Plasma sheath transmission factors for tokamak edge plasmas

Simple analytic relations are derived for the floating potential of a solid object in contact with a magnetized plasma as a function of the electron/ion mass ratio, the electron/ion temperature ratio, and the secondary electron emission coefficient. Simple analytic relations are also obtained for the sheath transmission factors, i.e., the particle and energy fluxes to floating and nonfloating surfaces. These analytic formulations, derived from a fluid model treatment of ion flow, are found to give results in close agreement with results derived from more complex analysis based on kinetic theory and numerical models. Tokamak scrape-off plasmas are often characterized by ion distributions which have finite drift velocities at the point where the ions enter the scrape-off plasma from the main plasma (via cross-field diffusion). The Bohm criterion governing the drift velocity of ions as they enter the electrostatic sheath in front of a limiter, divertor plate, or probe is generalized for this case.