Velocity Distributions for Elastically Colliding Electrons

Morse, Philip Μ.; Allis, W. P.; Lamar, E. S.

doi:10.1103/physrev.48.412

Cited by 148 publications

(38 citation statements)

References 4 publications

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“…This distribution was determined theoretically by Morse, Allis, and Lamar (1935) for the particular case when only elastic collisions take place in the gas, but its form is not known for the more complex situation when inelastic collision processes also occur. For this reason the01'etical calculations of the coefficientrx/ p, which were made some years ago (EmeIeus, Lunt, and Meek 1936), were based on an assumed distribution of electron velocities and the subsequent comparison with experimental values used as a criterion for assessing the validity of any particular distribution.…”

Section: Introductionmentioning

confidence: 99%

The Theoretical Evaluation of the Townsend Coefficient a/p For Hydrogen

Blevin¹,

Haydon²

1957

Aust. J. Phys.

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IntroductionThe theoretical evaluation of the first Townsend ionization coefficient rx/p (ionizations cm-1 (mm Hg)-l) requires a knowledge of the precise form of the velocity distribution of electrons in the gas. This distribution was determined theoretically by Morse, Allis, and Lamar (1935) for the particular case when only elastic collisions take place in the gas, but its form is not known for the more complex situation when inelastic collision processes also occur. For this reason the01'etical calculations of the coefficientrx/ p, which were made some years ago (EmeIeus, Lunt, and Meek 1936), were based on an assumed distribution of electron velocities and the subsequent comparison with experimental values used as a criterion for assessing the validity of any particular distribution. For the particular case of hydrogen, assuming a Maxwellian distribution of' velocities, values of rx/p were calculated as a function of the parameter E/p (V cm-1 (mm Hg)-l) throughout the range 13 30, there is a considerable discrepancy at the lower values of E/p. It is clear that as E/p is reduced a greater proportion of electron collisions must be elastic and for this low range of E/p Deas and EmeIeus (1949) assumed an elastic collision distribution function based on the condition that the mean free path l is independent of the electron veloctiy u. The agreement, however, was even less satisfactory. In hydrogen, a more valid assumption may

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Section: Introductionmentioning

confidence: 99%

The Theoretical Evaluation of the Townsend Coefficient a/p For Hydrogen

Blevin¹,

Haydon²

1957

Aust. J. Phys.

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“…The electron energy distribution function f can be determined with the aid of the Boltzmann transport equation which is the phase space continuity equation for electrons (2) af + C + v vf+ a v v f (1) where C is the net rate at which electrons appear in an element in phase space, v is the velocity, a the acceleration, t the time, and Vv the gradient operator in velocity space.…”

Section: The Boltzmann Equationmentioning

confidence: 99%

Microwave Determinations of Average Electron Energies and the First Townsend Coefficient in Hydrogen

Varnerin

Brown

1950

Phys. Rev.

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“…Theoretical analyses of the mobility and diffusion of electrons in neutral gases under the influence of an applied electric field have traditionally relied upon the so-called two-term approximation (Lorentz 1916;Davydov 1935;Morse, Allis, and Lamar 1935;Margenau 1946;Allis 1956), in which the distribution function is approximated by the first two terms of an expansion in Legendre polynomials, is thus reduced to two coupled differential equations for jO(c) andJ1(c). In equations (2) and (3) the 0 subscripts refer to the neutral gas while the other notation is standard.…”

Section: Introductionmentioning

confidence: 99%

On the Validity of the Two-term Approximation of the Electron Distribution Function

Robson¹,

Kumar²

1971

Aust. J. Phys.

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The Boltzmann equation for electrons moving in a neutral gas under the influence of an externally applied field is solved by expanding the electron distribution function in terms of Legendre and Sonine polynomials. The solution is given in terms of infinite matrices which have elements ordered by the Sonine polynomial index, and which are dependent upon the field strength. From the structure of the formulae, it is possible to infer that truncation of the Legendre polynomial expansion after two terms is a good approximation at all field strengths. This is supported by calculations of the electron drift velocity at low field strengths, which show that the error introduced by making the two-term approximation is small, even when the deviation from equilibrium is significant. The convergence of the Sonine polynomial expansion is shown to be strongly depende:r;J.t upon field strength, and large matrices are required in the drift velocity formula at even small field strengths.

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Velocity Distributions for Elastically Colliding Electrons

Cited by 148 publications

References 4 publications

The Theoretical Evaluation of the Townsend Coefficient a/p For Hydrogen

The Theoretical Evaluation of the Townsend Coefficient a/p For Hydrogen

Microwave Determinations of Average Electron Energies and the First Townsend Coefficient in Hydrogen

On the Validity of the Two-term Approximation of the Electron Distribution Function

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