Electromagnetic rogue waves in beam–plasma interactions

Abstract

The occurrence of rogue waves (freak waves) associated with electromagnetic pulse propagation interacting with a plasma is investigated, from first principles. A multiscale technique is employed to solve the fluid Maxwell equations describing weakly nonlinear circularly polarized electromagnetic pulses in magnetized plasmas. A nonlinear Schrödinger (NLS) type equation is shown to govern the amplitude of the vector potential. A set of non-stationary envelope solutions of the NLS equation are considered as potential candidates for the modeling of rogue waves (freak waves) in beam–plasma interactions, namely in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov–Ma breather. The variation of the structural properties of the latter structures with relevant plasma parameters is investigated, in particular focusing on the ratio between the (magnetic field dependent) cyclotron (gyro-)frequency and the plasma frequency.