Ionization electron energy distribution

The unusual complex potential derived for He(2 S)-Ar does not lead to contradictions with other experimental data, such as total ionization cross section and electron energy distribution, but rather explains some of the observed differences between the systems He(2l5 ) Ar and He(235) Ar. 

Spontaneous Ionization in Slow Collisions 3. Electron Energy Distributions... 

Plasmas typical of C02 laser discharges operate over a pressure range from 1 Torr to several atmospheres with degrees of ionization, that is, nJN (the ratio of electron density to neutral density) in the range from 10-8 to 10-8. Under these conditions the electron energy distribution function is highly non-Maxwellian. As a consequence it is necessary to solve the Boltzmann transport equation based on a detailed knowledge of the electron collisional channels in order to establish the electron distribution function as a function of the ratio of the electric field to the neutral gas density, E/N, and species concentration. Development of the fundamental techniques for solution of the Boltzmann equation are presented in detail by Shkarofsky, Johnston, and Bachynski [44] and Holstein [45]. 

Provided that very accurate ionization-efficiency data are available, the second differential of the ionization efficiency curve can yield ionization potentials in good agreement with spectroscopic values without assumptions about the relative amounts of sample and reference compounds (Morrison, 1951). Different molecular energy levels may be discerned, but there are difficulties caused by scatter in the ionization-efficiency data and lack of knowledge of the electron-energy distribution in any given experiment (Morrison, 1963). 

Most of the last-named difficulty has been removed in a simple mathematical treatment which effectively removes a major part of the high-energy side of the electron beam (Winters et al., 1966). An experimental factor b, accounting for the lack of knowledge of electron energy distribution, has been found to be quite close to that calculated from the Maxwell-Boltzmann distribution. Recently it has been claimed that the 0 0 ionization and vibrational fine structure of acetylene had been detected (J. H. Collins et al., 1968), and this energy distribution difference (E. D. D.) method appears to be both simple and accurate. 

Specified electron energy distribution function The EEDF is specified, normally assumed Maxwellian (Eq. 9). The electron energy balance (Eq. 31) is solved assuming an adiabatic condition for electron temperature at the wall. The Maxwellian assumption is very common in the literature [100, 125, 126, 130, 133, 135-137]. Measured EEDFs in ICPs, however, have a Maxwellian bulk (due to electron-electron collisions), and a depleted tail due to inelastic losses and escape of fast electrons to the walls. Thus a bi-Maxwellian distribution may be more appropriate [154]. A Maxwellian distribution is not expected to have a great effect on ion densities since the ionization rate is self-adjusted to balance the loss rate of ions to the walls and the latter depends only very weakly on the EEDF. The good agreement with experimental data [101, 130, 148, 152] is an indirect evidence that the Maxwellian EEDF is reasonable for obtaining species densities and their distributions. Other forms of... 

The upward-directed electric field accelerates the ambient thermal energy electrons of mean energy = 1.5 kT to a new distribution fimction that depends upon the local E field and neutral composition and density. The connection between the spatial E field and the electron energy distribution function is made through solution of either the Boltzmann equation (Pitchford et al., 1981 Phelps and Pitchford, 1985) or the derived Fokker-Planck equation (Milikh et al., 1998a). In either case, a full database of cross sections for electron-molecule (N2, O2) excitation, ionization (both direct and dissociative), and attachment (for O2) is needed for reliable solutions. Electron-ion and electron-atom (N, O) scattering are usually neglected because of the small product of electron and ion or atom densities. 

Useful formulas for estimations of the direct ionization cross sections can be also found in Barnett (1989). The ionization rate coefficient A i(7 ) canthenbe calculated by integration of the cross section cri (e) over the electron energy distribution function (see (2-7)). Assuming the Maxwellian EEDF, the direct ionization rate coefficient can be presented as... 

Figure 2-31. Electron energy distribution between different excitation and ionization channels in water vapor.

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