Characterization of early current quench time during massive impurity injection in JT-60SA

Characteristics of the early current quench (CQ) time in mitigated disruptions are studied for a full-current (5.5 MA) scenario in the JT-60SA superconducting tokamak. Self-consistent evolution of the plasma temperature and current density profiles during the early CQ phase before the plasma moves vertically is simulated using the axisymmetric disruption code INDEX for given impurity source profiles. It is shown that the hollow (flat) impurity density profiles peaks (flattens) the current density, and it causes a temporal change in the internal inductance in this phase. However the resultant CQ time is found to be insensitive to the impurity source profile for the same assimilated quantity. The simulation results are interpreted by the L/R model including the temporal change in the internal inductance as well as the effect of a gap between the plasma and the conducting vessel structures and stabilizing plates. This results will improve the accuracy to estimate the amount of impurity assimilated into plasma from the observed CQ rate in the massive gas injection (MGI) experiment planned in JT-60SA. The accessible range in which the CQ time can be scanned as well as the electron densities to suppress runaway electrons is also shown for different injected amounts of neon, argon, and their deuterium mixture under the limitation of the MGI gas amount. Mitigated disruptions in JT-60SA typically lead to the CQ time shorter than the vessel wall time, which is expected to produce relevant contributions to disruption mitigation in ITER and future reactors.


Introduction
JT-60SA is a large superconducting tokamak device with a high plasma current of up to 5.5 MA, and disruption mitigation is one of the major issues addressed in the JT-60SA project to make relevant contributions for ITER and future reactors [1,2].For disruption mitigation experiments, a massive gas injection (MGI) system will be installed in JT-60SA after the integrated commissioning phase [3].Although axisymmetric simulations of major disruptions and vertical displacement events (VDEs) have previously been performed using the DINA code to specify the maximum wall loads for in-vessel component design [4], more detailed study is also required to evaluate main characteristics of mitigated disruptions in preparation for the coming experiment.
Since a toroidal loop resistance of the vessel structure of JT-60SA is low, the current quench (CQ) time in disruptions caused by the MGI in JT-60SA is expected to be shorter than decay time of wall eddy current.Such a conducting wall limit is also expected to be the case in ITER, although the delivery of massive material is made in a different way using shattered pellet injection (SPI) scheme [5].Note that although JT-60SA will operate with the carbon divertor target and the sputtered impurity will dominate the physics of natural disruptions, disruption mitigation supplies more neon or argon quantities than intrinsic carbon impurities and can be discussed on the same basis as the metal ITER-like wall environment.The impurities injected as pellets or gas for disruption mitigation assimilate into the plasma and enhance radiation loss to reduce heat loads to in-vessel components during the thermal quench (TQ) and lead to a rapid decay of the plasma current.It is necessary to control the CQ time within an appropriate time window to reduce both the electromagnetic load caused by the eddy current, which is dominant in fast CQ, and that caused by the halo current, which is dominant in slow CQ [6].For example, the ITER DMS is required to make the CQ time between 50 and 150 ms at a full plasma current of 15 MA [5].
MGI has been studied in many tokamaks such as ASDEX Upgrade [7,8], Alcator C-Mod [9], DIII-D [9,10], Tore Supura [11], TEXTOR [12], EAST [13], and JET [14].It was shown that the CQ time became shorter with more impurities, and argon impurity leads to faster CQ than neon in the JET experiment [14].The CQ time was almost saturated when a large amount of gas was injected into the plasma in the ASDEX Upgrade experiments [8].From the perspective of analyzing MGI experiment, it is required to know the amount of impurity assimilated into plasma, which is difficult to measure directly.A standard way used in the previous studies is to calculate it from the plasma resistance, assuming a balance between ohmic heating and radiation loss [14][15][16].For such an evaluation, the current decay rate in the early CQ phase, before the plasma moves vertically, is considered to estimate post-TQ plasma parameters in order to exclude the effect of the halo current in VDE [17].In the present paper, we study the relationship between the early CQ time and the impurity assimilation in JT-60SA using the axisymmetric disruption code INDEX [18,19].It will be shown that the zero-dimensional (0D) L/R decay model including a temporal change of the internal inductance as well as the effect of a gap between the plasma and the conducting vessel structures and stabilizing plates (SPs) in the JT-60SA geometry can capture major trends in the simulation.
The assimilated impurities and the electric field in the early CQ phase also affect the generation of runaway electrons (REs).In previous MGI experiments, REs were observed in DIII-D and JET with injection of pure neon and argon [14,20].Although, because of the low avalanche gain, the extrapolation of the experimental data in present tokamaks to ITER is not straightforward, the mixture injection of noble gas and deuterium gas has been observed to suppress RE generation.JT-60SA can supply large amounts of impurity gas mixed with deuterium up to 5.3 kPa m 3 from two MGI valves [3].In the present study, an accessible range of the CQ time and the electron densities to suppress REs is analyzed for different injected amounts of neon, argon, and their deuterium mixture.
The paper is organized as follows: in section 2, the simulation setup for the INDEX code is explained.A reference of mitigated disruptions for a full-current scenario of I p = 5.5 MA is described in section 3.In section 4, the relationship between the simulated early CQ times and assimilated impurity quantities is studied.The simulation results are interpreted using the 0D L/R model.The effect of deuterium mixture injection on CQ, considering the injection capability of the MGI system in JT-60SA, is discussed in section 5. Finally, section 6 concludes this paper.

