Enhancement of Ohmic heating by Hall current in magnetized capacitively coupled discharges

In low-pressure capacitively coupled discharges, a heating mode transition from a pressure-heating dominated state to an Ohmic-heating dominated state is known by applying a small transverse magnetic field. Here we demonstrate via particle-in-cell simulations and a moment analysis of the Boltzmann equation that the enhancement of Ohmic heating is induced by the Hall current in the ${\boldsymbol{E}}\times {\boldsymbol{B}}$ direction. As the magnetic field increases, the Ohmic heating in the ${\boldsymbol{E}}\times {\boldsymbol{B}}$ direction dominates the total electron power absorption. The Ohmic heating induced by the Hall current can be well approximated from the Ohmic heating of unmagnetized capacitively coupled discharges.