Localization of 3D inertial Alfvén wave and generation of turbulence

Abstract

The present paper deals with the nonlinear interaction of Inertial Alfvén wave (IAW) and fast magnetosonic wave in the low beta plasma, where beta is the ratio of thermal pressure to the background magnetic pressure. In this paper, the localization and turbulent spectra of IAW along with the density dips correlated with the fast magnetosonic wave have been investigated. Variation of parallel electric field along and across the field lines has also been studied. Taking ponderomotive nonlinear effect in the dynamics of fast magnetosonic wave, couple of dimensionless equations has been derived. These coupled equations have been simulated numerically using the pseudo-spectral method. The obtained results reveal that the Kolmogorov scaling is followed by a steeper scaling in magnetic power spectrum, which is consistent with the observations by the FAST and Hawkeye spacecraft in auroral region. The relevance of present investigation has been discussed for auroral plasmas.

Appendix: Expressions for ponderomotive force

The components of ponderomotive force for electrons due to 3D IAW are

$$ F_{ex} = \biggl( \frac{e^{2}\lambda_{e}^{2}k_{0 \bot}^{2}}{4m_{e}c^{2}} \biggr)\frac{\partial \vert A_{z} \vert ^{2}}{\partial x} $$

(15)

$$ F_{ey} = \biggl( \frac{c^{2}\alpha^{2}m_{e}k_{0x}k_{0y}}{4B_{0}^{2}} \biggr) \frac{\partial \vert A_{z} \vert ^{2}}{\partial x} $$

(16)

and

$$ F_{ez} = - \biggl( \frac{e^{2}\lambda_{e}^{4}k_{0 \bot}^{4}}{4m_{e}c^{2}} \biggr)\frac{\partial \vert A_{z} \vert ^{2}}{\partial z} $$

(17)

Similarly the components of ponderomotive force for ions due to 3D IAW are as follows:

$$\begin{aligned} F_{ix} =& \biggl( - \frac{m_{i}P^{2}c^{2}k_{0y}^{2}\alpha^{2}}{4B_{0}^{2}} - \frac{m_{i}Q^{2}c^{2}k_{0x}^{2}\alpha^{2}}{4B_{0}^{2}} \biggr) \frac{\partial \vert A_{z} \vert ^{2}}{\partial x} \\ &{} + \biggl( \frac{eQck_{0x}k_{0z}\alpha^{2}}{4\omega_{0}B_{0}} - \frac{eQ\alpha k_{0x}}{4B_{0}} \biggr) \frac{\partial \vert A_{z} \vert ^{2}}{\partial z} \end{aligned}$$

(18)

$$\begin{aligned} F_{iy} =& \biggl( \frac{m_{i}P^{2}c^{2}k_{0x}k_{0y}\alpha^{2}}{4B_{0}^{2}} - \frac{m_{i}Q^{2}c^{2}k_{0x}k_{0y}\alpha^{2}}{4B_{0}^{2}} \biggr) \frac{\partial \vert A_{z} \vert ^{2}}{\partial x} \\ &{} + \biggl( \frac{eQck_{0y}k_{0z}\alpha^{2}}{4\omega_{0}B_{0}} - \frac{eQ\alpha k_{0y}}{4B_{0}} \biggr)\frac{\partial \vert A_{z} \vert ^{2}}{\partial z} \end{aligned}$$

(19)

and

$$ F_{iz} = \biggl( \frac{eQck_{0x}k_{0z}\alpha^{2}}{4\omega_{0}B_{0}} \biggr) \frac{\partial \vert A_{z} \vert ^{2}}{\partial x} + \biggl( \frac{e^{2}\alpha k_{0z}}{2\omega_{0}cm_{i}} \biggr)\frac{\partial \vert A_{z} \vert ^{2}}{\partial z} $$

(20)

Here

$$\begin{aligned} &{P = \frac{\omega_{ci}^{2}}{\omega_{ci}^{2} - \omega_{0}^{2}},\qquad Q = \frac{\omega_{ci}\omega_{0}}{\omega_{ci}^{2} - \omega_{0}^{2}}\quad \mbox{and}}\\ &{\alpha = \frac{\omega_{0}}{ck_{0z}} \bigl( 1 + \lambda_{e}^{2}k_{0 \bot}^{2} \bigr)} \end{aligned}$$