Numerical simulation of the electrical arc, burning in the long cylindrical channel, is carried out. Assumptions of steady state, axisymmetry, local thermodynamic
equilibrium and optically thin plasma are adopted in a two-dimensional MHD modeling of thermal plasma. A control volume method and the SIMPLE algorithm are used as the
numerical scheme for solving the governing conservation equations of mass, momentum, energy, coupled with Maxwell's equations and the Ohm's law. Distributions of the
temperature, the velocity, and the electrical field in plasmatrons are obtained. Calculations are carried out for the determination of the thermal stabilizing length, the dynamical stabilizing length, and the electrical stabilizing length. Dependencies of these stabilizing lengths on the
gas flow rate, the electrical current, and the channel diameter are found.