A multi-machine scaling of halo current rotation

PAPER A multi-machine scaling of halo current rotation To cite this article: C.E. Myers et al 2018 Nucl. Fusion 58 016050 View the article online for updates and enhancements. Related content The ITPA disruption database N.W. Eidietis, S.P. Gerhardt, R.S. Granetz et al. - The halo current in ASDEX Upgrade G. Pautasso, L. Giannone, O. Gruber et al. - Characterization of disruption halo currents in the National Spherical Torus Experiment S.P. Gerhardt, J. Menard, S. Sabbagh et al. - Recent citations KSTAR Status and Upgrade Plan Toward Fusion Reactor Jong-Gu Kwak et al - Dependence of disruption forces on the plasma position inside the vacuum vessel in tokamaks V D Pustovitov - Overview of disruptions with JET-ILW S.N. Gerasimov et al - This content was downloaded from IP address 37.158.234.192 on 20/07/2020 at 12:09 1© 2017 Princeton University Plasma Physics Laboratory Printed in the UK 1. Introduction When a tokamak plasma disrupts, large electric currents are driven in the conducting walls that surround the plasma [1–8]. A portion of these wall currents are eddy currents induced by the disrupting plasma [9], while the remainder are so-called halo currents that are driven when the plasma makes direct contact with the wall [10, 11]. Inside the wall, both eddy and halo currents can flow across magnetic field lines and produce large J×B Lorentz forces that can jeopardize the structural integrity of the machine [9, 12, 13]. Given the increasing size and parameters of next-generation tokamaks such as ITER, these wall-current-generated forces pose a significant threat to the viability of the tokamak as a fusion reactor concept [14– 20]. As such, it is imperative to understand how the various disruption wall current phenomena will scale in next-gener- ation devices. In this paper, we focus on the behavior of halo currents, which flow along a hybrid current path that connects the scrape-off layer of the plasma to the wall of the machine. This plasma-wall circuit enables the direct measurement of the halo currents as they enter or exit the first wall [21, 22]. Such measurements reveal that halo currents often develop toroidal asymmetries [3–8, 23–26] that are attributed to a magnetohydro dynamic kink mode [27–31] that destabilizes when the Nuclear Fusion A multi-machine scaling of halo current rotation C.E.Myers1, N.W.Eidietis2, S.N.Gerasimov3, S.P.Gerhardt1, R.S.Granetz4, T.C.Hender3, G. Pautasso5 and JET Contributorsa 1 Princeton Plasma Physics Laboratory, Princeton, NJ 08543, United States of America 2 General Atomics, San Diego, CA 92186, United States of America 3 CCFE, Culham Science Centre, Abingdon, OX14 3DB, United Kingdom 4 MIT Plasma Science and Fusion Center, Cambridge, MA 02139, United States of America 5 Max-Planck-Institüt für Plasmaphysik, D-85748 Garching, Germany E-mail: [email protected] Received 23 May 2017, revised 29 September 2017 Accepted for publication 24 October 2017 Published 12 December 2017 Abstract Halo currents generated during unmitigated tokamak disruptions are known to develop rotating asymmetric features that are of great concern to ITER because they can dynamically amplify the mechanical stresses on the machine. This paper presents a multi-machine analysis of these phenomena. More specifically, data from C-Mod, NSTX, ASDEX Upgrade, DIII-D, and JET are used to develop empirical scalings of three key quantities: (1) the machinespecific minimum current quench time, τCQ ; (2) the halo current rotation duration, trot ; and (3) the average halo current rotation frequency, fh . These data reveal that the normalized rotation duration, trot /τ CQ , and the average rotation velocity, vh , are surprisingly consistent from machine to machine. Furthermore, comparisons between carbon and metal wall machines show that metal walls have minimal impact on the behavior of rotating halo currents. Finally, upon projecting to ITER, the empirical scalings indicate that substantial halo current rotation above fh = 20 Hz is to be expected. More importantly, depending on the projected value of τCQ in ITER, substantial rotation could also occur in the resonant frequency range of 6–20 Hz. As such, the possibility of damaging halo current rotation during unmitigated disruptions in ITER cannot be ruled out. Keywords: tokamak, disruptions, halo currents (Some figuresmay appear in colour only in the online journal) C.E. Myers etal A multi-machine scaling of halo current rotation Printed in the UK 016050 NUFUAU © 2017 Princeton University Plasma Physics Laboratory 58 Nucl. Fusion NF 10.1088/1741-4326/aa958b Paper 1 Nuclear Fusion IOP International Atomic Energy Agency a See the author list of ‘Overview of the JET results in support to ITER’ by Litaudon etal [52]. 