic wave ω2≃k2c2 scos θ2, (2.61) also called slow wave because its phase velocity is cs(much smaller than vA). This wave is equivalent to a sonic wave in the presence of a magnetic field. In order to summarize this section, figure 2.3 depicts the surface described by ω¯ k/k2 for the dispersion relations of the transverse and the longitudinal waves. 2.2.3 Alfvén Eigenmodes The previous section described the shear Alfvén waves, which require special attention for their implication in D-T fusion plasmas. Fusion-born αparticles have an energy of 3.5 Mev, corresponding to a velocity larger than Alfvénic speed, resonating with those waves during the slowing down of the αparticles. The shear Alfvén waves are particularized to a toroidal geometry, having in mind the toroidal and poloidal periodicity of a tokamak, the fluid displacement (ξ) could be described by 2.2. MHD waves in tokamaks 27 FIGURE 2.3: Surface described by ω¯ k/k2as a function of θ(angle between ¯ B0and ¯ k). Extracted from [26]. a spatial Fourier decomposition in poloidal (m) and toroidal (n) harmonics, ξ(ρpol,φ,θ) = ∑ m,n ξm,n(ρpol)ei(nφ−mθ−ωt). (2.62) The definition of q(ρpol)(equation 1.11) implies a helical toroidicity which can be included in the shear Alfvén wave dispersion relation 2.52, ω=kkvA→ω=nq −m qR vA. (2.63) This results on the definition of the Alfvén continuum, implying that all frequencies can propagate in the plasma as singular local oscillations. Nonetheless, phase mixing produce exponential decay on the amplitude of these oscillations [27]. Gaps on the Alfvén continuum are produced by the periodic variations of vA along the magnetic field lines produced by B∼R−1. In these gaps a discrete spectrum of Alfvén Eigenmodes (AE) can exist which do not suffer from phase mixing. By considering the Bragg frequency produced by periodic variations in the refraction index, one can calculate the frequency width of these gaps, f=¯ v 2∆z. (2.64) The average phase velocity is ¯ vand ∆zis the distance between the periodic varying refraction index. Periodic variations spaced ∆z=q2πRare induced by the toroidal geometry of a tokamak, which would produce the so called toroidicityinduced Alfvén eigenmode (TAE) gap centered at ωTAE =vA 2qR. (2.65) The width of this TAE gap is proportional to the inverse aspect ratio of the tokamak 28 Chapter 2. Theoretical Background ε=r/R. These eigenmodes are deleterious to fast-ion confinement despite their low amplitude (δB/B∼10−4). These modes are easily destabilized by fusion-born αparticles, and in turn they can cause a global loss of confinement via resonant transport. ICRH and NBI can be used in medium size tokamaks to generate the fast-ion distribution necessary to destabilize TAEs. To illustrate this, a simulation of a NBI driven TAE on AUG tokamak is depicted in figure 2.4. These TAEs can produce both convective and diffusive fast-ion losses which is routinely measured by the FILD systems [12]. FIGURE 2.4: Radial velocity field of a simulated n=3 TAE on the AUG tokamak. A trapped fast-ion interacting with the TAE and being measured by the different FILD systems is depicted. 2.2.4 Other instabilities Besides the waves previously described, there are other instabilities that can cause fast-ion losses and can be therefore detected by the fast-ion loss detector. •Kink: It is an ideal MHD instability driven by radial gradients of the current density. It results on a fluid displacement on a resonant surface. Despite this fluid displacement, the flux surfaces remain nested. This mode does not propagate along field lines, it is static on the plasma frame. However it rotates as a rigid body at the plasma rotation velocity. The mode interacts with fast-ions, producing radial transport and a clear convective pattern on the FILD signal at the plasma rotation frequency. 2.2. MHD waves in tokamaks 29 •Magnetic islands: It consist on a fluid displacement of a resonant surface, where the magnetic topology is broken due to magnetic reconnection in Tearing Modes (toroidal current driven) and Neoclassical Tearing Modes (driven by pressure gradients). A resistivity (η6=0) is needed to develop. These modes rotate with the plasma (as a kink mode) producing convective losses. The broken topology is at the so-called resistive layer, where the Xand Opoints are formed. Inside this resistive layer, due to parallel conductivity along field line and stochasticity, the temperature and density profiles are flattened. •Sawtooth oscillations: It occurs when q=1 at the plasma core, producing quasi-periodic relaxation events with an associated drop in temperature and density. Its name refers to the signal produced on the diagnostic temporal traces. An internal m=1 kink or tearing mode is produced at the core, growing to replace the core and producing q>1. Once this relaxation process is over, the flattened qprofile is again peaked since the core has reheated and the current diffused into the core, so the relaxation process can take place again. The core current density is limited by this instability. Although sawtooth oscillations produce radial fast-ion transport mostly at the core, it can affect trapped particles exploring both the core and plasma periphery, which are captured by FILD. •Fishbones: Fast-ion drive an instability similar to an internal kink or a tearing mode as in sawtooth oscillations. Its name is given after the temporal evolution of the magnetic signal produced on the Mirnov coils. •Edge localised modes (ELMs): They are inherent to the high confinement mode (H-mode), in which an edge transport barrier produces a pedestal structure on the edge, adding an onset to the pressure profile of the whole device. These ELMs are periodic relaxation events located at the edge and driven by the plasma current and pressure gradient at the pedestal [28]. They have beneficial effects, for instance help flushing out impurities, but they also produce large heat fluxes into the SOL which ultimately reaches the divertor jeopardizing its integrity. ITER will operate in H-mode but the heat fluxes expected to be produced by the ELMs cannot be withstood by its divertor tiles. Therefore, ELM control techniques must be developed. Fast-ions interact with the electromagnetic fields associated with the ELMs, so their associated fast-ion losses are easily observed by FILD. Furthermore, the FILD detector was used to observe an acceleration of beam ions correlated with the ELMs, indicating that there can be an energy exchange between ELMs and fast-ions [29]. 30 Chapter 2. Theoretical Background 2.3 Heat loads on plasma facing components In order to provide information on how the MHD waves interact with the fast-ions, FILD needs to be inserted in the scrape off layer, facing the plasma and therefore receiving heat flux. The heat fluxes reaching the plasma facing components and divertor target have radiative and convective components [30]. The radiative is neglected on nowadays devices, while the convective heat flux dominates, which consists on thermal particles being transported from the plasma core out to the SOL and down to the divertor following the magnetic field lines (being the parallel particle transport much larger than the perpendicular transport). The convective heat flux can be further classified into: •Steady state heat flux: This axisymetric heat flux can be found in L-mode and the inter-ELM periods in H-mode. Its parallel component is dominated by electron conduction, being the radial heat transport mainly localized at the outer midplane due to unfavourable curvature in the poloidal plane. Exponential decay is obtained for the parallel heat flux profile (qk(s)) when the perpendicular transport is assumed to be diffusive, qk(s) = qk,0 ·exp −s λqfx, (2.66) being sa radial coordinate defined on the divertor, λqthe fall-of length and fx the flux expansion (used to remap the heat flux upstream). •Transient heat flux: These non-axisymmetric heat fluxes are produced by the filaments expelled by the ELMs. Their main implication is the large temperature increase produced on the divertor tile (∆T) in the time scale of the ELM crash event (τELM) [31]: ∆T∝∆WELM AELM 1 √τELM , (2.67) being AELM the divertor wetted area and ∆WELM the energy associated to the ELM. Since τELM ∼1ms, the temperature increase determines the material transient limits. However, the repetition rate of the ELMs fELM is not so large, producing an averaged steady state power load (PELM) given by PELM =∆WELM ·fELM ≃0.2 −0.3Pheat. (2.68) Infrared (IR) thermography is applied to measure the temporal evolution of the superficial divertor temperature and to infer the total convective fluxes. This technique is based on the photon flux (Γ(λ,T)) emitted by a body depending on its temperature Tat each wavelength λ, as described by the Planck’s law, Γ(λ,T) = e(λ,T)2πc λ4 1 ehc λkBT−1, (2.69) 2.4. Finite elements analysis 31 where eis the emissivity of the object, cthe speed of light, kBthe Boltzmann’s constant and hthe Planck’s constant. Since the divertor temperature is expected to reach up to 2500 K [32], equation 2.69 is evaluated on that temperature interval for different wavelengths. Figure 2.5 shows how a sudden increase on the emitted photon flux is produced for λ=1µm. This short range of wavelengths is employed in measurements for machine protection, to detect areas being overheated. Longer wavelengths (λ∼5µm) are employed on IR thermography because larger photon flux is emitted at lower temperatures. Even longer wavelengths (λ∼10µm) have the disadvantage of producing a flux less sensitive to temperature changes above 1200K. The implementation of the tomography system in AUG is found in [33], having a 500 1000 1500 2000 2500 Temperature (K) 1026 1028 1030 1032 Photon flux (s-1m-3) 1 m 5 m 10 m FIGURE 2.5: Photon flux of a black body (e=1) radiator for different values of wavelength λ. sampling rate up to 2100 frames/s and a spectral range of λ=4.7 ±0.15µm. The measured temporal evolution of the superficial temperature fields can be used to reconstruct the heat flux solving the heat diffusion equation ρcp ∂T ∂T=∇κ∇T, (2.70) being cpthe specific heat, ρthe density and κthe heat conductivity. This is evaluated in AUG using the THEODOR (THermal Energy Onto DiverOR) [34] that uses the temporal evolution of a temperature profile T(s,t)as an input, returning the evolution of the heat flux density q(s,t). These measurements of the heat flux will be employed on section 4.2 to estimate the evolution of the probe head temperature. 2.4 Finite elements analysis The heat flux defined in the previous section induces a evolution of the temperature field on the FILD probe head. To study this process, a finite elements analysis (FEA) is employed. FEA is defined as a numerical method that approximates solutions to 32 Chapter 2. Theoretical Background boundary value differential equations. It can be employed to a wide range of partial differential equations (PDE) with arbitrary domains. It will be used on section 4.2 for a thermomechanical analysis and subsection 4.1.3 for a stress analysis. It consists on discretizing the model body into an equivalent system comprised of smaller bodies (finite elements) interconnected at common points (nodes). Each variable on the PDE are approximated by a field variable, which take discrete value at the position of the nodes and can approximate the values at non-nodal points using shape functions. The values of these field variables are treated as unknown values to be determined. The shape functions are usually polynomial forms of the independent variables, derived to satisfy certain conditions at the nodes. The degree of freedom of a single finite element will be equal to the product of the number of nodes and the number of field variables. The stiffness matrix of a finite element represents the resistance of the element to change when subjected to external forces. In a stiffness stress analysis, this matrix indicates the resistance of the element to deformation when loaded. But it can also be defined, for instance, in thermal analysis, as the resistance to heat transfer. There exist commercial software used to discretize the body, and define the stiffness matrix based on the model. These models have implemented different solvers to obtain the field values. The commercial software used on this thesis is ANSYS Workbench. 33 Chapter 3 Scintillator-based FILDs in AUG In tokamaks, a large variety of fast-ion diagnostics can be found. All these different techniques aim at the same goal - diagnostic the energetic ion population at the highest phase-space and temporal resolutionsbut their working principle varies significantly. For example, the spectrometers employed to analyze the light emitted by fast-ions that are neutralized by injected neutrals, are completely different from the detectors based on collimators that re-ionize and measure the neutralized fast-ions after they have exited the plasma. Moreover, different diagnostics cover different regions of the fast-ion phase-space, so different diagnostics need to be combined to obtain a more complete information. In this context, the fast-ion loss detectors, used to obtain velocity-space measurements at very high resolution, suffer the drawback of being only able to measure ions at the vessel first wall. This limitation can be overcame by the installation of more than one FILD at different locations on the wall providing simultaneous measurements. This chapter describes the FILD predecessors, its working principle, the relevance of simultaneous measurements of multiple FILDs and the spatial distribution of FILD detectors in AUG, including FILD5 and FILD4 which are developed in the frame of this thesis. 3.1 Working principle 3.1.1 Brief history of fast-ion loss diagnostics In 1985, a diagnostic able -for the first time- to directly measure energetic αparticles was developed to measure the significant production of αparticles of ICRH heated plasmas in the PLT reactor [35]. It consisted on a collimator slit located below the plasma and a CR-39 plastic track detector. The detector was extracted and etched for 6 hours in a NaOH solution at 70 ºC after each plasma discharge. About 4 hours of reading with a 400X microscope was needed to extract the measurements from the edging. Given the relative position of the collimator slit and track detector, the gyroradius and pitch angle of the incoming trajectories was obtained from the etches. This diagnostic produced therefore a signal integrated in time, loosing its temporal resolution. 40 Chapter 3. Scintillator-based FILDs in AUG be measured. This results on a binary map (measurable or not measurable) in gyroriadius and pitch angle which is performed at different FILD locations. Combining the resulting binary maps one can construct contour plots similar to figure 3.6. The color scale in this plot indicates the minimum insertion needed to measure a specific orbit. We can clearly observe that at, at least for that specific plasma configuration, FILD5 already covers a large region of phase space at an insertion of less than 2 cm. In [47] one can observe that, even assuming a 2D wall, the phase-space coverage varies from one FILD to the other. For instance, FILD5 would need to be more inserted than FILD4 to measure ions with small gyroradius (rL<2.5cm) while FILD4 would have more difficulties to capture passing orbits λ∼30 °. This analysis depends on the plasma equilibrium and should be executed to the interest scenarios when designing a new FILD probe. FIGURE 3.6: Velocity-space coverage diagram of FILD5 for shot no. 34570 at 3.4 s, showing full coverage for the FILD’s outermost position. When FILD is inserted less than 15 mm, coverage is zero since the collimator slit is behind the wall. Extracted from [41]. 3.3 FILD5 set up A detailed description of the diagnostic setup including probe head is given in 3.3.1. Remotely-controlled reciprocating system is explained in 3.3.2 and optics relay and DAQs in subsection 3.3.3. First measurements observed during the last experimental campaign (including NBI prompt losses and MHD induced fast-ion losses) are discussed in subsection 3.3.4. 3.3.1 Detector head design and location The design of this new FILD is based on the three already existing detectors. The graphite cup (diameter 7 cm) protecting sensitive components from heat and particle fluxes is D-shaped to maximize the number of fast-ions entering the scintillating 3.3. FILD5 set up 41 chamber. The ion entrance aperture (0.5 mm width, 2 mm long and 10.5 mm deep) is placed 5 mm away of the scintillator plate, whose position within the light acquisition systems can be determined lighting up a halogen lamp embedded on the head. To track the heat shield temperature, a thermocouple contacts the inner surface of the graphite cup. Additionally, a secondary plate has been implanted behind the scintillator plate, acting as a Faraday cup and allowing a complementary method for absolute measurements of fast-ion losses. A more detailed description of FILD probe heads can be found in [25]. To maintain the magnetic field lines lying on the scintillator plate and parallel to the collimator slit, the detector head is at 45 degrees with respect to the mid plane and 12 degrees around its own axis. It rests between B-coils IL3 and IL4 right above the divertor as shown in figure 3.5. When FILD is not being used, the probe head outermost surface remains sheltered by the two surrounding B-coil protection parts, which were milled to accommodate the diagnostic. 3.3.2 Reciprocating system In order to expose the collimator slit to fast-ion orbits, movement from the out-vessel driving unit needs to be transmitted to the off-axis rod which holds the probe head (figure 3.7). For this reason, a rotary feedthrough is coupled to a worm-gear by means of a 1-meter double-cardan joint along a radial port originally dedicated to the B-coils. The worm-gear transmits its linear movement to the off-axis rod via two crank shafts (one on each side of the detector). The movement of the off-axis rod is restricted by a set of 4x2 bearings, which are clamped to a holder armed with two in-vessel end-of-stroke electrical switches. Signals provided by the switches are used by the Discharge Control System (DCS) to determine whether the programmed discharge is compatible with the current configuration of the FILDs. FIGURE 3.7: Computer-aided design (CAD) view of the FILD system embedded on the AUG vessel. One can observe the in-vessel mechanical driving unit, including double-cardan joint, worm-gear, crank shaft and bearing set. Additionally, the electrically isolated case containing the lenses relay together with the pipe enclosing the image bundle are displayed. Extracted from [41]. The set of forefront mechanical elements is fastened to a metallic case which encloses part of the lenses relay. Since this case is fixed to the PSL, electrical insulations made of vacuum-compatible polymers such as Polyether Ether Ketone (PEEK)[48] and Vespel are used to contact components at vessel potential. 