Exact Quadratic Longitudinal Response of a Maxwellian Plasma and its Application to the Rate of Electrostatic Decay

Physics – Plasma Physics

Scientific paper

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[7827] Space Plasma Physics / Kinetic And Mhd Theory, [7839] Space Plasma Physics / Nonlinear Phenomena, [7847] Space Plasma Physics / Radiation Processes, [7868] Space Plasma Physics / Wave/Wave Interactions

Scientific paper

Langmuir waves driven by electron beams are commonly observed in both space and laboratory plasmas. Once generated, these Langmuir waves may undergo a variety of mode conversion processes, in which wave energy is transferred between wave modes. One such process is electrostatic decay, in which a Langmuir wave decays into a product Langmuir wave and an ion-sound wave; this is an important mechanism in the generation of electromagnetic radiation at multiples of the plasma frequency, known as plasma emission. Until now the rate of electrostatic decay has been calculated using an approximate expression for the quadratic longitudinal response (otherwise known as the second-order longitudinal susceptibility), which describes the coupling between three electrostatic waves. We derive an exact expression for the quadratic longitudinal response in terms of generalized plasma dispersion functions. This expression reduces to the approximate result in the appropriate limit. We develop numerical expressions for the generalized plasma dispersion functions, correcting various aspects of previous calculations and positioning us to calculate the rate of electrostatic decay.

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