Approach to Stability of a Plasma

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Abstract
The stabilization of a spatially homogeneous plasma by the collision term of the new kinetic equation of Balescu for a weakly unstable plasma is shown for a simplified model. The one‐particle velocity distribution consists of two symmetrically displaced Lorentz distribution functions in which the displacement velocity and velocity spread are functions of time. For this distribution function, the collision term decreases the displacement velocity and increases the velocity spread until the plasma is quite stable. Physically this process can be viewed as conversion of relative energy to kinetic energy. This is demonstrated to be equivalent to the passage of the zero of the plus dielectric constant from the upper half complex plane, characterizing an unstable plasma, to the lower half complex plane, characterizing a stable plasma.

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