Modelling of pulsed low-pressure plasmas and electron re-heating in the late afterglow

Experimental studies of pulsed low-pressure discharges reveal that the mean electron energy exhibits high constant values in the afterglow. Therefore, energy losses in (quasi-)elastic collisions with neutral atoms and through particle losses to the walls must be compensated by some electron re-heating mechanism. The spatio-temporal dynamics of the discharge and the electron re-heating are examined with a hybrid model. The electron energy distribution function is calculated using the non-local approximation. Coulomb collisions among electrons are treated as well as collision processes between electrons and atoms in their ground or metastable states. A hydrodynamic model is used to describe the spatially resolved ion transport. Poisson's equation is solved throughout the plasma volume allowing for a spatial resolution of the plasma boundary sheaths. The re-heating of the electron gas from metastable atoms in the late afterglow is treated in detail. It is shown that superelastic collision processes from the upper to the lower metastable state give the dominant contribution. A further important contribution to the re-heating is established by the chemo-ionization process involving the dominant metastable state. Calculations are presented for argon and helium. The simulations are compared with experimental results in argon and excellent agreement is found.