Momentum transfer cross section

Referring back to equation 47, the other quantity necessary in calculating the gas conductivity is the coUision cross section, Gases contain at least four types of particles electrons, ionized seed atoms, neutral seed atoms, and neutral atoms of the carrier gas. Combustion gases, of course, have many more species. Each species has a different momentum transfer cross section for coUisions with electrons. To account for this, the product nQ in equation 47 is replaced by the summation where k denotes the different species present. This generalization also aUows the conductivity calculation to... 

Campeanu (1982), using data of McEachran, Stauffer and Campbell (1980) — —, Campeanu (1982), using momentum transfer cross sections calculated by Schrader (1979). Xenon -------, Wright et al. (1985) — —, Campeanu... 

As shown in Figure 6.18, electron drift velocities below e/p = 1 Td (= 1017 V cm2) are at least four times larger than those for positrons. Bose, Paul and Tsai (1981) attributed this difference to higher momentum transfer cross sections for positrons than for electrons at very low (i.e. 

The first discussion of the thermalization of positronium appears to have been that of Sauder (1968), who derived a general (classical) expression for moderation by elastic collisions of a particle in a medium, allowing for the thermal motion of the atoms or molecules of the medium. By assuming that the momentum transfer cross section, om, is a constant he found that the time dependence of the mean positronium kinetic energy,... 

Fig. 7.19. The time dependence of the mean ortho-positronium kinetic energy measured in silica aerogel under vacuum (o) and with 0.92 amagat of helium gas added ( ). The two curves were simultaneously fitted to the data by Nagashima et al. (1998), to obtain estimates of the Ps-He momentum transfer cross section. Reprinted from Journal of Physics B31, Nagashima et al, Momentum transfer cross section for slow positronium-He scattering, 329-339, copyright 1998, with permission from IOP Publishing.

Momentum-transfer cross section for slow positronium-He scattering. J. Phys. B At. Mol. Opt. Phys. 31 329-339. 

Momentum-transfer cross sections are normally determined by the electron swarm technique. A detailed discussion of the drift and diffusion of electrons in gases under the influence of electric and magnetic fields is beyond the scope of this book and only a brief summary will be given. The book by Huxley and Crompton (1974) should be consulted for a full description of the experimental methods and analysis procedures. 

The analysis and experimental procedures are very demanding in obtaining accurate cross-section data and there are particular problems in obtaining unique cross sections (see Huxley and Crompton (1974) and Kumar (1984) for details). If only the elastic channel is open the momentum-transfer cross section can be obtained reliably and accurately in some cases (e.g. He, 2%). With the addition of inelastic channels the uncertainty in the derived cross sections due to lack of uniqueness increases. 

Figure 5 (Kurachi and Nakamura, 1990) presents a survey of electron collision cross sections of CF4. In addition to the momentum-transfer cross section q , it shows the vibrational-excitation cross sections q T, and q (for two different vibrational modes), the (total) electronic-excitation cross section q, the dissociation cross section q j , the electron-attachment cross section qg, and the (total) ionization cross section 9,. Each of the cross sections is a function of the electron kinetic energy and reflects the physics of the collision process, which is being clarified by theory. The cross sections designated as total can be discussed in greater detail in terms of different contributions, which are designated as partial cross sections.

Commonly this equation and Eq. (35) are used to determine the normalized isotropic distribution. Consideration of Eq. (36) shows that various quantities of the collision processes and a few plasma parameters are involved in its coefficients and naturally have an immediate impact on its solution. With respect to the atomic data of the various collision processes, these are the momentum-transfer cross section Q (U), the total cross sections Qj U), the corresponding excitation or dissociation energies of the ground-state atoms or molecules, and the mass ratio m jM. With regard to the plasma parameters, the electric field strength E and the density N of the atoms or molecules occur, but only in the form of the reduced field strength E/N. All these quantities have to be known for a specific weakly ionized plasma in order to determine the isotropic distribution MU) by solving Eq. (36). 

Since it is usually in the direction of the applied electric field, the drift velocity is usually denoted as the scalar Vj. a ie) is known as the momentum-transfer cross section and is defined by... 

Fig. 3. C2F6 elastic and momentum-transfer cross sections.

The momentum-transfer cross section is easily calculated for any of the various elastic cross sections discussed in the preceding section. A momentum-transfer cross section can also be defined analogously for inelastic processes, although the concept is most useful in the elastic case. 

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