JT-60SA simulation using the INDEX code
In the present paper, the axisymmetric disruption code INDEX [18,19] has been used to model the disruptions caused by MGI.The INDEX code is based on the 1.5D tokamak model, which couples 1D transport equations in the magnetic flux coordinates and two-dimensional (2D) Grad-Shafranov equilibrium calculation .The time series of a freeboundary tokamak equilibria are followed with iterations with the 1D magnetic diffusion equation and the circuit equation to describe the eddy current flowing in the vessel.The model of the conductive structures, including vacuum vessel, superconducting poloidal field coils, plasma position control coils, and SP, is the same as that used in the MHD equilibrium control simulator, which is used to develop a control scheme for the plasma shape and position in JT-60SA [21,22].The main structure of the JT-60SA tokamak is shown in figure 1.The vacuum vessel consists of SS316L double wall with 18 mm thickness with 72 ports [23,24].The SP consists of SS316L double wall with 10 mm thickness and covered by graphite tiles [25].In the present simulation, the vacuum vessel and the SP are modeled as toroidally circulating conducting elements and the superconducting coils (CS and EF) and in-vessel coils called fast plasma position control (FPPC) are modeled using the same number of turns as the real device [26].Note that the FPPCs are treated as passive CS like the elements that constitute the VV and SP in the present study.
In the present simulation, self-consistent evolution of the plasma temperature and current profiles are modeled using the 1D transport equations with given impurity sources, where the density of the ion species is modeled separately for the different charge states based on the ionization and recombination rates extracted from the OpenADAS database [27,28].For more details of the INDEX code, see the appendix in [18].Particle and thermal diffusivities used in the present simulation are fixed to D = 1.0 m 2 s −1 and χ = 5.0 m 2 s −1 over the simulation time.Such a level of the radial transport coefficients tacitly assumes that the magnetic flux surfaces reform after the TQ, and should be carefully validated.In this regard, recent ITER simulations have suggested that a significant fraction of the magnetic surfaces maintains to be destructed over the long time [29].
Figure 1 shows the reference equilibrium considered in this study, where I p = 5.5 MA and other main parameters are summarized in table 1.In the present study, mitigated disruptions are triggered by introducing artificial transport loss and additional impurity sources as described below.

