The effect of weak collisionality on damped modes and its contribution to linear mode coupling in gyrokinetic simulation

Abstract

We revisit the characteristics of stable, damped modes originating from the Landau damping by employing a discretized gyrokinetic Vlasov simulation and also eigenvalue analysis in an unsheared slab geometry. By comparing results between gyrokinetic simulation and an eigenvalue analysis, we found that there exists a critical collisionality βc⋆ at which the Case-van Kampen (CvK) modes are damped down to the analytically estimated Landau damping rate and an eigenmode consistent with Landau's theory emerges. Consequently, the recurrence phenomenon disappears so that the Landau damping can be properly reproduced. The critical collisionality βc⋆ depends on the resolution in velocity space; i.e., a higher (lower) resolution requires a lower (higher) collisionality, while tends to zero (βc⋆→0) as Δv→0. It is found through a reduced model that even in the collisionless case with marginally stable CvK modes, the linear mode coupling between unstable and stable/damped components through a tertiary mode and the resultant energy transfer can be properly calculated such that the stable/damped mode persists as an eigenstate.