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This paper analyzes a situation which is common for magnetized technicalplasmas such as dc magnetron discharges and HiPIMS systems, where secondaryelectrons enter the plasma after being accelerated in the cathode fall andencounter a nearly uniform bulk. An analytic calculation of the distributionfunction of hot electrons is presented; these are described as an initiallymonoenergetic beam that slows down by Coulomb collisions with a Maxwelliandistribution of bulk (cold) electrons, and by inelastic collisions withneutrals. Although this analytical solution is based on a steady-stateassumption, a comparison of the characteristic time-scales suggests that it maybe applicable to a variety of practical time-dependent discharges, and it maybe used to introduce kinetic effects into models based on the hypothesis ofMaxwellian electrons. The results are verified for parameters appropriate toHiPIMS discharges, by means of time-dependent and fully-kinetic numericalcalculations.

Analytic model of the energy distribution function for highly energetic electrons in magnetron plasmas