Mitigated disruption with plasma current of 5.5 MA in JT-60SA
Figure 2 shows an example of the simulated mitigated disruptions with neon impurity injection.For the initial 3 ms of simulation, the plasma temperature is decreased until it is below 50 eV in average by the artificial transport loss term.From 3 ms to 3.5 ms, as highlighted by the gray zone in figure 2, the impurity source is introduced to make the impurity density uniform in the plasma.
As illustrated in figure 3, the direction of VDE is upper, which is common to all disruptions discussed in the present paper.Note that the direction of VDE depends on the initial plasma position and the neutral point where the VDE direction is switched to the downward direction can be analyzed numerically [30,31].With such an analysis, it has been found that the initial position of the present case in figure 1 is about 6.4 cm upwards from the neutral point.As discussed in section 1, the present work focuses on the current decay rate in the early CQ phase, where the dashed vertical lines in figures 2(a)-(e) represent when I p crosses 90% and 80% of the initial value, respectively.In the time window between them, the vertical position of plasma axis does not change significantly.After the VDE started to grow, the internal inductance l i and the safety factor at plasma surface q surf show non-monotonic changes when the lower X-point disappears and upper X-point appears at t = 12.7 ms.

L/R model
The equation for magnetic energy evolution carried by a rigid plasma column which does not move is expressed as follows: Here, I p , L p , and R p are the plasma current, plasma inductance, the plasma resistance, respectively, whereas V em represents the electromotive force induced by the external current I c in the conductor.The total plasma inductance L p of the torus plasma is expressed as the sum of the external inductance L e , where R 0 and l i are the plasma major radius and normalized internal inductance, respectively.Assuming that the external conductor is perfectly conducting, ∂ (I p + I c ) /∂t = 0. Therefore, V em is given in terms of the mutual inductance between the external conductor and the plasma M pc as follows: Inserting equations ( 2) to (1), one obtains From equation ( 3), the CQ rate τ CQ is derived as follows: In the present paper, the current decay in the early CQ phase, in which the VDE does not grow, is mainly considered as described in section 3. Assuming that changes in L p , R p , and dL p /dt are small so that τ CQ is constant in such a short duration, I p in the early CQ phase can be regarded to decay exponentially as follows: where I p0 is the initial plasma current.
If we assume that the plasma inductance L p is constant during the CQ and approximate that L e ∼ M pc , which is equivalent to ignoring the contribution of magnetic energy in the vacuum region between the plasma surface and the conductors, equation ( 4) reduces to the following form: Since the plasma resistance R p = 2π R 0 η p /S is determined by the Spitzer formula [32] in terms of the electron temperature T e and effective charge Z eff , the current decay time τ CQ has often been employed to estimate T e and Z eff during CQ.

