Fundamental limitations of the local approximation for electron distribution function and fluid model in bounded plasmas

Abstract

It is shown that the local approximation for computing the electron distribution function depends both on the ratio between the energy relaxation length and a characteristic plasma length and on the ratio between heating and ambipolar electric fields. In particular, the local approximation is not valid at the discharge periphery even at high pressure due to the fact that the ambipolar electric field practically always is larger than the heating electric field.

Ambipolar field role in formation of electron distribution function in gas discharge plasma

“…As preliminary studies have shown (see also refs 17,18 ), the main reason for EDF radial dependence occurrence when fulfilling λ ε  >  R locality condition is the influence of E a ambipolar field. This field, as is known 2–4 , increases from the plasma center to periphery, and where it (soon or late) begins to exceed the heating field.…”

“…The research in this paper has continued 17,18 . It is shown that the local approximation (4) for EDF and other characteristics of electron gas at plasma periphery determination, where ambipolar field is dominant, is not applicable even when L  >  λ ε criterion is satisfied.…”

“…As is shown in previous papers 17–22,25 , the subject of research was DC discharge positive column (PC). As is known, the heating field in PC is directed in longitudinal (axial) direction, while ambipolar field - in radial direction, i.e.…”

“…(4). As a rule, for numeric simulations by various calculating codes 15–17 , that E total field, which is found from solution of Poisson’s equation, is substituted into kinetic equation.…”

“…literary sources 1–6 predicate the local approximation applicability). Positive discharge column simulations performed both in atomic (argon) 17–23 ] and molecular (nitrogen and oxygen) 24 gases show that at plasma periphery, where E a ambipolar field (soon or late) exceeds E h heating field, excitation response increase is observed, due to additional heating of fast electrons exactly by ambipolar field.…”