Numerical estimation of arc plasma thermodynamic parameters of electromagnetic macro-particles launcher

An approach that allows to estimate the non-ideal thermodynamic plasma parameters of the arc-driven electromagnetic launcher is proposed. Plasma is considered to be incompressible quasineutral gas with properties which vary only through the direction of motion. The 2D distribution of the magnetic field in the vicinity of the arc plasma is studied. It is assumed that atoms are once ionized, and electrons, ions, and neutral atoms have the same temperature. The degree of ionization is calculated by Saha equation, and the electrical conductivity of the arc plasma is calculated in the approximation of Spitzer.
The resulting system of equations is complemented by the experimental data (current in the circuit of the launcher, the voltage drop at the launcher muzzle, the arc plasma length defined on the basis of B-dot probe traces). Arc plasma behavior is defined by the parameter of non-ideality and temperature iteratively. The experimental arc plasma length is compared with the arc plasma length calculated by obtained relations. Statistical weights of atoms and ions are determined by interpolation of data given in the table which depend on the pressure and temperature.
Processing of experimental data was done to estimate non-ideal arc plasma parameters. It is shown that: 1) at the current density of about 80 kA/cm$^2$ the character of temperature and conductivity dependence on the plasma current density is changed; 2) the electrical conductivity of arc plasma is described by the approximate dependence of $\sigma(T)=\sigma(T/T_0)^n$, where $\sigma_0=1.556\,\Omega^{-1}$ sm$^{-1}$; $n=1.988$, $Т_0=1\,000$ K.