Impurity density scan
As a main part of the present analyses, the INDEX simulation has been performed over a wide range of the injected impurity density.The current decay rate τ CQ is characterized by fitting equation ( 5) to the I p waveform for the time interval between t 90% and t 80% , at which I p crosses 0.9 × I p0 and 0.8 × I p0 , respectively, which means τ CQ is equivalent to the extrapolation of the initial phase of the CQ.As illustrated in figure 2, the vertical displacement of the plasma in the early time interval between the vertical dashed lines is still small.Note that for some technical reasons of the simulation setup and data processing, the initial current I p0 in the following dataset was recorded using the average value of I p in the initial 1 ms of the simulation but it does not affect any conclusion of this study.
Figure 4 shows the relationship between τ CQ and the injected impurity density of neon and argon.In the present analyses, all of τ CQ are shorter than decay time of wall eddy current of τ wall ≈ 72.6 ms, which is shown by a horizontal dashed line in figure 4. Here, τ wall is estimated using the conductor model described in section 2. τ CQ with argon is smaller than that with neon while the input n imp is similar, which is consistent with the experimental results reported in JET [14].The color dotted curves in figure 4 show the results of curve fitting.As compared in table 2, curve fitting using a functional form with minimum values matches well with the simulation results, and the root mean square errors are much smaller than those estimated for the curve fitting without minimum values.
These facts shows that the relationship between the input n imp and τ CQ is like a power-law form with a minimum value.Such a trend that the CQ time saturates with much impurity has also been reported in ASDEX Upgrade experiments with the MGI [8] and DIII-D experiments with the SPI [17].Figure 5 shows the plasma parameters related to the CQ for the neon density scan shown in figure 4. According to figure 5, the plasma resistance R p also saturates when τ CQ saturates with high neon density.The electron cooling rate data with neon  decreases by more than two orders of magnitude with the electron temperature in the range from 10 eV to 1 eV, as can be seen from that calculated from the Open ADAS data [27,28].In this high neon density region, therefore the radiation loss power P rad saturates and ⟨T e ⟩ decreases only slightly.We also note that the volume averaged effective charge ⟨Z eff ⟩ decreases with the increase of lowly charged neons, which compensates a slight decrease of the ⟨T e ⟩; therefore, the plasma resistance is kept almost constant so that the change in τ CQ becomes small.
According to figure 4 and table 2, the minimum τ CQ with argon has been estimated by curve fitting as 4.2 ms, which is smaller that with neon of 5.9 ms.This suggests that the achievable minimum CQ time induced by MGI depends on the injected impurity species.Furthermore, gas/pellet assimilation efficiency is expected to degrade at such a low temperature below 5 eV, which also limits accessible short CQ time with given injected quantities.A comparison between the minimum τ CQ and the linear CQ time for natural disruptions in the multimachine database in appendix.

