On the theory of Alfven vortices

Abstract

The revision of the previous theory of the shear Alfven vortices in a homogeneous plasma is given. The necessity of such a revision is due to the fact that in the previous papers the solutions were not matched adequately on the singular line of the vortex so that these solutions do not satisfy to the charge conservation law. The influence of the magnetic viscosity on the character of the admitted discontinuities in the shear Alfven vortices is studied. The nonlinear equations of the shear Alfven waves in the usual approximation of cold ions and also with the allowance for the ion temperature are obtained. The solution of these equations in the form of the dipole vortex with the spatially decreasing ampitude is found. The specific character of the obtained solution consists in a power decreasing of the transverse potential on sufficiently far vortex periphery. It is shown that the integral characteristics of the vortices (energy, generalized enstrophy) are finite. The numerical analysis of the obtained solution is performed.

Drift-ballooning modes in the presence of charged dust impurities in a nonuniform rotating magnetoplasma

“…This exercise has been carried out by Mikhailovskii et al 14 and Liu and Horton, 15 and explicit expressions for the various constants had been found.…”

Effects of parallel ion dynamics on drift-Alfvén vortices in plasmas

“…The important point to be noted here is that for a uniform plasma (L n -*oo), the lower bound u/a > c s is clearly attributed to the inclusion of the nonlinear parallel ion dynamics. Such an effect has been overlooked in previous studies (Shukla et al , 1986Liu & Horton 1986;Mikhailovskii et al 1987;Kaladze et al 1987). The inner solution of (25) is given by ( r\ uB A 3 J 1 (k 1 r)+A i I 1 (k 2 r) + -\-^R costf,…”

“…2 v 2 A )/p 2 . Equation (25) is a fourth-order inhomogeneous partial differential equation, whose solution can be found following Liu & Horton (1986) and Mikhailovskii et al (1987).…”

“…It is found that the parallel ion motion restricts the vortex speed.Recently, a number of authors (Shukla 1985;Shukla, Yu & Varma 1985;Shukla, Yu & Stenflo 1986;Liu & Horton 1986;Mikhailovskii et al 1987;Kaladze et al 1987) have investigated the formation of drift-Alfven vortices in plasmas. However, all of these studies have been restricted to the twodimensional ion-fluid and three-dimensional electron-fluid motions.…”

Radial quantum number of Laguerre-Gauss modes

“…These modes are ultimately suitably rescaled wave functions of the stationary states of a two-dimensional quantum oscillator, under the Schrödinger equation [27]. Since this latter system can properly model other interesting vortices arising in different media (as in plasmas [28], superfluids [29], and Bose-Einstein condensates [29]), the oscillator will serve as our thread, bearing in mind that the results can be immediately translated to the optical case.…”