Effects of electron-to-ion mass ratio in driving magnetic oscillations of magnetohydrodynamic plasmas and self-organized criticality

Evolutions of nonlinear magnetic fields have been shown to be governed by a set of coupled nonlinear equations of second order in magnetohydrodynamic (MHD) plasmas by Lee and Parks [Geophys. Res. Lett. 19, 637-640 (1992)]. We have considered the same set of coupled nonlinear equations for further analysis in this work by neglecting the presence of external forcing term in it. Different modes of oscillations of magnetic field have been found to exist in special limiting cases of this set of undriven second order coupled nonlinear equations having frequencies that are multiples of lower hybrid frequency. Numerical solutions of these coupled equations have been analysed revealing a quasi-periodic route to chaotic oscillations of the nonlinear magnetic fields as electron-to-ion mass ratio signifying presence of linear coupling effects is increased. Some signatures of the phenomenon of self-organized criticality (SOC) in typical quasi-periodic oscillations of magnetic field have also been noticed using Fourier analysis. The presence of long range correlations has been witnessed in quasi-periodic oscillations whereas both long range correlations and anticorrelations are found in chaotic oscillations using rescaled range analysis. Concluding remarks are provided in addition to various results and discussions.