scholarly journals Inelastic Collisions in the Townsend?Huxley Diffusion Experiment

1971 ◽  
Vol 24 (4) ◽  
pp. 841 ◽  
Author(s):  
JLA Francey ◽  
PK Stewart
Keyword(s):  
Distribution Function ◽  
Energy Loss ◽  
Cross Sections ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Inelastic Collisions ◽  
Diffusion Experiment ◽  
Inelastic Energy Loss ◽  
The Mean ◽  
Range Of Values

The Boltzmann equation, including density gradients, is solved for the electron distribution function in the Townsend-Huxley experiment. Elastic and inelastic collisions with constant cross sections are assumed to occur, the inelastic energy loss per collision being small compared with the mean energy. The inelastic energy loss and the electron mean energy are calculated and tabulated over a range of values of EIP.

Solution with Third-order Accuracy for the Electron Distribution Function in Weakly Ionized Gases (or in Intrinsic Semiconductors): Application to the Drift Velocity

1981 ◽  
Vol 34 (4) ◽  
pp. 361 ◽  
Author(s):  
G Cavalleri
Keyword(s):  
Distribution Function ◽  
Legendre Polynomials ◽  
Taylor Expansion ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Mean Free Path ◽  
Third Order ◽  
Order Accuracy ◽  
Weakly Ionized ◽  
The Mean

The first four components 10, I" 12 and 13 of the expansion in Legendre polynomials of the electron distribution function I are shown to be of order t:D, et, e2 and e3 respectively, with e = (m/M)'/2 where m and M are the masses of the electron and molecule respectively. This allows the solution of the so-called P3 approximation to the Boltzmann equation applied to a weakly ionized gas (or to an intrinsic semiconductor) in steady-state and uniform conditions and for dominant elastic collisions. However, nonphysical divergences appear in 10 and in the drift velocity W. This can be understood by the equivalence of the Boltzmann-Legendre formulation and the mean free path formulation in which a Taylor expansion is performed around the 'origin', i.e. for a -+ 0, where a = eE/m is the acceleration due to an external electric field E. Indeed, one sees that the expansion under the integral sign (integrals appear in the evaluation of transport quantities) leads to divergent integrals if the expansion is around a = O. Fortunately, it is easy to perform a Taylor expansion around a oft 0 in the mean free path formulation and then to find the corresponding expansion in Legendre polynomials outside the origin. In this way, explicit convergent expressions are found for 10, I" 12, 13 and W, with third-order accuracy in e = (m/M)'/2. This is better than the best preceding expression, that by Davydov-Chapman-Cowling, which has first-order accuracy only (it is the solution of the P, approximation to the Boltzmann equation).

Inelastic collisions at low energies

1969 ◽  
Vol 47 (10) ◽  
pp. 1723-1729 ◽  
Author(s):  
A. Dalgarno
Keyword(s):  
Energy Loss ◽  
Cross Sections ◽  
Low Energy ◽  
Inelastic Collisions ◽  
Low Energies ◽  
Low Energy Electrons ◽  
The Cross ◽  
Loss Rates

A summary is presented of the processes by which low energy electrons lose energy in moving through the atmosphere and estimates are given of the cross sections and energy loss rates. The mechanisms by which thermal electrons cool are described and the cooling efficiencies are listed.

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