42 Chapter 3. Scintillator-based FILDs in AUG To reach its outermost position, FILD head needs to move 25mm along its axis, which correspond to a total of 20 turns of the rotary feedthrough. The rotation of this element is provided by the out-vessel driving unit [49] (figure 3.8). It consists of a stepper motor (MICRON XTRUE 60), an absolute rotary encoder (PROFIBUS-DP class 2), a transmission belt and a spring torque limiter. The torque limiter connects the stepper motor and the rotary encoder protecting the rotary feedthrough. Comparing the rotary encoder signal with the embedded motor encoder allows identifying slipping caused by in-vessel worm gear clogging. Both the motor and the rotary encoder are controlled by a Programmable Logic Computer (PLC) S7 SIMATIC. The most sensitive elements such as the main PLC and the motor controller are placed in the transfer room so they are protected from the electric and magnetic fields that could harm them. The FILD operator can remotely communicate with the PLC using the human-machine interface system WinCC. FIGURE 3.8: Assembly of the different elements of the out-vessel remotely controlled driving unit (stepper motor, rotary encoder, transmission belt and torque limiter). Additionally, the antireflectioncoated vacuum window can be spotted next to the driving unit. Extracted from [41]. 3.3.3 Optics relay and light acquisition systems The light pattern emitted by the scintillating plate is transferred to the light acquisition systems outside of the vacuum via an in-vessel optics set. Four components can be distinguished. First, a 3D printed titanium body occupies all the room from 4cm to the scintillator plate until the end of the off-axis rod, holding a total of 8 lenses as shown in figure 3.9. This is needed to deviate the scintillating image through the off-axis rod. The titanium body was milled to accommodate the thermocouple case, calibration lamp and Faraday cup wires. Secondly, already inside the PSL-clamped case, a set of 2 mirrors is used to deflect the light towards the radial port. Then, 3.3. FILD5 set up 43 a set of 4 lenses hold by an electrically insulated structure, projects the light on an in-vessel coherent image guide. The image guide consists on 40x50 quartz-made optic fibers, whose transmission is not harmed by the neutron radiation. Finally, the light goes through an anti-reflection coated vacuum window which filters out light outside the bandwidth emitted by the scintillator. FIGURE 3.9: FILD in-vessel optics. Green lines depict how the light coming from the scintillator rod is conducted towards the radial port and projected onto the image guide end. Extracted from [41]. The light beam coming from the vacuum window is diverted into two light acquisition systems via a drilled mirror which acts as an optimized beam splitter. The light acquisition systems are a Charge Couple Device (CCD) camera [50], for high velocity-space resolution, and an 8x8 channels Avalanche Photo Diode (APD) camera [51], for high temporal resolution (up to 2MHz). The APD camera replaces Photo Multiplier Tubes (PMTs) used in former FILDs. It can be directly installed near the vessel, saving the long fiber bundle needed by PMTs to carry the light from the torus hall to the transfer room. The detector chip of the APD camera is covered by an array of small lenses to focus all the incoming light into the sensitive regions of the detector. The APD camera communicates with a dedicated server in the control room via a 10Gbits optic connection. Additionally, it receives an interlock trigger signal and a clock signal of 2MHz. The CCD camera 2m ethernet cable is insulated by a copper mesh against Ion Cyclotron Resonance Frequency (ICRF) cross-talk. Its signal is sent to the control room via optic wire using a data converter. Once in the control room, the signal is transferred to a Linux PC using a PCI card. When the DCS communicates the beginning of the discharge via an interlock signal, the PC start recording with a sample rate of 50 frames per second. 44 Chapter 3. Scintillator-based FILDs in AUG 3.3.4 First measurements The new FILD has been operating since the 2017 AUG experimental campaign. After measuring prompt and MHD-induced fast-ion losses in dedicated experiments, it was successfully used in other scenarios where FILDs normally have complications (e.g. upper single null). In this subsection, the most conspicuous results are shown as proof of principle, leaving the rest of the observations for forthcoming analysis. AUG has excellent qualities for fast particle experiments. Its heating system consists of 6 MW of IRCH, 2 MW of ECRH and 20 MW of NBI, distributed among 8 different sources at 60/93 keV with different injection geometries, being the 93 keV beams right above the new FILD. Part of the NBI injected ions are born in unconfined orbits, depending on magnetic equilibrium, kinetic profiles and applied beam, these particles (also known as prompt losses) are usually observed by FILD detectors. Figure 3.10 shows the heating power time trace of NBI injector #8 matching the scintillating light recorded by APD camera channel 8 during a discharge with a toroidal current of Ip= 0.45 MA and a toroidal field of Bt= 2.4 T. This confirms that light emitted by the scintillator plate is produced by fast-ion injected by the NBI source. FIGURE 3.10: Time trace of NBI #8 applied power together with measured fast-ion losses with APD channel 8 corresponding to energy E∼93 keV and pitch angle α∼45°. Extracted from [41]. Besides, the velocity-space of the escaping ions can be inferred as follows. FILDSIM [40] simulations are used to build a strike map containing the synthetic gyroradius and pitch angle distribution on the scintillator plate. The resulting strike map depends on the collimator slit dimensions and magnetic field vector near the probe-head. The halogen lamp embedded in the graphite head is used to obtain a backlighted image of the scintillator plate which helps to overlay the strike map on its correct position. The losses are observed to be centred around Larmor radii ρL∼2.7 cm corresponding to deuterium ions injected at 93 keV (given the magnetic 3.4. FILD4 set up 45 field at FILD position B=2.3 T). Moreover, the strike map is used for CCD frame triangulation, to obtain the image shown in figure 3.2, allowing an easier comparison among experimental data and simulations. On the other hand, during 4 MW ICRH heated discharges with a plasma current of Ip=0.7 MA and a toroidal magnetic field of Bt=2.5 T, a neoclassical tearing mode (NTM) evolves as shown in figure 3.11 magnetic spectrogram. Analysis of Mirnov coils signals is used to calculate poloidal (m=2) and toroidal (n=1) mode numbers. Using electron cyclotron emission (ECE) fast measurements, the magnetic island is determined to be located at ρpol =0.6. FIGURE 3.11: Magnetic spectrogram showing a (2,1) magnetic island (top). Spectrograms of the signals of FILD5 APD channel 57, FILD1 PMT channel 8 and FILD2 PMT channel 14 are depicted. A (2,1) magnetic island is clearly observed in all spectrograms, indicating coherent MHD induced fast-ion losses. FILD APD camera adjacent channels show the same trace on the spectrogram during the saturated phase of the magnetic island, indicating coherent fast-ion losses produced by the NTM. 3.4 FILD4 set up The mechanical assessment of the FILD4 diagnostic is described in this section together with its conceptual design, mechanical details and optical system. 46 Chapter 3. Scintillator-based FILDs in AUG 3.4.1 Detector head design and location The FILD4 system is located about 2 meters above the 93 keV NBI box, ∼45° below the AUG mid-plane right below the mid-plane manipulator (where FILD1 is mounted). The diagnostic head of this FILD is oriented as FILD1 and FILD2, having its longitudinal axis horizontally and aligned with the tokamak major radius. This way, the collimator slit is the head component that is closer to the plasma, optimizing the FILD signal while reducing convective loads. As FILD1 and FILD2, the head is tilted along its own axis 12° so the collimator slit is parallel to the magnetic field for typical values of the magnetic field helicity. The available room at the FILD4 location is scarce, so the entire system had to be clamped to the holder of an ECRH mirror as shown in figure 3.12. The diagnostic is designed to never interfere with the ECRH beam path. The mirror is a critical component of the ECRH launcher, so it can not be drilled to hold FILD4. Henceforth, a single-pieced holder is designed to be clamped at the same bolts to which the ECRH mirror holder is fixed. This solution ensures that FILD4 does not add any additional stresses on the ECRH mirror holder itself, only on its bolts (the forces are directly transferred to the vessel). FIGURE 3.12: The new FILD installed on AUG. The system is clamped to a mirror holder from an ECRH launcher. Probe head, collimator slit, driving coil, image guide, and protection limiters can be identified. Extracted from [45]. The movable rod and its housing is drilled to a vertical rectangular face on the 3D printed holder that is shown in figure 3.13. This vertical face has a 102mm drill 3.4. FILD4 set up 47 to enable the retraction of the FILD4 moving rod. Parallel to this surface, 7 cm behind it, a rod of 11 mm diameter is installed to hold the retaining spring that pulls the movable rod (hence the probe head) to the retracted position. The 3D holder has another vertical face, outside the mirror holder volume, that is used to clamp the holder of the magnetic coil. The 3D holder is made of 3D printed titanium because its complex shaping. All the surfaces in contact with FILD4 components and bolts from ECRH mirrors are milled to ensure the required tolerances. Like all the other diagnostic components, the 3D holder was tested to be vacuum compatible by being heated in a vacuum oven and monitoring the out-gassing. The magnetic permeability is also measured and demonstrated to be below µ<1.05. FIGURE 3.13: 3D printed holder CAD model showing holes for clamping to the ECRH mirror, rod for pulling spring and magnetic coil holder. When FILD is not being used, its probe head must be protected from convective heat loads. For this purpose, two massive tungsten-coated carbon tails are installed (one on each side of the probe head) as shown in figure 3.12. To effectively protect FILD4 and receive as little heat load as possible, these tails are tangent to the revolution surface produced by the ICRH limiters. Besides the convective heat flux, radiation emitted by the plasma (for instance, X-rays) can be deleterious to sensitive components such as plastic-made switches, wires, vespel insulation and the driving coil itself. Fort this purpose, the main body of FILD4 is protected by a 2mm thick case which protects these sensitive elements (figure 3.14). The case has a 10 cm circular hole so the probe head can slide out and another slot to accommodate the image guide. in order to avoid misalignment in case FILD4 suffers small displacements with respect to the vessel, the case is directly clamped on the FILD4 fixed body. Besides the scintillator itself, the diagnostic head houses some components that are needed to successfully operate FILD. An halogen lamp, for instance, is placed about 4 cm away from the scintillator plate, as close as possible to the head surface to avoid blocking the emitted scintillator signal on it path to the vacuum window. 48 Chapter 3. Scintillator-based FILDs in AUG FIGURE 3.14: FILD4 case protecting sensitive elements from radiation. Each pin of the lamp is wired to 3 in-vessel cables that are exiting the vacuum via a customized 9 pins feed-through. Each of these 3 pins are welded outside outside the vacuum and a 30 meters cable connects the electrical feedtrhoguh to a power supply located in the reactor basement. This basement has components that are electrically connected to the reactor, so it cannot be accessed during operation, but it is protected from neutron radiation, so these sensitive elements can be located there. The power supply is operated in no-operational days or before the FILD experiments, so the cameras can be aligned with respect to the edges of the scintillator. The probe head also contains a thermocouple that monitors the inner head temperature, which could be compared against infrared measurements from the video real time system. A pin is also located on the scintillator plate. The impugning ions are decelerated generating a voltage on the metallic plate, which can be measured on the pin. A metallic plate of similar dimensions is installed right behind the scintillator plate (isolated by a ceramic plate) and can be used to cancel the electromagnetic noise. This system helps having an additional measurement of the absolute incoming fast-ion flux. The wires from both thermocouple and Faraday cup are carried to the reactor basement in a similar way to the calibration lamp. The wires from all the elements on the head move together with the diagnostic when it is being inserted or retracted, so they ware fixed to the rod to avoid blocking the emitted light. The wires have curvature radius of about 3 cm that enables the relative displacement of the rod and fixed components. These wires are fixed to the vessel and extracted to a plug next to the vacuum window where the image guide 3.4. FILD4 set up 49 light exit the plasma (subsection 3.4.3). 3.4.2 Reciprocating system In order to allow gyro-orbits reach the scintillator plate, the collimator slits has to be inserted in the scrape off layer. Therefore, part of the probe head will be exposed beyond the protection limiters, where both convective heat load and disruption 1 are a threat to the probe head integrity. FILD therefore needs to alternate between retracted and inserted position. The limited room forced the designer to optimize the stroke of the diagnostic so the probe head can be introduced as much as possible without colliding with the ECRH mirror during a retraction. These constraints restricted the maximum stroke to 8 cm. For the cases when the probe head is pulled at large speed, there is a rear spring that avoid any collision with the ECRH mirror. Figure 3.16 shows a schematic of the reciprocating system, where one can observe how the moving rod (in yellow) holds the probe head along its longitudinal axis. The movable rod is hollow to reduce its mass and to accommodate the wires and emitted scintillator light. It is 4mm thick and relays on a fixed component that is cylindrical inside and octagonal outside (depicted in green in figure 3.16). Different components needed for functioning are placed on the eight outer surfaces, such as 4 pairs of bearings (white in figure figure 3.12 and red in figure 3.16). The bearings penetrate the fixed part and hold the moving rod via eight slots made on the fixed faces. The insertion of each bearing holder can be adjusted ∼5 mm, so the moving rod has a smooth movement by only contacting the fixed part via the bearings, producing reduced friction. The movable rod has two small rods, one above and one below, as depicted on figure 3.15. The axis of these rods is along the radial component of the main movable rod, so the small rods are perpendicular to its surface. Each of these rods is contains two independent and separated guiding ball bearings: one bearing contacts the guiding slot (so the main rod can not tilt around its axis) and the other bearing contacts the pushing arm (that rotates with the coil as a rigid body) transferring the force to the moving rod. The pushing arm has similar slot as the ones in the octagonal part. The bearing moves along the moving arm when the coil rotates, so the probe head moves along its axis. The pushing arms are welded to the base in which the coil holder is clamped. No eddy currents are expected to be induced on the pushing arms because they move parallel to the magnetic field. On the contrary, the coil holder base moves with respect the magnetic field, so magnetic flux crossing that area varies as the coil rotates. To avoid eddy currents, the holder is made in a cross shape (as seen in figure 3.16), minimizing the eddy currents and its associated mechanical damping. A protuberance (similar to the rods used for pushing the probe head) is used to act on the mechanical switches. There are three sets of two switches each: a set 1As described in section 1.2.3, a disruption is an event in which the plasma current flows towards the wall, exerting large and deleterious j×Bforces on the vessel 56 Chapter 3. Scintillator-based FILDs in AUG coils. Soft x-ray measurements at high temporal resolution helps measuring the radial location of the instability around a normalized radius of ρpol =0.6. Figure 3.21 b) shows the spectrogram from one of the APD channels that measures the beammodulated losses. Fast-ion losses produced by the NTM are identified. The slit of the FILD collimator remains fixed about R∼2.02 m during that time window. After the beam is turned off at 2.0 seconds, the NTM is still visible on the Mirnov coil spectrogram but disappear from the FILD spectrogram. This can be explained by the fact that the beam stops injecting prompt losses that are radially transported by the NTM towards the FILD probe. FIGURE 3.21: An NTM observed in (a) Mirnov coil spectrogram (b) FILD APD channel 19 spectrogram. Extracted from [45]. The traces on the FILD4 spectrogram are explained as the mode producing an orbit deflection on the ions. The orbit deflection depends on the phase of the perturbation, and since it rotates, the orbit deflection is modulated in time, producing losses on the wall as a rotating lighthouse. These losses, modulated at the mode frequency in the laboratory frame, are called coherent losses and are well captured by FILD not only for NTMs but also for alfvénic modes such as TAEs and BAEs, which are important to study fast-ion confinement but are not under the scope of this project. 57 Chapter 4 Smart FILD 4.1 Magnetically-driven actuator Special attention is paid to the FILD4 reciprocating magnetic system, which represents a novel compact and cost effective approach when compared to the other FILDs. Magnetically driven manipulators have already been used for reciprocating Langmuir probes [53],[54],[55] in tokamak devices. They consist in an in-vessel coil, that when externally energized, creates a magnetic moment of value µ=NIA, where Nis the number of windings in the coil, Ais the coil transversal area and I is the current flowing to through the coil. This magnetic moment tries to align with the existing tokamak toroidal magnetic field, producing a torque τcoil =µBcos(θ), where Bis the magnitude of the tokamak toroidal magnetic field and θthe angle between the coil transversal area and the magnetic field. If the coil axis is located in the radial direction, i.e. θ≈0°, the torque would be maximized and could be used to rotate the pushing arms described in section 4.2. This FILD manipulator is based on the same working principle. 