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On the theory of the recombination of ions in gases at high pressures

Published online by Cambridge University Press:  24 October 2008

W. R. Harper
W. R. Harper
Affiliation:
St John's College; Wills Research Student, University of Bristol
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Extract

Previous theories of the recombination of ions in gases are shown to be inapplicable to high pressures. An approximate quantitative theory which takes into account all the relevant phenomena is developed. The effect of both thermal agitation and mutual attraction in determining encounters of ions of opposite sign is considered, and the frequency of encounters which lead to recombination calculated. The criterion for an encounter to lead to recombination is that the drift of the ions towards each other due to their mutual attraction must be greater than their tendency to separate due to their Brownian movement. Excellent agreement is obtained with such experimental results as are available. Preferential recombination between an ejected electron and its parent ion is also discussed.

I am indebted to various members both of the Wills Physics Laboratory and of the Cavendish Laboratory for discussion of the problems dealt with in this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 2 , April 1932 , pp. 219 - 233
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

* Ann. de Phys. 28, 433 (1903).Google Scholar

† Electricity in Gases, Chap. VI.

‡ Phil. Mag. 10, 242 (1905).Google Scholar

§ Phil. Mag. 18, 341 (1909).Google Scholar

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‡ Greater than a few atmospheres.

§ Loeb and Marshall (loc. cit.) have dealt with this question by the following procedure. From the equations of motion of the two ions all terms due to the random bombardment are eliminated, and the equation is integrated. An unjustified substitution followed by various transformations then leads to an equation which, for important physical conditions, makes the root mean square distance between the pair of ions imaginary. I shall not criticise the conclusions drawn from this equation.

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* See p. 228.

* It might therefore be thought that as in section 2 this would require D 1 to be replaced by D 1 + D 2, but in reality there is no analogy. In section 2 the motion of the two ions was derived as a function of one position variable only, whereas the present problem with both ions moving cannot be reduced to such a simple form. Moreover, in section was necessarily positive, whereas in the present problem it is negative for part of the-time and has a mean value equal to zero. Note however that although is not given by (2·1) and are given by the Einstein-Smoluchowski equation, leading to the two values for τ′ already obtained—for only the one or the other ion moving. In section 5 an equation will be derived in which is negative, but it is inapplicable here since the class of tracks to which it applies is different.

* See Thomson, , Conduction of Electricity through Gases, 3rd ed., p. 22.Google Scholar

† The distance is only a few times smaller than σ0.

* This comes from an extension of the theory that cannot be dealt with in the present paper.

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‡ Loc. cit.

§ Thomson, , Conduction of Electricity through Gases, 3rd ed., p. 123Google Scholar. The low value for k 2 is chosen, since the gas used in the recombination experiments was not specially purified.

* Thomson, , Conduction of Electricity through Gases, 3rd ed., p. 123Google Scholar. The low value for k 2 is chosen, since the gas used in the recombination experiments was not specially purified.

† Ann. der Phys. 32, 148 (1910).Google Scholar

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* Loc. cit.

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* However, in a letter to the Phys. Rev. 38, 1565 (1931)Google Scholar, A. H. Compton, Bennet and Stearns claim to have obtained quantitative results based on the Thomson theory of recombination. As no details are given it is impossible to say whether the reasons given in this paper for rejecting the Thomson theory apply to their results or not. They have observed an increase in the ionisation current at high pressures with a rise in temperature, and adduce this in support of their theory, but the observations of Erikson (loc. cit.) show that the effect is not susceptible of so simple an explanation. They also find that preferential recombination is more probable in air than in nitrogen, and conclude that the range of the ejected electron is less in air. But it may equally well be due to a difference in the time required for the electron to become a negative ion, since impurity molecules to which it could attach itself would be present to a much greater extent in air.

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