Predictive simulations for plasma scenarios in the SMART tokamak

Fusion Engineering and Design 192 (2023) 113833 Available online 28 May 2023 0920-3796/© 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Contents lists available at ScienceDirect Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes Predictive simulations for plasma scenarios in the SMART tokamak A. Mancini a,b,∗, L. Velarde b,c, E. Viezzer a, D.J. Cruz-Zabala a, J.F. Rivero-Rodriguez d, M. Garcia-Muñoz a, L. Sanchis e, A. Snicker e, J. Segado-Fernandez b, J. Garcia-Dominguez b, J. Hidalgo-Salaverri b,c, P. Cano-Megias b,c, M. Toscano-Jimenez f, the PSFT Group aDepartment of Atomic, Molecular and Nuclear Physics, University of Seville, Seville, Spain bCentro Nacional de Aceleradores (U. Sevilla, CSIC, J. de Andalucia), Sevilla, Spain cDepartment of Energy Engineering, University of Seville, 41092 Seville, Spain dUnited Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK eDepartment of Applied Physics, Aalto University, Espoo, Finland fDepartment of Applied Physics III, University of Seville, Spain ARTICLE INFO Keywords: SMART ASTRA ASCOT5 FIESTA Plasma scenarios ABSTRACT The SMall Aspect Ratio Tokamak (SMART) is a new spherical machine that is currently being constructed at the University of Seville (Mancini et al., 2021; Agredano-Torres et al., 2021). The operation of SMART will cover three different phases reaching an inductive plasma current (𝐼𝑃) of more than 500 kA, a toroidal magnetic field (𝐵𝑇) of 1 T and a pulse length of 500 ms (Mancini et al., 2021; Agredano-Torres et al., 2021). The main goal of the SMART tokamak is to study high plasma confinement regimes in a broad triangularity range (-0.5≤𝛿≤0.5) (Doyle et al., 2021; Doyle et al., 2021). While in phase 1 the ohmic heating alone is expected to provide enough power to access the H-mode, in phase 2 and phase 3 the access to the H-mode will be ensured by applying Neutral Beam Injection (NBI) as external heating system. The NBI will consist of one injector at 25 keV and 1 MW of power. The overall design of the NBI, including injection geometry, energy and power have been optimized using the ASCOT5 code (Hirvijoki et al., 2021). The SMART scenarios have been developed with the help of the free boundary equilibrium solver code FIESTA (Cunningham, 2013) coupled to the linear time independent, rigid plasma model RZIP (Lazarus et al., 1990) to calculate the target equilibria for all the different operational phases. To assess the feasibility of those scenarios, predictive modelling needs to be included to evaluate properly the evolution of the temperatures, density profiles for both electrons and ions. To this extent, the 1.5D transport code ASTRA (Pereverzev and Yushmanov, 2002) has been used including models for the ohmic current, bootstrap current and current driven by NBI. This contribution discusses the electron and ion density and temperature profiles obtained for various scenarios for phase 1 and 2 and presents the design study of the NBI. 1. Introduction The SMall Aspect Ratio Tokamak (SMART) is a new spherical tokamak currently being constructed and assembled at the University of Seville [1,2]. SMART will operate through three phases that differ in value of the plasma current 𝐼𝑝up to more than 500 kA, toroidal magnetic field 𝐵𝑇up to 1 T and pulse length 𝜏up to 500 ms, see Table 1. Its versatility is the operation in single and double null configuration, and with positive and negative triangularity (−0.5≤𝛿≤ 0.5[3,4]). By phase 2, SMART will also be equipped with a Neutral Beam Injector (NBI) with a maximum power of 1 MW, to study the effects of fast-ion physics in high positive and negative triangularity scenarios. In this environment, the prediction of plasma performance ∗Corresponding author at: Department of Atomic, Molecular and Nuclear Physics, University of Seville, Seville, Spain. E-mail address: [email protected] (A. Mancini). of