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.
Veldes, G. P., Borhanian, J., McKerr, M., Saxena, V., Frantzeskakis, D. J., & Kourakis, I. (2013). Electromagnetic rogue waves in beam-plasma interactions. Journal of Optics (United Kingdom), 15(6), . https://doi.org/10.1088/2040-8978/15/6/064003