Effect of squeeze on electrostatic Trivelpiece-Gould wave damping

Abstract

We present a theory for increased damping of Trivelpiece-Gouid plasma modes on a nonneutral plasma column, due to application of a Debye shielded cylindrically symmetric squeeze potential φ1. We present two models of the effect this has on the plasma modes: a 1D model with only axial dependence, and a 2D model that also keeps radial dependence in the squeezed equilibrium and the mode. We study the models using both analytical and numerical methods. For our analytical studies, we assume that φ1/T≪1, and we treat the Debye shielded squeeze potential as a perturbation in the equilibrium Hamiltonian. Our numerical simulations solve the 1D Vlasov-Poisson system and obtain the frequency and damping rate for a self-consistent plasma mode, making no assumptions as to the size of the squeeze. In both the 1D and 2D models, damping of the mode is caused by Landau resonances at energies En for which the particle bounce frequency ωb(En) and the wave frequency ω satisfy ω=nωb(En). Particles experience a non-sinusoidal wave potential along their bounce orbits due to the squeeze potential. As a result, the squeeze induces bounce harmonics with n > 1 in the perturbed distribution. The harmonics allow resonances at energies En≤T that cause substantial damping, even when wave phase velocities are much larger than the thermal velocity. In the regime ω/k≫T/m (k is the wave number) and T≫φ1, the resonance damping rate has a |φ1|2 dependence. This dependence agrees with the simulations and experimental results.