Nonlinear oscillations in a warm plasma

Nonstationary magnetosonic wave dynamics in plasmas exhibiting collapse

In a Lagrangian fluid approach, an explicit method has been presented previously to obtain an exact nonstationary magnetosonic-type wave solution in compressible magnetized plasmas of arbitrary resistivity showing competition among hydrodynamic convection, magnetic field diffusion, and dispersion [Chakrabarti et al., Phys. Rev. Lett. 106, 145003 (2011)]. The purpose of the present work is twofold: it serves (i) to describe the physical and mathematical background of the involved magnetosonic wave dynamics in more detail, as proposed by our original Letter, and (ii) to present an alternative approach, which utilizes the Lagrangian mass variable as a new spatial coordinate [Schamel, Phys. Rep. 392, 279 (2004)]. The obtained exact nonlinear wave solutions confirm the correctness of our previous results, indicating a collapse of the magnetic field irrespective of the presence of dispersion and resistivity. The mean plasma density, on the other hand, is less singular, showing collapse only when dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas, and they are expected to be of special importance in the astrophysical context of magnetic star formation.

Wave-breaking limits for nonquasistatic oscillations in a warm one-dimensional electron plasma

In this work, wave breaking for general non-quasi-static oscillations in warm plasma is investigated using Lagrangian methods. In particular, the effects of secular behavior on wave-breaking limits are explored, and it is shown that thermal effects can sometimes prevent wave breaking by curbing secular behavior. The oscillation equations for fully relativistic warm plasma are cast into Lagrangian form, and wave-breaking limits are derived for waves in warm plasma having nonconstant density. These results have important applications in electron acceleration schemes that employ a wakefield or a slow beat wave propagating down a density gradient.

Nonlinear standing waves in bounded plasmas

An analytical model for nonlinear volume oscillations in a bounded cold plasma is developed. Although here the familiar propagating wave solutions do not exist, exact nonlinear standing waves subject to appropriate boundary conditions can nevertheless be found. The behaviors of the electrons and ions are described self-consistently in terms of Lagrangian variables. The analytical solutions are compared with that from particle-in-cell simulations. Good agreement is found in the regimes of interest.