Effect of the Electrode/Wall Area Ratio on the Plasma Potential in Discharge and Tokamak Plasmas

Plasma potential is a key parameter in plasma discharge or fusion plasma to control plasma–wall interaction or ExB drift. The magnitude of plasma potential depends on the overall energy transmitted to the plasma via direct current (dc) or radio frequency (RF) devices such as electrodes or antennas. Knowing the plasma potential from the exciting source is useful to prevent high energetic fluxes to the wall or to improve the plasma confinement or explaining shear velocity. The aim of the present model is to calculate this plasma potential with respect to a dc or RF source in a magnetized or unmagnetized plasma. This double saturated probe (DSP) model takes into account the electron saturation current and is able to derive the plasma potential as a function of the electrode/wall area ratio for a dc or RF discharge in a helium/argon plasma with or without a magnetic field. The results of the model are compared with Aanesland’s model in the case of unmagnetized capacitive sheath and particle-in-cell (PIC) simulations. The magnetized model is applied to a plasma column with a perpendicular capacitive current in an RF discharge. It appears that the plasma potential can increase to almost the RF potential value at a low wall/electrode area ratio ( $A_{\text {wall}}/A_{\text {el}}$ lower than 5), while the same potential collapses as soon as the area ratio (perpendicular over the parallel current area) is higher than the electron/ion saturation current ratio. This is directly due to the saturation of electron current, preventing the plasma potential from following the imposed RF potential by the electrode, so that the maximum value can be as lower as the floating potential. The perpendicular current involved is mainly a conduction current modeled as a resistive collisional current. In fusion plasma, the maximum plasma potential can rise to higher values than in plasma discharges, but the collapse of the potential still occurs for long collisional biased flux tubes.