02aE01
トカマクディスラプションにおける逃走電子発生の物理モデリングの進展
Progress in Disruption Modeling with Runaway Electrons for Tokamak Plasmas
松山 顕之
MATSUYAMA Akinobu
量研機構
QSTIntroduction - In the last decades, much effort has
been paid to the development of mitigation schemesof disruption loads in ITER, which is aimed atminimizing heat and electromagnetic loads due tothe plasma thermal and magnetic energies within
acceptable levels. However, an important challenge
still remains – the mitigation of runaway electrons.
While the current quench in metallic wall
environments such as JET-ILW [1] is observed tobe slow enough to avoid runaway generation, themassive impurity injection to mitigate thermal loads
shortens the current quench time, which results inrunaway generation [2]. A theoretical prediction [3]suggests that mitigated disruptions in ITER aresusceptible to runaway generation due to theavalanche growth. In [4], the estimation that a small
seed current on the order of 10-9MA can beamplified up to 1 MA runaway current has beenreported. A difficulty arises in a large gap of theavalanche growth gain between present tokamaks
and ITER [3], which prevents us fromstraightforward extrapolation of the experimental
data towards disruptions with 10 MA-order plasma
currents. Therefore – in addition to experimental
demonstration of runaway mitigation – to develop
predictive models is a mandatory as research insupport of ITER.
In this paper, we report our recent progress inmodeling of runaway electrons. The runaway
generation is governed by complex interaction
between various physical processes involved in themechanisms of thermal and current quenches. This
paper focuses on two mechanisms that we recently
studied: (1) the effects of MHD activity on runaway
generation and (2) mitigation mechanisms byimpurities. As the future prospects of our integrated
modeling, we also report a development of kinetic
modeling on the basis of Monte-Carlo code.
Effects of MHD activity on runaway generation Runaway electron generation is understood as theconversion of magnetic energy from Ohmic torunaway currents, where the resistive dissipation ina plasma and within the wall dominates its

conversion rate [4]. Since post-disruption plasmas
are characterized by the low electron temperaturearound 10 eV, it is natural to consider the resistive
instability [5] as a mechanism giving constraints on
the runaway current profile. To study such effectsof MHD activity, we have developed a resistive
MHD code EXTREM [6] that self-consistently
couples runaway generation and resistive MHD
modes. Figure 1 compares the evolution of runaway
current profile calculated by EXTREM with 1D
transport calculation, where a profile flattening due
to nonlinear resistive kink is simulated. We foundthat during the evolution of a resistive kink, theinductive electric field associated with the magnetic
flux expulsion plays a role of additional channel toenhance the primary current [6]. Figure 2 compares
the primary (left) and plateau (right) currents fordifferent electron temperatures; the effect of
inductive electric field is seen to be significant at
the low temperature and high resistivity condition.
Such condition is relevant to mitigated disruptions
and our simulation suggests that the resistive
instability plays an important role in the generation
and redistribution of primary runaway currents.
Mitigation by high Z impurity - Another important
topic is a mitigation mechanism of runaway
generation by high-Z impurities. Especially, inITER, massive impurity gases or solid pellets are
injected to dissipate thermal energy of bulk plasmas
with impurity radiation. We here apply the runaway
avalanche model including the contribution of
impurity collisions and synchrotron radiation [5]and evaluate the runaway current plateau for Argon
and Neon injection. Taking into account the balance
between the Ohmic heating and radiation loss ηj2 =nenZL(Te), one can evaluate the runaway generation
rate from the induced electric field E = ηj. The
evaluated runaway current plateau is plotted versus
the impurity density in Fig. 3 for ITER-likeparameters with a given seed current of 10-7MA. A
non-monotonic dependence on the impurity density
is observed here: At lower impurity density side (nZ< 1020m-3), the runaway current is seen to increase

with the impurity density because the induced
electric field increases with the resistivity.
Conversely, by further increasing the impurity
density up to 1021m-3, the parameter regime thatimplies the mitigation by impurity injection appears.
This region is characterized by the dissipation ofelectron energy due the synergetic effects of elastic
scattering by impurity atoms and the synchrotron
radiation [7]. The recent mitigation experiments
direct at the validation of this mechanism and atquantifying the damping rate of runaway current
against the impurity content for different gas
species.
Advanced Kinetic Modeling by Monte-Carlo
methods and Future Directions - Recent progressin the theory of runaway electrons has relied on
numerical study using Fokker-Planck codes.
Although these codes are accurate enough toanalyze the momentum space dynamics of electrons,
it is still cumbersome to extend such types of thecodes to analyze the spatial dynamics. In the fieldof energetic particle physics, orbit following Monte
Carlo codes are widely used for such purpose.
Motivated by this fact, to explore the possibility oforbit-following approach, we develop a newvariance reduction technique with the aid of weightwindow [8] to simulate the runaway distributionfunction by Monte-Carlo methods. Figure 4
illustrates that transient behavior of the distributionfunction during Dreicer acceleration is reproducedby our scheme. The new scheme helps us toperform numerical simulations of the runaway
dynamics even with weak electric fields near thecritical threshold [9]. We start to implement thisnew scheme to the guiding-center orbit-following
code ETC-Rel [10] and plans to address therunaway electron generation in stochastic magnetic
fields. The possibility of runaway mitigation bymagnetic perturbations is suggested earlier in thepioneering work by Yoshino, et al. [11] but remains
to be an open physics issue.
[1] P. C. de Vries, et al., Plasma Phys. Control. Fusion
54 (2012) 124032.
[2] C. Reux, et al., J. Nucl. mater. 463 (2015) 143.
[3] M. N. Rosenbluth and S. V. Putvinski, Nucl. Fusion
37 (1997) 1355.
[4] J. R. Martin-Solis, A. Loarte, and M. Lehnen, Phys.
Plasmas 22 (2015) 082503.
[5] P. Helander, et al., Phys. Plasmas 14 (2007) 122102.
[6] A. Matsuyama, et al., in 26th IAEA Fusion Energy
Conference, Kyoto, Japan, 17-22 October 2016,
TH/P1-34.
[7] J. R. Martin-Solis, A. Loarte, and M. Lehnen, Phys.
Plasmas 22 (2015) 092512.
[8] MCNP5 – A General Monte Carlo N-Particle

Transport Code, Version 5. LA-UR-03-1987.
[9] P. Aleynikov and B. N. Breizman, Phys. Rev. Lett.
114 (2015) 155001.
[10] A. Matsuyama, et al., Nucl. Fusion 54 (2014)
123007.
[11] R. Yoshino and S. Tokuda, Nucl. Fusion 40 (2000)
1293.

Figure 1: Primary current profiles calculated without(top) and with (bottom) resistive kink modes.

Figure 2: Electron temperature dependence of primary(left) and plateau (right) runaway currents, includingresistive (res) and inductive electric fields (ind) driven bym = 1 resistive kink modes.

Figure 3: Runaway current plateau with Iseed = 10-7MA
for ITER parameters (R=6.2m, a=2m, Ip=17MA,Bt=5.3T).

Figure 4: Nonthermal electron distribution function
during Dreicer acceleration calculated by Fokker-Planck(dashed) and Monte-Carlo codes (colored points).