4.1.1 Analytical characterization One can start by considering the current flowing through a coil in the absence of an electric field, I=1 RV−Lsel f dI dt , (4.1) where Vis the externally applied voltage and the self induction Lsel f =µ0N2A/h, being hthe coil height, limited by constructive constraints to a maximum of h=46 mm. If the coil is rotated on a magnetic field, the variable area perpendicular to the magnetic field would modify the magnetic flux, inducing a net electric current on the coil, I=1 RV−NBA d dt sin(θ)−Lsel f dI dt . (4.2) Therefore, the torque produced by the coil, τcoil, regardless the rest of the system, would be τcoil =NAB cos(θ) RV−NBA cos(θ)˙ θ−Lsel f ˙ I. (4.3) 58 Chapter 4. Smart FILD The other torques acting on the coil must also be considered, for instance, the pulling spring has a linear force along the moving rod, Fspring =k(x−xs) = kl(tan(θ)−tan(θs)), (4.4) where xis the probe head insertion, xsthe negative insertion that would relax the spring (which is always in tension). We have used the fact that x=ltan(θ), where lis the distance between the coil rotation axis and the moving rod axis. This longitudinal force should be compensated by a force normal to the pushing arm groove surface (i.e. a factor 1/ cos(θ)larger) that has a distance l/cos(θ)to the coil rotation axis. Therefore, the torque produced by the spring would be τspring =Fspring l cos2(θ)=kl2tan(θ)−tan(θs) cos2(θ). (4.5) If one considers that the mass of the probe head and moving rod are mrod, an inertial force can be defined as Finertia =−mrod ¨ x. Given that x=ltan(θ)(therefore ˙ x= l˙ θ/ cos2(θ)), so the inertia force would be Finertia =−mrodl2tan(θ) cos2(θ)˙ θ+1 cos2(θ)¨ θ. (4.6) Since this force is also longitudinal to the moving rod axis, (similarly to the spring force) it needs to be multiplied by a factor l/ cos2θto be converted into applied momentum at the coil rotation axis: τinertia =−mrodl2 cos4(θ)2tan(θ)˙ θ+¨ θ. (4.7) We can now consider that all the torques applied at the coil axis must be in equilibrium, this is ι¨ θ=τcoil +τspring +τinertia +τeddy, (4.8) where ιis the angular inertia of the coil and pushing arm. Since we are using an optimized shape for the coil structure, we could neglect as a first approach the induced eddy currents. On the other hand, the relatively large coil height hallows to neglect coil self induction Lsel f in conditions with small variations of coil voltage V. A non-linear one dimensional equation of the system is obtained by including the different coil torques in equation 4.8, ι¨ θ=NAB cos(θ) RV−NBA cos(θ)˙ θ−kl2tan(θ)−tan(θs) cos2(θ)−mrodl2 cos4(θ)2tan(θ)˙ θ+¨ θ. (4.9) Equation 4.9 has been obtained by simply imposing force balance. However it is also easily achievable using analytical methods through the Lagrangian of the system. This equation can be linearized around a point θ=θ0, defining the linear variable 4.1. Magnetically-driven actuator 59 θ0=θ−θ0and obtaining, ι¨ θ0=VNAB Rcos(θ0)−sin(θ0)θ0−(NAB)2 Rcos2(θ0)−2cos(θ0)sin(θ0)θ0˙ θ0 −kl2tan(θ0) cos2(θ0)+1 cos4(θ0)+2tan2(θ0) cos2(θ0)θ0−tan(θs)1 cos2(θ0)+2tan(θ0) cos2(θ0)θ0 −2mrodl2tan(θ0) cos4(θ0)+1 cos6(θ0)+4tan2(θ0) cos4(θ0)θ0˙ θ0−mrodl21 cos4(θ0)+4tan(θ0) cos4(θ0)θ0¨ θ0. (4.10) It is convenient to see how the equations look when FILD4 is half inserted (taking θ0=0 °) and neglecting second order terms, ι+mrodl2¨ θ0+ (NAB)2/R˙ θ0+kl2θ0=VNAB/R−kl2tan(θs). (4.11) This equation can be integrated to simulate the trajectory of the system when different values of voltage are applied. This is done and the results are compared against actual position measurements in section 5.1. 4.1.2 Selecting number of windings In equation 4.11 one can easily identify the equivalent mass M=ι+mrodl2as the sum of angular inertia of both coil and moving rod, the equivalent damping C= (NAB)2/R, resulting from the back electromotive force on the coil, and the generalized equivalent stiffness K=kl2. The first term on the right hand side corresponds to an external constant force on the system due to the spring force and the second term (−VNAB/R) is the force induced by externally applying a voltage to the coil. Using these parameters one can obtain the damping ratio of the system ξ, ξ|θ0=0=C 2√MK =(NAB)2 2Rpkl2(ι+mrodl2), (4.12) and observe that it depends quadratically on the magnetic field at the FILD position B. The coil area was maximized for having the largest coil torque but due to space limitations was constrained to A=0.0054 m2. Other parameters, such as mrod and l=10.5 cm are also limited by structural and functional constraints. The spring kis chosen such as can effectively pull the system back to its parked position (k=100 N/m pretended with a force of 4 N). The coil resistivity R=13 Ωis mostly given by vacuum feedtroughs and has little dependence on the number of windings N. Since the coil voltage is externally applied can be regulated to induce the necessary force to overcome the spring and insert the probe. Therefore, Nis selected so the system has critical damping (ξ|θ0=0=1) for the values of Bin which FILD is normally operated, resulting on N=250 windings. 60 Chapter 4. Smart FILD 4.1.3 Multibody modelling Friction of the movable elements of a reciprocating system can play an important role when the system is embedded in a vacuum chamber. The friction coefficient is increased, restricting the amount of movable parts and the maximum achievable angular velocity of worm gears such as the employed on FILD5 (see subsection 3.3.2). The contact of all movable elements of FILD4 is through ceramic bearings, producing negligible friction on the system. Nonetheless, in the unlikely (but still possible) case that these bearings stuck for some reason (e.g. ball breaking during a plasma disruption) the increase in the friction coefficient might cause the manipulator to retract much slower. To assess how this incident might affect the retraction times, one needs a model that includes the forces on the guiding bearings and pushing arms, which is not possible with the simple 1D model described on subsection 4.1.1. A simple method to include the effect of friction in the movement of the system is through a 2D multibody numerical model as illustrated on figure 4.1. FIGURE 4.1: Magnetically driven FILD sketch. A revolute joint (1) has been defined in the coil rotation axis. A circumference-line-type cam joint (2) models the contact between the pushing arm and the bearing. The contact between the probe head holder and each guiding bearing (3), (4), (5), and (6) has been defined as point-line-type cam joint. Extracted from [52]. The employed model uses three different bodies: (1) the vessel (reference body) including the guiding bearings and coil holder, (2) the assembly of magnetic coil and pushing arm, and (3) the assembly of the probe head and the moving rod. The movement of these bodies is restricted with kinematical joints to properly account for the different contacts and to include effects derived from friction. Each movable body has 3 coordinates, so there are 6 equations in total (equation 4.13a), to which the kinematical constraints are added (equation 4.13b) together with the coil dynamics (equation 4.13c). This ensemble results in a set of differential algebraic equations 4.1. Magnetically-driven actuator 61 [56], M(q)¨ q=Q(q,˙ q,λ,I,t), (4.13a) C(q) = 0, (4.13b) ˙ I=h(q,˙ q,I,V), (4.13c) where qis the generalized coordinates vector, Mthe generalized mass matrix, Qthe generalized external forces vector, and Cthe geometric constraints vector. To take into account the friction effect, the reaction forces in the joints have been evaluated through Lagrange multipliers, λ. The associated friction forces have been updated within each integration step. The equation can be evaluated using Newton-Raphson algorithm. The voltage is programmed to follow a PID algorithm that would produce the insertion of the probe before plasma breakdown. On figure 4.2 one can observe how the measurement cycle would be carried out for two different values of the friction coefficient, µ=0 and µ=0.6. On both simulations, four phases can be clearly identified: 1. An initial phase, where a constant voltage (meaning open loop) is being applied until the probe head reaches a pre-defined insertion. No fast insertion is needed here since the probe can use the toroidal magnetic field existing few seconds before breakdown. 2. The position is then controlled by a PID algorithm which would compare the probe head target and actual positions adjusting the delivered voltage on the coil to smoothly reach the maximum measurement stroke of 80 mm and maintaining a constant insertion. 3. The polarity is reversed on the power supply, applying a retraction voltage of 10 V. This produces a fast retraction of about 40 mm, which would be enough to reach the limiter shadow. As expected, the retraction time depends on the friction coefficient, which could be compensated by increasing the retraction voltage. 4. Finally, the detector has being fully retracted to its parking position, where it is safe from any heat load existing on the SOL. One can observe that the friction coefficient can modify, as expected, the retraction times a few tens of milliseconds. However, despite the large increase in µ, the delay is not significant, being the induced difference much smaller than the heating time scale of the probe head as described in section 4.2. The effectiveness of the realtime retraction is therefore not expected to be affected by changes on the friction coefficient. On the other hand, the pushing rod has been identified as the weakest structural element of the manipulator, and thus requires special attention. The temporal evolution of the force acting on the pushing rod can be obtained from the Lagrangian 62 Chapter 4. Smart FILD FIGURE 4.2: (a) Probe head position as a function of time. Different values for friction coefficient (µ= 0 and µ= 0.6) have been considered. Different retraction times (b) and reaction forces (c) in the pushing bearing (see figure 4.1) depending on the friction coefficient are shown during the retraction phase for Vret = 10 V. Extracted from [52]. multipliers λand is represented on figure 4.2 (b). One can observe, that friction might strongly affect the applied forces during the retraction phase. The mechanical stresses induced in the bearing rod are evaluated using the maximum force during the retraction phase. This force is included in a Finite Elements (FE) analysis using ANSYS as shown on figure 4.3. The maximum mechanical stress σmax is compared with the steel limit value (i.e. the yielding limit σy). A structural safety factor (SFs) for the manipulator can the be defined as SFs=σy σmax , (4.14) and will depend on the applied force. A set of simulations similar to the represented on figure 4.2 are performed scanning different values of the friction coefficient µand retraction voltage Vret. From that simulations set, the retraction times are stored along with the maximum value of the forces on the pushing rod. FE analysis of each force on the rod are performed to obtain the corresponding σmax values and therefore SFs. From that set of data, figure 4.4 can be constructed, representing the friction coefficient as a function of retraction time and safety factor. Isolines for Vret are also over plotted. One should note that, when SFsequals 1 or lower, local plasticity occurs in the pushing bearing rod. This is important to avoid permanent deformations that could produce poor 4.1. Magnetically-driven actuator 63 FIGURE 4.3: FE analysis performed on the pushing rod showing how the force is being applied and a zoom in the region where the mechanical stresses are being concentrated on the rod. Presented on the conference related to reference [52]. performance in the guiding system and gridlock. SFscan be used to define a minimum safe retraction time that should not produce too large retraction times so the real-time retraction is still possible. FIGURE 4.4: Structural safety factor of the FILD system as a function of the retraction time, the friction coefficient, and the voltage applied during the retraction phase. A system with µ= 0 and Vret= 10 V will retract in tsa f e ret = 0.08 s with a structural safety factor higher than 3. Extracted from [52]. 64 Chapter 4. Smart FILD 4.2 Thermomechanical assessment The thermal behaviour of the FILD probe head is simulated for different purposes. The simulated heat load can provide an estimation of the characteristic time of the heating process [57], helping to set upper boundary limits on the FILD real-time control. On the other hand, these heat loads can be used to predict the mechanical stresses produced by temperature gradients determining the role of fatigue on the probe head. 4.2.1 Estimated heat load on the probe head The applied parallel heat load is extrapolated from divertor target measurements using two different exponential decays [58] to account for the near and far scrapeoff layer. The extrapolated heat load on the divertor is mapped into ρpol so it can be used on any FILD head by just determining its poloidal location (figure 4.5), taking into account the flux expansion. This is done by using reconstructions of the plasma equilibrium performed with the CLISTE [59] code. For that remapping, equilibrium reconstructions of the time point of interest are employed. Moreover, the applied heat load on each FILD depends on the incident angle of the magnetic field line and probe head surface (α) as Q⊥=Q(ρpol)sin(α). (4.15) 1.00 1.02 1.04 1.06 1.08 1.10 1.12 0 50 100 150 200 Q (MW/m2) ρpol Measured (IR) Extrapolated FIGURE 4.5: Measured IR heat flux on the divertor and its extrapolation towards the FILD probe head. Extracted from [60]. Field line 3D tracing is used to calculate the wet (receiving heat flux) surfaces and field line length (Lf). The field line is followed using a 4th order Runge-Kutta integration scheme. If it does not hit an element of the realistic 3D wall for a collection length (Lcollection) [61] it is considered wet, and the perpendicular heat flux is obtained directly from the extrapolation of the IR measurements (QFILD ⊥=Q⊥). On the contrary, if the field line length is shorter than the collection length (Lf<Lcollection), 4.2. Thermomechanical assessment 65 the heat flux on the FILD head is corrected using QFILD ⊥=Q⊥ Lf Lcollection . (4.16) The collection length is evaluated using equation 5 in [61], Lcollection =d2cs/8D⊥, (4.17) where csis the sound speed in the SOL, d2the area of the grid node and the perpendicular diffusion coefficient approximated as D⊥∼9I−2 p(MA−2), being Ipthe plasma current. A mesh of the FILD probe head is created using ANSYS and has 10890 nodes, concentrating more nodes near the collimator aperture of the head. The mesh is illustrated on figure 4.6. The nodes are composed by tetrahedrons given the geometrical complexity of the body [62]. These tetrahedrons, which are called SOLID187 in ANSYS, are static elements with 10 nodes of general purposes. These tetrahedrons are commonly used in complex geometries. This element has 3 degrees of freedom on each node, the translation on the X,Yand Zaxis being the displacement interpolated using quadratic function shapes. This increases the computational cost, but since the problem already converges with such a low level of nodes no hexahedrons are used on the mesh. Since the region near the collimator is geometrically complex and with resulting large temperature gradients, the number of elements is manually increased by defining two spheres of influence on the corners of the hole. As shown in figure 4.6, the geometry is well resolved for both the (b) outer and (c) inner radius. On the rear side of the probe head, a larger size for the elements is used, since the thermal gradients and temperature are low. The mesh corresponding to the external surface of the probe head is exported to Matlab. A matrix is created containing the center of gravity of each triangular element of the external surface so the heat fluxes can be evaluated as previously described. This matrix has 3948 nodes. The evaluated heat fluxes are imported back to ANSYS using a External Data component system, so the heat fluxes can be interpolated to each point on the grid. Figure 4.7 shows an example of the heat fluxes obtained for FILD4. 4.2.2 Simulated temperature evolution The obtained heat fluxes are applied using a Finite Elements Analysis implemented on the Transient Thermal module of ANSYS [63]. The thermomechanical properties of the graphite are the same as used for the rest of graphite-made plasma facing components of AUG, which is an isostatic ultra-fine grain graphite manufactured by the company SIGRAFINE. The mechanical properties depend upon the employed grading. The FILD head correspond the the product R6710, whose properties are listed on table 4.1. The specific heat employed in the simulation is temperaturedependent. The Tungsten coating of the probe head is not included in the model 72 Chapter 4. Smart FILD • Ask for actual voltage and current output. • Ask for diagnostics on module temperature, noise levels etc. • Modify the parameters of the embedded PID controller. Thanks to the developed C++ library, all these functions are now available from any CentOS7 PC on the AUG network. The power supply is protected from any current peak coming from the coil since it has internal input fuses and an earth fuse. Extra protection is provided by an external fuse, which can be more easily replaced. This fuse is implemented together with a mechanical switch, used to manually disconnect the power supply from the coil when not used. The control loop of the power supply is executed as an application process (AP) of the DCS on a dedicated CentOS PC placed on the control room. The time reference of this PC is synchronized with the DCS time via a time to digital converter (TDC) on a PCI card. The PC is connected to the AUG network and is therefore able to communicate with the power supply. Currently, the AP performs the following steps: • Once initiated, the AP loads the voltage and time curves defined beforehand and stored locally. The user should reboot the AP if different FILD trajectory is desired. • The AP creates a network socket to establish communication with the power supply. • Once the shot numbers are distributed, the AP turns the power module on and waits for the TS06 trigger. The voltage is set to 0. Other trigger can be easily selected if FILD is required to be inserted before plasma breakdown. • Once the trigger is received, the predefined voltage curve is executed in a deterministic loop. Each 5ms the desired voltage is sent to the power supply, which responds acknowledging that the new set point is successfully defined. Within the same time step, the power supply is interrogated for the actual values of output voltage and amperage, which are stored as a matrix for post processing purposes. • In case that an error is received from the power supply during the loop, or if the DCS sends a discharge termination signal, the voltage on the coil is set to 0 and the power module is turned off. • At the end of the loop, the power module is turned off. A matrix is stored as an ASCII file containing the information of desired and actual voltage and delivered current. Each magnitude has an associated time stamp. • The AP reads again the voltage and time files, reestablishes the communication with the power supply and awaits for the next discharge. 