If the magnetic field is so strong as to impair collective transverse drifts, all the charges supplied to the probe come mainly from a long tube of force, whose section is about one Larmor radius larger than the probe; while a diffusion process, more efficient than ordinary drifts, continuously exchanges particles between the inside and the rest of the plasma. A one‐dimensional model of this process is proposed, leading to an integro‐differential Poisson's equation, which has been studied for the case in which the collected particles are very fast. The solution consists of a chargeless, slowly decaying potential which describes the geometrical screening effect of the probe; while in the sheath an approximate boundary‐layer solution matches with the probe's potential.

Topics
Electrostatics, Magnetic fields, Partial differential equations
1.
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3.
The method is similar to the one used in the early theory of probes: See, e.g.,
J. E.
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On this type of asymptotic expansions, see, e.g., M. Kruskal, in Rendiconti del Terzo Congresso Internazionale sui Fenomeni d’Ionizzazione nei Gas (Società Italiana di Fisica, Milan, 1959) p. 562.
5.
This “shadow effect” has been actually observed in the machine “Etude” at Project Matterhorn (private communication from L. L. Hoffman).
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See, for example,
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For the boundary layer theory in a fluid cf. S. Goldstein, Lectures on Fluid Mechanics (Interscience Publishers, Inc., New York, 1960), Chaps. 7–9.
7.
See, e.g., D. V. Widder, The Laplace Transform (Princeton University Press, Princeton, New Jersey, 1946), p. 181.
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© 1961 The American Institute of Physics.
1961
The American Institute of Physics
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