the machine is essential and can be achieved by using predictive modelling codes in order to compute the evolution of plasma profiles, such as temperature and density, for the three different phases. The aim of the paper is the description of the SMART performances in the first two phases and it is organized as follows. Section 2will provide a general description of the SMART tokamak, while the equilibrium obtained with FIESTA [3–5] and the transport model used in ASTRA [6] will be detailed in Section 3. Phase 1 in its baseline and positive triangularity scenarios will be addressed in Section 4, while Phase 2 will be discussed in Section 5with density and temperature profiles in 5.1 and the description of the optimization process of the NBI in 5.2. This work focuses solely in phase 1 and phase 2 in positive triangularity, https://doi.org/10.1016/j.fusengdes.2023.113833 Received 28 October 2022; Received in revised form 31 March 2023; Accepted 17 May 2023 Fusion Engineering and Design 192 (2023) 113833 2 A. Mancini et al. Fig. 1. Overview of the SMART tokamak together with the Neutral Beam Injector (NBI). Fig. 2. Phase 1 equilibrium from FIESTA. Baseline is depicted on the left while the positive triangularity case is on the right. while negative triangularity will be assessed in a separate work. The positive triangularity scenarios have been computed in order to assess the performance of the machine in terms of toroidal beta 𝛽𝑡, poloidal beta 𝛽𝑝, normalized beta 𝛽𝑁=𝛽𝑡∕(𝐼𝑝∕(𝑎𝐵𝑇)) and confinement time 𝜏𝐸. In addition, the evaluation of those scenarios will constitute a solid base for the design of many diagnostics, and for MHD and gyrokinetics analysis, and their validity will be proven once the machine will come into operation. 2. SMART tokamak The SMall Aspect Ratio Tokamak (SMART) is a compact spherical machine characterized by an overall height of 3 m and an overall diameter of 2 m. It is composed by an AISI 316 L stainless steel vacuum vessel having an inner wall diameter of 300 mm, outer wall diameter of 1600 mm and an inner height of 1600 mm. The vacuum vessel has an overall number of 44 circular ports and 2 rectangular ports mainly aimed for diagnostics and maintenance purposes. A set of twelve copper toroidal field coils (4 number of turns each) are capable of producing the desired toroidal magnetic field (𝐵𝑇) at the major radius (𝑅0) of the plasma for all the operative phases (see Table 1). Four poloidal field coils (PF1 and PF2), with 23 number of turns each, are needed for the vertical control and shaping of the plasma. Table 1 Operative stages of the SMART tokamak. Phase 1 Phase 2 Phase 3 𝑅0[m] 0.4 0.4 0.4 𝑎[m] 0.25 0.25 0.25 𝜅≤1.95 ≤2.00 ≤2.30 𝛿±0.4 ±0.5 ±0.5 𝐼𝑃[kA] 100 200 > 500 𝐵𝑇[T] 0.1 0.4 1 𝜏[ms] 0.100 0.150 0.500 𝑃𝐸𝐶𝑅𝐻 [kW] 6 (2.45 GHz) 6 (7.5 GHz) 200 𝑃𝑁𝐵𝐼 [kW] – 1000 1000 Table 2 ASTRA input model data. Phase 1 Phase 2 base @𝛿𝑚𝑎𝑥 base @𝛿𝑚𝑎𝑥 𝛥𝑠[m] 0.059 0.067 0.035 0.032 𝐼𝑃[kA] 30 30 200 200 𝐵𝑇[T] 0.1 0.1 0.4 0.4 𝜅1.83 1.48 1.95 1.79 𝛿0.23 0.4 0.35 0.4 𝑆𝑝[m2] 5.081 5.12 6.80 6.31 𝑉𝑝[m3] 0.68 0.70 1.03 0.90 𝛽𝑡1.74 2.46 2.92 3.3 𝛽𝑝0.337 0.395 0.325 0.322 𝛽𝑛1.25 1.77 1.46 1.61 The PF1 coils are placed outside the vessel while the PF2 are placed inside (see Fig. 1). Two pairs of divertor field coils (DIV1 and DIV2 in Fig. 1), all placed inside the machine, are needed to reach the desired elongation 𝜅and to operate the machine in single or double null configuration and in positive and negative triangularity [3,4]. The number of turns of these coils differs, being 35 for DIV1 and 23 for DIV2. A copper solenoid with 230 number of turns completes the magnetic system of the machine. SMART will be equipped with four vacuum pumps: two dry pumps of 80 m3h−1 and two turbomolecular pumps of 2300 lts−1 designed to obtain the required level of vacuum of 10−8torr with a maximum leakage of 10−8mbar ⋅lts−1. Additional heating systems such as Electron Cyclotron Resonance Heating (ECRH) and Neutral Beam Injector (NBI) will also be installed during the operational phases of the machine. The optimization process and the parameters for the NBI are discussed in Section 5.2. Additional information are detailed in [1,2]. 