4.3. Real-time control 73 Once the discharge is finished, the user can load the matrix and obtain, in post processing, the evolution of the insertion. This is done following a similar algorithm as described in [53]: By subtracting the delivered current to the current that would be delivered in the absence of magnetic field (i.e. V/R), the induced back electromotive current can be inferred. From there, the coil angular velocity is obtained, which integrated in time can allow having a measurement of the FILD probe insertion. 4.3.2 Video real-time protection of FILDs As described on section 2.3, Planck’s law (equaton 2.69) determines that a body at a temperature emits a photon flux depending on its wavelength. Optical filters can be used to select certain wavelength ranges to infer the temperature of an object by measuring its radiance Bλ. This is routinely used in tokamaks to estimate the temperature of in-vessel components during the a plasma shot. For instance, the AUG video real-time system consist on a set of about 24 CCD/CMOS cameras completely covering the divertor, the heat limiters on the LFS and almost the whole vessel surface. Details of the implementation of this system, which has been operational since 2007, can be found in references [32,68]. The cameras employed on the AUG VRT system are measuring the visible and near infrared range. Equation 2.69 is evaluated on reference [32] for different ranges of wavelength, concluding that the visible/near-infrared range has the shortest measurable temperature range, but the lower error. The image of the cameras is digitized using 8bits ADCs on a RedHawk system of 64 bits. During the plasma discharge, each frame acquired by the camera is prepossessed. This preprocessing consists on three steps. First, the background can be subtracted from a prerecorded frame. Secondly, the dynamic range is normalized from 0 (black) to 1 (white). Finally, the noise induced by the neutron flux (pixels with strong brightness) is eliminated applying a median filter of width 3x3. After the prepossessing, the light level associated with the elements that might suffer overheating can be calculated. For this, Regions of Interest (ROIs) covering the sensitive elements are defined on .xml files beforehand. These .xml files determine the pixels that are covering these elements, the threshold for discharge termination and the employed algorithm to analyze the ROI. Note that ROIs are defined with arbitrary topology and different ROIs can overlap on the same camera. The two different available algorithms to analyze the ROI are: •Brightness: The value of all the pixels composing the ROI are integrated. This algorithm is normally used for the divertor and limiters. •Hotspot: Local overheating can be identified by looking at the maximum value in a 2x2 pixel square. This method is normally used for manipulators (e.g. FILD) and allows locating the probe within the ROI besides monitoring its temperature. All this analysis is performed in between frame time (8 ms). Status signals are sent to the DCS each frame time. If a ROI overcomes its predefined threshold value, a 74 Chapter 4. Smart FILD warning status signal is sent to the DCS, which will terminate the discharge in a controlled rump-down. Particularly, the FILD array installed on AUG is well covered by the VRT system. In figure 4.13, one can observe a few examples on how FILD heads are covered by the ROIs defined on different cameras. White lines on the frames are constructed using a CAD of the vessel interior to identify the probes and sensitive elements and have a clearer definition of the ROIs. Some FILDs are covered by two different cameras from two different angles, protecting the probes more conservatively. FIGURE 4.13: Frames from different cameras in the VRT system covering the 5 FILDs installed on AUG. Figure 4.14 shows a frame from camera 07Eod in a discharge where FILD4 is being inserted. A zoom of the FILD4 ROI is illustrated. One can clearly see the spot corresponding to the diagnostic head and how the Hotspot algorithm can locate it. The temporal evolution of the value inferred from this ROI in a similar discharge is depicted on figure 4.15 together with its upper threshold. In this case, FILD4 is being sequentially inserted and retracted to obtain fast-ion radial profiles. The probe head is already overheated on the first cycle on figure 4.15, but the value of the ROI does not overcome its threshold. On the contrary, during the second cycle, that value is overcome and thus, the status signal is modified on the processing pipelines of the DCS. As a result, the discharge is terminated by turning off auxiliary heating systems and slowly ramping down the plasma current. Unlike other FILD probes, FILD4 can move during the plasma discharge. If a lower limit had been defined on the VRT system to command the DCS to retract the FILD probe head, the discharge would have continued. This is discussed in the next section. 4.3. Real-time control 75 FIGURE 4.14: Frames from VRT camera 07Eod with a zoom showing FILD4 being overheated. One can observe the ROI defined on the frame and how the Hotspot algorithm is able to locate FILD4 head in it. 4.3.3 Expanding the FILD operational limit FILD4 has been already expanding the FILD operational window since its installation. The fact that it can be inserted and retracted during the discharge, allowed to use it during short phases (i.e. 4 seconds) in long pulses with higher heating power in where convectional FILDs could not have been used. On the other hand, in the previous subsections we have described the different characteristic times of the process involved in the FILD head heating and positioning control. While the slowest process has been identified as the temperature increase on the probe head (∼100 ms), the FILD takes about 50 ms to retract to its parking position. On the other hand, the ROI values of the safety cameras are evaluated every 8 ms, which is slower for the time that the power supply would need to start retracting the FILD probe head. We can conclude, that the FILD4 diagnostic can react on real-time to changes on the temperature head (5 ms). Due to software problems with the DCS during the 2020 campaign, this algorithm, however could not be tested. So far, for controlling the FILD probe, the voltage is defined beforehand, and the position is inferred off-line. This corresponds to a feed-forward control, even if retraction is triggered by overheating detection. Nonetheless, the algorithm for inferring the position of the FILD probe head could be implemented on the AP, allowing to have a feedback control of the position of the head. This would guarantee that the FILD probe head remains at the same position in case it suffers a displacement from its target measurement. It is remarkable that a retraction time of 50 ms is 76 Chapter 4. Smart FILD 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 0.0 0.2 0.4 0.6 Ip(MA) 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 0.0 2.0 4.0 ne(10 -19 m-3) 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 0.0 0.2 0.4 0.6 FILD4 ROI 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 Time (s) 2 4 6 Insertion (cm) Core Edge #36524 07Eod-FILD4 Hotspot VPE Treshold (a) ( )b (c) ( )d FIGURE 4.15: Temporal evolution of (a) plasma current, (b) lineintegrated electron density, (c) FILD4 hotspot on camera 07Eod and (d) FILD4 insertion during discharge #36524. One can see that FILD is FILD4 is performing insertion-retraction cycles. During the second cycle the threshold for VPE is overcame and the discharge is terminated. If a lower threshold would have been defined, FILD4 could have retracted and the discharge would had continued. achieved by just turning the voltage of the coil to 0, and that smaller times could be achieved by using negative values of the voltage. 77 Chapter 5 Experimental Results This chapter describes the most relevant observations obtained with the new FILDs installed on AUG, namely the behaviour of the magnetically-driven reciprocating system of FILD4, simultaneous measurements obtained with multiple FILDs at different locations on the wall, radial profiles of fast-ion losses on the SOL and the modulation of the FILD signal in TAE control experiments using externally applied 3D magnetic perturbations. 5.1 Validation of the magnetically-driven actuator After the FILD4 system was installed on the machine wall, together with the rest of out-vessel components (power supply and out-vessel optics), a series of dedicated experiments were performed, ranging from the commissioning of the FILD magnetically driven reciprocating system to the data acquisition itself. This section reports the outcome of the validation of the magnetically-driven manipulator. The magnetically-driven reciprocating system requires an existing toroidal field for functioning. Without this external magnetic field, the coil would not suffer any torque regardless the applied voltage. Therefore, machine operation is required for commissioning. However, attempting to move the probe head for the first time during a plasma pulse has some intrinsic risks. For instance, if by any chance the communication with the power supply fails and the coil voltage is not reversed, the probe head might stay inserted for a sufficient time so that its integrity is jeopardized. For this reason, an scenario with the needed toroidal field and no plasma threatening the probe head is required. Therefore, the so-called probe tests are employed for the commissioning of the magnetically-driven actuator. In these probe test, the different AUG systems (magnets, discharge control system, etc.) are tested in a long pulse without plasma breakdown. In these shots, an on-axis magnetic field of BT=1 T is generated. This translates into a magnetic field value of BFILD4=0.85 T at the FILD4 location, which is well below the optimized value for which it was designed. However, the voltage on the coil can be increased to overcome the spring force in order to test the movement of the system. The FILD4 movement was tested recursively using these probe tests. A predefined trajectory was applied to the driving coil, and the actual position 78 Chapter 5. Experimental Results was inferred from back electromotive current. Different square pulses were systematically applied, finding that the system successfully reached the target insertion. A typical FILD trajectory in these probe tests is illustrated on figure 5.1 b). One can observe two main drawbacks of using FILD in this low BTregime: •The system overshoots: The low value of magnetic field on axis reduces the back electromotive damping force, which can be beneficial, since FILD moves faster. However, such a low value made the damping parameter ξ=0.29 meaning that the system is well underdamped and can overcome its target position during the transient regime, which could result in unexpected heat loads on the probe head. •Bouncing at parking position: When FILD is being retracted fast, the moving rod impacts the rear spring, bouncing for a couple of periods. This phenomena is also observed in the laboratory when manually inserting the probe head and realising the movement. The bounces are of small amplitude, not enough so the FILD probe head is exposed in the scrape-off layer, but should nevertheless be taken into account when applying faster retractions. A more damped regime is expected (and tested) to mitigate or suppress this bouncing. After FILD4 was proven to properly work on these vacuum shots, it was used in normal discharges with plasma. Figure 5.1 a) shows the FILD trajectory in a shot of BT=2.5 T, that has a magnetic field at the FILD4 location of BFILD =1.92 T. This is above the magnetic field to which FILD4 is designed to have critical damping. One can observe that despite the overshooting and back bouncing are avoided, the system takes much longer to reach the target position. This is because at the applied magnetic field, the damping ratio is ξ= 1.45, well overdamped. This kind of system would require a proportional derivative control algorithm which is proposed for future work. On the other hand, it is important to note that plasma scenarios with BT=1.8 T on axis would produce critical damping, avoiding overshooting and enabling the system to reach the target position much faster. FIGURE 5.1: Head target (black) and measured (blue) insertion for the overdamped (a) and underdamped regimes (b). In the overdamped regime, the probe head takes longer to reach the target position. In the underdamped regime, the probe head overshoots, which could result in unexpected heat loads on the head. Extracted from [45] To further characterize the system, the equation 4.11, which corresponds to the linearization around θ=0°, is integrated in time using a fourth order Runge-Kutta 5.2. Simultaneous measurements of multiple FILDs 79 algorithm. Time steps of 1 milliseconds were proven to be sufficient to have convergence on the solution. This model includes the spring pretension force of 4N and uses the applied coil voltage as a function of time. Figure 5.2 shows the movement of the system when consecutive steps in coil voltage are applied. The inferred position of the probe fairly agrees with the predicted movement. This sort of simulations can be used in the future to optimize the operation of the probe (e.g. optimize sweeping for radial fast-ion measurements) and commission the real-time retraction. FIGURE 5.2: Coil trajectory inferred from discharge #36498 together with the simulated trajectory and the voltage externally applied to the coil during a insertion scan performed to obtain radial profiles. 5.2 Simultaneous measurements of multiple FILDs The FILD array can be employed to obtain multiple measurement at the same time point. For instance, in discharge #38035, FILD1, FILD2, FILD4 and FILD5 were inserted and the obtained velocity-space patterns at 0.9 seconds are depicted on figure 5.3. In that instant, beams #6 and #7 were active, producing first (E1=93 keV) and second (E2=46.5 keV) signals on the FILD detectors. Different pitch angles are measured by each FILD. FILD1 has predominantly a pitch of 40°, while FILD2 measures mainly 50°, and some component and a weaker signal at 25°. FILD4 and FILD5 are measuring mainly the second injection energy, FILD4 only capturing ions centred around λ=55°while FILD5 measures three different pitch angles: 22°, 40°and 72°. A single MHD instability can induce convective losses measured by multiple FILDs at the same time window. An example is shown in figure 3.11, where the losses induced by a magnetic island and its multiple harmonics are depicted simultaneously for FILD1, FILD2 and FILD5. However, this is not always the case. For instance, on figure 5.4, TAEs and NTMs are producing losses on FILD1 and FILD4 during the same discharge, but at different time windows. Beam #6 is applied during the entire discharge, and as soon as beam #8 is turned on, TAEs are destabilized producing convective losses that are captured by FILD1, together with losses induced by NTMs. These losses are not visible on FILD4 until 4.25 seconds, when beams #6 and #8 are replaced by beam #3 and 4MW of ICRH injected at 36.5 MHz. These 80 Chapter 5. Experimental Results FIGURE 5.3: Simultaneous velocity-space measurements of discharge #38035 at 0.9s on FILD1, FILD2, FILD4 and FILD5. Different pitch angles are measured on the different probes. measurements can help determining the properties of the instabilities responsible for ejecting ions at different regions on the wall. 5.3 Radially resolved fast-ion loss measurements When FILD is inserted at a fixed location, its able to produce time-resolved velocityspace measurements at the edge of the fast-ion distribution function. For instance, the new FILD was able to identify passing (trapped) orbits produced by a sequence of applied tangential (radial) beams [45]. The new diagnostic technique reported on this paper consists on performing consecutive scans on the FILD insertion. If the plasma parameters are constant thought the scanning cycles, the time-resolved fast-ion measurements can be translated into radially-resolved velocity-space measurements of fast-ion losses. 5.3. Radially resolved fast-ion loss measurements 81 FIGURE 5.4: Spectrograms of the FILD4 (a,c) and FILD1 (b,d) signals during discharge #36568. Losses induced by NTMs and TAEs are identified on each FILD during different time windows. 5.3.1 (E, Pitch, R) measurements of fast-ion losses The FILD insertion/retraction cycles are applied to discharges with plasma current Ip=0.8 MA and magnetic field Bt=−1.8 T, producing critical damping (ξ≈1) on the FILD manipulator, and thus, enabling fast movement of the FILD head needed for performing insertion/retraction cycles. Figure 5.5 shows the time traces of a discharge in which 2.5 MW beam sources #3 (60 keV) and #8 (93 keV) are consecutively applied combined with eventual 2.9 MW of ICRH power at 30 MHz. Despite the temporal changes in the applied heating systems, the electron density remains practically constant at the core (ne=5.4 · 1019 m−3) and edge (ne=3.2 ·1019 m−3). The field-line helicity at the edge q95 =3.8 is also unperturbed during the whole shot, while electron temperature Teis sightly modified by the applied heating scheme, remaining relatively constant through each phase. The inferred evolution of the FILD insertion is depicted on figure 5.5 (e). One can observe that FILD is fully inserted once the first NBI beam has been applied. Then, after FILD reaches a steady inserted position, the voltage on the magnetic coil is sequentially reversed, forcing the system to oscillate 25 mm each 400 ms, modulating the measured FILD signal produced by the APD camera. This translates into 25 mm 88 Chapter 5. Experimental Results 4.2 4.4 4.6 4.8 0 10 20 30 Ipolsola (kA) 2 3 4 5 6 FILD insertion (cm) 4.2 4.4 4.6 4.8 Time (s) (a) (b) 0.00 0.05 0.10 0.15 0.20 FILD (a.u.) FIGURE 5.13: (a) Temporal evolution of the divertor target current, used as an ELM monitor along with FILD inferred insertion. (b) Measured FILD signal including spikes induced by ELMs. Extracted from [60]. dependence of ELM-induced fast-ion losses under different heating schemes, fieldline helicity and, as shown in that example, different applied magnetic fields. The statistics shown in figure 5.14 are however limited, and thus need to be improved before any physical interpretation of these measurements. 