Generalized sheath criterion for arbitrary degenerate plasmas

Abstract

In this research, we study the generalized sheath criterion for plasmas with an arbitrary degree of electron degeneracy and temperature, ranging from the classical dilute regime to the fully degenerate quantum plasmas. The latter may be relevant to warm dense matter and/or laboratory high energy density matter or even astrophysical stellar plasmas. The hydrostatic one dimensional model is used to establish the generalized Bohm's criterion for sheath entrance ion speed limits, and the small amplitude theory of the sheath problem, which accurately describes the sheath parameters for lower ion acoustic Mach numbers, is developed. Our results indicate that the sheath characteristic parameters such as electrostatic potential and density profiles, as well as the wall potential and the sheath length, are significantly affected by plasma parameters such as the ion and electron temperature and number densities in the plasma region. In particular, there are fundamental differences between sheath structures of the dilute classical plasmas and those of dense quantum ones.