NONLINEAR EVOLUTION OF LANGMUIR AND ELECTROMAGNETIC PULSES IN A WARM,UNMAGNETIZED PLASMA - MODULATIONAL INSTABILITY, INTEGRABILITY AND SELF-FOCUSING IN 2-DIMENSIONS(1)

The nonlinear dynamics of wave envelopes modulated in 2+1 dimensions i s considered for two systems in plasma physics: (i) Langmuir pulses an d (ii) intense (but weakly relativistic) electromagnetic (EM) pulses. Using singular perturbation techniques applied to an envelope approxim ation, both problems are reduced to the two-dimensional nonlinear Schr odinger (2DNLS) system, which describes the dynamics of two coupled sl owly varying potentials. The general 2DNLS system exhibits a rich vari ety of phenomena, including enhanced (compared with 'longitudinal' pro pagation) modulational stability and (1D) soliton formation; decay of 1D solitons over long time scales; self-focusing regimes (determined b y a virial-type condition); as well as integrability and 2D solitons. Applying our recent results on the 2DNLS system, we determine which of these phenomena can actually occur here and compute the parameter reg imes. (i) The 2DNLS system for the Zakharov equations is modulationall y unstable for all parameter values. It also has an integrable sector and a self-focusing regime. (ii) The 2DNLS system describes coupled 'l ongitudinal' and 'transverse' modulations of linearly or circularly po larized EM pulses propagating through a warm unmagnetized two-componen t neutral plasma with arbitrary masses (i.e. electron-positron or elec tron-ion). The pulse can accelerate particles to weakly (but not fully ) relativistic velocities; relativistic, ponderomotive and harmonic ef fects all contribute to the nonlinear terms. The resulting 2DNLS syste m does not admit a self-focusing regime. Parameter values leading to a n integrable case (the so-called 'Davey-Stewartson I' equations, which admit 2D soliton solutions) are computed; however, the required value s would not be attainable in a. laboratory or astrophysical setting. N one the less, the existence of new nonlinear modulational instabilitie s associated with the second spatial degree of freedom already represe nts an important potential limitation on any (1+1)-dimensional approac h to nonlinear evolution and modulational instability of plasma EM