Two-dimensional nonlocal model of axially and radially inhomogeneous plasma of cylindrical magnetron discharge.

A cylindrical magnetron discharge (CMD) with two coaxial electrodes, a uniform axially directed magnetic field, and discharge ends closed by the shields biased at the cathode potential is considered. The presence of the shields creates axial inhomogeneity of plasma, which is taken into account in this study. At low pressures and small magnetic fields the pronounced nonlocal regime of the electron distribution function (EDF) formation is realized. The electron component is analyzed on the basis of radially and axially inhomogeneous Boltzmann kinetic equation. Unmagnetized electrons that move in axial direction are trapped in the axial potential well, their energy relaxation length exceeds the discharge vessel length, and the kinetic equation can be averaged over axial flights of electrons. Using a model two-dimensional potential profile, the EDFs at the different axial positions are obtained and two-dimensional distributions of the electron density, ionization rate, and current on cathode are calculated. The results of the modeling and experiments are compared for the dc CMD in Ar at a pressure of 3 Pa, magnetic field strength of 10 mT, and current of 150 mA.