Theory of magnetized, coupled, rf-driven plasma sheaths in one dimension

A set of equations for magnetized plasma sheaths in rf capacitance discharges is developed within the adiabatic electron, fluid ion framework. It differs from previous approaches in that (a) ion demagnetization i.e., the detachment of the ion flow from the magnetic lines caused by electrostatic gradients, is introduced self-consistently, (b) the ion injection velocity from the presheath is reevaluated to ensure the ion-electron Aux balance, and (c) two symmetrically opposed coupled sheaths are driven by a sinusoidal driving voltage instead of a sinusoidal current. It is found that the sheath potential and thickness increase considerably with increasing magnetic inclination theta relative to the electric field compared to the unmagnetized results; the latter are recovered at the parallel magnetic field limit. Also, the ion injection velocity along the magnetic lines is subsonic and depends on the magnetic inclination. Finally, a sinusoidal ac voltage drives an anharmonic sheath current, while a sinusoidal current drives anharmonic voltage. [S1063-651X(99)09001-7].