Model of the cathode fall region in magnetron discharges

Using a 1D, two-fluid description, the influence of the magnetic field on the plasma boundary region adjacent to the cathode target in a magnetron has been investigated. Assuming the transport of magnetically confined electrons above the `race-track' to be dominated by diffusion and mobility, with plasma ions falling directly to the cathode, the spatial variation in the electron and ion densities and velocities in the sheath and pre-sheath have been determined, together with the electric field structure. By assuming an electric field remnant in the plasma, the fluid equations have been integrated through the space-charge sheath up to the cathode, allowing smooth joining of the sheath and pre-sheath regions. Modelling with both constant and spatially varying magnetic fields has shown that realistic secondary electron fluxes are predicted for only a limited range of initial discharge parameters, indicating that Bohm diffusion of electrons is the most appropriate transport mechanism.