Impact of impurity source profile
The impurity source used to produce figure 4 has been set to make impurity density uniform in the plasma, as described in section 2, and in this subsection, the impact of impurity source profiles on the CQ rate is studied.In realistic situations, the profile of impurities assimilated into the plasma is not necessarily uniform but depends on mixing by MHD activity [33,34].We have considered a variation of the impurity source profile using the parabolic function below.
Here, ρ is the square-root of normalized toroidal flux.By changing the coefficient A, the impurity source takes various distributions.The coefficient B is set to make the total amount of impurity source is equal to that when the impurity source is uniform, which corresponds to A = 0.When A > 0, the impurity source is hollow at the center, that is, peaks at the edge.When A < 0, the impurity source has a peak at the center.Figure 6 shows the simulation results when the coefficient A is 0, −1, or 1.In these cases, the volume average n imp is fixed to 2.0 × 10 19 m −3 .According to figure 6(a1), the impurity profiles do not affect the current decay rate but lead to different evolution of the internal inductance.Such a temporal change in L i is caused by the current diffusing into a more conductive region where T e is high.Comparing figure 6(b1-3), when the impurity profile is peaked, the current density at the plasma center decreases faster, which causes a faster decay of the internal inductance.In opposite, the current density at the center and the internal inductance increase when the impurity has a hollow profile.
Table 3 the simulation results with various impurity source profiles with two different volume average impurity densities of 1.0 × 10 20 m −3 and 2.0 × 10 19 m −3 .Here, the plasma resistance R p is defined as the averaged value across plasma as follows; According to table 3, R p gets smaller with the impurity distribution getting more hollow, which is because the plasma cooling differs among these cases.∆W mag /∆t becomes small as the impurity source profile becomes hollow, because R p decreases.In contrast, τ CQ takes similar value with the same n imp .
Because of the difference in R p , τ CQ estimated by the L/R model, τ L/R = L i /R p , varies with the impurity profile, which is not consistent with that τ CQ in the early CQ does not change so much.This can be explained by considering the time change of L i .The fourth column of table 3 shows that the average rate of change in the internal inductance L i between t 90% and t 80% , denoted as ∆L i /∆t, increases as the impurity distribution becomes more hollow.The L/R model is modified by including a temporal change in the plasma internal inductance as follows: As shown in the last column in table 3, τ ∆L i /∆t have taken similar values independently of the impurity profiles.This is consistent with the simulated τ CQ values, while τ ∆L i /∆t is about 40% smaller than τ CQ uniformly.To explain the uniform difference between τ CQ and τ ∆L i /∆t , we need to retain the full expression of equation ( 4), rather than equation ( 9); the latter assumes L e ∼ M pc in the 0D L/R model.This assumption holds true when the perfect conducting wall is close enough to the plasma surface.In reality, there is a gap between the plasma surface and the conducting wall, and the contribution of magnetic energy in the vacuum region is not negligible.To take into account such a contribution from the magnetic energy in the gap between the plasma and the conducting wall, we introduce the notation where the factor C is smaller than unity, which means that L e is partially canceled by M pc .Considering the assumption (10) and that the plasma internal inductance L i is not constant over time, the L/R model ( 4) is modified as follows: In this form, the simplified L/R model of equation ( 6) is augmented by including a temporal change in the internal inductance as well as the effect of a gap between the plasma and the conducting vessel.
Although the factor C can be determined by calculating the effective mutual inductance between the plasma and the vessel, here we consider an empirical method using the simulation result itself.We consider an appropriate subset of the simulation results, and the factor C is determined by the leastsquare method of the simulated τ CQ using equation (11).As an illustration, we determine the factor C using the simulation results with uniform argon and neon densities, where L e = µ 0 R (ln (8R/a) − 2) estimated at the initial equilibrium is used.It leads to C = 0.249 for that τ mod matches well with τ CQ , where the coefficient of determination R 2 is 0.981.
Using the determined C, equation ( 11) is applied to reproduce the whole simulation database in figure 7. It shows that τ mod matches well with τ CQ under various conditions.The R 2 values with the data described in figure 7 are summarized in table 4, where we see that the agreement is quite good.The results of table 4 support the proposed recipe for determining C. Once the factor C is determined using a a small number of the simulations, equation ( 11) can be applied to the interpretation of the simulation or experimental results for more general conditions of the impurity density and profiles.
4.4.2.Discussion on the factor C. Finally, we address how much the factor C depends on the geometrical configuration of the plasma and the conducting wall.In JT-60SA, the outboard gap between the plasma and the conducting wall is determined by the location of the SP.To test the sensitivity, the SP has been moved in the INDEX simulation from the actual position between 5 cm closer to plasma and 15 cm farther from plasma, as shown in figure 8(a).
The relationship between the SP position and the factor C is shown in figure 8(b).In these calculations, a neon impurity source of n imp = 1.0 × 10 20 m −3 with flat profile (A = 0) has been assumed.The factor C increases as the SP moves farther from the plasma.This result is expected because the factor C is related to the magnetic flux in the vacuum region, which depends on the geometry of the plasma and conductors around it.As being clear with its definition, when the conducting wall is moved infinitely far from the plasma or when the wall is highly resistive, C approaches unity and the L/R time is given by L p /R p , where L p = L e + L i is the total plasma inductance.Such a resistive limit was previously considered to interpret the CQ time much longer than the wall time, such as in the case of JT-60U [16].Conversely, the mitigated disruptions in JT-60SA are expected to typically lead to a CQ much faster  than the wall time (∼73 ms), and the present analysis provides a good basis to analyze the CQ rate in the similar conducting wall limit to ITER.

