Fully nonlinear dust kinetic Alfvén waves

Abstract

Exact localized nonlinear dust kinetic Alfvén waves are investigated by retaining the complete dust nonlinearity and by invoking small but finite-β effects in a collisionless plasma, whose constituents are electrons, ions and negatively charged dust grains. Sub-Alfvénic, as well as super-Alfvénic, solitary waves consisting of smooth density humps or dips are found to exist. Further, super-Alfvénic kink type solitons are also found to occur. The soliton amplitude depends upon various plasma parameters along with the soliton propagation speed. The results of the present investigation may be useful in the diagnostics of dust in magnetized plasmas and in understanding the formation of coherent soliton structures in space and laboratory plasmas.

Exact nonlinear dust kinetic Alfvén waves in a dust–ion plasma

“…Equation (8) represents similar dispersion relations to those obtained in [30]. However, in the present model we have completely omitted the concentration of electrons.…”

“…From equations (3)- (4c), we obtain the same normalized equations as equations (11)-(12c) of [30]. We now seek quasistationary localized solutions of these three normalized equations along with equations (9) and (10).…”

“…Assuming that all dependent variables are functions of η only and using the boundary conditions given by equation (11), one can reduce [30] the normalized equations (9), (10) and equations (11)-(12c) of [30] to the following nonlinear differential equation for N :…”

“…Equation (1) is derived from the Maxwell equations whereas equation (2) gives the density of the thermal ions [29]. Equations (3)-(4c) describe the dynamics of cold and magnetized dust grains [30]. Finally, to close the system of equations (1)- (4c), we use the following charge neutrality and current continuity equations:…”

“…According to their analysis solitons involving smooth density dips and cusped density humps can coexist. Later, Mahmood et al [30] investigated how cusped density humps become smoother when finite-β effects are taken into account. They also found the existence of kink-type solitons [31] in dust-contaminated plasmas.…”