Modulational instability and associated rogue structures of slow magnetosonic wave in Hall magnetohydrodynamic plasmas

Abstract

The modulational instability and associated rogue structures of a slow magnetosonic wave are investigated for a Hall magnetohydrodynamic plasma. Nonlinear Schrodinger equation is obtained by using the multiple scale method, which shows a modulationally unstable slow magnetosonic mode evolving into bright wavepackets. The dispersive effects induced by the Hall electron current increase with the increase in plasma beta and become weaker as the angle of propagation increases. The growth rate of the modulational instability also increases with the increase in plasma beta. The growth rate is greatest for the parallel propagation and drops to zero for perpendicular propagation. The envelope wavepacket of a slow magnetosonic is widened with less oscillations as plasma beta increases. But the wavepacket becomes slightly narrower and more oscillatory as the angle of propagation increases. Further a non-stationary envelope solution of the Peregrine soliton is analyzed for rogue waves. The Peregrine soliton contracts temporally and expands spatially with increase in plasma beta. However, the width of a slow magnetosonic Peregrine soliton decreases both temporally and spatially with increase of the propagation angle. (C) 2014 AIP Publishing LLC.