抄録
This study presents a new theoretical model for describing a rectilinearly channeled negative surface discharge, sometimes called a guided discharge. The discharge consists of a passive region in the channel in plasma state and an active region at the channel tip in ionized state, the channel tip moving at a propagation speed. In the former region, a nonlinear diffusion equation holds valid under the assumption that the current in the channel consists of moving electrons supplied from the electrode. The boundary conditions at the channel tip are the current continuity condition and the condition that the propagation speed of the channel tip is proportional to the gradient of second power of the potential of the channel at the tip. From these boundary conditions it follows that the potential at the tip is held constant. By means of appropriate scaling of relevant quantities, a one-parameter family of general solutions of the equations is shown to be uniquely determined. This study presents how to apply the experimental data to the theoretical solution. It becomes clear in accordance with the discussion that the potential at the channel tip and the mobility will be essentially important. Moreover we discussed in relation to applied voltage and mobility based on the previously obtained experimental data.
