2024/03/19 by Strauss, Walter A., Suzuki, Masahiro · 1 citation
#35B32 #35B35 #35M33 #76X05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2403.13174
We consider a plasma that is created by a high voltage difference λ, which is known as a Townsend discharge. We consider it to be confined to the region Ω between two concentric spheres, two concentric cylinders, or more generally between two star-shaped surfaces. We first prove that if the plasma is initially relatively dilute, then either it may remain dilute for all time or it may not, depending on a certain parameter κ(λ, Ω). Secondly, we prove that there is a connected one-parameter family of steady states. This family connects the non-ionized gas to a plasma, either with a sparking voltage λ^* or with very high ionization, at least in the cylindrical or spherical cases.