Steady nonlinear electrostatic plasma wave in a weak transverse magnetic field

Abstract.The structure of a stationary electrostatic plasma wave propagating at a right angle to a weak magnetic field is studied. It is shown that the periodic finite amplitude wave is close in its physical structure to Bernstein-Greene-Kruskal wave of a perfectly definite type. The distinguishing feature of such a nonlinear wave is the absence of the resonant particles trapped by the wave. The electron distribution function, density perturbation and the shape of the wave electrostatic potential are found. The nonlinear dispersion relation is derived to determine the frequency shift due to the perturbation of the distribution function in the resonant region.