2018 1741-4326 1741-4326/18/016050+15$33.00 https://doi.org/10.1088/1741-4326/aa958b Nucl. Fusion 58 (2018) 016050 (15pp) C.E. Myers etal 2 edge safety factor drops below q95 ∼2 [32]. The resulting helically kinked plasma only makes contact with a finite toroidal sectionof the wall such that the halo currents are preferentially driven in a toroidally localized region. This generates toroidally asymmetric forces that manifest themselves, for example, as strong lateral impulses in large tokamaks such as JET [9, 23, 25]. Given that toroidal halo current asymmetries are largely ameliorated by disruption mitigation systems such as massive gas injection (MGI) [33, 34], we focus in this paper on halo currents generated during unmitigated disruptions. An additional consideration regarding asymmetric halo currents is that the location of the asymmetry often rotates toroidally during the disruption [3, 7, 35–37]. At first glance, this rotation might seem to be beneficial because it reduces the directional coherence of the lateral or vertical impulse delivered to the machine. This benefit becomes a detriment, however, if the halo currents complete 2–3 full rotations at a frequency that resonates with critical machine components. Such resonant rotation can produce dynamically amplified forces that enhance the overall structural loads. For ITER, the critical coil and vessel resonances are in the 3–8 Hz range, while integrated system resonances extend into the 10–20 Hz band [18, 19]. Thus, the rotating halo current problem in ITER can be summarized in a single question: Are halo currents in ITER likely to complete 2–3 full rotations at frequencies below 20 Hz? The goal of this paper is to answer this question by developing an empirical scaling of halo current rotation that can be extrapolated to ITER. Though halo current rotation has been observed in a number of devices [3, 7, 35–37] and explored with theory [38, 39] and simulations [40], no experimental investigation of how it scales with machine parameters has yet been conducted. The approach used here is to assemble a multi-machine database of toroidally resolved halo current measurements and then to process these data within a common analytical framework. This undertaking, which is conducted under the auspices of the International Tokamak Physics Activity (ITPA), facilitates the development of empirical scalings for three key quantities: (1) the machine-specific minimum current quench time, τCQ ; (2) the halo current rotation duration, trot ; and (3) the time-averaged halo current rotation frequency, fh . When combined, the latter two quantities characterize the total rotation count, Nrot , at a given rotation frequency: Nrot =  fh · trot = v h  2πR· trot , (1) where vh is the time-averaged toroidal rotation velocity and R is the major radius of the machine. In this paper, we use a newly constructed ITPA halo current rotation database to empirically determine how τCQ , trot , and fh scale with key machine parameters. Once these scalings are established, a prediction can be made as to which rotation frequencies are likely to complete at least 2–3 rotations in ITER. The remainder of the paper is organized as follows: in section2, the format and contents of the ITPA halo current rotation database are described. Then, in section3, a scaling of the machine-specific minimum current quench time, τCQ , is developed. This scaling ultimately facilitates the projection of the behavior of rotating halo currents to ITER. Next, in section4, we analyze the properties of rotating halo currents, including their rotation frequency and velocity as well as their preferred direction of rotation. Then, in sections5.1 and 5.2, we use the results of sections3 and 4 to develop empirical scalings of the halo current rotation duration, trot , and rotation frequency, fh . In section5.3, these scalings are used to project the behavior of rotating halo currents in ITER. Finally, in section6, we close with a discussion of candidate physical mechanisms that may explain some of the halo current rotation phenomena reported here. 2. The ITPA halo current rotation database In order to develop a multi-machine scaling of halo current rotation, a new database of toroidally resolved halo current measurements is required. The approach taken here is to collect raw halo current data (e.g. shunt tile waveforms) from a number of devices that have deployed toroidally resolved halo current sensor arrays. The resulting ITPA halo current rotation database therefore contains a substantial amount of raw data that are processed within a common analytical framework. The new ITPA halo current rotation database includes data from five tokamaks: Alcator C-Mod [3], DIII-D [35], ASDEX Upgrade (AUG) [7], NSTX [36], and JET [34, 37]. These machines collectively span a wide range of spatial scales and equilibrium parameters so that the scaling of halo current rotation with a variety of machine parameters can be assessed. The impact of the wall material (metal versus carbon), for example, is a key concern when extrapolating from presentday tokamaks to ITER, which will use a tungsten-and-beryl- lium metal wall. As such, data from both carbon and metal wall machines are included in the database. Table1 lists the various datasets in the ITPA halo current rotation database, separated