The Mathematical Analysis On The Effect Of Strong Nonlinearity On Steady-State Self-Focusing And Filamentation Of Whistlers In A Plasma

A high-power Gaussian Whistler propagating in a magnatoplasma becomes self-focused because of (i) ponderomotive force and (ii) nonuniform heating nonlinearities (i) being dominant for t << T and (ii) being dominant for t > t E . On short time scale (t << t E ) whistlers of all frequencies can be focused (the self – focusing length is very large for ω=  /2 and decreases rapidly on both sides), whereas on the long time scale (t > t E ) only high frequency whistlers (ω>  /2) are focused. At very high powers the plasma is depleted almost completely from the axial region and self-focusing does not occur, rather, defocusing takes place. A plane uniform whistler of high intensity is seen to be unstable for small scale fluctuations, i.e., it must break up into filaments in course of it propagation. The growth rate increases with decreasing scale length of perturbation and is seen to be a saturating function of power density of the beam.