Nonlinear modulational stability and propagation of an electromagnetic pulse in a two-component neutral plasma

Abstract

We study nonlinear effects including possible modulational instability of an intense electromagnetic pulse propagating through a fully ionized unmag-netized plasma. (The pulse is assumed to be sufficiently strong to accelerate particles to weakly, but not fully, relativistic velocities.) The envelope is shown to evolve over long time scales in general according to a vector form of the well-known cubic nonlinear Schrödinger (NLS) equation. Three distinct nonlinear effects contribute terms cubic in the amplitude and thus can be of comparable magnitude: ponderomotive forces, relativistic corrections and harmonic generation. In contrast with previous work, our calculation takes all three effects into account. Integrability and modulational stability of any given system are shown to depend on polarization, frequency, composition and temperature, and these dependences are given. We first carry out the calculation in detail for the case of zero temperature. In the special case of a cold positron-electron plasma, in contrast with the predictions of Chian & Kennel (1983), the model is strictly modulationally stable for both linear and circular polarization. We then generalize our result by giving the dependence of the nonlinear coefficients on temperature. As it turns out, finite-temperature effects are qualitatively important only near a critical frequency (<3/2ωp) just above the plasma frequency for which the group velocity is comparable to either (or both) of the sound velocities. The results have important implications for pulsar micropulse observations and possible technological applications.

Green’s function-stochastic methods framework for probing nonlinear evolution problems: Burger’s equation, the nonlinear Schrödinger’s equation, and hydrodynamic organization of near-molecular-scale vorticity

“…As with Burger's equation, (47) and its variants appear in a wide range of contexts, including nonlinear optics [6], hydrodynamics [49], and plasma physics [50].…”

Fast magnetohydrodynamic cnoidal waves and solitons in electron-positron plasma

“…However, e-p plasma can emit energy through cyclotron radiations to cool down and may exist in nonrelativistic regimes as well. 16 Scientists have shown a substantial interest in the study of nonlinear propagation of electrostatic and electromagnetic waves in e-p plasmas [18][19][20][21][22] due to its existence in astronomical objects such as in early universe, [23][24][25] in quasars 26 and active galactic nuclei (AGN), 27 black holes, 28 solar flares, 29 the pulsar magnetosphere, 30 in γ-ray bursts, 31,32 and at the center of the Milky Way galaxy 33 etc. The production [34][35][36][37] and trapping 38 of positrons in the laboratory has paved the way for experimental studies of e-p plasma.…”

Self-guiding electromagnetic beams in relativistic electron–positron plasmas

“…The existence of stable localized envelope solitons of EM radiation has been suggested as a potential mechanism for the production of micro-pulses in AGN and pulsars [6][7][8]. In the early Universe localized solitons are strong candidates to explain the observed inhomogeneities of the visible Universe [9,10], and vortex soliton can be considered to play a significant role for the formation of the observed structure of the Universe [11].…”