Relaxation of a nonideal magnetohydrodynamic plasma in a cylindrical column

The time evolution of a nonideal magnetohydrodynamic (MHD) plasma is investigated. An approach for the reduction of the nonlinear vector MHD equations for a current carrying plasma with a strong longitudinal external magnetic field to a set of scalar partial differential equations is supposed. Analytical time-dependent solutions of the nonlinear resistive and dissipative MHD equations for a cylindrical plasma column are presented. It is shown that the internal magnetic field and the velocity have different damping times and that in the asymptotic limit t→∞ the plasma slowly relaxes toward the static equilibrium state. Analytical reduced MHD solutions describing slowly evolving states in tokamaks are found.