The spoke origin based on the coupling-induced wave model in high-power impulse magnetron sputtering plasma

Spokes, identified as the source of anomalous across-B field transport during the high-power impulse magnetron sputtering (HiPIMS) discharge, have been considered as a result of plasma instability. This paper investigates the evolution of the coupling between two azimuthal waves in HiPIMS plasma by revisiting the dispersion relation. A coupling-induced wave model is proposed for the origin of the spoke. The ion sound wave can be strongly coupled with a Doppler-shifted electron Bernstein wave, inducing a long-scale (cm size) electric field oscillation waving at the frequency difference. The spoke appears to be a collective behavior of ion rearrangement guided by the difference frequency wave along the azimuthal direction. The direct comparison of spoke characteristics, such as rotating velocity, frequency and dynamic features, given by this model with experimental and simulation results from the literature shows a good qualitative agreement. Moreover, the evolution of spoke behavior following on from the model are presented, including rotating velocity and mode number along the racetrack. Their variation tendency matches well with experimental findings, from the literature.