2.02 2.03 2.04 2.05 2.06 RFILD(m) 0.00 0.05 0.10 0.15 0.20 0.25 FILD ELM spikes (a.u.) #36498 Bt=-2.5T #36036 Bt=-1.8T FIGURE 5.14: Measured spikes on the FILD signal induced by ELMs during two different discharges at different magnetic field on axis. Extracted from [60]. 5.3. Radially resolved fast-ion loss measurements 89 Radially-resolved orbit deflection induced by magnetic islands FILD was programmed to radially sweep in scenarios with existing magnetic islands producing the first radially-resolved measurements of coherent fast-ion losses induced by internal perturbations. Figure 5.15 depicts the time-traces of an example discharge where electron density and plasma current are constant through the entire pulse. 2MW of ECRH power are applied together with a total of 5MW of NBI using sources #6 and #7. At 2.5 seconds, source #7 is replaced by #8. This discharge has a plasma current of Ip=0.8 MA and a magnetic field of Bt=−2.5 T, overdamping the FILD movement and thus restricting the achievable number of cycles/second. The FILD trajectory is depicted on figure 5.15(c) together with the spectrogram of the APD recorded signal, in which the coherent MHD-induced fast-ion losses are visible. The intensity of the measured coherent losses is clearly amplified when the FILD probe is inserted. The Light Ion Beam Probe (LIBP)[71,72] technique is applied 1 2 3 (MW) 0.0 0.5 1 2 3 4 5 Time (s) NBI sources #6 #7 #8 ECRH Ip (MA) Core n (10 m ) e -3-19 Edge n (10 m ) e -3-19 FILD4 APD #36521 5 10 15 Frequency (kHz) 2.00 2.02 2.04 2.06 2.08 R (m) FILD FIGURE 5.15: Overview of discharge #36521 showing (a) temporal evolution of plasma current, core and edge electron densities, (b) applied NBI and ECRH heating and (c) spectrogram of FILD signal showing MHD-induced coherent losses modulated by the FILD insertion. Extracted from [60]. to these radial measurements. This technique provides an experimental estimation of the fast-ion orbit radial displacement (ξ) by means of analyzing the modulated FILD signal (∆F) induced by ions which are lost on their first poloidal transit after a single pass through the internal perturbation, ξ≈(∆F/¯ F)Li. (5.3) ¯ Fis the unperturbed (mean) fast-ion flux and Liis the ionization scale length at the orbit birth location, which can be substituted by the density scale length near the 90 Chapter 5. Experimental Results edge due to the strong linear dependence of the ionization profile on edge electron density ne. The LIBP technique is applied to the time window from 3.3 to 3.7 seconds, when, as seen on figure 5.15, electron density, applied heating and frequency of the MHD instability are constant. A spectrogram of a magnetic pick-up coil is illustrated in figure 5.16(a) showing the evolution of the perturbation which has been identified as a Double Tearing Mode (DTM) radially expanding from ρpol =0.35 to 0.65 and having toroidal and poloidal periodicities of (n,m)=(1,3). Figure 5.16(b) shows the spectrogram of the coherent FILD signal from the APD camera during the time window of interest. Coherent losses observed at the spectrogram are not only modulated by the FILD insertion, but also by the DTM amplitude. To disentangle this effect, the mode amplitude is tracked as shown on figure 5.16(a) and smaller time windows on the FILD signal are selected at each local maximum, resulting on samples of FILD measurements at almost constant DTM amplitude and frequency. 2 4 6 8 10 12 14 Frequency (kHz) 2 4 6 8 10 12 14 Frequency (kHz) 3.3 3.4 3.5 3.6 3.7 0 0.2 0.4 0.6 FILD (a.u.) (c) (b) (a) #36521 Raw FILD ΔF F FIGURE 5.16: (a) Magnetic spectrogram of DTM with overlaid tracked amplitude. (b) Spectrogram of the FILD signal showing coherent losses at the same frequency as the DTM. (c) Samples of raw FILD signal together with its mean values and oscillating component at the mode frequency. Extracted from [60]. The samples of the raw FILD signal, plotted as scattered points on figure 5.16(c), can be averaged obtaining ¯ Fand Fourier-transformed to obtain the fluctuating component at the DTM frequency (∆F). The resulting values of (¯ F,∆F)are analyzed by applying equation 5.3 to produce time-resolved estimations of the orbit deflection. Since FILD is performing a insertion/retraction cycle, the radial profile of the orbit deflection is obtained as shown on figure 5.17(a). This radial profile corresponds to the outer banana leg of the measured trapped orbits. Velocity-space measurements reveal that these ions are captured with an energy of E=93keV and pitch 5.4. FILD measurements during TAE control experiments using externally applied 3D fields 91 angle of 65°. This information is used to track the measured orbits backwards in time to connect the FILD location (RFILD) with the innermost flux surface explored by each orbit, helping to remap the radial profile against the minimum ρpol of the internal banana leg. This internal profile is compared against the reconstructed mode structure obtained by ECE (figure 5.17(b)). Despite the limited radial range covered by FILD, the measured dependence of the orbit deflection seems to agree with the reconstructed ECE profile, having FILD a larger spatial resolution. The FILD internal radial range could be expanded by combining orbits measured by different APD pixels. 2.02 2.03 2.04 2.05 RFILD (m) 0.0 0.5 1.0 1.5 2.0 (cm) 0.2 0.4 0.6 0.8 pol 0.0 0.5 1.0 1.5 2.0 (cm) 0 0.1 0.2 0.3 0.4 FFT (ECE) (a) (b) FIGURE 5.17: Radial profile of orbit deflection at the FILD location (a) and at the innermost ρpol of the measured orbit (b) together with DTM radial structure measured by ECE. Extracted from [60]. 5.4 FILD measurements during TAE control experiments using externally applied 3D fields As explained on section 2.2, Alfvénic waves can interact with fast-ions, producing radial transport and eventually losses, which jeopardize the performance of a future fusion reactor. For this reason, there is a worldwide effort to develop actuators that are able to suppress (or maintain under tolerable levels) these instabilities. A comprehensive review of the leading techniques available to control these instabilities can be found in [73]. One could classify these control techniques depending on whether they affect the damping rate of the instability γD([74,75,76]) or the drive produced by fast-ions γEP. The latter ones consist on modifying the gradients on the fast-ion phase-space that are responsible of destabilizing the mode. One example is 92 Chapter 5. Experimental Results applying outboard beam injection to suppress global Alfvén Eigenmodes [77]. Another example consist on using externally applied 3D magnetic perturbations (MPs) to mitigate Alfvénic activity as done in NSTX [78,79]. This section describes how a method similar to the one detailed in references [78, 79] is employed to control the amplitude of the TAEs, assessing, for the first time, the impact of the poloidal spectrum of the applied MPs on the instabilities. 5.4.1 Saddle coils in AUG Externally applied magnetic perturbations are used in many tokamaks to degrade the edge confinement, reducing the pressure gradient and avoiding the appearance of ELMs [10,80]. In AUG, these externally applied fields are produced by a set of 16 saddle coils [81]. They are divided in an upper and a lower set of 8 coils each. Figure 5.18 shows how the coils are equally spaced along the toroidal direction. Each FIGURE 5.18: A sketch showing the AUG saddle cois producing an n=2 perturbation. The Brcomponent of the applied field is observed on the separatrix and on a poloidal cut. coil consists on 5 loops that withstand up to Icoil =1.3kA of current each (1kA at full toroidal magnetic field). The coils are powered modularly [82], allowing to produce MPs with a given toroidicity n. For instance, figure 5.19 shows how the upper and lower set of coils are powered to produce a n=2 MP. Different phases can be applied to the upper (φU) and lower (φL) set of coils, which results on a differential phase shift (∆φUL =φU−φL), tailoring the poloidal mode spectra of the applied perturbation. 5.4.2 TAE control using n=2 fields The experiment discussed in this subsection were carried out in identical ELMy H- mode plasmas with a toroidal magnetic field at the magnetic axis of Bt=2.5 T, a plasma current of Ip=0.6 MA, a normalized ratio of plasma pressure to magnetic pressure, βN=1.2 and a collisionallity ν∗ e≈0.2. Traces of these discharges are depicted in figure 5.20. 5 MW of early NBI heating together with 1.5 MW of on-axis counter Electron Cyclotron Current Drive (ECCD) produced an elevated q-profile. Figure 5.20(b) shows static n=2 MP pulses of 200ms that were applied by two sets of eight ELM control coils, one above the midplane and one below [81]. The current flowing through the lower set of coils was kept at the same toroidal phase (φL) in 5.4. FILD measurements during TAE control experiments using externally applied 3D fields 93 FIGURE 5.19: A sketch showing how the upper and lower set of coils produce a n=2 pattern. The contour plot in the middle shows the resulting magnetic perturbation as a function of the toroidal (φ) and poloidal (θ) angles. Magnetic field lines are overlaid in black. both discharges, while the upper set of coils (φU) was rotated to introduce a differential phase shift (∆φUL =φU−φL), tailoring the poloidal mode spectra of the applied perturbation. The two different coil phasings (∆φUL =100° and ∆φUL =−50°) applied on each discharge, produce a similar density pump out (figure 5.20 (c)). On the contrary, the effect of the poloidal spectrum of the applied perturbation is especially clear in the fast-ion loss detector (FILD) measurements, where a higher fast-ion loss flux is detected when pulses of ∆φUL =100° are applied. In these discharges, there are Alfvénic instabilities (BAEs and TAEs) and a low frequency magnetic island. Analyzing the signal from multiple Mirnov coils, the toroidal and poloidal mode numbers of the island are found to be n=1 and m=3. The cross power spectral density of adjacent channels on the ECE diagnostic, the mode can be localized between ρpol ≈0.2 −0.3 and ρpol ≈0.6. At those 2 locations, the phase jump between adjacent channels is found to be π(which is a sign of X- point) indicating that the low frequency mode is a Double Tearing Mode (DTM). This DTM enables us to conclude that the magnetic field line helicity is q=m/n=3/1 at the radial location of the two X- points, being the q-profile reversed, which is explained by the large fraction of applied on axis counter ECCD. This information on the qprofile is used as a constraint to reconstruct the magnetic equilibrium. During the entire flattop phase, the suprathermal population of deuterium ions injected by the NBI destabilizes different branches of Alfvén eigenmodes, whose amplitude evolution is affected by the applied magnetic perturbations. One can observe BAEs at frequencies ranging from 50-80 kHz and TAEs from 80-110 kHz. The toroidal mode numbers of the TAEs were identified to range from n= 2 to n= 94 Chapter 5. Experimental Results 0 2 4 6 0.0 0.5 1.0 0 2 4 0 5 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time [s] 0.2 0.4 0.6 0.8 NBI [MW] ECRH [MW] Icoil [kA] Plasma current [MA] Core electron density [10-19 m3] Edge electron density [1019 m-3] Core electron temperature [keV] Edge electron temperature [keV] FILD [a.u.] AUG #34570, #34571 (a) (b) (c) (d) (e) FIGURE 5.20: Temporal evolution of (a) auxiliary heating, (b) plasma and ELM control coil current, (c) electron density, (d) temperature and (e) fast-ion losses. Black (blue) traces correspond to discharge #34570 (#34571) where coil phasing ∆φUL =100° (∆φUL =−50°) was applied. 5. These TAEs are of especial interest since their amplitude is strongly modulated by the applied MPs. The spectrograms on figure 5.21 show how TAEs are clearly suppressed when the MPs are applied on discharge #34570. This result is similar to the NSTX experiments reported on [78,79]. Contrarily, on #34571, the amplitude of the existing TAEs is largely amplified by the applied MPs, minimizing the detected fast-ion flux on FILD. Since both plasmas are having the same density, qprofile and are heated by the same fast-ion sources (same applied NBIs), the determining factor to suppress or amplify the TAEs was the applied differential coil phasing ∆φUL. The pattern of the measured FILD signal on both discharges is depicted on figure 5.22 (a). One can observe that different populations are affected by the 3D fields, with the dominant populations at the NBI injection energy at two different pitch angles. The trajectories of both pitch angles are calculated and projected on the poloidal plane on figure 5.22 (b). This helps identifying that the most affected ions are on trapped orbits while the dominant signal is being produced by barely trapped ions. Both trajectories explore regions of space near the saddle coils and therefore large perturbed fields. The different levels on the FILD signal produced by different differential coil phasing ∆φUL can be explained by the existence of a edge resonant transport layer (ERTL) [11] as will be simulated on chapter 6. 5.4.3 TAE control using n=4 fields n=4 MPs produce a weaker perturbation that minimizes the impact on the kinetic profiles, but can still have an impact on the fast-ion phase-space and TAEs. The 5.4. FILD measurements during TAE control experiments using externally applied 3D fields 95 FIGURE 5.21: TAEs and FILD signals during shots #34570 and #34571 showing suppression and excitation of TAEs depending on the applied differential coil phasing ∆ΦUL. FIGURE 5.22: (a) Measured fast-ion velocity space. (b) Trajectories of the two dominant pitch angles measured by FILD at the NBI injection energy. n=4 pattern on the applied MPs can be produced by reversing the current flowing through each saddle coil (of the total of 8) along the toroidal direction. For each row, there will be only two possible configurations, that come from reversing the currents on every coil. Considering both sets of saddle coils, there are 4 possible configurations of the n=4 MPs, given the two coil phasing of the lower set of coils (φL=0° and φL=180°) and the differential phasing (∆φUL =0° and ∆φUL =180°). Since the number of possible configurations of the n=4 MPs is limited to 4, it takes 96 Chapter 5. Experimental Results a relative small number of discharges to assess its impact on Alfvénic activity and fast-ion losses. Figure 5.23 shows the traces of two identical discharges where the only difference is the phase of the lower set of coils (∆φL). Both discharges have 5 MW of NBI and about 2.7 MW produced by 4 ECRH gyrotrons. These two discharges have similar densities both on axis and at the location of the TAEs. Intermittent phases of 200 ms are applied in which the MPs differential phase (∆φUL) is reversed. This helps studying the impact of the coil phasing on the TAEs and fast-ion losses while keeping the density as constant as possible, as shown in figure 5.23 c). FIGURE 5.23: Time traces of identical discharges where only the phase of the lower set of coil is modified: (a) Applied heating, (b) plasma and saddle coil currents (c) electron density at the core and edge (d) temperatures at the core and TAE location. The destabilized TAEs are depicted on figure 5.24. These experiments do not aim at controlling the TAEs in the early phase of the discharge, where elevated q-profile and fast-ion pressure produce a drive (γEP) too high to control the modes. The beam was changed from sources #6 and #7 to sources #7 and #8 to produce marginal stability of the TAEs. The spectrogram shows how the TAEs become weaker and their amplitude is strongly modulated by the applied ∆φUL. Green arrows indicate the TAEs being amplified by applied ∆φUL =180° on both discharges. Figure 5.25 shows the spectrograms of both discharges for the regions where the TAE is modulated by the applied ∆φUL. One can observe that due to the matched and constant density, the TAE have a very steady frequency. In the marginally stable phase, the only existing TAEs are identified as n=2 and n=3. A simple frequency tracking algorithm is used to calculate the evolution of the amplitude of the n=2 5.4. FILD measurements during TAE control experiments using externally applied 3D fields 97 FIGURE 5.24: Spectrograms of discargues #37698 and #37699 showing TAEs becoming marginally unstable and being affected by the applied coil phasing ∆φUL. TAEs, which is depicted on figure 5.25 c) and d). One can observe here more clearly that the mode amplitude is increased with ∆φUL =180°. At the end of figure 5.25 d) the MPs are turned off and the TAE amplitude decreases. FIGURE 5.25: Spectrograms of discargues #37698 and #37699 showing TAEs becoming marginally unstable and being affected by the applied coil phasing ∆φUL. Figure 5.26 shows the FILD signal on discharge #37698 being clearly modulated by the applied ∆φUL. The FILD signal from discharge #36371 is over plotted. Both discharges are identical, but one of the lower saddle coil was miswired during the 104 Chapter 6. Modelling therefore the information of a single marker is transferred to a different memory unit when the particle moves from one core to another. The simulations performed in the frame of this thesis are run in the Marconi HPC [94]. A typical simulation to destabilize a single toroidal harmonic and reach saturation can take about 24h using 256 cores (i.e. ∼6000 CPUh). 