Abstract
This article is divided into five parts according to the mathematical method used, rather than according to the physical situation. In part I we attempt to follow the motion of an individual particle under a Lorentz force including the effects of gradients of the magnetic field. This is no longer possible with the introduction of collisions in part II, but one may yet follow the motion of an average particle. One is then tempted to expect that a swarm of particles will have the behavior of the average particle, and this is remarkably close to the truth for high values of E/p, the ratio of the continuous to the stochastic force, and has the advantage of being more intuitive than the distribution function methods which follow.
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General References
Alfven, H.: Cosmical Electrodynamics. Oxford: Clarendon Press 1950. — Has a chapter on the motion of charged particles similar to part I of this article.
Chapman, S., and T. G. Cowling: The Mathematical Theory of Non-uniform Gases. Cambridge University Press 1939. — Deals exhaustively with small departures from thermal equilibrium.
Kihara, Taro: Mathematical Theory of Electrical Discharges in Gases. Rev. Mod. Phys 24, 45 (1952);
Kihara, Taro: Mathematical Theory of Electrical Discharges in Gases. Rev. Mod. Phys 25, 844 (1953). — Covers the area of part III of this article.
Spitzer, L., and R. Harm: Phys. Rev. 89, 977 (1953). — Compute the conductivity of an ionized plasma by the method of part V.
Wannier, G. H.: Phys. Rev. 83, 281 (1951). — This is the most recent work on ion mobilities.
Wax, Nelson: Noise and Stochastic Processes. Dover Publ. Co. 1954. — Contains reprints of the basic articles by Chandrasekhar and Uhlenbeck.
The following references to electron distribution functions are given in historical order:
Druyvesteyn, M. J.: Physica, Haag 10, 69 (1930).
Morse, P.M., W. P. Allis and E.S. Lamar: Phys. Rev. 82, 412 (1935).
Davydov, B.: Phys. Z. Sowjet. 8, 59 (1935).
Smit, J. A.: Physica, Haag 3, 543 (1937).
Tonks, L., and W. P. Allis: Phys. Rev. 52, 710 (1937).
Holstein, T.: Phys. Rev. 70, 367 (1946).
Margenau, H.: Phys. Rev. 73, 297, 309 (1948).
Macdonald, A. D., and S. C. Brown: Phys. Rev. 75, 411 (1949).
Allis, W. P., and S. C. Brown: Phys. Rev. 87, 419 (1952).
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© 1956 Springer-Verlag OHG. Berlin · Göttingen · Heidelberg
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Allis, W.P. (1956). Motions of Ions and Electrons. In: Electron-Emission Gas Discharges I / Elektronen-Emission Gasentladungen I. Encyclopedia of Physics / Handbuch der Physik, vol 4 / 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45844-6_5
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