Nonlinear interaction between ions and multiple electrostatic waves

Abstract

The nonlinear interaction of ions with multiple electrostatic waves propagating perpendicularly across a uniform magnetic field is investigated both analytically and numerically. Applying a multiscale expansion method with the wave amplitude as the perturbation parameter, a general nonlinear resonance condition is analytically derived. Under this condition, it is confirmed that multiple waves even below the cyclotron frequency and small amplitude are capable of effectively producing acceleration or stochastic heating by numerical simulation. Compared to the single wave situation, the stochastic threshold for heating by multiple waves with frequencies satisfied with a nonlinear resonance condition is significantly reduced because the nonlinear interaction of ions with multiple waves leads more easily to overlapping of islands and spreading of the stochastic layer in phase space. The above result is helpful to understand the energization mechanism of ions in the solar corona.