Particle-In-Cell simulations of the filamentation process in magnetized radio-frequency plasmas

Abstract: In a uniform radio-frequency (RF) plasma between a large electrode pair, the addition of an axial magnetic field induces diverse longitudinal filaments. To reveal its pattern dynamics, we conduct two-dimensional (2D) Particle-In-Cell (PIC) simulations, capturing the entire evolution of the filamentation process. We found that the entire evolution experiences two dynamic stages. In the first stage, electrostatic standing waves and plasma density ripples grow synergistically, forming filamentary pattern. Our results show that the plasma ripples and RF electrostatic standing waves are modulated. In addition, each filament equips a double-humped peak. The spectrum reveals that the oscillations are mainly RF and its higher harmonics. Subsequently, the plasma shifts towards a dynamic regime governed by the competition between Lorentz and thermal pressure forces, characterized by the chaotic evolution of filaments. Through RF-cycle averaging, our force analysis demonstrated that electrons and ions are governed by the magnetic force and electric force respectively. The time-averaged magnetic force drives electrons to accumulate at plasma density maxima, while time-averaged electric force pushes ions into the same regions, jointly molding the filaments. These novel clues pave the way for a theoretical understanding of filamentation instability and provide essential references for effectively manipulating magnetized plasmas.