Kruskal’s perturbation method for stochastic ion resonance in a magnetized medium driven by electrostatic wave packet

Nonlinear differential equations and mathematical methods for solving them have many applications to study the dynamics of the nonlinear systems. One of the nonlinear systems in physics is plasma, where more than 99% of the universe is in this state, from neutron stars to lightning. In a plasma, wave-particle interaction occurs frequently, which causes random resonance of charged particles and consequently nonlinear behavior of particles in the medium. In this paper, the theoretical model and mathematical-analytical method are presented to investigate the behavior of the magnetized medium perturbed by electrostatic wave packet, heating and turbulence of the medium. The results show that in the strong perturbation due to the wave packet, the transport of ion resembles anomalous behaviour, altering between diffusive and trapped motion. The results of this study provide a model to describe wave-particle interaction in the medium driven by periodic forces under non-uniform time varying magnetic field, such as solar winds during solar activity.