by machine and wall material. Four of the datasets (DIII-D, NSTX, AUG-C, and JET-C) were acquired during carbon wall operations, while the three remaining datasets (C-Mod, AUG-W, and JET-ILW) were acquired during metal Table 1. Contents of the ITPA halo current rotation database. Seven total datasets, delineated by machine and wall material, are sourced from five different machines. Only unmitigated disruptions are included. In total, the database contains 813 shots, each of which terminates with an asymmetric vertical displacement event (VDE). Note that the database does not necessarily include all of the unmitigated disruptions from each machine. For example, the 150 shots in the JET-ILW dataset are the 150 most asymmetric disruptions out of ∼6500 total disruptions recorded for JET-ILW. Machine Wall material Sensor type Shots C-Mod Molybdenum Partial rogowskis 148 NSTX Carbon Shunt tiles (1 row) 141 AUG-C Carbon Shunt tiles (2 rows) 129 AUG-W Tungsten Shunt tiles (2 rows) 49 DIII-D Carbon Shunt tiles (5 rows) 51 JET-C Carbon Ip asymmetry 145 JET-ILW ITER-like Ip asymmetry 150 Total 813 Nucl. Fusion 58 (2018) 016050 C.E. Myers etal 3 wall operations. The specific metals used in each machine (molybdenum, tungsten, or ITER-like tungsten and beryllium) are listed in table1. The dual datasets from AUG (carbon and tungsten) and JET (carbon and ITER-like) are particularly valuable in that they provide intra-machine comparisons of how halo currents are modified by metal walls. The machines in the ITPA halo current rotation database employ several types of halo current sensors. As shown in figure 1, the halo current sensor arrays in three of the machines, AUG, NSTX, and DIII-D, are comprised of shunt tiles, which resistively measure halo currents flowing from the plasma into the wall. The AUG shunt tile sensor set (figure 1(a)) is comprised of an inboard array (DUIm, 9 tiles) and an outboard array (DUAm, 8 tiles) [7]. The NSTX sensor set (figure 1(b)) is comprised of a single row of 6 shunt tiles on the outboard side of the divertor [8, 22, 36]. The DIII-D sensor set (figure 1(c)) is comprised of five concentric rings of shunt tiles with 5–10 tiles each [21, 35]. In C-Mod, on the other hand, halo currents are measured using an array of 10 partial rogowski coils (figure 1(d)) [3]. Each partial rogowski coil measures the poloidal current in a toroidally localized region of the inner vessel wall. Two toroidally continuous rogowski coils (not shown) measure the total poloidal wall current in the upper and lower divertors. These measurements confirm that the poloidal wall currents measured in the lower divertor during a downward-moving disruption are dominated by halo currents rather than by eddy currents [3]. JET uses a third technique for measuring halo currents: the identification of toroidal asymmetries in the plasma current. Here, poloidally distributed arrays of poloidal magnetic field sensors (figure 1(e)) act as toroidally localized plasma current rogowski coils. Four of these sensor arrays are deployed in various ‘octants’ of the JET vessel such that toroidal asymmetries in the plasma current, Ip , can be identified [37]. These Ip asymmetry measurements quantify the net toroidal current difference between octants due to halo currents. While there is intense debate about the physical mechanism(s) that generate the Ip asymmetries [9, 28, 37], the JET Ip asymmetry measurements can be used in the same way as poloidally localized measurements in other machines to characterize halo current phenomena [41]. Finally, each entry in the ITPA halo current rotation database includes a set of auxiliary waveforms that are associated with each disruption. These waveforms include quantities such as the plasma current, Ip , the toroidal magnetic field, BT , and various equilibrium parameters such as the major radius, R, the minor radius, a, the elongation, κ, the edge safety factor, q95 , the internal inductance, i , and the stored energy, WMHD . In some cases, additional data is available concerning the evolution of the plasma’s vertical position, Zp, and cross-sectional area, S. In this paper, however, the analysis of auxiliary waveforms is limited primarily to Ip and BT . In total, the ITPA halo current rotation database includes more than 800 discharges (shots) spread across seven datasets from five different machines. Table 1 summarizes the machine, wall material, sensor type, and shot count for each of the seven datasets. Importantly, since disruption mitigation schemes such as massive gas injection (MGI) are known to suppress halo current asymmetries [33, 34], only unmitigated disruptions are considered in this study. To ensure that this is the case, information on the triggering of various disruption mitigation systems is also included in the database. This information, along with an analysis of the asymmetry of the halo currents (section 4), is used to filter the database to include only unmitigated disruptions that terminate in an asymmetric vertical displacement event (VDE). All 