Specificity of the electron energy distribution function in a low-pressure nitrogen plasma

In this work, self-consistent simulations of a glow discharge positive column in low-pressure nitrogen plasma are presented. The electron energy distribution function (EEDF) was calculated by solving the complete (i.e. nonlocal) Boltzmann kinetic equation for electrons in both the energy and coordinate (space) variables. The accuracy and range of applicability of the two limiting cases are considered when the kinetic equation is reduced to a dependence on only one variable: kinetic energy in the local approximation or total energy in the so-called totally nonlocal (Holstein-Tsendin) approximation. It is shown that the Holstein-Tsendin approximation, when electron spatial transport dominates the electron energy relaxation (i.e. the ratio between the typical plasma inhomogeneity characteristic length Lambda and the electron energy relaxation length lambda(epsilon)), can be used at low nitrogen pressures (when the parameter pR <= 0.05 Torr). With a further increase in pressure, there is a large intermediate region where the EEDF is nonlocal in the sense that the full kinetic equation must be solved. So, even at pR approximate to 0.5 Torr, the EEDF in nitrogen plasma is nonlocal. Therefore, the use of a local approximation to find the EEDF, when all terms with spatial gradients and an ambipolar field can be discarded in the kinetic equation, requires careful verification. Particular attention should be paid to the periphery of the discharge volume, where the self-consistent ambipolar field inevitably exceeds the external electric field that heats the electrons and produces plasma.