The plasma transport equations for a weakly collisional plasma have previously been derived for four different time scales. This paper is devoted to the derivation of the plasma transport equations for the two other complementary regimes: the intermediately collisional regime (ICR) (i.e. for the case where the transit time w1 is of the same order as the collision time is of the same order as the collision time ), and the strongly collisional regime (SCR) (i.e. for the case of ) for different time scales. It is shown that the lowest-order gyromotion is unperturbed by collisions. On the Alfvén time scale, one merely obtains for both the intermediately collisional case and the strongly collisional case the single-fluid ideal MHD equations, if certain additional requirements are satisfied. On the MHD-collision time scale, one arrives at the full set of transport equations, where in both cases, contrary to the weakly collisional case, no turbulent terms are found. On the resistive diffusion timescale, one ends up with the known transport equations, with the addition of turbulent contributions.

Ideal MHD equilibria with an ignorable space variable are investigated. It is shown that only three classes of these symmetric equilibria exist: the systems with a straight, a (cylindric) helical, and a circular magnetic axis.

The time evolution of an incompressible non-ideal magnetohydrodynamic (MHD), current-carrying plasma with mass flow is investigated. An approach for the reduction of the nonlinear vector MHD equations to a set of scalar partial differential equations is supposed. Analytical time-dependent solutions of this system are presented. They describe kinetic plasma equilibria both with well-defined nested-in magnetic and velocity surfaces and in the form of vortices. The obtained solutions may be called ‘diffusion-like’, since their temporal structure is very similar to the solutions of the diffusion problem. It is shown that the magnetic field and the velocity have different dumping rates. In the asymptotic limit t→∞, the plasma slowly relaxes towards the hydrostatic equilibrium of gravitating systems.

The effect of finite plasma rotation on the equilibrium of an axisymmetric toroidal magnetic trap is investigated. The nonlinear vector equations describing the equilibrium of a highly conducting, current-carrying plasma are reduced to a set of scalar partial differential equations. Based on Shafranov's well-known tokamak model, this set of equations is employed for the description of a kinetic (stationary) plasma equilibrium. Analytical expressions for the Shafranov shift Δ are found for the case of finite plasma rotation, where two regions of possible plasma equilibria are found corresponding to sub- and super-Alfvénic poloidal rotation. The shift Δ itself, however, turns out to depend essentially on the toroidal rotation only. It is shown that in the case of a stationary plasma flow, the solution of the Grad–Shafranov equation is at the same time also the solution of the stationary Strauss equation.