813 shots listed in table1 satisfy these criteria. Figure 1. The toroidally resolved halo current sensor arrays in the ITPA halo current rotation database. (a) Two shunt tile arrays (DUIm, DUAm) in the lower divertor of ASDEX Upgrade. Reproduced courtesy of IAEA. Figure from [7]. Copyright 2011 IAEA. (b) A single shunt tile array in the lower outboard divertor of NSTX (red). Reproduced courtesy of IAEA. Figure from [36]. Copyright 2013 IAEA. (c) Five shunt tile arrays (Rows 10–14) in the lower divertor of DIII-D [21]. (d) A single partial rogowski array in the lower inboard divertor of C-Mod. Reproduced courtesy of IAEA. Figure from [3]. Copyright 1996 IAEA. (e) Four octants of poloidal field sensor arrays (red) to measure plasma current asymmetries in JET. Reproduced courtesy of IAEA. Figure from [37]. © 2014 EURATOM. Nucl. Fusion 58 (2018) 016050 C.E. Myers etal 4 3. Disruption current quench analysis Each disruption in the ITPA halo current rotation database is first analyzed for its current quench properties. In this section, we analyze these current quench properties in detail because, as will be shown in section5, the scaling of halo current rotation is intimately linked to the scaling of the current quench. We begin by establishing the procedure for determining the discharge-specific current quench time, tCQ . Figure2 shows the current quench analysis for a typical DIII-D discharge. In figure2(a), a disruption timing algorithm is applied to the plasma current waveform, Ip(t) , to determine the disruption time, tD , the pre-disruption plasma current, IpD ≡Ip(tD) , and the 80% and 20% times, t80 and t20 . The algorithm searches for a current spike and determines the disruption time based on a threshold applied to dIp/dt (see figure2(b)). Here, a threshold value of |dIp/dt|=50 MA s−1 is used in all cases. For JET discharges specifically, the disruption time, tD , is determined using the algorithm of Gerasimov etal, which monitors the loop voltage in addition to dIp/dt [34, 37]. In either case, the resulting discharge-specific current quench time is defined as tCQ ≡(t20 −t80)/0.6 [14]. To highlight the timing of the halo currents with respect to the current quench, figure2(c) shows the RMS halo current waveform, |Ih(t)| , from one of DIII-D’s toroidally resolved shunt tile arrays (Row 10, see figure1). Here, the |Ih(t)| waveform is defined as  Ih(t)  =     Nsens  i ∆φi δφi  Ih(t,φi)  2 , (2) where Nsens is the number of sensors in the array, φi is the toroidal location of the ith sensor, δφi is the toroidal extent of the ith sensor, ∆φi is the toroidal extent of the vessel sector represented by the ith sensor, and Ih(t,φi) is the halo current measured by the ith sensor. The resulting |Ih(t)| waveform represents the toroidally integrated halo current flowing into or out of a poloidally localized region of the divertor. The sample |Ih(t)| waveform in figure2(c) rises with the plasma current spike at the start of the disruption and persists well into the current quench. We note here that, in most cases, the halo current measured by a given sensor array is only a fraction of the total halo current since most of the arrays are poloidally localized. The current quench analysis procedure described in figure2 is applied to all disruptions in the ITPA halo current rotation database. Figure3 shows the resulting database-wide variation of the shot-specific current quench time, tCQ . Here, the x-axis separates the data by machine, while the y-axis plots the measured values of tCQ . The horizontal width of each dataset Figure 2. The disruption current quench analysis procedure. (a) The plasma current waveform, Ip(t) , is processed to identify the disruption time, tD , the pre-disruption plasma current, IpD , and the 80% and 20% times, t80 and t20 . The discharge-specific current quench time is defined as tCQ ≡(t20 −t80)/0.6 [14] and is shaded in gray. (b) A threshold of |dIp/dt|=50 MA s−1 is used to identify the current spike (if there is one) and to identify the disruption time, tD . (c) The RMS halo current waveform, |Ih(t)| , for the Row 10 shunt tiles as determined from equation(2) shows that the halo current rises sharply at the time of the current spike and persists well into the current quench. Figure 3. Measured current quench times, tCQ , across the ITPA halo current rotation database, sorted by machine. The horizontal width of each dataset is a histogram of the distribution of current quench times in that dataset. Though a wide range of quench times are observed, each machine is subject to a sharp lower limit on how quickly the plasma current can quench during a disruption. The empirical values for this minimum current quench time, τCQ , are defined as the lower bound of the first histogram bin that contains 20% as many points as the fullest histogram bin. The resulting τCQ values are plotted as horizontal black lines and listed in the legend. The histogram bins are distributed logarithmically such that the error in each τCQ value is ±5%. Note that the τCQ values for AUG-W versus