Description of Large-Scale Processes in the Near-Earth Space Plasma

Abstract

We suggest a solution of the problem of the description of magnetic and electric fields occurring during large-scale nonradiative processes in the collisionless space plasma. The key idea is that the quasi-neutrality condition and the field-aligned force equilibrium of electrons should be taken into account. Equations describing the plasma are divided into two parts, namely, a system of transport equations which describes the plasma motion, and a system of equations for fields. The fields are defined in the instantaneous action approximation via the current spatial distributions of hydrodynamic plasma parameters and boundary conditions obtained from the system of elliptic equations containing no partial time derivatives. Three forms of the generalized Ohm’s law corresponding to different levels of plasma magnetization are considered. It is shown that, depending on the form of a system of transport equations derived for each plasma component, five key variants of the equation system describing the plasma can be obtained from the three forms of the Ohm’s law. The first form of the generalized Ohm’s law refers to the general case in which all plasma components unmagnetized and the system of transport equations represents the Vlasov equations for each plasma component. The second form of the Ohm’s law corresponds to the case of unmagnetized ionic plasma components, while electrons are magnetized and their pressure tensor is expressed through their longitudinal and transverse pressures as well as through the magnetic field. In the latter case two variants of the system of transport equations are possible, and the ions are described by Vlasov equations in both of them. In the first variant, the electrons are described by the Vlasov equation in the drift approximation. In the second variant, the electrons are described by the system of Chew–Goldberger–Low equations of magnetogasdynamics. The third variant of Ohm’s law corresponds to the case in which all plasma components are magnetized, and the pressure tensor of each component is replaced by its expression through the longitudinal and transverse pressure, as well as through the magnetic field. In this case, two variants of the transport equation system are also possible. In the first variant, each component is described by the Vlasov equation in the drift approximation. In the second variant, each component is described by the system of the Chew–Goldberger–Low equations of magnetogasdynamics.