Recently, the initial boundary conditions for proforce waves with a substantial current behind the shock front have been derived. Computer solutions of the Electron Fluid Dynamical equations meet the expected boundary conditions at the end of the sheath region. This paper will compare the wave structure for proforce waves with and without current behind the shock front.
Hemmati, Mostafa and Young, Steven
"Proforce Waves: The Effect of Current Behind the Shock Front on Wave Structure,"
Journal of the Arkansas Academy of Science: Vol. 49, Article 14.
Available at: https://scholarworks.uark.edu/jaas/vol49/iss1/14