Impurity amount scan with deuterium mixture
JT-60SA will prepare a significant injection capability of the MGI, which is aimed at addressing its impact on RE avoidance and mitigation at a full plasma current of up to 5.5 MA.
The early CQ phase considered in this work is also relevant to determine the avalanche gain of RE generation.In order to investigate the effects of deuterium mixture injection on RE generation and CQ, the neon impurity amount has been scanned in the INDEX code with and without an additional source of deuterium.Figure 9 shows the results of the neon impurity amount scan with three different amount of deuterium, that is, n D = 0.0, 1.0 × 10 20 , and 1.0 × 10 21 m −3 .The impurity source profiles are fixed to be flat with A = 0 in equation (7).It is clear that τ CQ is affected by additional deuterium when the electron density is significantly higher than that without deuterium.Increasing the electron density yields more radiation power, which shortens τ CQ .Under such conditions, the dependency of τ CQ on neon density is still observed.It is known that the RE growth rate by the avalanche effect Γ avl is proportional to the parallel electric field normalized by the critical electric field E ∥ /E C at the plasma center [35,36].
Here, E C is defined as follows [37]: According to the n Nq scan result without deuterium in figure 9(d), E ∥ /E C increases with n Ne until it reaches 5.0 × 10 19 m −3 then decreases.The suppression of E ∥ /E C with high n Ne is thought to be the enhancement of the bounded-electron friction force [35].The observed decrease in E ∥ /E C with n D suggests that an additional deuterium source is useful to reduce the avalanche growth rate.We simulate the RE generation with three different impurity conditions, that is, flat argon impurity source of n Ar =2.0 × 10 19 m −3 with no deuterium, n D = 1.0 × 10 20 m −3 , and n D = 1.0 × 10 21 m −3 .For simplicity, the seed current is assumed as 2.0 kA in total and is set to be proportional to the distribution of T e .The diffusion coefficient of REs is fixed to 10 m 2 s −1 , although it has been pointed out that the REs are mostly lost because the stochastic magnetic field enhances the transport during the early CQ phase [38].The purpose of simulating the RE generation in the present paper is not to estimate the level of RE current in the JT-60SA MGI experiment but to investigate the trends of the generated REs when deuterium is mixed into the MGI gas.
From figure 10, it is seen that the growth of the RE becomes slow when the E ∥ /E c is reduced by the deuterium mixture, but in all three cases, the RE current plateau are reached more than 3 MA.This could be explained partially by that raising the electron density shown in figure 10(d) results in an increase of the target electrons available for the avalanche.As discussed in recent ITER simulation [39], an increase of injected deuterium amount does not necessarily mean RE suppression.Additionally, the suppression of the seed electrons needs to be addressed.It requires self-consistent simulation of TQ including stochastic loss of fast electrons [40], which is outside the scope of the present study and remains a future work.

Remarks for experiment in JT-60SA
In JT-60SA, two MGI valves will be installed behind the SPs at the 180 • opposite position [3].The maximum gas amount in each valve is 5300 Pa m 3 , and it is designed to inject at least 400 Pa m 3 of gas.As a mitigation gas, a small amount of noble gas and a large amount of H 2 or D 2 will be mixed to study the RE.
Figure 11 shows the relationship between τ CQ and the amount of injected impurity within the capability of the JT-60SA MGI system, including both noble gas and deuterium, assuming that between 40% and 10% of the injected impurities assimilate into the plasma.The range of gas amounts injected  The errorbars indicate the range of assimilation rates between 10% and 40%.The colored dashed lines show the deuterium amount N D .The deuterium mixture rates N D /N inj in less deuterium case (orange) are between 11.1%-95.2%,while those in more deuterium case (green) are between 55.6%-99.5%.The vertical solid lines correspond to the minimum and maximum gas amounts that the JT-60SA MGI valves can inject, and the black dashed line corresponds to the minimum gas amount that a single MGI valve can inject, respectively.by the MGIs is also shown by the vertical solid lines in the figure.The minimum gas amount assumed here is not based on the engineering limit but on the technical specification for the valve design.Therefore, the actual limit for gas injection needs to be tested experimentally.Nevertheless, even if the gas injection of one tenths of the minimum gas amount assumed here is feasible, it is expected not to obtain CQs with a wide range of τ CQ values by pure noble gas injection.In contrast, figure 11 shows that a relatively wide range of the CQ time is accessible when we use the deuterium mixture, as indicated by the green triangles.Because the injection of a large amount of hydrogenic species and a small amount of neon is currently envisaged for the ITER DMS [41], the model validation of the CQ time in such a regime of the deuterium mixture injection and in the conducting wall limit will make a key contribution from the JT-60SA MGI experiment to ITER.