6.2 Simulation set up This section describes the employed set up to calculate the plasma response and to resolve propagating TAEs on 2D and 3D fields using the MEGA code. 6.2.1 Equilibrium, kinetic profiles and fast-ion population For the time point of interest (i.e. discharge #34570 at 3.5 seconds), magnetic equilibrium (i.e. magnetic flux matrix and pressure profile) are reconstructed using both the CLISTE [59] and the IDE [95] codes. In both codes, constraints on the q-profile based on the measured DTM are imposed. The obtained equilibrium from both codes are in good agreement. MEGA uses the output generated by CLISTE because its larger poloidal resolution. Pre-processing MEGA subroutines translate the flux matrix into cylindrical coordinates of the equilibrium magnetic field vector Band remap the bulk plasma pressure profile into the cylindrical grid. On the other hand, radial profiles of electron temperature (Te), density (ne) and plasma rotation (ωtor) are obtained fitting the information of different diagnostics in a time window centered around the time point of interest, as shown on figure 6.2. Since MEGA follows a single-fluid approach, the ion temperature and density are assumed to be equal to the fitted electron temperature and density. The measured density is employed as initial value for the MHD variable, while the temperature is only employed to calculate the fast-ion critical velocity (vcrit), not having a direct impact on the MHD grid. MEGA internally translates the fitted plasma rotation frequency into rotation velocity following vtor =ωtorRˆ φ. The simulations reported on this thesis use the δfmethod to model the fast-ion distribution. MEGA distributes markers homogeneously in real space (R,φ,Z). Then, assigns a randomized negative value to the pitch angle (λ). Note that the pitch angle is defined as λ=vk/vwith respect to the direction of the magnetic field, so the markers are initiated in the same direction of the plasma current. The markers are also randomly initiated in energy Ebut placing more markers at larger energies. The weightings corresponding to F0are assigned following a built-in function to reproduce an anisotropic slowing down distribution, F0(R,Z,Λ,v) = exp −(1−ψ(R,Z)/ψmax) scaleψ×1 2er f c v−vbirth ∆v ×1 v3+vcrit(R,Z)3×exp(−(Λ−Λ0)2 ∆Λ2), (6.3) 6.2. Simulation set up 105 FIGURE 6.2: Radial profiles of electron temperature (Te), density (ne) plasma rotation (ωtor) and safety factor (q) inferred from the time point of interest and used as inputs for the MEGA simulations. where Λis the normalized pitch angle3,vthe particle energy, ψthe flux at the particle position, vbirth the injection energy and er f c(x)the complementary error function. The first term accounts for the radial profile of the particle distribution. It can be modified to account for an off-axis distribution. The second term slowly cuts off the energy distribution at the injection energy. The value of vbirth corresponding to a deuterium beam of 93 keV is used. The third term takes into account the slowing down distribution and the last term for the pitch angle of the distribution. The parameters scaleψ,∆v,Λ0and ∆Λ0are tuned so the resulting fast-ion distribution resembles the results of a TRANSP/NUBEAM [96] run. The weight of each marker is denormalized so the fast-ion pressure matches a normalized fast-ion pressure on axis βEP that is included an ad-hoc simulation parameter. The number of markers depends on the grid resolution, having at least 2 markers per cell. 6.2.2 Convergence on discretization and diffusive parameters The cylindrical grid of MEGA is expanded beyond the separatrix, so the trapped particles exploring both the scrape off layer and the plasma core are not lost and can be computed. A binary mask is applied to the evolution of the plasma fluid velocity v, density ρand pressure poutside ρpol =0.98 so the perturbations cannot propagate towards the scarpe off layer region with negligible density. Multi-nTAE runs were performed changing the resolution of the grid to observe modifications of the obtained frequencies, growth rates and poloidal structure of the modes. It was found that the resolution NR×Nφ×NZ=128 ×128 ×256 already converges with the results at higher resolution, while the results employing a lower 3The normalized pitch angle is Λ=µB0/E, being µthe magnetic moment of the particle and B0the value of the magnetic field on axis. Λaccounts for the ratio of (on axis) perpendicular energy to the total energy. 106 Chapter 6. Modelling resolution NR×Nφ×NZ=128 ×128 ×128show discrepancies in the frequency and poloidal structure. A similar study was performed for the plasma response simulations as reported in subsection 6.1. The diffusive parameters in MEGA have an impact on the TAE damping rate and on the saturation value of the plasma response. The finite spatial resolution in the explicit integration scheme of MEGA produce an intrinsic level of numerical damping. Employing a resolution of NR×Nφ×NZ=128 ×128 ×256, the growth rate is observed to be unmodified for values of the diffusive parameters below ν= νn=χ=η/µ0=5·10−7vAR0, being vAthe Alfvén velocity on axis and R0the radial location of the magnetic axis. This means that below that value numerical damping dominates. Therefore, for TAE runs using that resolution, the normalized diffusive parameters are set to be equal and η=5·10−7µ0vAR0, which is a value a factor 2500 larger than the physical (Spitzer) resistivity (ηs). For TAE runs, a normalized time step of dt =0.04/ωci is employed, being ωci the gyrofrequency of a deuterium ion at the magnetic axis (given by equation 2.5b), which results in typical values of dt ≈0.35 ns for AUG plasmas. The evolution of the bulk plasma are rather insensitive to dt due to the high stability of the employed 4th order Runge-Kutta algorithm. However, the simulation crashes when increasing dt up to a level where the Courant-Friedrichs-Lewy (CFL) [97] condition is not satisfied. 6.2.3 Imposed 3D fields The VACFIELD code [98] is employed to calculate the 3D fields induced by each saddle coil. This code discretizes the saddle coil geometry and uses the the Biot- Savart’s law4to calculate the components of the magnetic field on a cylindrical grid. An output is generated for each coil when subjected to a 1kA current. In order to prepare the inputs for MEGA, these outputs are loaded and corrected to account for the coil currents of the case of study before the independent fields are merged. The resulting cylindrical grid containing the total externally applied magnetic field is remapped using a cubic interpolator into another cylindrical grid with the poloidal resolution of the MEGA simulation. The toroidal resolution of this grid is 320 points regardless the resolution of the MEGA simulation. The three components of the magnetic field are Fourier-transformed along the toroidal direction, to obtain the value corresponding to each toroidal harmonic n. The finite number of coils generate sidebands following nSB =n±8p, being p and integer. For instance, when n=2 is applied, sidebands at nSB =−6 and at nSB =8 are induced. The sideband at nSB =8 is barely visible and the sideband at nSB =−6 is an order of magnitude smaller than n, so both are neglected in the present thesis. For each component of the magnetic field vector, a 2D (poloidal) matrix is exported into a separated ASCII file to account for the real and imaginary part of the Fourier decomposition. Each 4In a position in space r, the magnetic field is given by B(r) = µ0 4πRCI dl×r0 |r0|3, being Ithe coil, µ0the vacuum magnetic permeability, Cthe coil path and r0=r−lthe full displacement vector of the wire element (dl). 6.3. Results 107 poloidal matrix is loaded by MEGA and reconstructed along the toroidal direction given the toroidal harmonic n. 6.3 Results The simulation set-up described above can be used to obtain the plasma response to externally applied 3D fields (subsection 6.3.1), the TAEs propagating in these fields and in an axisymetric equilibrium (subsection 6.3.2). The last subsection (6.3.3) is devoted to discuss the relation of the externally applied 3D fields and the destabilized TAEs. 6.3.1 Plasma response to externally applied 3D fields Prior to the time integration of the system, MEGA calculates the MHD mismatch (∂ρ/∂t|t=0,∂v/∂t|t=0,∂p/∂t|t=0and E|t=0) as the right hand side terms of equations 6.1a,6.1b,6.1c and 6.1e. These terms are subtracted to the calculated timederivatives during time integration, ensuring that the system remains in equilibrium and the MHD variables do not evolve unless an initial perturbation is applied. Since both pressure and magnetic field are given by an axisymetric equilibrium, the MHD mismatch of the initial system is generally small. However, the externally applied 3D magnetic fields perturb this equilibrium. Therefore different results will be obtained depending whether these 3D fields are included before or after the initial MHD balance. If they are applied before, the MHD mismatch accounts for these discrepancies, and the system remains in equilibrium unless fast-ions destabilize AEs (that will propagate in a 3D equilibrium as described in subsection 6.3.2). On the other hand, if these 3D fields are applied after the initial MHD balance, the effect of the fields is not included on the MHD mismatch and MEGA calculates the response of the plasma to these externally applied 3D fields. In this plasma response simulations, kinetic effects are neglected, and thus the evolution of the markers is not calculated in MEGA to save computational time. The applied edge binary mask ensures that the magnetic field at the plasma boundary remains constant, acting as an internal simulation boundary. However, this requires to modify the input plasma rotation (dashed grey line on figure 6.2) to ensure that ωφ=∂ωφ/∂ρpol =0 at the position of the binary mask, avoiding artificial electric fields at the boundary that may terminate the simulation. To validate the plasma response simulations, the applied coil configuration from discharge #34570 (n=2, ∆φUL =−50°) is employed. All the components different than n=2 are filtered out to reduce numerical noise. Different simulations were run applying this filter each 10, 100, 200 and 500 time steps finding the same results. Convergence on the simulation time-step is found as long as CFL condition is satisfied. Figure 6.3 shows the temporal evolution of the kinetic and magnetic energies when the poloidal resolution is modified while maintaining Nφ=32. In these n=2 108 Chapter 6. Modelling simulations, only half of the toroidal geometry is simulated. One can observe that a resolution larger than NR=NZ=256 is required to find stabilization of the plasma response and that convergence is achieved with resolutions above NR=NZ=512. The time derivatives of these energies are not strictly zero at the end of the simulation. However, their value is very small, and the poloidal structure of the associated perturbations (shown in figure 6.4) is observed to remain constant. Therefore, this final state is assumed to be a stabilized plasma response. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.000 0.005 0.010 0.015 Ekin (a.u.) 128 256 320 448 512 576 640 704 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Time (ms) 0.00 0.50 1.00 1.50 2.00 2.50 3.00 Emag (a.u.) 10-4 (a) (b) FIGURE 6.3: Convergence test performed changing the poloidal resolution while maintaining NR=NZ. The kinetic (a) and magnetic (b) energies converge with with a resolution of NR=NZ=512. The values employed on the diffusive parameters also have an impact on the simulation. Figure 6.5 shows the evolution of the kinetic energy for different values of normalized resistivity η/(vAR0µ0). This simulations are set with NR×Nφ×NZ= 512 ×32 ×512 and the applied n=4 poloidal spectrum from discharge #37698. The other diffusive parameters are set to ν=1·10−7vAR0and χ=5·10−7vAR0. One can observe that the results η/(vAR0µ0) = 1·10−10 and η/(vAR0µ0) = 1·10−9are identical. This is produced by the intrinsic numerical damping of MEGA, that limits the minimum achievable resistivity for a given spatial resolution of the MHD grid. A simulation using Spitzer resistivity (ηS) would require unfeasible spatial resolution, therefore, a resistivity η/(vAR0µ0) = 1·10−8is employed in these simulations. The toroidal flow of the bulk plasma (ωtor) is proven to screen the plasma response. This phenomenon is typically reproduced by numerical studies [99]. To observe this screening effect in MEGA, a scan of 6 simulations were performed. 6.3. Results 109 FIGURE 6.4: Poloidal structure of the plasma response for magnetic field along the major radius δBRand toroidal flow velocity δvφ. 0.0 0.2 0.4 0.6 0.8 1.0 Time (ms) 0.0 0.5 1.0 1.5 2.0 2.5 Ekin 10-3 = 1 10-7vAR00 = 5 10-8vAR00 = 1 10-8vAR00 = 1 10-9vAR00 = 1 10-10vAR00 FIGURE 6.5: Scan on normalized plasma resistivity (η/vAR0µ0), for a n=4 run with NR×Nφ×NZ=512 ×32 ×512, ν=1·10−7vAR0 and χ=5·10−7vAR0. Each run uses a plasma rotation (ωsim) that is obtained by multiplying the experimental rotation profile ωexp by a constant. The final value of the radial magnetic field is shown in figure 6.6, where one can observe how it is mitigated when ωsim is increased. To further validate these plasma response simulations, the resulting MEGA fields are compared with calculations performed with the MARS-F [100,101] and VMEC 110 Chapter 6. Modelling FIGURE 6.6: Radial magnetic field obtained for different simulated toroidal flows. The total magnetic field is reduced when increasing the simulated toroidal flow (ωsim). [102] codes, using the same equilibrium and kinetic profiles. VMEC is an ideal MHD code and thus provides solutions with nested flux surfaces only. On the other hand, MARS-F is a linear resistive MHD code, whose implicit integration scheme allows to obtain steady a state solution performing an integration step only. The MARS-F code is run with and without parallel slow wave damping. The poloidal spectrum calculated by these codes is shown in figure 6.7 as the radial magnetic field Bralong the minor radius (ρpol) for all the different poloidal harmonics (m). The over plotted dashed lines correspond to the product of the safety factor (q) and the toroidicity of the applied 3D fields (n), indicating the regions of the spectrum that are pitchaligned with the bulk plasma. One can observe that all results are similar, showing an internal kink at (ρpol =0.7) and an edge-peeling response near the plasma boundary. However, the ideal MHD spectrum calculated by VMEC agrees with MARS-F without parallel slow wave damping. On the other hand, when this damping mechanism is included in MARS-F, it resembles more to the MEGA spectrum. This can be explained by the fact that MEGA uses a larger resistivity and has a finite damping associated with its integration scheme. 6.3.2 TAEs destabilized in axisymetric and 3D equilibriums When the MHD mismatch is calculated and kinetic effects are included, the fast-ion resonate with an initial random perturbation and AEs grow until reaching a saturation state. The fast-ion population is modelled by adjusting the parameters of equation 6.3 to resemble the distributions calculated by the TRANPS code. The initial distribution is depicted on figure 6.8 in real and velocity-space. One can observe that the injection energy is 93 keV, the critical energy ranges between 30 keV and 50 keV and the pitch angle is centered around vk/v=0.6, corresponding to a rather co-passing fast-ion population, typically produced by beam sources #6 and #7. The distribution is centered on axis, having a negative radial gradient along the whole 6.3. Results 111 FIGURE 6.7: Poloidal spectrum of the radial magnetic field Brcalculated with (a) MEGA (b) VMEC (c) MARS-F (d) and MARS-F including parallel slow wave damping. FIGURE 6.8: (a) Initial real-space of the fast-ion distribution integrated in velocity-space. (b) Initial velocity-space of the fast-ion distribution integrated in real-space. radius. The colorbar is in arbitrary units and the effective fast-ion content is determined by the fast-ion on-axis normalized pressure parameter β0 EP. Using the fast-ion distribution function described above and the axisymetric equilibrium fields, the TAEs are destabilized and saturated after 0.13 ms. Figure 6.9 112 Chapter 6. Modelling shows the temporal evolution of the kinetic energy for the different toroidal harmonics. An auxiliary time axis is added showing the time normalized by the Alfvénic frequency (ωA0=vA/R0). The evolution of the energy is plotted on a logarithmic scale to observe the linear growth of the modes. One can observe that the dominant toroidal harmonics are n=2,3,4 and 5, as observed in the experiment, while n=1 has a much smaller growth rate. FIGURE 6.9: Temporal evolution of the kinetic energy associated to each toroidal harmonic during a multi-nsimulation. One can identify these instabilities as TAEs for two main reasons: • The modes, growing exponentially during the linear phase, are located in the continuum gap. For instance, the temporal evolution at each minor radius of the n=4 perturbation is Fourier transformed and plotted together with the shear Alfvén wave (SAW) continuum 5in figure 6.10. • Both the radial component of the velocity field (vr) and toroidal component of the electric field (Eφ) have a ballooning structure in the poloidal plane. On the contrary, the radial component of the magnetic field (δBr) shows an antiballooning structure (the perturbation has its maximum on the high field side). This is observed for the calculated instabilities and shown in figure 6.11 for a n=4 harmonic. The frequency and poloidal structure of these modes normally do not depend on the total fast-ion content. However, its growth rate (measured as the time-derivative of the logarithmic of the mode amplitude) does linearly increase with applied fastion pressure. Figure 6.12 shows the normalized growth rates for different values of β0 ep. The extrapolated value at β0 ep = 0 corresponds to the total damping associated with the TAE. Contrarily to β0 ep, the obtained TAEs depend upon the shape of the initial fastion distribution. For instance, one could modify equation 6.3 to include an stepper 5More information on the shear Alfvén wave continuum can be found in section 2.2 and reference [103]. The plotted continuum is obtained evaluating equation 19 on reference [104] for the axisymetric equilibrium. 6.3. Results 113 FIGURE 6.10: Shear Alfvén continuum (white solid lines) and Fourier decomposition of the mode evolution at each radial position. FIGURE 6.11: Poloidal structure of a n=4 TAE, showing normalized Vr,Eφand δBr. and hollow fast-ion distributions. This modification of the radial profile changes the location of the fast-ion drive and thus, moves the TAE in the continuum radially, as shown in figure 6.13. When 3D fields are included in the initial equilibrium, the TAEs are destabilized as well. These TAEs are observed to have the same location in the SAW continuum. The growth rate seems to depend on the applied differential coil phasing (∆φUL) of the 3D fields. For instance, figure 6.14 shows the evolution of the n=3 TAEs for β0 ep=0.3, 0.4 and 0.5 % under the differential coil phasings from discharges #34570 and #34571. Similarly to the experiment, the coil configuration employed in #34571 produces more unstable TAEs. Simulations are run with the same fast-ion distribution described above and the 3D equilibriums including the plasma response calculated in section 6.3.1. This plasma response fields are not observed to have a significant impact on the growth rate nor the location of the destabilized TAEs. 120 Chapter 7. Summary and conclusions modulate the FILD signal and the observed TAEs. The hybrid kinetic-MHD MEGA code is applied to model the impact of externally applied 3D fields on both FILD signal and observed TAEs. The code is employed for the first time to calculate the plasma response to externally applied 3D fields finding good agreement with VMEC and MARS-F. The code is employed to calculate TAEs in both axisymetric and 3D equilibriums, finding an overlap of the induced edge resonant transport layer and the fast-ion drive of the TAEs. 7.1 Outlook The new diagnostics installed will help expanding the operational window for FILD measurements. The plasma pulse is aborted when the video real time informs that one of the probe heads is overheated. One could define a lower threshold on the video real time system so that FILD is retracted and cooled down before the discharge termination trigger is released. The radial FILD measurements can be expanded to externally applied 3D fields and a larger variety of MHD instabilities such as NTMs, TAEs, BAEs, EHOs. It can also be employed to radially characterize the quiescent population of escaping ions in other scenarios, such as L-mode and I-mode. The MEGA code can be used to calculate the impact of the fast-ion population on the plasma response to the externally applied 3D fields via resonant interaction and modification of the equilibrium fields. 