Excitation of left-hand-polarized nonlinear Alfvén waves by an ion beam in a plasma

The nonlinear problem of MHD wave excitation in plasma by an ion beam with a ring distribution function was solved. We studied how the steepened wave profiles grew out of low‐frequency Alfvén fluctuations excited by the ion beam in plasma. Two types of nonlinearities are taken into account: (1) strong nonlinearity of resonant ions (beam ions) due to trapping and bounce‐oscillation effects and (2) weak nonlinearity of nonresonant particles (plasma particles) that leads to mode coupling and steepening of the wave profile. The spectral method in concert with a hybrid method of resonant simulation was used in this study. The wave excitation, saturation, and subsequent nonlinear evolution were studied.