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Continuum Theory of Spherical Electrostatic Probes
1.I. Langmuir and H. M. Mott‐Smith, Phys. Rev. 28, 727 (1926).
2.J. E. Allen, R. L. F. Boyd, and P. Reynolds, Proc. Phys. Soc. (London) B70, 297 (1957).
3.I. B. Bernstein and I. N. Rabinowitz, Phys. Fluids 2, 112 (1959).
4.R. L. F. Boyd, Proc. Phys. Soc. (London) B64, 795 (1951).
5.B. Davydov and L. J. Zmanovskaja, Zh. Tekhn. Fiz. 3, 715 (1936).
6.For an absorbing surface, the values of and on the probe surface are of order of mean free path (between charged and neutral particles) divided by a characteristic length. For the latter, a factor of is needed. Within the continuum formulation they are taken to be zero.
7.A. Guthrie and R. K. Wakerling, Characteristics of Electrical Discharges in Magnetic Fields (McGraw‐Hill Publishing Company, Inc., New York, 1949).
8.Although ε is dropped from the equation, it is still retained in the transformed variables
9.H. S. Tsien, in Advances in Applied Mechanics (Academic Press Inc., New York, 1956), Vol. IV.
10.The same result can be obtained by first interchanging the variables and then expanding in powers of
11.I. Cohen, Phys. Fluids 6, 1492 (1963).
12.This problem is treated in reference 11. See Sect. VI of the present paper.
13.For moderate probe potentials, the sheath thickness can be shown to be of order of Debye length based on the value of charge density at the edge of the sheath.
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