LIGKA: A linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks

Abstract

In a plasma with a population of super-thermal particles generated by heating or fusion processes, kinetic effects can lead to the additional destabilisation of MHD modes or even to additional energetic particle modes. In order to describe these modes, a new linear gyrokinetic MHD code has been developed and tested, LIGKA (linear gyrokinetic shear Alfvén physics) [Ph. Lauber, Linear gyrokinetic description of fast particle effects on the MHD stability in tokamaks, Ph.D. Thesis, TU Mü nchen, 2003; Ph. Lauber, S. Gü nter, S.D. Pinches, Phys. Plasmas 12 (2005) 122501], based on a gyrokinetic model [H. Qin, Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks, Ph.D.Thesis, Princeton University, 1998]. A finite Larmor radius expansion together with the construction of some fluid moments and specification to the shear Alfvén regime results in a self-consistent, electromagnetic, non-perturbative model, that allows not only for growing or damped eigenvalues but also for a change in mode-structure of the magnetic perturbation due to the energetic particles and background kinetic effects.Compared to previous implementations [H. Qin, mentioned above], this model is coded in a more general and comprehensive way. LIGKA uses a Fourier decomposition in the poloidal coordinate and a finite element discretisation in the radial direction. Both analytical and numerical equilibria can be treated. Integration over the unperturbed particle orbits is performed with the drift-kinetic HAGIS code [S.D. Pinches, Ph.D. Thesis, The University of Nottingham, 1996; S.D. Pinches et al., CPC 111 (1998) 131] which accurately describes the particles' trajectories. This allows finite-banana-width effects to be implemented in a rigorous way since the linear formulation of the model allows the exchange of the unperturbed orbit integration and the discretisation of the perturbed potentials in the radial direction.Successful benchmarks for toroidal Alfvén eigenmodes (TAEs) and kinetic Alfvén waves (KAWs) with analytical results, ideal MHD codes, drift-kinetic codes and other codes based on kinetic models are reported.

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

“…In its general behaviour STAE-K is closest to NOVA-K. Note that for this comparison an older version of NOVA-K [25,27], which does not include FOW-and FLR effects, was used, which makes the underlying physical model very similar to that of STAE-K. Just like STAE-K, LIGKA [28] is a non-perturbative eigenvalue code but with a much more complex model, and it is not surprising that these two codes show differences. It can also be noted that for fast-ion velocities less than approximately v A,0 /2, the mode is still damped.…”

“…The fully kinetic codes predict a much stronger frequency change for high temperatures. Curves other than STAE-K taken from [26,28]. Comparison of STAE-K to analytic theory in the limit of very small inverse aspect ratio for various fast-particle temperatures.…”

Global particle-in-cell simulations of fast-particle effects on shear Alfvén waves

“…Numerically, the TAE modes have also been studied by many authors. For example, they have been simulated using the reduced kinetic approach [13], the first-principle global gyrokinetic eigenvalue approach [14,15], the electron-fluid ion-kinetic hybrid gyrokinetic model [16,17], and using the global gyrokinetic particle-in-cell (PIC) code [18].…”

Global particle-in-cell simulations of plasma pressure effects on Alfvénic modes

“…[19,20] (global eigenvalue code LIGKA) to study the continuum and radiative damping mechanisms. The electron-fluid ion-kinetic hybrid gyrokinetic model has been benchmarked vs. the theoretical predictions for the TAE mode in Refs.…”