Loss cone effects and monotonic sheath conditions of a partially magnetized plasma sheath

In this Letter, we propose the conditions for monotonic plasma sheaths adjacent to a floating wall in the presence of an applied, oblique magnetic field. The electron velocity distribution function (VDF) at the sheath edge obtained from a kinetic model exhibits a loss cone shaped truncation. Using an approximation of the truncated VDF, we derive an analytical framework of the sheath edge condition (i.e., Bohm condition), namely, the relation of ion injection velocity and sheath potential drop as a function of the magnetic field angle. The results show that the sheath edge velocity and total potential drop decrease for a steady-state sheath, which eventually collapses when the magnetic field lines become parallel to the wall.