Plasma Fluctuations Induced by Subthreshold Pump Fields

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Abstract
We present in this work three equivalent methods to calculate stable plasma density fluctuations induced by a uniform oscillating electric field near the plasma frequency, somewhat below threshold for generation of parametric electrostatic instabilities. The first method is essentially that of Silin and Sanmartin which is based on the electron and ion Vlasov equations, each transformed to their respective oscillating frames of reference, but here we include effects associated with atomicity of the charges to obtain plasma density fluctuations below threshold. The second approach, which is a more straightforward development of the pumped plasma fluctuations, uses the 'dressed test particle' concept and the nonlinear Poisson equation in the frame of reference oscillating with the electrons. These equations are given for any number of waves and the two results agree exactly. The third and most demanding derivation undertaken here is a modified DuBois–Goldman theory, limited to three waves plus pump, developed by one of us from the rest frame nonlinear Poisson equation for parametric stability analysis. Contrary to an assertion by Hagfors and Gieraltowski, the modified DuBois–Goldman method gives the same results as the other two to second order in field strength.

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