Self-consistent system of equations for a kinetic description of the   low-pressure discharges accounting for the nonlocal and collisionless   electron dynamics
  For low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the nonMaxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the nonMaxwellian EEDF. The importance of accounting for the nonuniform plasma density profile on both the current density profile and the EEDF is demonstrated. 
Igor D. Kaganovich