Integrable, oblique travelling waves in quasi-charge-neutral two-fluid plasmas

Abstract

A Hamiltonian description of oblique travelling waves in a two-fluid, charge-neutral, electron-proton plasma reveals that the transverse momentum equations for the electron and proton fluids are exactly integrable in cases where the total transverse momentum flux integrals, <i>P</i>_<i>y</i>^(<i>d</i>) and <i>P</i>_<i>z</i>^(<i>d</i>), are both zero in the de Hoffman Teller (dHT) frame. In this frame, the transverse electric fields are zero, which simplifies the transverse momentum equations for the two fluids. The integrable travelling waves for the case <i>P</i>_<i>y</i>^(<i>d</i>)=<i>P</i>_<i>z</i>^(<i>d</i>)=0, are investigated based on the Hamiltonian trajectories in phase space, and also on the longitudinal structure equation for the common longitudinal fluid velocity component <i>u</i>_<i>x</i> of the electron and proton fluids. Numerical examples of a variety of travelling waves in a cold plasma, including oscillitons, are used to illustrate the physics. The transverse, electron and proton velocity components <i>u</i>_<i>jy</i> and <i>u</i>_<i>jz</i> (<i>j</i>=<i>e</i>, <i>p</i>) of the waves exhibit complex, rosette type patterns over several periods for <i>u</i>_<i>x</i>. The role of separatrices in the phase space, the rotational integral and the longitudinal structure equation on the different wave forms are discussed.