負極性直線状沿面放電のモデリング

抄録

This study presents a new theoretical model for discribing a rectilinearly channeled negative discharge generated on PET film (δ=50μm) under atmospheric conditions. The channel is modeled using a RC distributed constant circuit with the front potential Vl and moving at propagation speed υl.
A conduction equation (∂U/∂t=μ√U ∂2U/∂2z, U=V2, with V; Potential and μ; electron mobility) is introduced under the assumption that the generated current consists of only electrons. This equation can be solved using the boundary conditions and speed condition in which the speed is considered as being proportional to the gradient of U. (υl=-β∂U/∂z, β; const)
Although it is difficult to solve the conduction equation analytically under the boundary condition and the speed condition, using the simplified boundary condition and the length l (t) instead of the speed condi- tion, the conduction equation is solved numerically. And the U (z, t) are caluculated and compared with the experimental results.
I proposed that one of the best approach to the discussion of the conduction equation is using the solution of Stefan problem which corresponds to the fusion phenomenon occuring in a column of ice. The solution of Stefan problem are also compeared with the above numerical solution.