121 Appendix A Manufacturing Drawings After FILD4 and FILD5 were designed, over 200 manufacturing drawings were needed for their successful construction. In this annex, the most relevant assembly drawings of these two diagnostics are included: • FILD5 diagnostic: –Diagnosticoverview ................................................122 –Innercase...........................................................123 –Rollerholder .......................................................124 –Pushingarm ........................................................125 –Cardan-feedthroughconnector ......................................126 –Doublecardanjoint .................................................127 • FILD4 diagnostic: –Diagnosticoverview ................................................128 –Coilholderandpusher .............................................129 –Pushingarm ........................................................130 –Movingrod .........................................................131 • Common components: –Bearingrodholder ..................................................132 122 Appendix A. Manufacturing Drawings B A C D E F G H J K L M 14 15 1613121110987654321 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 M L K J H G F E D C B A DIN ISO 2768-mK 1:1 - - ASDEX Upgrade DUH-1000-C 1 FILD5 Main Assembly Herrmann Pruefer javgomar (089)3299-1214 16.05.2016 dd.mm.yyyy - . .- 1 dd.mm.yyyy . - - - Bearbeitet mit Catia V5R23 DIN A1 - - The reproduction, distribution and utilization of this document as well as the communication of its contents to others without express authorization is prohibited. Offenders will be held liable for the payment of damages. All rights reserved in the event of the grant of a patent, utility model or design. title scale tolerance weight electrochemical polished: sheet-No. Drawing No. Revision IPP Supervisor: stock -No . material status revisiontext relative permeability: µr <= namedate phone wrought material rev -No . sheet size checked drawn b y Project of sheets Pos Menge Benennung Zeichnung-Nr Werkstoff Lagernummer Bemerkung 1 1 Vespel Box DUH-0031-D Vespel SP1 . - 2 2 Down Joint 1 DUH-0029-D 1.4311 . - 3 2 Lateral Roller 1 DUH-0027-D 1.4311 . - 4 1 Bronze Rod 3 DUH-0039-D ALBROMET-W200 . - 5 1 Bronze Rod 4 DUH-0040-D ALBROMET-W200 . - 6 1 Worm Gear DUH-0041-D 1.4311 . - 7 1 Worm Gear Clamping DUH-0042-D 1.4311 . - 8 1 Slide Shaft DUH-0043-D ALBROMET-W200 . - 9 4 Cooper Bearing 1 DUH-0038-D ALBROMET-W200 . - 10 2 Lateral Roller 2 DUH-0070-D 1.4311 . - 11 10 Sicherungsring DIN471-14x1 A2 . - 12 1 Screw Help DUH-0022-D 1.4301 . Clamping Cylinder 13 1 Clamping DUH-0032-D 1.4311 . - 14 1 Main Part DUH-0033-D 1.4311 . - 15 8 Part 3 DUH-0074-D 1.4311 . - 16 8 Part 1 DUH-0072-D 1.4311 . - 17 8 Part 2 DUH-0073-D 1.4311 . - 18 8 Bearing DUH-0075-D 1.4311 . - 19 1 Tube DIN 2395 - A - 50x50x2 DUH-0025-D 1.4311 . - 20 1 Optic Pipe Support DUH-0026-D 1.4311 . - 21 1 Pipe DUH-0035-D 1.4311 . - 22 1 Clamping DUH-0036-D 1.4311 . - 23 1 Sheet 1 DUH-0002-D 1.4311 . - 24 1 Sheet 2 DUH-0003-D 1.4311 . - 25 1 Main Part DUH-0018-D 1.4301 . - 26 1 Sheet DUH-0021-D 1.4311 . - 27 1 Main Part DUH-0045-D ALBROMET-W200 . - 28 4 Shell 1 DUH-0046-D Vespel SP1 . - 29 2 Shell 2 DUH-0047-D Vespel SP1 . - 30 2 Slide Shaft DUH-0048-D 1.4311 . - 31 2 Slide Shaft Head DUH-0049-D 1.4311 . - 32 4 Link Bar SH DUH-0050-D 1.4311 . - 33 2 Link Bar Cil DUH-0051-D ALBROMET-W200 . - 34 2 Shaft DUH-0053-D 1.4311 . - 35 2 Small Part DUH-0054-D 1.4311 . - 36 2 Big Part DUH-0055-D 1.4311 . - 37 1 Slider DUH-0057-D 1.4311 . - 38 2 Link Bar DUH-0058-D 1.4311 . - 39 2 Link Bar Cyl DUH-0059-D ALBROMET-W200 . - 40 2 Link Bar Sh DUH-0060-D 1.4311 . - 41 1 Coupling Peek DUH-0061-D PEEK . - 42 1 Clamping DUH-0062-D 1.4301 . 43 3 Vespel Isulating DUH-0023-D Vespel SP1 . teil6 FILD3 44 1 . - 45 1 . - 46 1 . - 47 3 . - 48 1 . - 49 1 . - 50 1 . - 51 1 . - 52 1 . - 53 1 . - 54 1 . - 55 1 . - 56 1 Pipe Contact DUH-0005-D 1.4311 . - 57 1 Holder DUH-0006-D 1.4311 . - 58 2 Peek Ring DUH-0007-D PEEK . - 59 1 Piple Contact DUH-0009-D 1.4311 . - 60 1 Holder DUH-0010-D 1.4311 . - 61 1 Screw Help DUH-0019-D 1.4301 . - 62 1 Top Support DUH-0012-D 1.4311 . - 63 1 Support Plate DUH-0013-D 1.4311 . - 64 2 Coupling Cover DUH-0015-D 1.4311 . - 65 1 Coupling Rod DUH-0016-D 1.4311 . - 66 4 SKF W 61700 DUH-0017-D 1.4311 . - 67 1 Bushing DUH-0067-D 1.4311 . - 68 1 Outter Coupling DUH-0086-D 1.4311 . - 69 1 Inner Coupling DUH-0087-D 1.4311 . - 70 2 wellengelenk_teil1_varia nte2_FILD5 DUH-0082-D 1.4301 . - 71 1 wellengelenk_teil1_varia nte3 DUH-0085-D 1.4301 . - 72 4 wellengelenk_asche2 DUH-0081-D 1.4311 . - 73 2 wellengelenk_teil3 DUH-0079-D 1.4311 . - 74 2 wellengelenk_asche1 DUH-0080-D 1.4311 . - 75 1 wellengelenk_teil1_varia nte4 DUH-0083-D 1.4301 . - Front view Scale: 1:3 13 14 15 16 17 18 19 1 2 3 5 6 7 8 21 23 24 9 10 11 2526 12 27 28 29 30 31 32 34 35 36 37 38 39 40 41 42 52 43 56 57 58 59 60 61 62 63 64 65 72 73 74 70 71 75 68 69 Bottom view Scale: 1:3 FIGURE A.1: FILD5 diagnostic overview. Originally A3 format. Appendix A. Manufacturing Drawings 123 D 1 A 2345678 7 8654321 B C E F F E D C B A title scale tolerance weight electrochemical polished: sheet-No. Drawing No. Revision IPP Supervisor: stock -No . material status revisiontext relative permeability: µr <= namedate phone wrought material rev -No . sheet size checked drawn by Project of sheets The reproduction, distribution and utilization of this document as well as the communication of its contents to others without express authorization is prohibited. Offenders will be held liable for the payment of damages. All rights reserved in the event of the grant of a patent, utility model or design. DIN ISO 2768-mK 1:1 - - ASDEX Upgrade DUH-0028-C 1 FILD5 Optic Assembly Assembly Herrmann Pruefer javgomar (089)3299-1214 16.05.2016 dd.mm.yyyy - . .- 1 dd.mm.yyyy . - - - Bearbeitet mit Catia V5R23 DIN A3 - - Pos Menge Benennung Zeichnung-Nr Werkstoff Lagernummer Bemerkung 1 1 Peek Box DUH-0031-D Vespel SP1 . - 2 2 Down Joint 1 DUH-0029-D 1.4311 . - 3 2 Lateral Roller 1 DUH-0027-D 1.4311 . - 4 1 Bronze Rod 3 DUH-0039-D ALBROMET-W200 . - 5 1 Bronze Rod 4 DUH-0040-D ALBROMET-W200 . - 6 1 Worm Gear DUH-0041-D 1.4311 . - 7 1 Worm Gear Clamping DUH-0042-D 1.4311 . - 8 1 Slide Shaft DUH-0043-D ALBROMET-W200 . - 9 4 Cooper Bearing 1 DUH-0038-D ALBROMET-W200 . - 10 2 Lateral Roller 2 DUH-0070-D 1.4311 . - 11 10 Sicherungsring DIN471-14x1 A2 . - 12 1 Screw Help DUH-0022-D 1.4301 . Clamping Cylinder 13 1 Assembly DUH-0034-C . - 14 1 Optic Case 2 DUH-0024-C . - 15 1 Optic Pipe DUH-0037-C . - 16 1 PSL Clamping Product DUH-0001-C . - 17 1 Optic Case 1 DUH-0020-C . - Front view Scale: 1:3 13 14 15 16 17 1 2 3 5 6 7 8 9 10 11 12 Right view Scale: 1:3 FIGURE A.2: FILD5 case. Originally A3 format. 124 Appendix A. Manufacturing Drawings D 1 A 2345678 7 8654321 B C E F F E D C B A title scale tolerance weight electrochemical polished: sheet-No. Drawing No. Revision IPP Supervisor: stock -No . material status revisiontext relative permeability: µr <= namedate phone wrought material rev -No . sheet size checked drawn by Project of sheets The reproduction, distribution and utilization of this document as well as the communication of its contents to others without express authorization is prohibited. Offenders will be held liable for the payment of damages. All rights reserved in the event of the grant of a patent, utility model or design. DIN ISO 2768-mK 1:1 - - ASDEX Upgrade DUH-0034-C 1 FILD5 Slider Support Assembly Herrmann Pruefer javgomar (089)3299-1214 16.05.2016 dd.mm.yyyy - . .- 1 dd.mm.yyyy . - - - Bearbeitet mit Catia V5R23 DIN A3 - - Pos Menge Benennung Zeichnung-Nr Werkstoff Lagernummer Bemerkung 1 2 Switch Support 1 DUH-0088-D 1.4301 . - 2 1 . - 3 4 . - 4 4 . - 5 1 Clamping DUH-0032-D 1.4311 . - 6 1 Main Part DUH-0033-D 1.4311 . - 7 8 Part 3 DUH-0074-D 1.4311 . - 8 8 Part 1 DUH-0072-D 1.4311 . - 9 8 Part 2 DUH-0073-D 1.4311 . - 10 8 Bearing DUH-0075-D 1.4311 . - 5 62 Front view Scale: 1:1 Rz16 A 0,15 A Left view Scale: 1:1 Top view Scale: 1:1 Isometric view Scale: 1:1 1 2 a2 141 5 7 8 6 9 10 3 4 FIGURE A.3: FILD5 holder for 8 rollers. Originally A3 format. Appendix A. Manufacturing Drawings 125 D 1 A 2345678 7 8654321 B C E F F E D C B A title scale tolerance weight electrochemical polished: sheet-No. Drawing No. Revision IPP Supervisor: stock -No . material status revisiontext relative permeability: µr <= namedate phone wrought material rev -No . sheet size checked drawn by Project of sheets The reproduction, distribution and utilization of this document as well as the communication of its contents to others without express authorization is prohibited. Offenders will be held liable for the payment of damages. All rights reserved in the event of the grant of a patent, utility model or design. DIN ISO 2768-mK 1:1 - - ASDEX Upgrade DUH-0044-C 1 FILD5 Pusher Assembly Herrmann Pruefer javgomar (089)3299-1214 16.05.2016 dd.mm.yyyy - . .- 1 dd.mm.yyyy . - - - Bearbeitet mit Catia V5R23 DIN A3 - - Pos Menge Benennung Zeichnung-Nr Werkstoff Lagernummer Bemerkung 1 1 Main Part DUH-0045-D 1.4311 . - 2 4 Shell 1 DUH-0046-D Vespel SP1 . - 3 2 Shell 2 DUH-0047-D Vespel SP1 . - 4 2 Slide Shaft DUH-0048-D 1.4311 . - 5 2 Slide Shaft Head DUH-0049-D 1.4311 . - 6 4 Link Bar SH DUH-0050-D 1.4311 . - 7 2 Link Bar Cil DUH-0051-D ALBROMET-W200 . - Front view Scale: 1:2 Bottom view Scale: 1:2 Auxiliary view A Scale: 1:2 Isometric view Scale: 1:1 1 2 3 4 5 67 FIGURE A.4: FILD5 pushing arm. Originally A3 format. 126 Appendix A. Manufacturing Drawings D 1 A 2345678 7 8654321 B C E F F E D C B A title scale tolerance weight electrochemical polished: sheet-No. Drawing No. Revision IPP Supervisor: stock -No . material status revisiontext relative permeability: µr <= namedate phone wrought material rev -No . sheet size checked drawn by Project of sheets The reproduction, distribution and utilization of this document as well as the communication of its contents to others without express authorization is prohibited. Offenders will be held liable for the payment of damages. All rights reserved in the event of the grant of a patent, utility model or design. DIN ISO 2768-mK 1:1 - - ASDEX Upgrade DUH-0011-C 1 FILD5 Port Hoder Assy Herrmann Pruefer javgomar (089)3299-1214 03.05.2016 dd.mm.yyyy - . .- 1 dd.mm.yyyy . - - - Bearbeitet mit Catia V5R23 DIN A3 - - Pos Menge Benennung Zeichnung-Nr Werkstoff Lagernummer Bemerkung 1 1 Top Support DUH-0012-D 1.4311 . - 2 1 Support Plate DUH-0013-D 1.4311 . - 3 2 Coupling Cover DUH-0015-D 1.4311 . - 4 1 Coupling Rod DUH-0016-D 1.4311 . - 5 4 SKF W 61700 DUH-0017-D 1.4311 . - 6 1 Bushing DUH-0067-D 1.4311 . - 1 2 3 4 5 A A Section view A-A FIGURE A.5: FILD5 connector of feedthrough and double cardan. Originally A3 format. Appendix A. Manufacturing Drawings 127 G F E D C B A 87654321 9 10 11 12 A B C D E F G H 121110987654321 H Weitergabe sowie Vervielfältigung der Unterlage, Verwertung und Mitteilung ihres Inhalts nicht gestattet, soweit nicht ausdrücklich zugestanden. Zuwiderhandlungen verpflichten zu Schadenersatz. Alle Rechte für den Fall der Patenterteilung, oder Gebrauchsmustererteilung vorbehalten. DIN ISO 2768-mK 1:2 - ASDEX Upgrade kreuzgelenk_teleskopwelle 1 Benennung 3 Benennung 2 kreuzgelenk_teleskopwelle - Leitenstern Leitenstern (089) 3299-1701 07.04.2014 07.04.2014 - - -- 1 TT-MM-JJJJ - - - - Bearbeitet mit Catia V5R20 DIN A2 - - Änderung Gepr. Bearb. Tel.: Werkstoff Zeichnungs-Nr.: zul. Abw.: IPP Betreuer: Benennung Blatt Änderungs-Index: Maßstab Lager-Nr.: Format Zust. Anz. Projekt: Datum Name relative Permeabilität: µr <= elektrochemisch poliert: v.BL. Halbzeug Gewicht: 600 255 Vorderansicht Maßstab: 1:2 2 134 Stückliste Menge Benennung Pos. Zeichnungs-Nr. Werkstoff Hersteller 1 wellengelenk_seite1 1 1.4301 1 wellengelenk_seite2 2 1.4301 1 teleskopwelle-keilwelle 3 A6x11x14 / 255 mm lang 1.4301 Hans Buehler 1 teleskopwelle-keilnabe 4 A6x11x14 / 600 mm lang 1.4301 Hans Buehler 6 FIGURE A.6: FILD5 double cardan joint. Originally A3 format. 128 Appendix A. Manufacturing Drawings G F E D C B A 87654321 9 10 11 12 A B C D E F G H 121110987654321 H DIN ISO 2768-mK 1:1 - - ASDEX Upgrade DUH-2000-C 1 FILD4 Assy Herrmann Pruefer javgomar (089)3299-1214 04.06.2016 dd.mm.yyyy - . .- 1 dd.mm.yyyy . - - - Bearbeitet mit Catia V5R23 DIN A2 - - The reproduction, distribution and utilization of this document as well as the communication of its contents to others without express authorization is prohibited. Offenders will be held liable for the payment of damages. All rights reserved in the event of the grant of a patent, utility model or design. title scale tolerance weight electrochemical polished: sheet-No. Drawing No. Revision IPP Supervisor: stock -No . material status revisiontext relative permeability: µr <= namedate phone wrought material rev -No . sheet size checked drawn by Project of sheets Pos Menge Benennung Zeichnung-Nr Werkstoff Lagernummer Bemerkung 1 Main Body DUH-1010-D 1.4311 . - 8 Part 3 DUH-0074-D 1.4311 . - 8 Part 1 DUH-0072-D 1.4311 . - 8 Part 2 DUH-0073-D 1.4311 . - 8 Bearing DUH-0075-D 1.4311 . - 2Hard Stop Cylinder DUH-1013-D 1.4311 . - 1 Hard Stop 1 DUH-1011-D 1.4311 . - 1 Hard Stop 2 DUH-1012-D 1.4311 . - 6 . - 6 . - 3 Benennung1 xxx-yyyy 1,4311 . - 1 Switch Rod DUH-1020-D 1.4311 . - 1 Main Body DUH-1015-D 1.4311 . - 2 Transmision Rod DUH-1016-D 1.4311 . - 2Transmision Washer DUH-1017-D 1.4311 . - 2Transmision Washer 2 DUH-1018-D 1.4311 . - 4 SKF 604 DUH-1019-D 1.4311 . - 1 Spring Support DUH-1005-D 1.4311 . - 1 Sheet 1 DUH-1002-D 1.4311 . - 1 Sheet 2 DUH-1003-D 1.4311 . - 2 Sheet 3 DUH-1004-D 1.4311 . - 1 Sheet 5 DUH-1006-D 1.4311 . - 1 Sheet 6 DUH-1007-D 1.4311 . - 1 Sheet 7 DUH-1008-D 1.4311 . - 2 Coil Holder DUH-1025-D 1.4301 . - 1 I Support DUH-1022-D 1.4311 . - 1 Support Plate DUH-1023-D 1.4311 . - 2 Isolation Plate DUH-1024-D PEEK . - 2 Lagerscheibe DNA-D-0079 1,4301 . - 2Kugellager_694_VA_1 DNA-0062-D 1,4311 . - 2 Conexion Rod DUH-1030-D 1.4301 . - 1 Sheet 1 DUH-1027-D 1.4301 . - 1 Sheet 2 DUH-1028-D 1.4301 . - 1 Sheet 3 DUH-1029-D 1.4301 . - 1 Driving DUH-1034-D Vespel SP1 . - 1 Inner Core DUH-1031-D 1.4301 . - 1 Enclosure DUH-1032-D 1.4301 . - 1 Outter Core DUH-1033-D PEEK . - 1 . - 1 . - 1 . - 1 . - 1 . - 3 . - 1 . - 2 . - 1 . - 1 . - 1 . - 1 . - 1 . - 1 . - 1 . - 1 . - 1 . - Front view Scale: 1:2 Top view Scale: 1:2 Isometric view Scale: 1:2 FIGURE A.7: FILD4 diagnostic overview. Originally A3 format. Appendix A. Manufacturing Drawings 129 D 1 A 2345678 7 8654321 B C E F F E D C B A title scale tolerance weight electrochemical polished: sheet-No. Drawing No. Revision IPP Supervisor: stock -No . material status revisiontext relative permeability: µr <= namedate phone wrought material rev -No . sheet size checked drawn by Project of sheets The reproduction, distribution and utilization of this document as well as the communication of its contents to others without express authorization is prohibited. Offenders will be held liable for the payment of damages. All rights reserved in the event of the grant of a patent, utility model or design. DIN ISO 2768-mK 1:1 - - ASDEX Upgrade DUH-1036-C 1 FILD4 Driving System Assy Herrmann Pruefer javgomar (089)3299-1214 04.06.2016 dd.mm.yyyy - . .- 1 dd.mm.yyyy . - - - Bearbeitet mit Catia V5R23 DIN A3 - - Pos Menge Benennung Zeichnung-Nr Werkstoff Lagernummer Bemerkung 1 2 Coil Holder DUH-1025-D 1.4301 . - 2 1 I Support DUH-1022-D 1.4311 . - 3 1 Support Plate DUH-1023-D 1.4311 . - 4 2 Isolation Plate DUH-1024-D PEEK . - 5 2 Lagerscheibe DNA-D-0079 1.4301 . - 6 2 Kugellager_694_VA_1 DNA-0062-D 1.4311 . - 7 2 Conexion Rod DUH-1030-D 1.4301 . - 8 1 Sheet 1 DUH-1027-D 1.4301 . - 9 1 Sheet 2 DUH-1028-D 1.4301 . - 10 1 Sheet 3 DUH-1029-D 1.4301 . - 11 2 Driving DUH-1034-D Vespel SP1 . - 12 1 Inner Core DUH-1031-D 1.4301 . - 13 1 Enclosure DUH-1032-D 1.4301 . - 14 1 Outter Core DUH-1033-D PEEK . - Front view Scale: 1:1 Left view Scale: 1:1 1 2 3 4 5 7 8 9 10 11 12 13 14 Isometric view Scale: 1:2 FIGURE A.8: FILD4 coil, holder and pushing arm. Originally A3 format. 136 Appendix B. Publication Record dejado una enorme huella en mi forma de entender la ciencia y la ingeniería. Por úlitmo, agradecer todo el cariño que siempre he recibido de mi gran (y grande) familia, especialmente de mis abuelos. Quería agradecer a mi hermana Virginia, de quien estoy cada día más orgulloso, su apoyo y complicidad. Quería dar las gracias a Tere por compartir conmigo tantas alegrías (y sufrimientos), a tu lado la vida es simplemente mejor. Es imposible poner en palabras la gratitud que siento hacia mis padres por todo el cariño que he recibido durante toda mi vida. Mamá, Papá, gracias por vuestra confianza, apoyo y por educarme para hacer las cosas lo mejor posible. 137 List of Figures 1.1 Cross section σ(m2)as a function of reactant energy (keV) for different fusion reactions. ................................ 3 1.2 Schematic view of the main components of a tokamak. Modified from [3]. ........................................ 7 1.3 Poloidal plot of a tokamak magnetic equilibrium. Extracted from [4]. . 8 2.1 Helical trajectory of a particle with parallel vkand perpendicular velocity v⊥with respect to the magnetic field. ................ 16 2.2 Phase space diagram for ions at E=75 keV simulated for a realistic plasma equilibrium. .............................. 22 2.3 Surface described by ω¯ k/k2as a function of θ(angle between ¯ B0and ¯ k). Extracted from [26]. ............................ 