Excitation of nonlinear Alfvén waves by an ion beam in a plasma: 1. Right-hand polarized waves

A self‐consistent theory of MHD wave excitation in the solar wind plasma by a cold ion beam moving along the ambient magnetic field is developed. Using analytical and numerical technics, we investigate the linear stage of the exponential growth of wave amplitudes, their saturation due to trapping or pitch angle diffusion of resonant ions and the steepening of the wave profile due to plasma nonlinearity. The derivative nonlinear Schrödinger equation was used to describe the nonlinear input of plasma particles, and a hybrid method of incomplete numerical simulation was used to investigate strongly nonlinear motion of resonant particles. We have studied the temporal behavior of wave energy for waves propagating in both positive and negative directions in relation to the magnetic field, directions and we have found that in cases under consideration the steepening profile developed only for right‐hand polarized waves. The physical mechanism for wave steepening is higher harmonic generation due to plasma nonlinearity.