Scattering of magnetized electrons at the boundary of low temperature plasmas

Abstract

Magnetized technological plasmas with magnetic fields of 10–200 mT, plasma densities of 1017−1019 m−3, gas pressures of less than 1 Pa, and electron energies from a few to (at most) a few hundred electron volts are characterized by electron Larmor radii rL, that are small compared to all other length scales of the system, including the spatial scale L of the magnetic field and the collisional mean free path λ. In this regime, the classical drift approximation applies. In the boundary sheath of these discharges, however, that approximation breaks down: The sheath penetration depth of electrons (a few to some ten Debye length λD; depending on the kinetic energy; typically much smaller than the sheath thickness of tens/hundreds of λD) is even smaller than rL. For a model description of the electron dynamics, an appropriate boundary condition for the plasma/sheath interface is required. To develop such, the interaction of magnetized electrons with the boundary sheath is investigated using a 3D kinetic single electron model that sets the larger scales L and λ to infinity, i.e. neglects magnetic field gradients, the electric field in the bulk, and collisions. A detailed comparison of the interaction for a Bohm sheath (which assumes a finite Debye length) and a hard wall model (representing the limit also called the specular reflection model) is conducted. Both models are found to be in remarkable agreement with respect to the sheath-induced drift. It is concluded that the assumption of specular reflection can be used as a valid boundary condition for more realistic kinetic models of magnetized technological plasmas.