Neglecting collisions, we consider a kinetic approximation for the Boltzmann function of particle distribution with a longitudinal macroscopic velocity that does not depend on the coordinates. With it we solve the two-dimensional problem (∂/∂x≠0, ∂/∂y≠0, ∂/∂z=0) of the equilibrium configurations of an l-component plasma in self-consistent internal and external transverse magnetic fields (and also in electric fields caused by a non-compensation of plasma charge as a whole).The solution obtained with the given assumptions is a general one and permits one to make a broad analysis of equilibrium plasma configurations with longitudinal currents in self-consistent external and internal transverse fields. It is shown that existence of steady plasma states with a spatial-periodic structure is possible. This corresponds to the data of experiments in which it has been reliably established that a plasma arising in pinch discharges has a fibrous structure characterized by a definite space periodicity.
A solvable model for the basic properties of a simple magnetized plasma torus