3. Plasma scenarios modelling The development of the operative scenarios assume an important role in the design of tokamak devices, as they influence the operation of the machine, the assessment of the performance but also the design of several diagnostic systems which need an estimation of the profiles of electron and ion density (𝑛𝑒,𝑛𝑖) together with their temperature profiles (𝑇𝑒,𝑇𝑖). In the SMART design, the modelling of the plasma scenarios have been computed using the ASTRA code, a 1.5 D transport code which combines 2D equilibrium equations with a set of 1D transport equations [6]. The input parameters for the modelling are the major radius 𝑅0, minor radius 𝑎, elongation 𝜅, triangularity 𝛿, Shafranov shift 𝛥𝑠, plasma volume 𝑉𝑝and plasma surface 𝑆𝑝, which have been computed with the FIESTA code [5,7]. The equilibrium profiles for phase 1 and phase 2 are shown in Figs. 2 and 3with the main equilibrium parameters summarized in Table 2. The different beta (𝛽𝑁, 𝛽𝑡and 𝛽𝑝) included in Table 2 have been computed with FIESTA and verified with ASTRA. The transport simulations were carried out with ASTRA by considering a hydrogen plasma with 𝑍𝑒𝑓𝑓 equal to 2, a Greenwald fraction (𝑓𝐺𝑊 ) of 0.4 and a GyroBohm model [8] for the transport coefficients: 𝜒𝑖=𝐶1 𝑎2𝑇3∕2 𝑒 𝐵2 𝑡𝑜𝑟𝜇2 ∇𝑇𝑒 𝑇𝑒 (1) Fusion Engineering and Design 192 (2023) 113833 3 A. Mancini et al. Fig. 3. Phase 2 equilibrium from FIESTA. Baseline is depicted on the left while the positive triangularity case is on the right. 𝜒𝑒= 2𝜒𝑖(2) 𝐷=𝐶2𝜒𝑒(3) 𝑣=𝐶3𝑣𝑝𝑉′−𝐷 𝑅0(0.2𝑅0 𝐿𝑇 𝑒 + 0.1𝑠𝐶4)(4) being 𝜒𝑖the ion heat transport coefficient, 𝜒𝑒the electron heat transport coefficient (assuming pure Ion Temperature Gradient, ITG), 𝐷the diffusion coefficient, 𝑣the convective velocity, 𝑣𝑝=𝐸||∕𝐵𝑝the pinch velocity indicating with 𝐸|| the parallel component of the electric field and 𝐵𝑝the poloidal component of the magnetic field. Finally 𝐿𝑇 𝑒 =𝑇𝑒∕∇𝑇𝑒is the electron temperature gradient length scale and 𝑠the shear. The coefficients 𝐶1,𝐶2,𝐶3and 𝐶4have been chosen equal to [0.4, 0.2, 0.1, 1] to have comparable transport coefficients of machines with similar size/aspect ratio of SMART (i.e. GLOBUS-M [9] and Pegasus [10]) and to take into account also neoclassical effects. For the simulations in H-mode, 𝜒𝑖has been chosen equal to 4 m2s−1 with the edge transport barrier (ETB) placed at 𝜌𝑝𝑜𝑙 = 0.95 [9–11] and leaving the same approximation of the GyroBohm model for the other coefficients (see Section 5.1). 4. Phase 1 scenarios In this section the phase 1 scenarios will be discussed both in the baseline and positive triangularity case. Simulations for phase 1 equilibria have been run with the parameters included in Table 2. Figs. 4 and 5show the density and temperature profiles as a function of the normalized radius 𝜌𝑝𝑜𝑙 =√(𝜓−𝜓𝑏)∕(𝜓𝑏−𝜓0), being 𝜓𝑏and 𝜓0the value of the poloidal flux at the separatrix and in the centre respectively. The density increases with the triangularity both for ions and electrons. The core electron density 𝑛𝑒0increases from 0.865 × 1019 m−3 to 1.01 × 1019 m−3, while the core ion density 𝑛𝑖0increases from of 0.7 × 1019 m−3 to 0.8 × 1019 m−3. Temperature profiles show the same trend, with a maximum of 0.171 keV and 0.08 keV respectively for 𝑇𝑒 and 𝑇𝑖in the core. The benefits of increasing the triangularity is also manifested in the reduction of the transport coefficients 𝜒𝑖,𝜒𝑒and 𝐷 as shown in Fig. 6. In phase 1, no additional source of energy is used to heat the plasma apart from the intrinsically ohmic heating. The ohmic power, 𝑃𝑂𝐻 , can be estimated as [12]: 𝑃𝑂𝐻 [MW] = 7 × 10−2 𝑍𝑒𝑓𝑓 𝐵2 𝑇𝑉𝑝 𝑞2 𝑎𝑅2 0𝑇3∕2 𝑒 (5) Fig. 4. 𝑛𝑒and 𝑛𝑖profiles for phase 1 in the baseline scenario and in the positive triangularity case. Fig. 5. 