A. B. Mikhailovskii

On the theory of Alfven vortices

The revision of the previous theory of shear Alfven vortices in a homogeneous plasma is given. In the previous papers the solutions were not matched adequately on the singular line of the vortex so that they do not satisfy 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 allowance for the ion temperature are obtained. The solution, in the form of the dipole vortex with spatially decreasing amplitude, is found. The specific character of the solution obtained consists of a power decrease 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 solution obtained is performed.

Regularized magnetic islands. II. The role of polarization current

The role of polarization current in the problem of rotating magnetic islands in the absence of drift effects is discussed for the case of nonregularized and regularized velocity profiles governed by the perpendicular viscosity. The polarization current is calculated taking into account the finite ion Larmor radius effects. It is shown that, in correspondence with the general rule by Waelbroeck and Fitzpatrick [Phys. Rev. Lett. 78, 1703 (1997)], this current is destabilizing. The destabilizing contribution of the polarization current into the generalized Rutherford equation for the magnetic island width does not depend on whether the profile function is regularized or not. It is shown that the Larmor corrections to the current consist of the sum of two oppositely directed currents and do not contribute into the generalized Rutherford equation.

On collisionality dependence of the neoclassical tearing modes

The problem of validity of the semi-phenomenological model of collisionality dependence of the polarization current contribution into the generalized Rutherford equation for neoclassical tearing modes proposed by Wilson H R et al (1996 Plasma Phys. Control. Fusion 38 A149) and later discussed and analysed by Maraschek M et al (1999 Plasma Phys. Control. Fusion 41 L1) is considered. It is shown that the collisionality dependence of the polarization current in this model contradicts that in the theory of linear MHD instabilities. Because of this, the above model is, to some extent, ad hoc . Since this model cannot be substantiated by any theory developed up until now, it should be used with care for evaluation of the plasma behaviour in ITER. The discussed disagreement between experiments, for which interpretation of this model was used, and a recent theory of magnetic islands may serve as a stimulus for further development of the theory.

An approach to calculation of magnetic island rotation frequency

The problem of magnetic island rotation is analyzed. It is noted that for the correct solution of this problem the nonstationarity of profile functions should be taken into account. An approach to solving equations for nonstationary profile functions is developed for cases when drift and neoclassical effects can be neglected. The principal role of perpendicular viscosity in determining island rotation frequency is emphasized. The possibility of the existence of stationary magnetic islands in tokamaks with a rotating plasma and a resistive wall is shown.

Regularized magnetic islands. I. Hyperviscosity and profile functions

The problem of the magnetic island profile functions is analyzed. An idea is suggested that discontinuities of the profile function derivatives at the island separatrix, which appear in simplified plasma models, can be eliminated by means of more complete description, i.e., the profile functions can be regularized. As an example, the regularization of the electrostatic potential profile function is considered for the case of a slab geometry when its formation is governed by the perpendicular viscosity. It is shown that for regularization of such a profile function one should keep in the viscosity expression the terms with higher derivatives of the velocity, usually referred to as hyperviscosity terms. A model expression for the hyperviscosity is derived by the Grad-type method. Physically, the regularization is related to the appearance of a part of the profile function localized in the Larmor transition layer near the island separatrix.

Rotation-transport threshold model of neoclassical tearing modes

A rotation-transport threshold model of neoclassical tearing modes (NTMs) is suggested. It is assumed that weakening of the bootstrap current effect is determined by competition of perpendicular transport and island rotation, which is in contrast to the known transport threshold models dealing with the parallel transport or parallel convection instead of island rotation. It is shown that for sufficiently strong island rotation the perpendicular transport does not lead to decreasing the bootstrap current contribution into the island width evolution equation. It is explained that the island rotation can prevail over the parallel transport/convection mainly for the case of ion contribution into the bootstrap current effect. Interrelation between the rotation-transport threshold model and the known ones is discussed. A generalized transport threshold model of NTMs describing the competition of the perpendicular transport with the island rotation, parallel transport and parallel convection is formulated. It is shown that the perpendicular transport can lead to weakening the bootstrap drive contribution only if it overpowers all the competitive effects.

Revision of the theory of drift solitons

Abstract The theory of drift solitons is revised. It is concluded that drift solitons may exist in a plasma with a homogeneous temperature but there is a nonvanishing lower threshold in the amplitude.

Alfven solitons in a relativistic electron-position plasma. I. Hydrodynamic theory

Nonlinear Alfven waves, propagating along an equilibrium magnetic field, are studied on the base of relativistic isotropic hydrodynamics. Alfven solitons of moving-wave and wave-packet type are considered. The results of Sakai and Kawata (1980) concerning the Alfven solitons of moving-wave type are revised. New expressions for the parameters characterizing these solitons are obtained.

Ballooning vortex in a magnetized plasma

Abstract The existence of a ballooning solitary vortex in an inhomogeneous plasma immersed in crossed magnetic and gravitational fields is demonstrated.

Electron drift solitons in an inhomogeneous magnetized plasma

Abstract It is shown that electron drift solitons can exist in an inhomogeneous magnetized plasma. Two such types of solitons are discussed, one which is similar to the solitons described by the one-dimensional Korteweg-de Vries equation, and a second which is an analog of the two-dimensional Rossby solitons.