Finite size effects on the dynamics of long wavelength modes in inhomogeneous one dimensional Vlasov plasmas

Collisionless damping of electron plasma waves is a well-known example of wave particle interaction phenomenon also termed as Landau damping [1] usually addressed for uniform plasmas. In the past, in an attempt linear Landau damping in 1D, periodic, inhomogeneous plasma was addressed using fluid model at large perturbation scales [2]. It was demonstrated that the presence of finite amplitude ion density background inhomogeneity efficiently manages to couple the electron plasma wave of long wavelength perturbations leading to damping of high phase velocity waves with v_Φ=ω/k, even though the resonance conditions are not satisfied [2]. Also, it was illustrated that in this cold plasma limit, the amplitude of the coupled modes will evolve in time t according to the Bessel function J_n(At/2) depending on the strength of inhomogeneity, where n is related to strength of inhomogeneity A [2]. 

In light of the above, we have studied linear Landau damping in a periodic inhomogeneous collisionless 1D plasma using a high resolution Vlasov-Poisson solver i.e VPPM-OMP 1.0 [3] without any approximations. In the work presented here, we ask ourselves as to what would happen to J_n(At/2) scaling, if the long wavelength limit is relaxed? Interestingly, for the parameters considered, it is found that for a given inhomogeneity strength A, the perturbation amplitude does not anymore follow J_n(At/2), for systems with finite size (L_x). We numerically demonstrate that at large L_x, our findings correctly asymptote to that of Ref [2]. In the following, we will address the various regimes of perturbation scales in an inhomogeneous plasma with kinetic electrons and immobile ions [4]. The details of this work will be presented.

References

[1] L. Landau, J. Phys. USSR 10, 25 (1946).

[2] P. K. Kaw, A. T. Lin, and J. M. Dawson, Phys. Fluids 16, 1967 (1973).

[3] Sanjeev Kumar Pandey, Rajaraman Ganesh, AIP Advances 11, 025229 (2021).

[4] Sanjeev Kumar Pandey, Rajaraman Ganesh, Under Preparation (2021).