Variational and transport properties of high-pressure arc plasmas

Abstract

One-dimensional steady-state transport equations are used to describe the equilibrium state of multiple species cylindrically symmetric arc plasmas. The effects of axial and azimuthal variations are introduced through the boundary conditions at the center. It is shown that the axisymmetric case of m=0 is actually the case of large m being smoothed out by thermal fluctuations where m is the azimuthal mode number. The conservation of mass density flux gives rise to mutual diffusion and a criterion is given to predict which neutral species should concentrate at the center and vice versa. By writing the energy balance equation in the form of action integral, it is clear that the power dissipation is always a minimum, thus proving the Steenbeck’s minimum principle. A local thermal equilibrium model is used to obtain the electron density. This model is tested against the experimental results of a helium arc with copper electrodes at atmospheric pressure. The steep positive density gradient of the copper is the consequence of pressure balance with the much higher density helium, and the steepness is directly related to the disparity of the two densities.