𝑇𝑒and 𝑇𝑖profiles for phase 1 in the baseline scenario and in the positive triangularity case. Fig. 6. 𝜒𝑖,𝜒𝑒and 𝐷profiles for phase 1 in the baseline scenario and in the positive triangularity case. where 𝑞𝑎= 5𝜅𝑎2𝐵𝑇∕𝑅𝐼𝑝is the safety factor at 𝑟=𝑎and 𝑇𝑒the average electron temperature in keV. Using this simple 0-D approximation, with the parameters included in Table 2, the ohmic power 𝑃𝑂𝐻 is 47 kW, similar to 50 kW estimated with ASTRA. The threshold power for the transition from L- to the H-mode (𝑃𝐿𝐻 ) can be evaluated with the following expression [13,14]: 𝑃𝐿𝐻 [MW] = 0.0488𝑛0.717 20 𝐵0.803 𝑇𝑆0.941 (6) where 𝑆= 4𝜋2𝑎𝑅√0.5(1 + 𝑘2)is the plasma surface area and 𝑛20 the electron average density expressed in 1020 unit. For phase 1, the Fusion Engineering and Design 192 (2023) 113833 4 A. Mancini et al. Fig. 7. Density profiles for phase 2 with and without NBI. threshold power is approximately 9 kW. The radiative power 𝑃𝑟𝑎𝑑 from the plasma, approximated by the sum of the Bremsstrahlung 𝑃𝐵𝑟 and cyclotron 𝑃𝑐𝑦𝑐𝑙 losses, can be neglected as approximately equal to 60 W. 𝑃𝐵𝑟 and 𝑃𝑐𝑦𝑐𝑙 have been estimated with the followingexpressions [15]: 𝑃𝐵𝑟[W] = 𝑍2 𝑒𝑓𝑓 𝑛𝑖𝑛𝑒𝑇0.5 𝑒 [7.69 × 1018]2𝑉𝑝(7) 𝑃𝑐𝑦𝑐𝑙[W] = 6.21 × 10−22𝐵2 𝑇𝑛𝑒𝑇𝑒𝑉𝑝(8) which gives results in accordance with ASTRA simulations. Therefore, neglecting the radiative power 𝑃𝑟𝑎𝑑 , it is expected that in phase 1 SMART will achieve the ohmic H-mode (𝑃𝑂𝐻 ≫ 𝑃𝐿𝐻 ). The energy confinement time has been approximated with the following scaling law valid at low densities and for ohmic heating [16]: 𝜏𝐸[s] = 0.07𝑛20𝑎𝑅2 0𝑞𝑐𝑦𝑙 (9) where 𝑞𝑐𝑦𝑙 = 5𝑎2𝐵𝑇∕𝐼𝑝𝑅the cylindrical safety factor. For phase 1, an energy confinement time of 0.33 ms is expected while ASTRA predicts 0.22 ms, slightly lower but of the same order of magnitude. The bootstrap current fraction 𝑓𝑏𝑠 is expected to increase with the triangularity 𝛿from 14.3% to 15.1% as there is a small increase in 𝛽𝑝, see Table 2. 5. Phase 2 scenarios 5.1. ASTRA results ASTRA simulations have been carried out in order to determine the profiles of density and temperature in phase 2 with and without the NBI. The parameters of the NBI used for the ASTRA simulations are the injected power (𝑃𝑁𝐵𝐼 ) of 1 MW and energy (𝐸0) of 25 keV as described in Section 5.2. Only the NBI heating has been included in the simulations. No ECRH heating has been considered as it will only be used for pre-ionization during the plasma start-up. The baseline case has been compared with the extreme positive triangularity, even though the two configurations differ slightly (see Table 2). Figs. 7 and 8show the density and temperature profiles in phase 2 where the blue curves represents the scenarios without NBI, and the red ones with the NBI. Dotted curves in both cases represent the scenarios in the highest positive triangularity case. With the NBI a rise in both density and temperature is expected. 𝑛𝑒0and 𝑛𝑖0will increase up to 4.7× 1019 m−3 and 3.8 × 1019 m−3. No big difference is expected between the baseline and the extreme positive triangularity case, as the difference in triangularity for those two cases is 0.1. A large increase is expected in the electron and ion temperature. 𝑇𝑒and 𝑇𝑖will increase up to 0.56 keV and 0.7 keV respectively in Fig. 8. Temperature profiles for phase 2 with and without NBI. Fig. 9. Transport coefficients with the ETB located at 𝜌𝑝𝑜𝑙 = 0.95. the baseline case. In the case of extreme positive triangularity, the ion temperature will be slightly higher up to 0.75 keV and the electron temperature up to 0.6 keV. Scenarios with NBI will enhance the 𝛽 parameters. In the baseline case, the 𝛽𝑡will rise up to 8.23%, 𝛽𝑝up to 0.7 and 𝛽𝑁up to 4.1, compared to the values reached in phase 1 (see Table 2). In the extreme positive case 𝛽𝑡will rise up to 9.1%, 𝛽𝑝of 0.69 and 𝛽𝑁up to 4.44. Moreover, ASTRA results foresee a bootstrap current fraction that increase from 𝑓𝑏𝑠 ≈ 15% in phase 1 to 