Simulation Studies of Resonant Excitation of Electron Bernstein Waves in Capacitive Discharges

The behavior of capacitive coupled plasma (CCP) discharges is investigated in a mildly magnetized regime, defined by the condition 1 $\leq$ $f_{ce}/f_{rf}$ $\lt$ 2, where $f_{ce}$ and $f_{rf}$ are the cyclotron and radio-frequencies (RF), respectively. This regime exhibits complex and distinctive plasma dynamics due to the interplay between RF fields and the externally applied magnetic field. Two prominent phenomena are observed in this regime. First, the plasma density profile becomes asymmetric across the discharge, deviating from the typical symmetric distribution seen in unmagnetized CCPs. Second, electron Bernstein waves (EBWs), high-frequency electrostatic waves, are excited and propagate within the bulk plasma, particularly along steep electron density gradients. As the strength of the magnetic field increases within this regime, the CCP discharge undergoes a transition from a symmetric configuration to an asymmetric one, and then returns to a symmetric profile at higher field strengths. Notably, the excitation and propagation of EBWs are strongly correlated with the presence of discharge asymmetry and localized density gradients. These waves play a significant role in energy transport and electron heating under mildly magnetized conditions. To gain deeper insight into the underlying physics, detailed numerical simulations are carried out using the particle-in-cell Monte Carlo collision (PIC-MCC) technique. These simulations capture the kinetic behavior of electrons and ions, including the collisionless effects and sheath dynamics essential to understanding the excitation of EBWs and the evolution of discharge symmetry. The study thus sheds light on the role of weak magnetic fields in shaping plasma behavior and highlights the importance of wave-particle interactions in magnetized CCPs.