Speaker
Description
Max Planck Institute for Plasma Physics
Energetic particles will play a central role in future burning plasma experiments, and their
confinement is an important aspect for a fusion reactor. Understanding the effects of energetic
particles (EPs) is essential, as they can strongly interact with the main plasma and drive
magnetohydrodynamic (MHD) instabilities. One notable example is the fishbone instability,
which arises from an internal kink mode with n=1 resonance to the precessional frequency of
EPs.
To investigate wave-particle interaction phenomena in tokamaks, numerical simulations serve
as a major research tool. This contribution focuses on applications and developments of the
nonlinear extended MHD code JOREK [1], which includes a kinetic module specifically for
energetic particles. In the present hybrid kinetic-MHD model implemented in JOREK, the
EPs are simulated using the particle-in-cell technique, while the bulk plasma is treated as a
fluid by solving the equations of MHD. A full-f formulation for the kinetic particles and an
anisotropic pressure coupling scheme to the fluid are used.
The kinetic particle module was applied to study toroidal Alfvén eigenmodes (TAE) and was
successfully validated in the linear regime [2]. The current setup is now being used to
investigate the fishbone instability both in the linear and in the nonlinear regime. Initial linear
simulations demonstrate good agreement with a benchmark case using the M3D-C1-K code
which is explained in [3].
Furthermore, a new hybrid kinetic-MHD model is currently under development for JOREK. It
aims at treating also the thermal ions kinetically and only describing the electrons as fluid.
The new model is based on the standard drift model. The ion density, parallel velocity and
pressure are determined through projections from the kinetic particles, while the electron
pressure and the MHD velocity are calculated using fluid equations. The new model is under
development in JOREK and we present the key concepts and the present state in this
contribution.
[1] M. Hoelzl et al. “The JOREK non-linear extended MHD code and applications to large-scale
instabilities and their control in magnetically confined fusion plasmas”. In: Nuclear Fusion
61.6 (May 2021), p. 065001. doi: 10.1088/1741-4326/abf99f. url: https://dx.doi.org/10.1088/1741-
4326/abf99f.
[2] T. J. Bogaarts et al. “Development and application of a hybrid MHD-kinetic model in JOREK”.
In: Physics of Plasmas 29.12 (2022), p. 122501. doi: 10.1063/5.0119435. eprint: https:
//doi.org/10.1063/5.0119435. url: https://doi.org/10.1063/5.0119435.
[3] C. Liu et al. “Hybrid simulation of energetic particles interacting with magnetohydrodynamics
using a slow manifold algorithm and GPU acceleration”. In: Computer Physics Communications, 275
(2022), p. 108313, url: https://doi.org/10.1016/j.cpc.2022.108313
