Abstract
The relativistic effects on strong Langmuir turbulence which arise from both relativistic plasma temperatures and high-amplitude oscillations (i.e. the oscillatory electron velocity in the wave approaches the speed of light) are considered. When relativistic effects arise primarily from high plasma temperature, a kinetic formalism is employed and a nonlinear Schrüdinger equation is derived from expansion of the Vlasov-Maxwell equations. The analysis is appropriate to either hydrogen or electron-positron plasmas, and the relativistic effect is found to provide a new type of nonlinear phase-amplitude coupling in three dimensions. A fluid treatment is used when the relativistic effects of high wave amplitudes predominate. Here, ion dynamics are ignored and the relativistic electron mass correction results in the same type of three-dimensional phase-amplitude coupling as in the kinetic analysis. A Lagrangian formalism for each limiting case is described which leads to a virial theorem from which thresholds for collapse of arbitrary wave packets can be derived.
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