AUG-C and JET-ILW versus JET-C are comparable, indicating that τCQ is largely unaffected by the wall material in this database of asymmetric VDEs. Nucl. Fusion 58 (2018) 016050 C.E. Myers etal 5 is a histogram of the distribution of current quench times. Figure3 shows that each machine exhibits a wide range of tCQ values that can vary by up to an order of magnitude within a given machine. A clear feature of these data is that each device is subject to a sharp lower limit on tCQ . We define this lower limit as the characteristic minimum quench time, τCQ . The τCQ value for each machine is determined here as the lower bound of the first histogram bin that contains 20% as many points as the fullest histogram bin (in order to avoid outliers). The resulting τCQ values, which are plotted as horizontal black lines in figure3, vary from 1.3 ms for C-Mod to 17.5 ms for JET-ILW. The histogram bins are distributed logarithmically such that the error in each τCQ value is ±5%. One key result is that the τCQ values for AUG-W and JET-ILW are not meaningfully different from their carbon-wall counterparts (AUG-C and JET-C, respectively). This implies that, while metal wall machines are capable of producing very long current quenches [33, 42], the minimum current quench time, τCQ , is largely unaffected by the wall material. These results are consistent with previous JET analyses, which show (1) that unmitigated ‘fast VDEs’ quench on equally rapid timescales in both JET-C and JET-ILW [33, 42]; and (2) that these fast VDEs are often asymmetric in nature [34]. Given the apparent insensitivity of τCQ to the wall material, the AUG and JET datasets will be combined for the remainder of this section. In order to project the observed current quench behavior to ITER, it is necessary to develop a scaling for the minimum current quench time, τCQ . Previously, Wesley etal used the ITPA Disruption Database to empirically connect τCQ to the L/R inductive decay time of the plasma [14, 17]. Reestablishing this connection for the present ITPA halo current rotation database is key because the L/R inductive decay time can be readily computed from the geometric parameters of each machine. The inductive decay time of the plasma is defined as τind =L/R , where L is the plasma inductance and R is the plasma resistance. The plasma inductance is well-described by that of a toroidal current ring: L =µ0R=µ0R  ln 8R a− 2+i 2, (3) where R is the plasma major radius,  is the normalized inductance, a is the plasma minor radius, and i is its internal inductance. The plasma resistance, R , on the other hand, is given by R =η 2 π R S, (4) where η is the plasma resistivity and S is its cross-sectional area. Combining equations(3) and (4), the plasma’s inductive decay time is given by τ ind = L / R = µ0 2πη S=C  η−1  S , (5) where C(η−1) is a prefactor that depends primarily on the characteristic resistivity of the disrupting plasma. Following Wesley etal, we now demonstrate the connection between the minimum current quench time, τCQ , and the inductive decay time, τind [14]. Figure4 plots the database-wide current quench times, tCQ , normalized to the product of the plasma cross-sectional area, S, and the nor malized inductance,  . The S, R, and a values used in the computation of the S· product are extracted from a pre-disruption equilibrium reconstruction of each discharge. In keeping with Wesley etal [14], a flat post-thermal-quench current profile is assumed ( i=0.5 ). The data in figure4, which are quanti tatively consistent with the ITPA Disruption Database [14, 17, 43], identify C (η −1 )= 1.2 – 4.2 ms m−2 as the range to be used when projecting τCQ to ITER. The machines that define the extrema in this range, C-Mod ( 4.2 ms m−2 ) and DIII-D ( 1.2 ms m−2 ), warrant further discussion. As derived in equations(3)–(5), the τind prefactor, C (η −1) , is expected to be a function of the characteristic resistivity of the disrupting plasma, η. This resistivity is set by the core temper ature in the post-thermal-quench plasma, which, in turn, is governed by the balance of two competing processes: ohmic reheating and radiative dissipation. Ohmic reheating injects energy into the post-thermal-quench plasma at a rate of ηJ2 , where J is the toroidal plasma current density. Radiative dissipation, on the other hand, sheds energy from the plasma at a rate that depends on the impurity content. In practice, the impurity content is largely determined by the wall material in the machine. Given the previous conclusion that the wall material has little impact on τCQ in this database of asymmetric VDEs, we focus here on the effect of ohmic reheating. In the C-Mod case, it is clear that increased ohmic reheating plays a substantial role in the current quench normalization. C-Mod is a high- BT machine that operates at current densities ( J∼2 –4 MA m−2 ) that are much higher than those of other tokamaks ( J∼0.2 – 0.6 MA m−2 ). The high current densities in C-Mod lead to observable reheating during the disruption [3], which is likely the cause of the