An analytical and numerical investigation of ion acoustic waves in a two-ion plasma

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Abstract
The ion acoustic dispersion relation for a plasma containing two distinct ion species is investigated over a wide range of plasma conditions. An approximate general analytic solution to the dispersion relation has been found, and is shown, by comparison to accurate numerical solutions of the individual modes, to be remarkably precise. This solution provides for the first time a systematic account of the totality of ion acoustic modes of the two‐ion system. It has been found that ion acoustic modes consist of two types of modes: (a) at least one, and, at most, two weakly damped modes for which ‖ωI/ωR‖≪1, and (b) an infinity of critically damped modes for which ωI/ωR≂−1. The critically damped modes are organized into two distinct categories: (a) modes for which ‖ω‖/k≳vF (vF is the thermal speed of the fast ion species); and (b) modes for which vS<‖ω‖/k<vF (vS is the thermal speed of the slow ion species). The critically damped modes with ‖ω‖/k≳vF are further organized into three distinct classes: (1) modes with phase speeds characterized by vF, (2) modes with phase speeds characterized by vFvS/√v2F−v2S, and (3) modes with phase speeds characterized by vS. The critically damped modes with vS<‖ω‖/k<vF belong to a single class, and are characterized by vS. Generally, it is found that there are one, or, at most, two modes with relatively small damping, while most of the remaining modes are too strongly damped to be physically realized. It has also been found possible to maximize the ion acoustic damping in a two‐ion plasma by a judicious choice of the relative ion concentrations. More specifically, an admixture of the lighter ion species will maximize the damping coefficient over a wide range of plasma conditions. This is important for certain gas‐filled, inertial‐fusion targets of current interest, where it is desirable to minimize the stimulated Brillouin backscatter process by maximizing the damping.

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