Second-Order Nonlinear Processes in Warm Unmagnetized Plasmas

Abstract

Nonlinear processes are commonly invoked to describe a wide range of phenomena in both space plasmas and laboratory plasmas, allowing wave energy in a particular mode to be transferred to different modes. Relevant processes include three-wave interactions and nonlinear wave-particle scattering. The strength of the wave coupling—and hence the nonlinear rates—for these processes is determined by the quadratic response tensor. The general expression for this tensor involves a number of velocity-space integrals of the velocity distribution function and denominators related to the Cerenkov resonance between waves and particles. Due to the difficulty of evaluating these integrals they are typically approximated by making assumptions about the phase speeds of the waves. However, the ranges of validity for these approximations are unclear, and the resulting approximate quadratic response tensors and nonlinear rates may be inaccurate in some regimes. Conversely, an exact expression for the quadratic response tensor of an unmagnetized Maxwellian plasma has been derived previously in terms of generalized plasma dispersion functions. This expression is valid for any phase speeds of the waves, but its length and complexity prevents its use in the calculation of nonlinear rates. What is lacking in the literature are more accurate explicit expressions for the quadratic response tensor that are appropriate for nonlinear rate calculations, from which also the accuracy of the typical approximations can be assessed. This thesis presents new, more accurate analytical expressions for the quadratic response tensor for various second-order processes in unmagnetized plasmas, and analytical and numerical calculations of the corresponding nonlinear rates. Comparisons are then made between these new nonlinear rates and the previous approximate rates, allowing the accuracy of the previous rates to be assessed and sharper bounds placed on their regimes of validity for the first time.