elevated Figure 4. Current quench times, tCQ , normalized to the product of the plasma cross-sectional area, S, and the normalized inductance,  (equation (5)). The AUG and JET databases are combined as per the discussion in the text. The black horizontal lines represent the normalized minimum quench times, C (η −1 ) ≡ τ CQ /( S·  ) , which are listed in the legend. These results, which are quantitatively consistent with the ITPA Disruption Database [14, 17, 43], identify C (η −1 )= 1.2 – 4.2 ms m−2 as the range to be used when projecting τCQ to ITER. Nucl. Fusion 58 (2018) 016050 C.E. Myers etal 6 C (η −1) value of 4.2 ms m−2 . For DIII-D, on the other hand, Wesley etal explored the role of a reduced external inductance as a possible explanation for the depressed C (η −1) value of 1.2 ms m−2 [17]. Regardless of the underlying causes of the variation in the values of C (η −1) in figure4, we adopt the observed range of C (η −1 )= 1.2 – 4.2 ms m−2 for projecting τCQ to ITER. A summary of the database-wide current quench results obtained in this sectionis given in table2. The extrapolated τCQ values for ITER are τCQ ≃37 –130 ms. One important timescale that does not enter into the Wesley scaling is the VDE growth time, τvert . This timescale is a machine-specific parameter that is set by the electrical conductivity of the passive structures that surround the plasma. Since τvert determines how fast the plasma can drift into the wall, it, too, is expected to play a role in setting the minimum current quench time, τCQ . This is especially true in events such as unmitigated ‘fast VDEs’ in JET where the core remains relatively hot (and therefore non-dissipative) throughout the current quench [33]. Instead of the L/R decay of the core plasma, the primary current quench mechanism in these cases is believed to be ohmic dissipation in the halo region as the plasma collides with the wall [44]. By happenstance, the VDE growth time in all five machines in the ITPA halo current rotation database is on the order of a few milliseconds. This τvert degeneracy prevents the development of a τCQ scaling that includes τvert , which is unfortunate given that ITER will have a much longer VDE growth time of τvert ∼0.5 s. The implications for ITER if the long VDE growth time increases τCQ beyond the values predicted by the Wesley scaling are discussed at the end of section5.3. 4. Halo current rotation analysis This sectiondescribes the halo current rotation analysis procedure developed for this multi-machine study. This procedure extracts the rotation duration, trot , and the rotation count, Nrot , from each set of toroidally resolved halo current measurements in the ITPA halo current rotation database. In conjunction with equation(1), these two quantities facilitate the development of empirical scalings of trot and the halo current rotation frequency, fh . The primary objective of the halo current rotation analysis is to track the toroidal rotation of the halo current asymmetry in time. In order to do so, the raw halo current data are fitted at each time point with an n=1 model function of the form Ih(φ)=h0+h1sin(φ−h2), (6) where φ is the toroidal angle, h0 is the n=0 amplitude, h1 is the n=1 amplitude, and h2 is the n=1 phase. In all cases, the toroidal angle, φ, is defined with respect to right-handed coordinates (φ increases counter-clockwise from above). Signed quantities such as Ip , BT , and Nrot are referenced to these right-handed coordinates. While equation(6) does not capture the full toroidal structure of the halo currents, it does provide a robust measurement of the toroidal phase of the halo current asymmetry. Sample results from this fitting procedure are presented in figure5, which considers the halo currents during a typical NSTX disruption. In figure5(a), the raw halo current data, Ih(t,φ) , are plotted in color. Here, the color scale is set so that the darkest red corresponds to the maximum halo current measured during this discharge. The black line that tracks the rotation is the fitted n=1 phase parameter, h2. In this sample discharge, an asymmetric lobe of halo current initially rotates in the negative toroidal direction (clockwise from above). It then locks at a fixed toroidal location ( φ∼300◦ ) for some time before resuming its clockwise rotation at the end of the disruption. Erratic halo current rotation patterns such as this are not uncommon; therefore, the halo current rotation analysis procedure must be robust to abrupt rotation locking or reversal. The next step after fitting the halo current measurements with equation(6) is to identify the ‘asymmetry intervals’ over which the halo current asymmetry has sufficient amplitude to warrant tracking the rotation. This is accomplished here by applying a threshold to the fitted n=1 amplitude, h1 (see figure5(b)). In practice, an h1 threshold of 10 kA works well for all of the halo current sensor arrays in the database. In the sample disruption in figure5, a single asymmetry interval is identified (the interval between the two vertical