Ion velocity distribution function in intrinsic gas plasma under conditions of resonance recharging as a main process. Theory

An analytical solution is found for the kinetic Boltzmann equation for ions in natural gas at the arbitrary electric field strength in plasma under conditions where the dominating process is resonance recharging. The ion distribution function in the strong field coincides with the function obtained by authors earlier, and in the weak field it is close to the Maxwell’s function with the temperature of atoms. For the ambipolar field of arbitrary value, the dependence of the cross-section of resonance recharging on the relative velocity is taken into account. It is shown that the ion velocity distribution function essentially differs from the Maxwell’s and is determined by two parameters. Good agreement between the results of calculations of the drift velocity of $\rm He^+$ ions in $\rm He$, $\rm Ar^+$ in $\rm Ar$ and the reduced mobility of $\rm N^+_2$ in $\rm N_2$ and known experimental data is obtained in a wide range of reduced electric field values. The analytical calculations of the average energy of ions at different values of the reduced electric field were compared with the results of the numerical simulation using the Monte Carlo method performed by other authors.