𝑓𝑏𝑠 ≈ 37% in phase 2 (𝐼𝑏𝑠 ≈66 kA), with a current fraction induced from the NBI (𝑓𝐶𝐷) of almost 15% which corresponds to an induced current 𝐼𝐶𝐷 ≈ 30 kA, in line with the results of GLOBUS-M [17]. ASTRA simulations predict that the total beam power 𝑃𝐶𝐷 is approximately 0.7 MW high enough to overcome 𝑃𝐿𝐻 , see formula (6), which is approximately 90 kW. The radiative power can be neglected as in phase 1. In fact, using the formulas (7) and (8), the radiative power can be estimated to almost 2.2 kW. Therefore it is expected that in phase 2 with the NBI, SMART will achieve the H-mode as 𝑃𝐶𝐷 ≫ 𝑃𝐿𝐻 . In addition without the NBI, the ohmic power (𝑃𝑂𝐻 ), evaluated with the formula (5), is approximately 0.22 MW similar to the 0.27 MW obtained with ASTRA. As the ohmic power is higher than the threshold power it is likely to expect that SMART will achieve in a H-mode regime also without the NBI. This justifies the approximation of using the transport coefficients with the profiles shown in Fig. 9 and described in Section 3. Fusion Engineering and Design 192 (2023) 113833 5 A. Mancini et al. As the operation will be in H-mode, the confinement time 𝜏𝐸can be estimated with the ITER IPB(y,2) scaling law [18]: 𝜏𝐸[s] = 0.145 𝐼0.93 𝑃𝑅1.39 0𝑎0.58𝑘0.78𝑛0.41 20 𝐵0.15 𝑇𝑀0.19 𝑃0.69 𝐻 (10) where 𝑃𝐻=𝑃𝑁𝐵𝐼 is the external heating power. For phase 2 we get a confinement time of 6.5 ms slightly lower but of the same order of magnitude of the one computed by ASTRA, 10 ms. A better estimation of the confinement time 𝜏𝐸is obtained when considering a NSTX-GyroBohm scaling law valid for spherical tokamaks [19]: 𝜏𝐸[s] = 0.21 𝐼0.054 𝑝𝐵0.91 𝑇𝑅2.14 0 𝑛0.05 𝑒𝑃0.38 𝐻 (11) which gives a 𝜏𝐸of almost 9 ms, in line with the ASTRA results. 5.2. NBI design and optimization To ensure H-mode in phase 2, 1 MW of Neutral Beam Injection (NBI) will be applied to positive-triangularity SMART plasmas. Beam height and width have been determined scaling NBIs of similar machines in size of SMART, such us Globus-M. The preliminary dimensions of the grid beams considered in the simulations are height and width of 30 cm and 33 cm respectively. The main parameters of the NBI have been optimized through the Monte-Carlo orbit-following code ASCOT5 [20], using the wall geometry and the magnetic equilibrium calculated with FIESTA (see Section 3) and the temperature and density profiles obtained with ASTRA without external heating, see Section 5.1. The optimization of the main NBI parameters has been performed with an iterative process, analysing the confinement of different particles injected at the separatrix (𝑟= 0.75 m and 𝑧= 0 m) and ionized inside the plasma. Here, the optimization of the injection geometry is presented, performed setting the NBI main beam energy, 𝐸0, to 25 keV. This has been considered as the best choice for phase 2 according to previous analysis, and matching the energy observed in other similar machines [9]. The energy of the beam is limited on one hand by the gyroradius of the resulting particles, that increases with energy (𝑟𝐿= 𝑚𝑣⟂∕𝑞𝐵 ∝𝐸0∕𝐵), and by the orbit drifts, thus affecting fast-ion losses. On the other hand, the higher the energy, the lower the cross-section of the global ionization processes between the injected neutrals and the thermal plasma [21], increasing the shine-through (i.e., the percentage of particles that travel through the plasma without getting ionized), and thus, decreasing the total efficiency. Therefore, the two main parameters employed to optimize the NBI geometry and energy are the prompt losses (i.e., particles that are lost before completing a toroidal period) and the shine-through. Moreover, a 25 keV injection energy provides a super-Alfvénic fast-ion distribution, as the Alfvén velocity at 𝜌𝑝𝑜𝑙 = 0.5is 𝑣𝐴∼ 1.6 × 106m∕s, while the velocity corresponding to the main injection energy is 𝑣= 2.2 × 106m∕s, making it possible to drive unstable a wide variety of Alfvén Eigenmodes, enabling