Conclusions
The characteristics of the current decay rate in the early CQ phase of mitigated disruptions have been studied for the fullcurrent 5.5 MA scenario in JT-60SA.In this study, the early CQ phase is focused because it is relevant to the experimental identification of assimilated impurities, as well as the RE generation via avalanche multiplication.In the impurity amount scan, the power-law-like relationship between the τ CQ and impurity amount has been obtained, which shows that the minimum values of τ CQ have depended on the impurity ion species.The simulated CQ rate in the early CQ phase has been interpreted using the 0D L/R model.We have shown that the simulation results match well with the model when it is modified to include a temporal change in the internal inductance dL i /dt and the effect of the magnetic flux outside the plasma.The INDEX simulation shows that the impurity profile in the plasma does not change τ CQ significantly despite that the plasma resistance is affected in the early phase of the CQ.This is because the current density profile is self-adapted to diffuse into a high T e (conductive) region, and the resultant L i change can compensate for the change in the CQ rate due to the change in the resistance.Another feature of the mitigated disruptions in JT-60SA is that the CQ time is typically shorter than the decay time of the eddy currents in the conducting wall.This is the same tendency as the MGI experiment in EAST, which has a superconducting coils [13], and in contrast to the previous CQ experiments in JET [14] and JT-60U [16].The analysis of the CQ time in such a conducting wall limit will provide a good basis for reliable extrapolation to ITER.
Although we have employed a prescribed impurity source instead of modelling the gas assimilation process selfconsistently, the relationship between the τ CQ and the impurity densities shown in the present parametric study can improve the accuracy of estimating the amount of impurity assimilated into the plasma from the observed CQ rate in the MGI experiment.Assuming a power balance between radiation loss and ohmic heating in the early CQ phase, we can estimate the plasma resistance R p from the measured τ CQ , which include the information of T e , Z eff , and assimilated impurities in the plasma.The modified L/R model of equation (11) can include the corrections due to a temporal change in the internal inductance, as well as the effect of the gap between the plasma and the conducting wall.Here, the numerical factor C can be determined from a small number of the simulations using pre-disruption equilibria.The internal inductance is expected to be obtained with magnetic sensor signals in the early CQ phase [16].Figure 12 illustrates the comparisons of T e and n imp between the actual volume-averaged values obtained at t = t 90 and the values estimated by the modified L/R model.Here, we also compare the results obtained from a simple estimate using L i /R p .With the modified L/R model, both T e and n imp are estimated well when T e is higher than a few eV.It is worth noting that the estimation of assimilated impurities from τ CQ and the plasma resistance does not work for too low T e because of such a low T e , τ CQ already reaches the lower bound and even becomes independent of the assimilated impurity.
One of the prioritized experiments in JT-60SA is to investigate the effect of massive deuterium injection to simulate the currently envisaged DMS scheme in ITER.Concerning the effect of deuterium mixture injection, we have examined the accessible range of the CQ time within the capability of the JT-60SA MGI system.It has been shown that a certain range of the CQ time can be scanned using a mixture of deuterium and noble gases under the limitation of the MGI gas amount.The insight obtained here will form a basis for designing the future JT-60SA MGI experiment.

Acknowledgment
This work was carried out using the JFRS-1 supercomputer system at Computational Simulation Centre of International Fusion Energy Research Centre (IFERC-CSC) in Rokkasho Fusion Institute of QST (Aomori, Japan).This work was partially supported by JSPS KAKENHI Grant Number JP21H01070.

