Electric Potential in Plasma and Sheath Regions with Magnetic Field Increasing toward a Wall

Electric potential near a wall in plasma with magnetic field increasing toward a wall is investigated analytically. A magnetic field that is symmetric about an axis and increases monotonically toward the wall is considered. The potential profile is analyzed by solving the plasma-sheath equation that gives the electric potential in the plasma region and the sheath region near the wall self-consistently. The potential in the plasma region depends on the profile of the magnetic field and the ion temperature. As the magnetic field near the wall increases and the ratio of the ion temperature to the electron temperature decreases, the potential drop in the plasma region decreases. The potential also depends on a ratio of the increase rate of the magnetic field to the decrease rate of the potential toward the wall. When the increase rate of the magnetic field is larger than the decrease rate of the potential, the potential drop in the plasma region becomes large compared with that in the magnetic field of which increase rate is smaller than the decrease rate of the potential.