Fluid simulation on effect of sidewall coil-generated magnetic field on plasma characteristics in low-pressure capacitive RF argon discharge in a cylindrical chamber

In capacitively coupled plasma devices, non-uniform magnetic fields generated by surrounding coils are an effective tool for regulating plasma spatial characteristics and optimizing process performance. In this study, a magnetic field model produced by a set of circular coils with rectangular cross sections surrounding a cylindrical chamber is developed. The magnetic vector potential is calculated using a 3D composite Simpson integration method, and the magnetic field is obtained by evaluating its partial derivatives via a finite difference method. Based on plasma fluid theory, a fluid model for low-pressure capacitive RF argon discharge in a cylindrical chamber is developed, incorporating magnetic field effects through the drift–diffusion approximation. The governing equations are discretized in space using a uniform grid with central difference schemes and in time using a fourth-order Runge–Kutta method. The results show that as the maximum magnetic field increases from 0 to 300 G, the peak positions of plasma density, electron power absorption, and ionization rate gradually shift toward the sidewall, accompanied by thinning of the sidewall sheath. The magnetic field near the sidewall is stronger than at the center, and enhanced electron cyclotron motion reduces radial electron losses, leading to improved confinement. When the maximum magnetic field exceeds 180 G, a strong electron energy absorption region appears near the sidewall; moreover, when the magnetic field configuration is asymmetric, the distribution of electron energy absorption also becomes noticeably asymmetric.