Propagation and Instabilities of Waves in Bounded Finite Temperature Plasmas

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Abstract
The quasistatic analysis is used to examine propagation and instabilities of waves in a plasma in which the transverse bounds and the temperature are important. A dispersion equation is derived by use of a dielectric tensor, which is correct within the quasistatic assumption and the assumption of longitudinal velocity, only. The dispersion curves have a smooth transition from the zero temperature case at long wavelengths to the unbounded finite temperature case at short wavelengths. The stop‐bands which appear in the zero temperature analysis become propagating regions in the more general case. Landau‐type damping is calculated; the cyclotron wave is strongly damped. The effect of the boundaries and the magnetic field on a double‐humped velocity distribution is examined. The transverse boundaries are stabilizing with respect to space‐charge waves, but the cyclotron interactions are strengthened. The temperature always exerts a stabilizing influence which is particularly marked for the interaction between the cyclotron waves. Curves of the limiting regions of stability, with respect to various parameters, are given, illustrating these effects. By the use of an example it is demonstrated that a moderate temperature can suppress the cyclotron instability. This result is in agreement with the experimental observation that a plasma, predicted to be unstable with respect to the cyclotron‐wave interaction, was actually stable.

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