Numerical study on the effect of the magnetic field generated by circular coils with rectangular sections on plasma characteristics in low-pressure capacitive RF argon discharges

Based on electromagnetic theory, a model of the magnetic field generated by three circular coils with a rectangular cross-section was developed. The magnetic vector potential is computed using three-dimensional composite Simpson integration, and the magnetic field is subsequently obtained by the finite difference method. According to plasma fluid theory, a two-dimensional, axisymmetric fluid plasma model was developed. The fluid model incorporated the effects of the magnetic field. To allow for the drift-diffusion approximation in the presence of a magnetic field, the inertia of electrons and ions was ignored. The plasma model was then discretized using a central difference scheme on a uniform mesh, and the fourth-order Runge–Kutta method was employed for temporal integration. These results show that when the same currents are applied to the three coils, the magnetic field is stronger near the coils and weakens as the distance increases. Increasing the magnetic field from 0 to 30 Gs led to a concomitant increase in the electron density at the chamber center. However, the greatest uniformity occurred at 20 Gs. Electron heating, electron ohmic heating, and electron pressure heating were all observed to increase at the chamber center.