Appendix. A lower bound of the CQ time for natural disruptions
In the literature, a lower bound of the CQ time for natural disruptions has been estimated with the multimachine database of the area-normalized linear quench rate between 80% and 20%, which indicates a lower bound of 1.67 ms m −2 in various tokamaks [42,43].Converting this lower bound of 1.67 ms m −2 as an exponential decay gives τ 80−20 CQ,min = 5.12 ms for JT-60SA.Here, assuming the full I p decay follows an exponential curve, time difference between 80% and 20% of I p0 is described as ∆t 80−20 = τ CQ (ln 0.8 − ln 0.2), and τ 80−20 CQ,min equivalent to the lower bound of 1.67 ms m −2 is obtained by solving the following equation: S is the poloidal cross-section area of 7.09 m 2 , as shown in table 1.The minimum early CQ time shown in figure 4 seems to be reasonable in comparison with the estimated lower bound for natural disruptions of 5.12 ms.

Figure 1 .
Figure 1.Initial equilibrium of the INDEX simulation.The blue and orange squares show the coils and conducting walls, respectively, that consists of the vacuum vessel and the stabilizing plate.

Figure 2 .
Figure 2. The time history of (a)Ip, (b)R axis (blue) and Z axis (red), (c)l i (blue) and q surf (red), (d) ⟨Te⟩, and (e) ⟨ne⟩ (solid) and ⟨n imp ⟩ (dashed).The impurity source is present during the interval highlighted by the grey region.The dashed vertical lines represent when Ip crosses 90% and 80% of the initial current, respectively.

Figure 3 .
Figure 3. Snapshots of the magnetic flux surfaces in the simulation of figure 2(a) at Ip = 0.9 × I p0 , (b) at Ip = 0.8 × I p0 , and (c) after the VDE grows.

Figure 4 .
Figure 4. Summary of impurity density scans for neon (blue) and argon (red).

Figure 6 .
Figure 6.The time history of (a1) Ip, (a2) plasma magnetic energy Wmag, (a3) Z axis , (a4) internal inductance L i , and (a4) plasma resistivity Rp of the cases with flat (A = 0), peaked (A = −1), and hollow (A = 1) impurity sources in blue, orange, and green lines, respectively.The volume average n imp is fixed to 2.0 × 10 19 m −3 .For these three cases, the current density profiles at times indicated by the vertical dotted lines in (a1-5) are shown in (b1-3).The grey region in (a1-5) shows the duration of the impurity source.The dashed-grey curves in (b1-3) show n imp at t = 3.5 ms.

Figure 7 .
Figure 7.Comparison between the characteristic time of the Ip decay τ CQ and that estimated by the L/R model (△), the L/R model considering ∆L i /∆t (□), and modified L/R model τ mod with C = 0.249 (•).The impurity ions and profiles of the data are shown by colors.

Table 4 .Figure 8 .
Figure 8.(a) The radial shift of stabilizing plate (SP) position and (b) the factor C when the SP is at each position.

Figure 11 .
Figure 11.τ CQ versus injected impurity amount N inj = N imp + N D , assuming that 30% of the injected impurity assimilates into the plasma.The errorbars indicate the range of assimilation rates between 10% and 40%.The colored dashed lines show the deuterium amount N D .The deuterium mixture rates N D /N inj in less deuterium case (orange) are between 11.1%-95.2%,while those in more deuterium case (green) are between 55.6%-99.5%.The vertical solid lines correspond to the minimum and maximum gas amounts that the JT-60SA MGI valves can inject, and the black dashed line corresponds to the minimum gas amount that a single MGI valve can inject, respectively.

Figure 12 .
Figure 12.Comparisons of (a) Te and (b) n imp between actual volume-averaged values and estimated values by conventional (white-outlined dots) and modified (colored dots) L/R models for neon impurities with deuterium mixture.

Table 1 .
Parameters of initial equilibrium.

Table 2 .
Comparison between curve fitting to τ CQ with and without a constant term.

Table 3 .
Parameter scan results while changing the impurity source profiles.Each value has been obtained at the beginning of the duration in which τ CQ is obtained (i.e.t 90% ).