Numerical solution of ionization equations using the fractional steps method

The fractional step method is used to solve the ionization equations for electron-ion plasma containing neutrals in relation to processes in stationary plasma thrusters (SPT). Splitting by physical processes is used: the evolution of plasma is presented as a superposition of pure transfer in an external field in phase space with subsequent ionization. To calculate the transfer, the macroparticle method was used. The ionization process in the case of plane symmetry is calculated using explicit analytical formulas. The obtained formulas of the fractional step method are compared with the numerical solution of the plasma evolution equation using a known physical model of ionization.