Effects of beam ions on stability properties of kinetic FRCs

Stability properties of kinetic FRCs (S*<10) with a significant beam ion population are investigated numerically using 2D and 3D hybrid simulations. It is shown that for beam ion distribution close to a double delta-function, with narrow energy and toroidal angular momentum spread, compressional Alfvén modes can be excited with low toroidal mode numbers. This is reactive-type instability, but being close to a resonant condition, when the average beam ion precession frequency matches the mode frequency, increases the beam-mode interaction. For TAE parameters, the n=2 mode is the most unstable, and its growth rate depends strongly on the beam ion distribution function and the FRC kinetic parameter. There was no significant difference in the properties of these modes in a simplified case of 1D equilibrium. For low beam ion densities, the instability saturates nonlinearly at low amplitude due to redistribution of the beam ions and significant changes in the beam ion current. The linear dispersion relation for compressional modes was derived to explain the simulation results. Similar n = 2 modes, but with small amplitudes, have been observed experimentally [1], and have been shown to be responsible for a significant redistribution of the beam ions [2].

[1] B. Deng et al, Nuc. Fusion 58, 126026 (2018)

[2] R. Groenewald et al., Phys. Plasmas 32, 072503 (2025)