27 2.4 Radial velocity field of a simulated n=3 TAE on the AUG tokamak. A trapped fast-ion interacting with the TAE and being measured by the different FILD systems is depicted. ................... 28 2.5 Photon flux of a black body (e=1) radiator for different values of wavelength λ.................................. 31 3.1 (a) FILD probe head and escaping fast-ion orbit reaching the aperture. (b) Scintillator plate where the collimated ions are dispersed using the tokamak magnetic field and characterized by their gyroradius and pitch angle. Extracted from [39]. ...................... 35 3.2 (a) CCD camera frame from FILD5 diagnostic with including calculated strike map. The measured losses correspond to rL∼2.8 cm and sim pitch angle α∼45°. (b) triangulated FILD signal that can be more easily compared against simulations and other diagnostics. Figure extracted from [41]. ............................... 36 3.3 Calculation using the hybrid kinetic-MHD code MEGA to calculate the deposition of fast-ions on the wall produced by externally applied 3D fields. It is observed that the n=2 pattern produced by the externally applied field would be visible in the region of the wall near FILD4 and FILD5 but would not be capture by the rest of the existing FILD systems. ................................. 37 138 List of Figures 3.4 Poloidal (a) and toroidal (b) distribution of the five FILD systems installed on the ASDEX Upgrade tokamak. The lines of sight of the different NBI systems are also included. Modified from [45]. ...... 39 3.5 ASDEX Upgrade vessel after FILD5 installation. The detector head can be spotted among the milled B-coil protection parts. The inset shows the FILD5 head during montage, surrounded by B-coils, divertor, and PSL. FILD1 location is visible although the probe head is not because mid-plane manipulator was dismounted at that time. Extracted from [41]. ............................... 39 3.6 Velocity-space coverage diagram of FILD5 for shot no. 34570 at 3.4 s, showing full coverage for the FILD’s outermost position. When FILD is inserted less than 15 mm, coverage is zero since the collimator slit is behind the wall. Extracted from [41]. ................... 40 3.7 Computer-aided design (CAD) view of the FILD system embedded on the AUG vessel. One can observe the in-vessel mechanical driving unit, including double-cardan joint, worm-gear, crank shaft and bearing set. Additionally, the electrically isolated case containing the lenses relay together with the pipe enclosing the image bundle are displayed. Extracted from [41]. ....................... 41 3.8 Assembly of the different elements of the out-vessel remotely controlled driving unit (stepper motor, rotary encoder, transmission belt and torque limiter). Additionally, the antireflection-coated vacuum window can be spotted next to the driving unit. Extracted from [41]. . 42 3.9 FILD in-vessel optics. Green lines depict how the light coming from the scintillator rod is conducted towards the radial port and projected onto the image guide end. Extracted from [41]. .............. 43 3.10 Time trace of NBI #8 applied power together with measured fast-ion losses with APD channel 8 corresponding to energy E∼93 keV and pitch angle α∼45°. Extracted from [41]. .................. 44 3.11 Magnetic spectrogram showing a (2,1) magnetic island (top). Spectrograms of the signals of FILD5 APD channel 57, FILD1 PMT channel 8 and FILD2 PMT channel 14 are depicted. A (2,1) magnetic island is clearly observed in all spectrograms, indicating coherent MHD induced fast-ion losses. ............................. 45 3.12 The new FILD installed on AUG. The system is clamped to a mirror holder from an ECRH launcher. Probe head, collimator slit, driving coil, image guide, and protection limiters can be identified. Extracted from [45]. .................................... 46 3.13 3D printed holder CAD model showing holes for clamping to the ECRH mirror, rod for pulling spring and magnetic coil holder. ..... 47 3.14 FILD4 case protecting sensitive elements from radiation. ........ 48 List of Figures 139 3.15 CAD model of FILD4 showing bearing holder, rear spring, pushing rod, strok limiter, switch and switch actuator. ............... 50 3.16 Magnetically driven FILD CAD design. Extracted from [52]. ...... 51 3.17 In-vessel (a) and out-vessel (b) optics of FILD. Light path is depicted in green while lenses are in purple. In the out-vessel optics relay, CCD and APD cameras are visible. Extracted from [45]. ............ 52 3.18 Port plug in sector 8 with the outer fibre bundle without the vacuum window. A zoom on the fibre bundle shows scintillator image during installation. .................................. 53 3.19 CAD model of port plug in sector 8 with the out-vessel optical set including large APD camera and its holder ................ 54 3.20 (a) Fast-ion loss signal generated by different NBI sources and recorded by both CCD and APD cameras. Fast-ion loss velocity space pattern produced by tangential beam #6 (b) and radial beam #8 (c). Extracted from [45]. .................................... 55 3.21 An NTM observed in (a) Mirnov coil spectrogram (b) FILD APD channel 19 spectrogram. Extracted from [45]. .................. 56 4.1 Magnetically driven FILD sketch. A revolute joint (1) has been defined in the coil rotation axis. A circumference-line-type cam joint (2) models the contact between the pushing arm and the bearing. The contact between the probe head holder and each guiding bearing (3), (4), (5), and (6) has been defined as point-line-type cam joint. Extracted from [52]. ............................... 60 4.2 (a) Probe head position as a function of time. Different values for friction coefficient (µ= 0 and µ= 0.6) have been considered. Different retraction times (b) and reaction forces (c) in the pushing bearing (see figure 4.1) depending on the friction coefficient are shown during the retraction phase for Vret = 10 V. Extracted from [52]. ........... 62 4.3 FE analysis performed on the pushing rod showing how the force is being applied and a zoom in the region where the mechanical stresses are being concentrated on the rod. Presented on the conference related to reference [52]. ................................ 63 4.4 Structural safety factor of the FILD system as a function of the retraction time, the friction coefficient, and the voltage applied during the retraction phase. A system with µ= 0 and Vret= 10 V will retract in tsa f e ret = 0.08 s with a structural safety factor higher than 3. Extracted from [52]. .................................... 63 4.5 Measured IR heat flux on the divertor and its extrapolation towards the FILD probe head. Extracted from [60]. ................. 64 140 List of Figures 4.6 Mesh employed by ANSYS to calculate the evolution of the temperature distribution and associated stresses showing (a) an overview of the head, (b) the hole for the collimator and (c) the internal radius where the maximum stress is found. .................... 66 4.7 Heat flux applied on FILD4 taking into account incident angle (α) and collection length (Lcollection). ......................... 66 4.8 Measured IR heat flux on the divertor and its extrapolation towards the FILD probe head. ............................. 67 4.9 Predicted evolution of the maximum temperature on the FILD head for different duty cycles. Extracted from [60]. ............... 68 4.10 For 0.5 and 4.0 seconds, probe head temperature distribution (a,b), stress on the entire head (c,d) collimator hole (e,f) and inner radius (e,g). 69 4.11 Fatigue test data with R=0 on PGX graphite. Extracted from [64]. . . . 70 4.12 Front view of the FAST-PS. Extracted from [66]. .............. 71 4.13 Frames from different cameras in the VRT system covering the 5 FILDs installed on AUG. ............................... 74 4.14 Frames from VRT camera 07Eod with a zoom showing FILD4 being overheated. One can observe the ROI defined on the frame and how the Hotspot algorithm is able to locate FILD4 head in it. ......... 75 4.15 Temporal evolution of (a) plasma current, (b) line-integrated electron density, (c) FILD4 hotspot on camera 07Eod and (d) FILD4 insertion during discharge #36524. One can see that FILD is FILD4 is performing insertion-retraction cycles. During the second cycle the threshold for VPE is overcame and the discharge is terminated. If a lower threshold would have been defined, FILD4 could have retracted and the discharge would had continued. .................... 76 5.1 Head target (black) and measured (blue) insertion for the overdamped (a) and underdamped regimes (b). In the overdamped regime, the probe head takes longer to reach the target position. In the underdamped regime, the probe head overshoots, which could result in unexpected heat loads on the head. Extracted from [45] .......... 78 5.2 Coil trajectory inferred from discharge #36498 together with the simulated trajectory and the voltage externally applied to the coil during a insertion scan performed to obtain radial profiles. ........... 79 5.3 Simultaneous velocity-space measurements of discharge #38035 at 0.9s on FILD1, FILD2, FILD4 and FILD5. Different pitch angles are measured on the different probes. ........................ 80 5.4 Spectrograms of the FILD4 (a,c) and FILD1 (b,d) signals during discharge #36568. Losses induced by NTMs and TAEs are identified on each FILD during different time windows. ................ 81 List of Figures 141 5.5 Time traces of the plasma discharge #38050 showing (a) evolution of applied NBI and ICRH, (b) evolution of plasma current Ipand edge field-line helicity q95, (c) core and edge electron densities ne, (d) electron temperatures Teat the core and at ρpol =0.7, (e) the insertion of the FILD detector and the fast-ion loss level measured by the channel #19 of the FILD APD camera. Extracted from [60]. ............ 82 5.6 3D contour plot of the measured fast-ion distribution on shot #38050 between 4.86 and 5.1 seconds as a function of particle energy (keV), pitch angle (º) and radial location of the FILD collimator slit (m). Extracted from [60]. ............................... 83 5.7 Measured velocity-space pattern at the innermost insertion for #38050 and 5.1s. Deuterium is assumed for reconstructing the measured energy. The artifacts produced by the image guide can be identified as localized spots on the ICRH region. Regions of interest used to produce figure 5.8 and pitch-angle interrogated on figure 5.9 are over plotted. Extracted from [60]. ......................... 84 5.8 Radially-resolved ROI values defined for NBI and ICRH ions over consecutive reciprocating cycles. The NBI ions are observed to have a larger radial gradient than the ICRH population. Extracted from [60]. . 84 5.9 Radially and energy resolved fast-ion loss measurements for the pitch angles corresponding to NBI ions (70°) and ICRH ions (56°). One can observe that ICRH ions with larger energy have smaller radial gradient than those with low energy. Extracted from [60]. ........... 85 5.10 (a) Measured velocity-space pattern produced by NBI sources #6 and #8. (b) Comparison of measured pitch angle profile at the injection energy (93keV) of measured FILD signal and ASCOT predictions. Extracted from [60]. ............................... 86 5.11 Poloidal (a) and toroidal (b) projections of the beam deposition profile calculated by ASCOT for particles reaching the FILD probe head with a pitch angle centered at 40°. (c) zoom on the FILD probe head region. 87 5.12 Measured radial profiles for beam #8 (ionized at the HFS) and #6 (ionized at the LFS). ASCOT simulations reproduce the measured beam deposition profile of source #8. Extracted from [60]. ........... 87 5.13 (a) Temporal evolution of the divertor target current, used as an ELM monitor along with FILD inferred insertion. (b) Measured FILD signal including spikes induced by ELMs. Extracted from [60]. ......... 88 5.14 Measured spikes on the FILD signal induced by ELMs during two different discharges at different magnetic field on axis. Extracted from [60]. ....................................... 88 142 List of Figures 5.15 Overview of discharge #36521 showing (a) temporal evolution of plasma current, core and edge electron densities, (b) applied NBI and ECRH heating and (c) spectrogram of FILD signal showing MHD-induced coherent losses modulated by the FILD insertion. Extracted from [60]. 89 5.16 (a) Magnetic spectrogram of DTM with overlaid tracked amplitude. (b) Spectrogram of the FILD signal showing coherent losses at the same frequency as the DTM. (c) Samples of raw FILD signal together with its mean values and oscillating component at the mode frequency. Extracted from [60]. .............................. 90 5.17 Radial profile of orbit deflection at the FILD location (a) and at the innermost ρpol of the measured orbit (b) together with DTM radial structure measured by ECE. Extracted from [60]. ............. 91 5.18 A sketch showing the AUG saddle cois producing an n=2 perturbation. The Brcomponent of the applied field is observed on the separatrix and on a poloidal cut. ......................... 92 5.19 A sketch showing how the upper and lower set of coils produce a n=2 pattern. The contour plot in the middle shows the resulting magnetic perturbation as a function of the toroidal (φ) and poloidal (θ) angles. Magnetic field lines are overlaid in black. ................. 93 5.20 Temporal evolution of (a) auxiliary heating, (b) plasma and ELM control coil current, (c) electron density, (d) temperature and (e) fast-ion losses. Black (blue) traces correspond to discharge #34570 (#34571) where coil phasing ∆φUL =100° (∆φUL =−50°) was applied. ..... 94 5.21 TAEs and FILD signals during shots #34570 and #34571 showing suppression and excitation of TAEs depending on the applied differential coil phasing ∆ΦUL............................... 95 5.22 (a) Measured fast-ion velocity space. (b) Trajectories of the two dominant pitch angles measured by FILD at the NBI injection energy. . . . . 95 5.23 Time traces of identical discharges where only the phase of the lower set of coil is modified: (a) Applied heating, (b) plasma and saddle coil currents (c) electron density at the core and edge (d) temperatures at the core and TAE location. .......................... 96 5.24 Spectrograms of discargues #37698 and #37699 showing TAEs becoming marginally unstable and being affected by the applied coil phasing ∆φUL....................................... 97 5.25 Spectrograms of discargues #37698 and #37699 showing TAEs becoming marginally unstable and being affected by the applied coil phasing ∆φUL....................................... 97 5.26 FILD signal being modulated by the ∆φUL of the applied n=4 MPs in discharge #37698 (right polarity) and #36371 (wrong polarity). . . . 98 5.27 Spectrogram showing TAEs when a mixed spectrum n=2+n=4 is applied. ..................................... 99 List of Figures 143 6.1 Scheme showing how externally applied 3D magnetic fields, fast-ion population and TAEs propagating on the bulk plasma interact with each other. ...................................101 6.2 Radial profiles of electron temperature (Te), density (ne) plasma rotation (ωtor) and safety factor (q) inferred from the time point of interest and used as inputs for the MEGA simulations. ..............105 6.3 Convergence test performed changing the poloidal resolution while maintaining NR=NZ. The kinetic (a) and magnetic (b) energies converge with with a resolution of NR=NZ=512. .............108 6.4 Poloidal structure of the plasma response for magnetic field along the major radius δBRand toroidal flow velocity δvφ..............109 6.5 Scan on normalized plasma resistivity (η/vAR0µ0), for a n=4 run with NR×Nφ×NZ=512 ×32 ×512, ν=1·10−7vAR0and χ= 5·10−7vAR0...................................109 6.6 Radial magnetic field obtained for different simulated toroidal flows. The total magnetic field is reduced when increasing the simulated toroidal flow (ωsim). ..............................110 6.7 Poloidal spectrum of the radial magnetic field Brcalculated with (a) MEGA (b) VMEC (c) MARS-F (d) and MARS-F including parallel slow wave damping. .............................111 6.8 (a) Initial real-space of the fast-ion distribution integrated in velocityspace. (b) Initial velocity-space of the fast-ion distribution integrated in real-space. ..................................111 6.9 Temporal evolution of the kinetic energy associated to each toroidal harmonic during a multi-nsimulation. ...................112 6.10 Shear Alfvén continuum (white solid lines) and Fourier decomposition of the mode evolution at each radial position. ............113 6.11 Poloidal structure of a n=4 TAE, showing normalized Vr,Eφand δBr.. 113 6.12 Obtained normalized linear growth rates for different values of β0 EP.. 114 6.13 Initial fast-ion distribution for a hollow (a) and core-localized (d) fastion distributions. Obtained modes propagating on the TAE gap (b,e) and associated poloidal structure (c,f). ...................114 6.14 Temporal evolution of TAEs growing during the linear phase including the externally applied 3D perturbations of discharges #34570 and #34571 for β0 ep=0.3,0.4 and 0.5 %. ......................115 6.15 ERTL in discharges #34570 (a) and #34571 (b). Transport induced by TAE (c) and poloidal projection of trajectories (d) overlaying (green) or missing the TAE (black). .........................116 6.16 (a) Calculated energy exchange during a hybrid simulation. (b) Predicted fast-ion drive (γEP) based on 6.7. ERTL in phase space for the externally applied 3D fields employed on discharges #34570 (c) and #34571 (d). ...................................117 144 List of Figures A.1 FILD5 diagnostic overview. Originally A3 format. ............122 A.2 FILD5 case. Originally A3 format. .....................123 A.3 FILD5 holder for 8 rollers. Originally A3 format. .............124 A.4 FILD5 pushing arm. Originally A3 format. ................125 A.5 FILD5 connector of feedthrough and double cardan. Originally A3 format. .....................................126 A.6 FILD5 double cardan joint. Originally A3 format. ............127 A.7 FILD4 diagnostic overview. Originally A3 format. ............128 A.8 FILD4 coil, holder and pushing arm. Originally A3 format. .......129 A.9 FILD4 pushing arm. Originally A3 format. ................130 A.10 FILD4 moving rod. Originally A3 format. .................131 A.11 Ceramic bearing holder. Originally A4 format. ..............132 145 Bibliography [1] J. A. Wesson. Tokamaks. 1st ed. Clarendon Press, Oxford, 1997. [2] J. D. Lawson. “Some criteria for a power producing thermonuclear reactor”. In: Proceedings of the Physical Society. Section B 70.1 (1957), pp. 6–10. ISSN: 03701301. DOI:10.1088/0370-1301/70/1/303.URL:https://iopscience. iop.org/article/10.1088/0370-1301/70/1/303. [3] S. 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