Nonlinear electromagnetic-wave interactions in pair plasma: (I) Non-relativistic regime

This paper is the first in a series devoted to the numerical study of nonlinear interactions of electromagnetic waves with plasma. We start with non-magnetized pair plasmas, where the primary processes are induced (Compton) scattering and the filamentation instability. In this paper, we consider waves in which electron oscillations are non-relativistic. Here, the numerical results can be compared to analytical theory, facilitating the development of appropriate numerical tools and framework. We distill the analytic theory, reconciling plasma and radiative transfer pictures of induced scattering and developing in detail the kinetic theory of modulation/filamentation instability. We carry out homogeneous numerical simulations using the particle-in-cell codes EPOCH and Tristan-MP, for both monochromatic waves and wave packets. We show that simulations of both processes are consistent with theoretical predictions, setting the stage for analyzing the highly nonlinear regime.