A fluid description for the discharge equilibrium of a divergent electron cyclotron resonance plasma source

A fluid description of the presheath of a magnetized plasma is used to model a divergent electron cyclotron resonance (ECR) plasma source. The fluid equations are moments of the time-independent Boltzman equation when cross-field particle motion occurs only through a static E×B drift. Closure is obtained by neglecting third-order moments. The electrons are assumed to have constant temperature along the magnetic field, to obey a Maxwell-Boltzmann potential-density relationship, and to be warmer than the ions. Interactions between plasma and neutral gas are included by specifying the profile of the gas density along the magnetic field and collision cross sections. A form of the equations is derived that can be used to study ions with anisotropic temperatures. The model is used to estimate the axial profiles of the density, ion flow, and ion temperature of an ECR plasma source. The calculated global relationships between (1) the electron temperature and the equilibrium neutral gas density, and (2) the absorbed microwave power and the equilibrium plasma density are comparable with experimental measurements. Furthermore, the calculated ion temperature is comparable to recently reported measurements [Appl. Phys. Lett. 57, 661 (1990) and Appl. Phys. Lett. 58, 458 (1991)].