Global particle balance in a 13.56 MHz magnetized parallel plate capacitive discharge

Global models have been extensively used by researchers in predicting the plasma parameters and scaling laws of diverse kind of discharges including the one with complex gas mixtures. The beauty of global model lies in its simplistic approach which enables it to be used readily in the discharges where fluid or kinetic simulation takes an enormous amount of computational time. Electron temperature is one of the plasma parameter commonly estimated by balancing the particles produced by ionization within a plasma volume to the flux of particles reaching the bounding surfaces [1-2]. The flux of the particles lost depends on the ratio of the electron density at the plasma sheath edge (ns) to the density at the center (n0). The factor hl= ns/ n0 has a critical dependence on the pressure and the dimension of the reactor. There are different solutions given in the literature on the basis on the working regime. However, we have used a Heuristic solution for hl, solved for a plane parallel geometry for the unmagnetized case. Due to the presence of transverse magnetic field the expression governing the particle and energy conservation gets modified as compared to the conventional unmagnified discharge model. In the present work, we have estimated the electron temperature from the global particle balance in a magnetized parallel plate capacitive discharge. To incorporate the effect of transverse magnetic field, the conventional form of hl has been modified and used in the particle conservation to estimate the electron temperature. The electron temperature obtained by particle balance exhibits a direct dependence with the gas pressure. The response of electron temperature to the pressure is found to be in agreement with the electron temperature measured by an rf compensated single Langmuir probe and also with the results obtained from the Comsol Multiphysics software. (author)