dashed lines in figures5(a) and (b)). Note that a minimum dwell time of τmin =0.3 τCQ is enforced during the identification of the asymmetry interval in order to ignore brief excursions across the h1=10 kA threshold. Once the asymmetry interval(s) are identified, the next step is to identify ‘rotation intervals’ within each asymmetry interval where the halo current asymmetry is coherently rotating. At this juncture, we compute the rotation velocity waveform as vh(t)=R·dh2/dt . After low-pass filtering vh(t) with a time constant of τfilt =τmin/2 , the rotation intervals are identified by applying a minimum velocity threshold of |vh|<0.5 km s−1 (see figure5(c)). Once again, a minimum dwell time of τmin =0.3 τCQ is enforced to ignore brief excursions across the velocity threshold. In the sample disruption in figure5, two distinct rotation intervals are identified (the two shaded regions in figure5(c)). In cases such as this where more than one rotation interval is identified, we select the Table 2. Summary of the current quench timing analysis of the ITPA halo current rotation database. The S· values for each machine in the database are computed as S· =τ CQ / C (η −1) . For ITER, on the other hand, S· is computed using the following nominal values: R=6.2 m, a=2 m, and κ=1.7 . The ITER τCQ values are calculated using the projected C (η −1) range of 1.2 – 4.2 ms m−2 determined from figure4. Machine S· (m2) τCQ (ms) C η −1 (ms m−2 ) C-Mod 0.32 1.3 4.2 NSTX 1.4 2.1 1.5 AUG 1.8 2.8 1.5 DIII-D 2.5 3.0 1.2 JET 5.9 15 2.5 ITER (min) 31 37 1.2 ITER (max) 31 130 4.2 Nucl. Fusion 58 (2018) 016050 C.E. Myers etal 7 interval with the longest duration as the main rotation interval. Figure5(d) shows the cumulative rotation count, Nrot(t) . The scalar rotation parameters reported for this discharge ( Nrot , trot , fh ) are extracted from the main rotation interval, which is shaded in gray. With the halo current rotation analysis procedure in hand, we now investigate sample halo current measurements from each machine. In the examples shown in figure6, the color of the various halo current measurements represents their polarity. More specifically, a positive halo current (red) is defined as halo current leaving the wall and entering the plasma, while a negative halo current (blue) is defined as halo current leaving the plasma and entering the wall. In the C-Mod, NSTX, AUG, and DIII-D examples, the halo currents possess a prevailing polarity that is associated with the poloidal localization of the halo current sensors. In the JET examples, on the other hand, the Ip asymmetry measurements are symmetric about zero such that no polarity information is available. It is interesting to note that the τCQ -normalized halo current measurements in figure 6 exhibit similar rotation durations across machines. This is a preliminary indication that τCQ factors prominently into the scaling of the rotation duration, trot . Before addressing this scaling, however, the polarities and rotation directions in figure6 warrant further investigation. First, with regard to polarity, the two predominantly positive (red) halo current measurements in figure6 (NSTX and AUG-C/DUAm) are acquired from halo current sensors on the outboard side of the divertor. Conversely, the three predominantly negative (blue) halo current measurements in figure6 (C-Mod, AUG-W/DUIm, and DIII-D/R11) are acquired from sensors on the inboard side of the divertor. Upon examining the polarity of halo currents across the entire ITPA halo current rotation database, it becomes clear that, in addition to the inboard or outboard location of the sensors, the polarity of the toroidal field, BT , controls the polarity of the halo currents. This conclusion is borne out in figure7, which plots the signed maximum halo current measured by each sensor array, Ih , against the signed toroidal magnetic field, BT . For the outboard sensor arrays in AUG, NSTX, and DIII-D, the halo current flows out of the wall for negative BT and into the wall for positive BT (figure 7(a)). For the inboard sensor arrays in C-Mod, AUG, and DIII-D, on the other hand, the halo current flows into the wall for negative BT and out of the wall for positive BT (figure 7(b)). These results, which are independent of the direction of the plasma current, indicate that the halo currents flow paramagnetically with respect to the toroidal field. The halo currents therefore act to conserve the toroidal flux in the disrupting plasma [11]. We note that the handful of NSTX and AUG data points that run counter to this trend represent a small number of disruptions ( ∼1% ) that contact the wall on the outboard (inboard) side of a nominally outboard (inboard) sensor array [8]. A second quantity of interest is the preferential direction of the halo current rotation. In figure6, five of the eight sample halo current pulses rotate in the negative toroidal direction (clockwise). As shown in figure8, it is the direction of the plasma current, Ip , that determines the preferential direction of the halo current rotation. In