7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Simulation of Compressional Alfvén Eigenmodes in Tokamak Disruptions andImpact on Runaway Electron Transport
Chang Liu1, Stephen Jardin1, Amitava Bhattacharjee1, Andrey Lvovskiy2, Carlos Paz-Soldan3
1
Princeton Plasma Physics Laboratory, 2 General Atomics, 3 Columbia University
e-mail (speaker): cliu@pppl.gov

The simulation results can be explained by considering
the resonance between the trapped REs and the CAEs[2]. The trapped REs affected by gradient drifts andmirror forces from δB∥ will have a net change ofcanonical angular momentum (Pϕ), which can cause thetrapped particle orbit to shift in the radial direction. This
resonance mechanism indicates that a radial gradient of
the trapped REs can lead to a drive of the mode. Unlike
the transit frequency of REs, which only depends onparticles’ velocity, the precession frequency of trapped

In summary, the excitation of current quench Alfvénic
mode can be explained by considering the resonancebetween CAEs and the precession motion of trapped
high-energy REs, and can be reproduced using kineticMHD simulation. There is still a discrepancy with theexperiments on the RE diffusion, which will be further
studied by updating the model with more kinetic effects.
References[1] Liu, C., et al., Comput. Phys. Commun. 275, 108313(2022).
[2] Liu, C., et al., Nucl. Fusion 61, 036011 (2021).
1.640

1.4

35

1.2

30

1.025

δB0.8
∥

20

0.6

150.4

100.2

50.04

68

101214
RE Energy (MeV)

16180

1.2
0.80.4Z (m)We conducted a series of linear simulations for the n=1mode with varying peak RE energy. It is found that thefrequency of the excited most unstable mode follows astaircase-like function with RE energy, and the spacing
between adjacent modes is about 0.2-0.4 MHz. The
mode frequency and the relationship with RE energy are
consistent with DIII-D experimental observation, as
shown in Fig. 1. However, the highest mode frequency
we found is around 1.4 MHz, which is smaller than in theexperiment. Each level of the staircase represents a
different mode structure in the poloidal plane. Analysisof the simulation shows that the mode has dominantly
compressional polarization (δB∥≫δB⊥), which is also
consistent with the recent diagnostic result.

We also did nonlinear simulations using a broad RE
energy spectrum and study the spatial diffusion of REs
driven by the mode exciation. However, we found that thediffusion effects from CAEs are too weak to explain fast
RE loss observed in experiments. We found that in orderto reach a short RE diffusion time of a few milliseconds,
the perturbed δB∥ must be larger than 0.5 Tesla. To reachsuch a high level of the mode amplitude, more trapped
REs are required, which may come from other pitch
angle scattering mechanisms than high-Z ion collisions,
including the avalanche generation and turbulence
scattering.

Growth/Damping Rate (103s 1 )In this work we present results of self-consistent kineticMHD simulations of RE-driven compressional Alfvén
eigenmodes (CAEs) in DIII-D disruption scenarios,
providing an explanation of the CQ modes. We use thekinetic-MHD code M3D-C1-K [1] to simulate theexcitation of CAEs driven by REs in the disruption case.

REs is proportional to the relativistic RE energy,
therefore the higher frequency mode can only be excitedwhen high-energy REs are present.

Frequency (MHz)Alfvénic modes in the current quench (CQ) stage oftokamak disruption have been observed in both DIII-Dand ASDEX Upgrade experiments. In DIII-D theexcitation of the mode is linked to the presence of highenergy runaway electrons (REs), and a strong mode
excitation is often associated with the failure of RE
plateau formation. The Alfvénic instabilities are being
explored in order to devise a complementary strategy for
RE mitigation in addition to impurity injection for ITER
and other tokamaks.

0.0
0.4
0.8
1.2
1.0 1.4 1.8 2.2R (m)Figure 1 (left) Linear simulation results of excited CAE
mode frequency (blue), growth rates (red) and damping
rate (green). (right) Mode structure of CAE ( f=0.9MHz)