By Benjamin Bederson and Herbert Walther (Eds.)
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The representations in Eqs. (10) and (1 I ) additionally show that, in a strict sense, the expression U'12fo(U,z, t ) represents the energy distribution of the electrons and (1/3)(2/m,)'12Ufi ( U ,z , t ) represents the energetic distribution of their particle current density. The latter possesses a component in the Zz direction only. 28 R. Winkler The substitution of the expansion in Eq. (9) into the kinetic equation, Eq. , 1980). This equation system includes the expansion coefficientsJr(U, z , t ) , and its approximate solution finally yields these coefficients and thus the velocity distribution.
D. Macroscopic Properties and Macroscopic Balances of the Electrons ....... 111. Electron Kinetics in Time- and Space-Independent Plasmas.................... A . Basic Equations and Consistent Macroscopic Balances ..................... B. Some Remarks on the Calculation of the Isotropic Distribution ............ C. Examples of Distribution Functions and Macroscopic Quantities ........... D. Kinetic Treatment of Gas Mixtures .......................................... E. Inclusion of the Electron-Electron Interaction ...............................
36) if it was extended to nonconservative collision processes. B. SOME REMARKS ON THE CALCULATION OF THE ISOTROPIC DISTRIBUTION Equation (36) represents a linear ordinary differential equation of second order with the additional terms fa(U Uf") involving the shifted energy arguments U U,?. These terms are caused by the occurrence of the various conservative inelastic electron collision processes with corresponding energy losses Uf" > 0 in these collision events. The solution of Eq. (36) is sought on an appropriate energy range 0 5 U 5 Urno, where the upper limit Uw has to be chosen in such a way + + THE BOLTZMANN EQUATION AND TRANSPORT COEFFICENTS 35 that the solution,&(U) becomes negligibly small for energies larger than the upper limit Urn.
Fundamentals of Plasma Chemistry by Benjamin Bederson and Herbert Walther (Eds.)