fact, all halo current pulses in the ITPA halo current rotation database that complete at least two full rotations ( |Nrot|>2 ) do so in the counter- Ip direction. Reversed- Ip data points from C-Mod confirm that the preferential direction of halo current rotation changes with a change in the direction of Ip . This result is obtained independent of the direction of BT since reversed BT data points are included for both C-Mod and DIII-D. While it is important to note that substantial co- Ip rotation is also frequently observed, any theory that seeks to explain halo current rotation must explain why the direction of rotation is preferentially counter- Ip . Figure 5. Sample halo current rotation analysis. The timebase is referenced to the disruption time, tD , and normalized to the minimum current quench time, τCQ . (a) The raw halo current data, Ih(t,φ) , is shown in color. Here, the toroidal angle, φ, is defined with respect to right-handed coordinates (φ increases counter-clockwise from above). The sensor locations are marked with horizontal dotted lines, and the black line that tracks the rotation is the fitted n=1 phase parameter, h2. (b) The fitted amplitude parameters, h0 and h1. The vertical dashed lines mark the asymmetry interval determined by applying an h1 threshold of 10kA and a minimum dwell time of τmin =0.3 τCQ . (c) The low-pass filtered rotation velocity waveform, vh(t) . Two rotation intervals (gray) are identified by applying a minimum velocity threshold of |vh|<0.5 km s−1 and the same minimum dwell time. (d) The cumulative rotation count, Nrot(t) . The scalar rotation parameters ( Nrot , trot , fh ) are extracted from the longer of the two rotation intervals, which is shaded in gray. Nucl. Fusion 58 (2018) 016050 C.E. Myers etal 8 5. Halo current rotation scalings The current quench and halo current rotation analysis procedures in sections3 and 4 provide the necessary data to develop empirical scalings for the halo current rotation duration and rotation frequency. In sections5.1 and 5.2, we develop these empirical scalings by performing least squares regression on the trot and fh data from the rotation analysis in section4. Then, in section5.3, the resulting scalings are used to project trot , fh , and Nrot to ITER. 5.1. The rotation duration scaling The empirical trot scaling developed in this sectionuses the machine-specific minimum current quench time, τCQ , as the independent variable in the least squares regression. At first glance, it may seem surprising that τCQ rather than the shotspecific current quench time, tCQ , is the best independent variable to choose. To qualitatively demonstrate why τCQ is the appropriate choice, figure9 explores the relationship between trot and tCQ . A quantitative comparison of the consequences of using tCQ versus τCQ in the least squares regression of trot is included later in this section. At this juncture, we down-select the ITPA halo current rotation database to include only halo current pulses that complete at least three-quarters of a rotation ( |Nrot|>0.75 ). This eliminates the locked or dithering cases that do not threaten to dynamically amplify the halo current forces. This downselection cuts the database nearly in half, leaving 478 rotating discharges. Returning to figure9, we see that, while there is a correlation between trot and tCQ ( rcorr ≃0.84 ), the longest current quenches in the database (toward the right) are strongly decorrelated from the measured rotation duration. The JET and NSTX databases, in particular, highlight the fact that trot spans a consistent range within each machine, regardless of the value of tCQ . While the decorrelation between tCQ and trot is not well understood, the fact that trot is more consistent from disruption to disruption than tCQ hints that the conditions in Figure 6. Rotating halo current examples sourced from across the ITPA halo current rotation database. The timebases are referenced to an arbitrary time point, tref, and normalized to the minimum current quench time, τCQ . In the C-Mod, NSTX, AUG, and DIII-D examples, the prevailing color of the halo currents indicates their polarity (red = positive = out of the wall; blue = negative = into the wall). In the JET examples, the Ip asymmetry measurements are symmetric about zero such that no polarity information is available. Several parameters of interest are listed for each discharge including the toroidal field, BT , the plasma current, Ip , the total rotation count, Nrot , and the average rotation frequency, fh . The signed quantities ( BT , Ip , and Nrot ) are referenced to right-handed toroidal coordinates. The vertical dashed lines delineate the asymmetry intervals over which the rotation is analyzed (see figures5(a) and (b)). The details of the halo current polarity and the direction of rotation are discussed in the text. Nucl. Fusion 58 (2018) 016050 C.E. Myers etal 15 [6] CounsellG.F., MartinR., PinfoldT., TaylorD. and The MAST Team 2007 Plasma Phys. Control. 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