Electron energy distribution function EEDF

For low-pressure plasmas containing mainly inert gases the electrons can be characterized by a Maxwellian electron energy distribution function (EEDF). How-... 

A time-varying electron energy distribution function (EEDF) was calculated from the Boltzmann equation. For convenience, all of the free electrons were placed near 5keV to approximate an initial nonequilibrium EEDF. The population densities were given by the time-dependent solution to the rate... 

Electron energy distribution functions (EEDFs) in non-thermal discharges can be very sophisticated and quite different from the quasi-equilibrium statistical Boltzmann distribution discussed earlier, and are more relevant for thermal plasma conditions. EEDFs are usually strongly exponential and significantly influence plasma-chemical reaction rates. 

Electron Energy Distribution Functions (EEDFs) in Non-Thermal Plasma... 

Figure 3-4. Comparison of Maxwell and Druyvesteyn electron energy distribution functions (EEDFs) at the same value of mean electron energy. Statistical weight effect related to the pre-exponential factor 5 and resulting in /(O) = 0 is taken into account.

Figure 5-38. Electron energy distribution function (EEDF) in glow discharge at different currents (1) 70 mA, (2) 30 niA.

On the other hand, it is also quite important to study reaction kinetics in nitrogen plasmas to understand quantitative amount of various excited species including reactive radicals. Many theoretical models have been proposed to describe the number densities of excited states in the plasmas. Excellent models involve simultaneous solvers of the Boltzmann equation to determine the electron energy distribution function (EEDF) and the vibrational distribution function (VDF) of nitrogen molecules in the electronic ground state. Consequently, we have found noteworthy characteristics of the number densities of excited species including dissociated atoms in plasmas as functions of plasma parameters such as electron density, reduced electric field, and electron temperature (Guerra et al, 2004 Shakhatov Lebedev, 2008). 

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... 

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... 

In the present analysis, the EEDF is determined by solving the Boltzmann equation as a fimction of the reduced electric field E/N so that the electron mean energy equals 3/2 times the electron temperature experimentally measured by the probe. The Boltzmann equation is simultaneously solved with the master equations for the vibrational distribution function (VDF) of the N2 X iZg+ state, since the EEDF of N2-based plasma is strongly affected by the VDF of N2 molecules owing to superelastic collisions with vibrationally excited N2 molecules. A more detailed account of obtaining the EEDF is given in the next section. 

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