Electron collision frequency

Shimamori and Hatano (1976) describe a Febetron-injected microwave cavity apparatus for measuring electron concentration following pulse irradiation. Its application to thermalization in Ar and CH4 is similar to the method of Warman and Sauer (1975). In a related experiment, Hatano et al. (private communication) measure the electron collision frequency directly. 

A necessary condition for the two-term expansion of the distribution function of equation (2) to be valid is that the electron collision frequency for momentum transfer must be larger than the total electron collision frequency for excitation for all values of electron energy. Under these conditions electron-heavy particle momentum-transfer collisions are of major importance in reducing the asymmetry in the distribution function. In many cases as pointed out by Phelps in ref. 34, this condition is not met in the analysis of N2, CO, and C02 transport data primarily because of large vibrational excitation cross sections. The effect on the accuracy of the determination of distribution functions as a result is a factor still remaining to be assessed. 

Here g and gg are functions of the electron collision frequency as evaluated by Wilkins and Gyftopolous P). 

Phelps, A.V., and J.L. Pack, Electron collision frequencies in nitrogen and in the lower ionosphere. Phys Rev Lett 3, 340, 1959. 

For Oj = He = n 10 cm" and kT 2 eV, Ad 105 nm. If D is a characteristic plasma reactor dimension, then Ad must be plasma oscillations) can develop if the electron collision frequency for elastic collisions is considerably lower than the plasma frequency cOp. Again for the simplest case ... 

The application of (3.3 to derive the electron concentration for the measured attenuation requires a knowledge of the electron collision frequency. Belcher and Sugden, who compared the attenuation at various values of to, found this to be 8-8 X 10 s . Later work - showed that this was too low by a factor of 3, and that the electron concentrations measured by them, and subsequent workers, were therefore too small. - These low electron concentrations were ascribed to the presence of OH ions, and the use of the later and higher values of the collision theory obviates the necessity of invoking OH as a significant ionic constituent. Page, Soundy and Williams have examined the temperature dependence of the collision frequency, and shown that the collision frequency is related to the temperature and composition by... 

The Q s are the electron collision cross sections, Z is the electron collision frequency and n the particle density. The Thompson probability factor is now defined in terms of the collision cross section, rather than the electrostatic energy. Taking Bulewicz and Padley s value of 40 x 10 cm for the mean electron collision cross section, the probability factor become 4-4 x 10 , and... 

The mean free path of electron is a direct function of the electron collision frequency. Electrons can collide with other electrons, lattice, defects, grain boundaries, and surfaces. 

Microwave discharges at pressures below 1 Pa witli low collision frequencies can be generated in tlie presence of a magnetic field B where tlie electrons rotate witli tlie electron cyclotron frequency. In a magnetic field of 875 G tlie rotational motion of tlie electrons is in resonance witli tlie microwaves of 2.45 GHz. In such low-pressure electron cyclotron resonance plasma sources collisions between tlie atoms, molecules and ions are reduced and the fonnation of unwanted particles in tlie plasma volume ( dusty plasma ) is largely avoided. 

All of these time correlation functions contain time dependences that arise from rotational motion of a dipole-related vector (i.e., the vibrationally averaged dipole P-avejv (t), the vibrational transition dipole itrans (t) or the electronic transition dipole ii f(Re,t)) and the latter two also contain oscillatory time dependences (i.e., exp(icofv,ivt) or exp(icOfvjvt + iAEi ft/h)) that arise from vibrational or electronic-vibrational energy level differences. In the treatments of the following sections, consideration is given to the rotational contributions under circumstances that characterize, for example, dilute gaseous samples where the collision frequency is low and liquid-phase samples where rotational motion is better described in terms of diffusional motion. 

Electrons from a spark are accelerated backward and forward rapidly in the oscillating electromagnetic field and collide with neutral atoms. At atmospheric pressure, the high collision frequency of electrons with atoms induces chaotic electron motion. The electrons gain rapidly in kinetic energy until they have sufficient energy to cause ionization of some gas atoms. 

For collision frequencies large compared with the frequency of the electric field, the current remains in phase with the electric field in the reverse case, the current is 90° out of phase. The in-phase component of the current gives rise to an energy loss from the field (Joule heating loss) microscopically, this is seen to be due to the energy transferred from the electrons to the atoms upon collision. 

In a nonattaching gas electron, thermalization occurs via vibrational, rotational, and elastic collisions. In attaching media, competitive scavenging occurs, sometimes accompanied by attachment-detachment equilibrium. In the gas phase, thermalization time is more significant than thermalization distance because of relatively large travel distances, thermalized electrons can be assumed to be homogeneously distributed. The experiments we review can be classified into four categories (1) microwave methods, (2) use of probes, (3) transient conductivity, and (4) recombination luminescence. Further microwave methods can be subdivided into four types (1) cross modulation, (2) resonance frequency shift, (3) absorption, and (4) cavity technique for collision frequency. 

Here the left-hand side is the ratio of power loss at time t, when the mean electron energy is (E), to that at thermalization, and C and n are determinable constants. This idealized equation is not expected to be valid in presence of the Ramsauer effect, but Warman and deHaas apply it anyway to N2, Ar, and He at atmospheric pressure. The method relates the gradual decrease of collision frequency to an increase in conductivity, which finally rides to a plateau interpreted to be the thermal conductivity. The time needed to reach 90% of the thermal conductivity is called the thermalization time (see Table 8.1). 

Sowada and Warman (1982) have described a dc conductivity method for Ar gas at 295 K and 45 atm. Following a 20-ns pulse of irradiation, the conductivity rises to a peak at -50 ns, due to the Ramsauer effect, before settling to a plateau, which is ascribed to thermal conductivity since the collecting field is very low. Since there is little electron loss, the conductivity profile is proportional to the mobility profile this in turn can be considered a kind of image of collision frequency as a function of electron energy. The time to reach the conductivity plateau, -150 ns, is the measure of thermalization time in the present case. At a density of -9 X 1021 cm-3, the conductivity maximum vanishes, indicating the disappearance of the Ramsauer minimum according to Sowada and Warman. 

Early theoretical models were based on fractional energy loss 2m/M per elastic collision (for details, see LaVeme and Mozumder, 1984, Sect. 3, and references therein). Thus, frequently, the energy loss rate was written as —d (E)/dt = (2m/M)((E)-3feBT/2)vc, where vc is the collision frequency and (E) is the mean electron energy over an unspecified distribution. The heuristic inclusion of the term 3feBT/2 allowed the mean energy to attain the asymptotic thermal... 

Holroyd (1977) finds that generally the attachment reactions are very fast (fej - 1012-1013 M 1s 1), are relatively insensitive to temperature, and increase with electron mobility. The detachment reactions are sensitive to temperature and the nature of the liquid. Fitted to the Arrhenius equation, these reactions show very large preexponential factors, which allow the endothermic detachment reactions to occur despite high activation energy. Interpreted in terms of the transition state theory and taking the collision frequency as 1013 s 1- these preexponential factors give activation entropies 100 to 200 J/(mole.K), depending on the solute and the solvent. 

The transmission coefficient k is approximately 1 for reactions in which there is substantial (>4kJ) electronic coupling between the reactants (adiabatic reactions). Ar is calculable if necessary but is usually approximated by Z, the effective collision frequency in solution, and assumed to be 10" M s. Thus it is possible in principle to calculate the rate constant of an outer-sphere redox reaction from a set of nonkinetic parameters, including molecular size, bond length, vibration frequency and solvent parameters (see inset). This represents a remarkable step. Not surprisingly, exchange reactions of the type... 

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