Relaxation of the electron gas in spatially decaying plasmas

Abstract

In the spatial decay region immediately adjacent to the active zone of weakly ionized plasmas, the spatial relaxation of the electron gas is studied in the inert gases Ne and He, the metal vapour Hg and in molecular nitrogen. In these gas plasmas, the spatial decay behaviour of the isotropic and anisotropic part of the velocity distribution as well as of all important macroscopic properties of the electrons is investigated and analysed on a rigorous kinetic basis developed for field-free relaxation conditions. In particular, the rather different decay features of the electron gas in different gases and the relevant spatial scales involved in the decay process could be clearly elaborated and well characterized by deducing an energy-resolved, lumped energy dissipation length. In addition to the energy-resolved characterization of the velocity distribution, especially the spatial decay of the electron energy flux, of the power transfer rates to the gas particles in electron collisions and of the mean electron energy is evaluated. Furthermore, the influence of a variation of the boundary conditions, necessarily imposed at the margins of the spatial decay region, on the resultant decay behaviour is critically investigated.

What really happens with the electron gas in the famous Franck‐Hertz experiment?

“…Within the framework of the two term approximation, the boundary condition of the kinetic problem at the anode for 0 ≤ U ≤ U ∞ has been fixed by the relation [19][20][21] f r (U, r a ) = 3 2…”

“…where n(r c ) is the electron density at the cathode and T is the absolute temperature of the thermionic cathode. Within the framework of the two term approximation, the boundary condition of the kinetic problem at the anode for 0 ≤ U ≤ U ∞ has been fixed by the relation [19][20][21] f r (U, r a ) = 3 2…”

A multi-term solution of the space–time Boltzmann equation for electrons in gases and liquids

“…The prototypical example of non-hydrodynamic phenomena is the Frank-Hertz experiment [26,27], which helped lay the foundations for quantum and atomic physics. Extensive theoretical studies of non-hydrodynamic electron phenomena have been performed including field free spatial relaxation [28], and spatial relaxation in the presence of uniform [29][30][31][32], non-uniform [33] and periodic electric fields [34][35][36]. Similar kinetic studies on the spatial relaxation of electrons in uniform and spatially periodic fields have been performed by Golubovskii et al.…”

Progress of the Electron Kinetics in Spatial and Spatiotemporal Plasma Structures

“…The electron kinetics of a wide spectrum of problems could successfully be analysed extending from basic ones in model plasmas up to problems in real discharge arrangements. Examples of these problems are the radially varying kinetics of the electrons (i) in the column plasma of dc glow discharges [6][7][8][9][10][11][12][13][14][15][16][17] and (ii) in cylindrical hollow cathode configurations [18], (iii) the properties of the electron gas in the surrounding of emitting and absorbing electrodes as in the cathode and anode regions of dc glow discharges [18][19][20][21][22][23][24][25], (iv) the reaction of the electron gas to strongly modulated spatially periodic fields like those being present in various types of striations in inert gas discharge plasma columns [1,[26][27][28][29], (v) the behaviour of the electron gas in the spatial decay to the remote plasma region [30][31][32], (vi) the kinetics of trapped electrons under the impact of a potential valley in the plasma [32] and (vii) the response of the electrons to spatial transitions of the electric field from accelerating to retarding fields occurring in grid-controlled arrangements [33] as that of the famous Franck-Hertz experiment.…”