to study their behaviour as a function of plasma shape and triangularity. Higher injection energies, up to 35 keV, will also be considered during the optimization process. In order to optimize the injection configurations, the fast-ion birth distribution has been modelled with a set of 106markers (high enough to achieve good statistics, according to previous analysis), whose orbits are followed for 1 ms. The different sets of markers have been generated with the BBNBI code [22], by varying the tangency radius of the beam centre line, as shown in Fig. 10. Then, by means of the ASCOT5 code, the ionized particles have been followed in a collisionless and MHD- quiescent environment, in order to calculate the percentages of prompt losses (as mentioned, particles lost before completing a toroidal period, and thus, not affected by Coulomb collisions). The selected simulation time is sufficient to account for the prompt losses. The shine-through has also been calculated for each of the 9 cases studied, with the aim to minimize the total amount of particles that are lost. Fig. 10. Sketch of the toroidal view of the SMART NBI configuration. The black circles represent the vessel walls and the red ones the toroidal section of the separatrix. The yellow line represents the beamline. The perpendicular distance from the beam to the centre of the device is represented by the blue circle and line, indicating the tangency radius, 𝑅𝑡. Fig. 11. NBI birth distribution in the toroidal projection for the most extreme configurations, #1 (up) and #9 (down). The results for the different configurations studied by varying the chosen optimization parameter, 𝑅𝑡, are shown in Fig. 12. As the plasma inner and outer radius is located at 0.243 mand 0.747 m,𝑅𝑡has been modified from 0.280 mto 0.735 m. The toroidal view of the birth distribution of the particles generated with these two extreme configurations are shown in Fig. 11. The minimum total amount of losses is provided by configurations #3 and #4, see Fig. 12. The rise in the shine-through with 𝑅𝑡is explained considering that, as the tangency radius is increased, the beam travels a shorter path through the plasma, in a region with lower density. On the contrary, increasing the tangency radius, the beam aligns with the magnetic field lines, decreasing the prompt losses to Fusion Engineering and Design 192 (2023) 113833 6 A. Mancini et al. Fig. 12. Evolution of the resulting losses for the different configurations (red circles) studied for the NBI system. Fig. 13. Slowing down distribution for the optimum configuration, #4, in pitch-energy. a negligible level. Hence, configurations from #5 to #9 should be discarded, as the shine-through is too high, as well as configurations #1 and #2, due to their higher result in prompt losses in comparison to the others. As configurations #3 and #4 show similar results, the shine-through and the prompt losses have been computed at higher injection energies, up to 35 keV, for both geometries. This criteria has been chosen in order to assess their performance in the possible case of an increase in the energy of the beam in the future [23], which would be performed without changing the injection geometry of the NBI. 35 keV is set as the maximum permitted injection energy, as it allows maintaining the shine-through below 10% with the current plasma profiles. The results in Table 3 show that, as the energy increases, the prompt losses in configuration #3 rise rapidly. The shine-through, on the contrary, increases for both configurations, and its absolute value is comparable. This evolution of the prompt losses with the energy has led to choose configuration #4 as the optimum one, showing that the injection energy of the NBI system could be increased in the future if desired, and the prompt losses would stay in an admissible range, while preserving an acceptable evolution of the shine-through fraction, always kept