A model for evaluating compression effects in the mθ=1 diocotron instability

Abstract

Herein is presented a refinement of the theory published by Finn et al. (1999) for the mθ=1 diocotron instability. A rigorous definition of the plasma length is introduced and the expression for the velocity field is improved, inasmuch as the effect of the finite size of the plasma column is included. The effect of the perturbation of the plasma length is considered rigorously by using a Green-function approach. A parametric study of the instability for a hollow profile is shown.

Rigorous fluid model for 3D analysis of the diocotron instability

“…The set of equations can be written in a more compact way by defining the quantity T (r, 0, z, t) = 0 (r, 0, z, t) -0, (r, 0,t), which represents the correction to the potential in a trap of finite length, with respect to the one in a trap of infinite length. Finally, the following system of equations is to be solved: A modified Rayleigh criterion for linear stability and the conservation of canonical angular momentum and of the energy of the system can be deduced fiorn system (9) [6]. The criterion proves that when cTo(r) is a monotonic function, the system is linearly stable.…”

“…However, the theory by Finn et al neglects the finite electron temperature and the effects of the perturbation of the plasma length in the axial direction are treated in a simplified manner. These two issues are treated rigorously in a recent work by the Authors [6].…”

“…[6] is reviewed and comparisons with experimental data provided by Kabantsev and Driscoll [4] are presented.…”

Diocotron spectrum with compression effects

“…New fluid-dynamics models have been developed for a non-neutral plasma, trying to solve the problem of the I = 1 diocotron instability [3,4]. These works show that a possible explanation of the instability comes from the finite curvature of the ends of the plasma column due to the confining voltage (i.e.…”

“…We focus our attention on a simplified version of the model developed by some of the authors in Ref. [4]. In normalized units, the model is the following:…”