Methods and Applications of Analysis

Volume 29 (2022)

Number 1

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part IV

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Steady states of gas ionization with secondary emission

Pages: 1 – 30



Walter A. Strauss (Department of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island, U.S.A.)

Masahiro Suzuki (Department of Computer Science and Engineering, Nagoya Institute of Technology, Showa-ku, Nagoya, Japan)


We consider the steady states of a gas between two parallel plates that is ionized by a strong electric field so as to create a plasma. There can be a cascade of electrons due both to the electrons colliding with the gas molecules and to the ions colliding with the cathode (secondary emission). We use global bifurcation theory to prove that there is a one-parameter family $\mathcal{K}$ of such steady states with the following property. The curve $\mathcal{K}$ begins at the sparking voltage and either the particle density becomes unbounded or $\mathcal{K}$ ends at an anti-sparking voltage. These critical voltages are characterized explicitly.

Received 22 March 2020

Accepted 14 May 2020

Published 10 June 2022