S11-4
Simulation Research on Runaway Electrons in Tokamak Disruption Events
ディスラプション時の逃走電子シミュレーション研究
Akinobu Matsuyama
松山 顕之Japan Atomic Energy Agency, Rokkasho, Aomori 039-3212, Japan
日本原子力研究開発機構 〒039-3212 青森県上北郡六ヶ所村大字尾駮字表舘2-166
The goal of our project “DISRUPT” using the Helios supercomputer at IFERC-CSC is to develop an
integrated simulation code for describing whole duration of major disruptions including its 3D nature. Ourcurrent scope is runaway electrons (REs), which may unacceptably shorten the lifetime of the plasma
facing components in ITER and DEMO. The present experiments have pointed out that low-order MHD
instabilities play a significant role in the RE generation as well as the RE current plateau termination. We
propose two different approaches to incorporate MHD events into RE modeling, which is based on (1)nonlinear MHD codes for internal modes and (2) linear MHD codes for external modes.

1. Introduction
Runaway electrons (REs) produced during
major disruptions can gain the energies above 10
MeV and their localized wall loads may
unacceptably shorten the lifetime of plasma
facing components. In ITER, even a small seedcurrent can be amplified by an avalanche
mechanism, and the formation of multi-MA RE
beams poses a serious problem. Therefore, thedevelopment of mitigation schemes has become
one of the most important topics in ITER.
Up to present, 2D axisymmetric modeling ofdisruptions has widely been used, which arepowerful tools for the parametric study tointerpret the experiments and to predict thedisruption scenarios. On the other side, thenecessity of improved modeling taking into
account 3D nature of disruptions is recognizedespecially if we focus on the toroidal asymmetryof the energy deposition on the vessel wall aswell as of the electromagnetic loads. Concerning
REs, enhanced RE losses have been observedwith the excitation of magnetic fluctuations,typically being n = 1 mode (n: toroidal modenumber), which results in toroidally localized
wall loads in the RE discharge termination phase.
In addition, the proposed mitigation schemes suchas massive gas injection and resonant magnetic
perturbations require 3D modeling of disruptions
and RE generation processes.
From 2012, we have initiated a project“DISRUPT” in IFERC-CSC, which is aimed atdescribing whole duration of major disruptions
including its 3D nature by simulations. Under thisproject, ETC-Rel [1,2] has been developed andcontinuously improved as 3D modeling of REs,
which solves relativistic guiding-center equationsfor Monte-Carlo test particles. In this paper, ourrecent progress is described especially focusing
on the study for examining how REs respond to
the excitation of low-order MHD instabilities.
3. Redistribution of REs by Internal Modes
The MHD modes that arise in the early phase ofa current quench has been considered to mitigate
the RE generation [3]. Because REs are produced
predominantly in the core region near the magnetic
axis, the main contribution is expected to be due tointernal modes. When we consider their impact on
the RE confinement, the saturated island widths area key parameter because REs are redistributed at alarge parallel velocity along the stochastic magnetic
fields once magnetic islands at different radial
locations are overlapped. For treating such aphenomenon, we integrate a nonlinear reducedMHD code Extreme [4] (based on the spectral
method in the poloidal and toroidal directions) withETC-Rel. Figure 1 shows the evolution of (a)magnetic energy, and (b) radial profile of seed REs
calculated, where a resistive kink mode isconsidered as an example of the MHD mode thatcauses the RE redistribution in the core plasma.
Here, an initial MHD equilibrium with the peaked
current profile (q(0) ~ 0.6) is chosen for theresistive kink to be unstable. The simulation has
shown that REs immediately respond to the changeof magnetic field topology associated with the kinkgrowth, and the timescale of RE redistribution isdominated by the mode growth, independently of
the RE energy. The physics involved is considered
to be similar to the relaxation of fast-ion densities in
the presence of sawteeth and fishbone. On the otherside, since REs are sensitive to the perturbing fields
because of its small gyroradii, short-wavelengthmagnetic turbulence can also enhance the radialtransport of REs. To improve the resolution, an
application of R4F [5] which can treat higher nmodes on the basis of pseudo-spectral method withmassively parallel computer is also underway.

4. Summary and Future Work
Progress in the project “DISRUPT” has beenreported, focusing on the RE physics. As the next
step, the simulation codes will be extended as an
MHD+PIC hybrid model for studying theinteraction between REs with MHD. Anotherimportant task is to treat slow plasma boundary
evolution on the transport timescale, taking into
account vertical displacement events (VDEs),
which dominates a final loss position of REs. In
addition, for the development of RE control schemesuch as collisional dissipation [8], the equilibrium
and linear stability models for the RE current
plateau will also become important.

Fig.1. Evolution of magnetic energy and of the radial
profile of 19 MeV REs in the nonlinear saturation phaseof resistive kink mode calculated by Extreme [5], where
the time T is normalized by the Poloidal Alfvén unit.

3. RE Loss Flux Driven by External Modes
Another important contribution of MHD modes
to REs is the RE current plateau termination driven
by external modes. Although the stability propertiesof the RE current plateau have not yet been
elucidated, the experimental correlation of prompt
RE losses with the surface safety factor values arerather clear. It suggests the contribution of
external-kink type modes. Following this idea, wedevelop a simulation model combining the linear
stability code MARG2D [6] with ETC-Rel. Figure
2 shows the Poincaré map of the RE drift orbit
recorded on the outer equatorial plane in thepresence of m = 4 external kink perturbations forδB/B ~ 1%. (Here, q(a) is selected to be 3.8.) Near
the plasma edge, such a strong perturbation causes aprompt loss of REs even in the absence ofstochastic fields. For edge perturbations like RMPs
and external MHD modes, the energy dependenceof RE losses are dominated by horizontal shift of
the resonant position against the MHD modes dueto the curvature drift motion. The simulation showthat REs are lost to the vessel wall as if the current
channel outside qK > 3 is scraped off, where qK is aneffective safety factor measured along the drift
surface. Because the loss pattern to the wall isgoverned by the radial magnetic field that is felt byparticles [7] when they are lost from the boundary
between closed and open field lines, the wall loads
exhibit the n = 1 toroidal asymmetry.

Fig.1. Poincaré map of 1-100 MeV RE drift orbit on
the outer equatorial plane in the presence of external kinkmode calculated by MARG2D, where δB/B ~ 1%. Red
segments indicate the magnetic separatrix and the blue
curve indicates qK = 3 drift surface.

Acknowledgments
The author would like to thank Drs. M. Yagi, N.
Aiba, and Y. Ishii for their collaboration. This work
was supported in part by Grants-in-Aid for
Scientific Research (23246163, 26820404, and23561009). The computation was carried out using
the HELIOS supercomputer system at IFERC-CSC.
References[1] S. Tokuda and R. Yoshino, Nucl. Fusion 39 (1999)
1123.
[2] A. Matsuyama, et al., Nucl. Fusion (2014) in press.
[3] P. Helander, et al, Plasma Phys. Control. Fusion 44(2002) B247.
[4] Y. Ishii, et al., Nucl. Fusion 43 (2003) 539.
[5] M. Yagi, et al., Nucl. Fusion 45 (2005) 900.
[6] N. Aiba, et al., Comput. Phys. Commun. 175 (2006)
269.
[7] G. Papp, et al., Plasma Phys. Control. Fusion 54(2012) 125008.
[8] E. M. Hollmann, et al., Nucl. Fusion 53 (2013)
083004.