below 10%. The slowing down distribution for configuration #4 and a 25 keV injection energy has also been analysed. For this simulation, the injected particles are allowed to interact with the bulk plasma via Coulomb collisions for 1 s, which is found sufficient for most of the fast-ion distribution to thermalize. The markers are stopped when they reach either the selected thermal limit of 1 keV, or the maximum simulation Fig. 14. Birth distribution of the particles generated with the optimized configuration (#4). Toroidal (up) and poloidal (down) projections. The latter includes a typical confined orbit. Table 3 Resulting losses for configurations #3 and #4, and different injection energies. ID Energy Shine-through Prompt losses Total losses 25 keV 4.9% 0.1% 5.0% 3 30 keV 6.9% 0.4% 7.3% 35 keV 9.0% 1.1% 10.1% 25 keV 5.3% 0.0 % 5.3% 4 30 keV 7.4% 0.1 % 7.5% 35 keV 9.6% 0.5 % 10.1% time. As shown in Fig. 13, most of the particles have a pitch angle above 0.9, meaning that they will describe passing orbits. This is desirable in order to reduce possible losses due to the drift of trapped orbits, and results in a better confinement of the beam particles. Hence, the birth distribution for the selected configuration (#4) is shown in Fig. 14, where an example of a passing orbit has been plotted in the poloidal projection of the distribution. 6. Conclusions Reference scenarios for the SMART tokamak have been computed with the 1.5D transport code ASTRA coupled with FIESTA to predict the density and temperature profiles needed primarily for the assessment of the performances of the machine. Only the baseline and maximum positive triangularity scenarios have been considered for phase 1 and phase 2. In phase 1 the parameters chosen here suggest that the machine will access the H-mode with a maximum 𝑛𝑒0and 𝑛𝑖0of 1×1019 m−3 and 0.8×1019 m−3. Maximum temperature 𝑇𝑒0and 𝑇𝑖0of 0.171 keV and 0.080 keV will be achieved with a maximum confinement energy time 𝜏𝐸of 0.2 ms, lower than the one estimated with the confinement scaling law for ohmic heating but of the same order of magnitude. Phase 2 will be equipped with a Neutral Beam Injector whose characteristics have been presented together with the optimization of its parameters, Fusion Engineering and Design 192 (2023) 113833 7 A. Mancini et al. in particular energy and injection geometry. The best configuration has been determined, opening the possibility of increasing the NBI energy without changing the injection geometry in the future. ASTRA simulations for phase 2 predict that SMART will access H-mode with and without NBI as both the Ohmic Power (𝑃𝑂𝐻 ) and the NBI coupled power (𝑃𝐶𝐷) are sufficiently higher than the threshold power (𝑃𝐿𝐻 ) as long as the experiments will confirm that the radiative power losses will be negligible. Core densities up to 4.65 × 1019 m−3 will be reached with a core temperature of 0.75 keV. Beta normalized 𝛽𝑁will increase up to 4.4 with a toroidal 𝛽𝑡up to 9%. A bootstrap current fraction of 𝑓𝑏𝑠 of 37% will be reached and a NBI current drive fraction 𝑓𝐶𝐷 of 15% is expected. Negative triangularity profiles will be assessed in a separate work, exploring also the phase 3 scenario. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request Acknowledgements This work received funding from the Fondo Europeo de Desarollo Regional (FEDER) by the European Commission under grant agreement numbers IE17-5670 and US-15570. The authors gratefully acknowledge the financial support of the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 805162). References [1] A. Mancini, et al., Mechanical and electromagnetic design of the vacuum vessel of the SMART tokamak, Fusion Eng. Des. 171 (2021). [2] M. Agredano-Torres, J.L. Garcia-Sanchez, A. Mancini, et al., Coils and power supplies design for the SMART tokamak, Fusion Eng. Des. 168 (2021). [3] S.J. Doyle, D. Lopez-Aires, A. 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