SIII-4
高エネルギー粒子駆動型不安定性のシミュレーション研究
Simulation Study of Energetic Particle Driven Instabilities
藤堂 泰Y. Todo
核融合研、総研大NIFS, Graduate Univ. Advanced Studies
Energetic particle driven instabilities (e.g.
Alfvén eigenmodes) are one of the mostimportant issues for the ITER plasmas because
they lead to energetic alpha particle
redistribution and losses. Computer simulation
is expected to predict the stability of Alfvén
eigenmodes and the associated energetic
particle transport for ITER operation scenarios.
In a Lighthouse Project of the IFERC-CSC
Supercomputer Helios, this issue has beeninvestigated using MEGA that is a hybrid
simulation code for energetic particles andmagnetohydrodynamics (MHD). In this paper,
we will present the results of MEGA code [1]for performance benchmark test on Helios,
Alfvén eigenmode stability and energetic
particle transport in ITER steady operation
scenario, and nonlinear MHD effects on Alfvén
eigenmode evolution and bursts. We will
discuss the future work on the energetic particle
driven instabilities.

Fig. 1 Strong scaling of MEGA code vs.
number of nodes on Helios.

I. Performance benchmark test of MEGA codeon Helios
The computational performance of MEGA
code was investigated using Helios. The
numbers of grid points and computationalparticles are (256, 256, 512) for (R, , z)coordinates and 34 million, respectively. Figure
1 shows the computational performance vs.
number of nodes on Helios. We see anexcellent strong scaling up to 512 nodes with8192 CPU cores.
II. Alfvén eigenmode stability and energetic
particle transport in an ITER steady state
operation scenario
Stability of Alfvén eigenmodes and theassociated transport of energetic alpha particles

Fig. 2 Spatial profiles of TAE modes in thelinearly growing phase (top) and in thesaturation phase (bottom).

Fig. 3 Beta value perturbations for energeticalpha particles and beam deuterium
particles, and safety factor profile.

and beam deuterium particles were investigatedfor an ITER steady state operation scenario
using MEGA code. The equilibrium data
provided on the ITER web site is used for thesimulation. The specific parameters are major
radius 6.2m, minor radius 2m, and total plasma
current 9MA. The particle simulation method isapplied to both alpha particles and beam
deuterium particles. The finite Larmor radiuseffects are taken into account for both thespecies.
It was found that toroidal Alfvén
eigenmodes (TAE modes) with toroidal mode
number from 12 to 22 are unstable and thesaturation level of the magnetic fluctuation is
0.2% normalized by the toroidal field. Figure 2
shows the spatial profiles of the TAE modes in
the linearly growing phase and the saturation
phase. Figure 3 shows the beta value
perturbations for alpha and beam deuterium
particles. Slight redistributions take place foralpha and beam deuterium particles with beta
value perturbations 0.03% and 0.01%,respectively.
III. Nonlinear MHD effects on Alfvéneigenmode evolution
We have recently investigated nonlinear
MHD effects on Alfvén eigenmode evolution
using MEGA code [2, 3]. In addition to fully
nonlinear code, a linear-MHD code was used
for comparison. The only nonlinearity in thatlinear code is from the energetic-particle
dynamics. No significant difference was foundin the results of the two codes for low
saturation levels, δB/B~10−3. In contrast, when

the TAE saturation level predicted by the linear
code is δB/B~10−2, the saturation amplitude in
the fully nonlinear simulation was reduced by afactor of 2 due to the generation of zonal (n=0)
and higher-n modes. This reduction isattributed to the increased dissipation arisingfrom the nonlinearly generated modes. The
fully nonlinear simulations also show thatgeodesic acoustic mode is excited by the MHD
nonlinearity after the TAE mode saturation.
MEGA code has been extended to simulate
recurrent bursts of Alfvén eigenmodes byimplementing the energetic-particle source,collisions and losses [4]. The Alfvén
eigenmode bursts with synchronization ofmultiple modes and beam ion losses at eachburst are successfully simulated with nonlinear
MHD effects for the physics condition similar
to a reduced simulation for a TFTR experiment.
It is demonstrated with a comparison between
nonlinear MHD and linear MHD simulation
results that the nonlinear MHD effects
significantly reduce both the saturation
amplitude of the Alfvén eigenmodes and thebeam ion losses. The Alfvén eigenmode bursts
take place for higher dissipation coefficientswith roughly 10% drop in stored beam energy
and the maximum amplitude of the dominantmagnetic fluctuation harmonic δBm/n/B~
5×10−3 at the mode peak location inside theplasma. Quadratic dependence of beam ion loss
rate on magnetic fluctuation amplitude is found
for the bursting evolution in the nonlinear
MHD simulation. The beam ion pressure
profiles are similar among the different
dissipation coefficients.
These results on nonlinear MHD effects
indicate the coupling of Alfvén eigenmode andzonal structures, and suggest the beam ion
profiles might reach close to a marginallystability state in the self-consistent evolution.
An important development of Alfvén
eigenmode simulation using Helios will be an
extension of the simulation model with kinetic
thermal ions and electrons.
[1] Y. Todo and T. Sato, Phys. Plasmas 5, 1321
(1998).
[2] Y. Todo et al., Nucl. Fusion 50, 084016 (2010).
[3] Y. Todo et al., Nucl. Fusion 52, 094018 (2012).
[4] Y. Todo et al., Nucl. Fusion 52, 033003 (2012).