**1. Introduction**

Alfven in his work [1] noted that the approach which does not take into account the corpuscular aspect of the electric current does not allow to fully describe many processes in the cosmic plasma. Relying on the concept of continuity, it is impossible in continuum mechanics to take into account fluctuations of hydrodynamic functions formed due to the molecular structure of the medium. It is known that at the hydrodynamic level of description, taking into account the corpuscular structure leads to the Langevin equation, in which the parameters of the medium are described by random sources [2]. These sources are responsible for fluctuations of density, velocity, temperature and, being the unavoidable properties of the medium, cannot be excluded. In turn, the model of "collisionless" plasma based on the Vlasov equations, in principle, does not contain fluctuations, since it is collisions that lead to fluctuations and, as a consequence, to dissipation. Naturally, magnetohydrodynamic equations (MHD equations) obtained in the drift approximation from the Vlasov equation through the moments of the distribution function also do not take into account dissipative processes (see, for example, [3]). In a magnetized plasma, the distribution of electrons and ions can have axial symmetry with respect to the magnetic field. In the absence of heat flux along the magnetic field lines (or it can be neglected), slow plasma motions obey MHD equations with anisotropic pressure. In a number of interesting cases, the description of the plasma behavior without collisions in the hydrodynamic approximation can be used as a heuristic tool for obtaining qualitatively correct results [3]. It should be noted that a significant part of the work on the macroscopic description of plasma behavior is devoted to clarifying the question of how much a real plasma can differ from its ideal twin under the assumption, for example, of an ideally conducting liquid [4].

Therefore the problem arises to try to obtain the MHD equations not from the Vlasov equations, but on the basis of another approach, in which the drift equations themselves, in the conclusion of which the perturbation theory lies [1], are the initial ones. Such a possibility opens in the case of application of the principles of the least dissipation of energy of Onsager [5] and the least production of entropy of Prigozhin [6], combined by Gyarmati into one variational principle [7]. In this case, the fluxes corresponding to the observed transport processes in a magnetized plasma are represented in the drift approximation. In turn, the drift approximation, being oneparticle, simultaneously admits fluctuations within the accuracy of this approximation *TL=H*∣*dH*∣< < 1, where *TL* is the period of the Larmorian rotation.

The application of variational principles allows one to obtain a hydrodynamic system of equations, which in the linear approximation describes in the drift approximation the dynamics of a collisionless plasma located near the equilibrium state. Unlike the Vlasov equation and the equations of hydrodynamics that follow from it (or postulated on the basis of known conservation laws), the resulting system of equations is completely self-consistent and takes into account the fluctuation interaction of local currents with electric and magnetic fields within the accuracy of the used drift approximation. Fluctuations are taken into account by introducing an additional term in the expression for the pressure, which is responsible for its nonequilibrium part, which is analogous to the postulation of a Langevin source in describing Brownian particles in hydrodynamics.
