In DC glow discharge during operation the Cathode and Anode materials gets heated up. The heat it receives depends on current density (Flux of particles) and particle type velocity etc. Are the relation between these plasma parameters and heat on surface available? Please refer me if any work you came across in these area. (Google doesn't seem to help).
This paper may be helpful for you :
Thomann, A.-L., Semmar, N., Dussart, R., Mathias, J., Lang, V.
Diagnostic system for plasma/surface energy transfer characterization
(2006) Review of Scientific Instruments, 77 (3), art. no. 033501.
doi: 10.1063/1.2166467
Dependence of characteristics of helium ion diffusion and drift in own gas on its temperature
RI Golyatina, SA Maiorov - Bulletin of the Lebedev Physics Institute, 2012
the variation on flux of electrons is proportional to the flux of electrons and the length they are traveling, in other words, the probability to strike a neutral and become ionize, is proportional to how many electrons are arriving at that place and for how long they are traveling. (check attached file), therefore if you know the flux, and the charge, you can calculate how many are striking and we can calculate how much energy are taking from the field, and then how much energy is reflected, and how much energy is absorbed by the electrode. Some of this will be use to sputtered material from the electrode and some to shake the net and heat the electrode. There is a software called SRIM, which calculate how the energy is scattered on the substrate by high energy ions. Also there is a experimental paper which measure where part of this energy is absorbed. For certain condition of flux and energy you can bury defects on the lattice or heal defects which are not too deep.
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