Mathematical modeling of hollow cathode processes with integral equations using

A mathematical model of hollow cathodes is presented in the form of a system of integral and differential equations describing physical processes occuring in the plasma of the hollow cathode active zone, at the plasma-cathode interface, on the cathode surface and in the transition zone between neutral gas and plasma. The model, algorithm and computer program permit mathematically closed calculation of local and integral hollow cathode parameters (channel walls temperature, cathode potential drop, electron concentration and electron temperature, ionization degree, plasma pressure including input channel pressure, voltage drop) given discharge current, plasma-forming gas flow rate, cathode channel geometry, heat removal nature and physical properties of plasma-forming gas and cathode material. The mathematical model makes it possible to predict the parameters of plasma active zone and the cathode temperature in the case of functioning of the external surface of the hollow cathode channel in discharge. The influence of functioning of the external cathode channel surface was investigated by mathematical modeling method. The results of calculating experiments are in good agreement with known experimental data for a number of parameters.