On some effects of velocity distribution in electron streams
Author:
S. V. Yadavalli
Journal:
Quart. Appl. Math. 12 (1954), 105-116
MSC:
Primary 78.0X
DOI:
https://doi.org/10.1090/qam/64633
MathSciNet review:
64633
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Abstract: Based on the Liouville theorem an integral equation is obtained for the solution of electron beam problems having a velocity spread. Assuming a rectangular velocity distribution (which is justified later) the integral equation is solved by Laplace Transforms to obtain the solution of the problems of small-signal velocity modulation in a drifting electron stream, and a drifting electron stream initially possessing full shot noise in each velocity class.
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F. B. Llewellyn and L. C. Peterson, Proc. I.R.E. 32, 144 (1944).
D. Bohm and E. P. Gross, Phy. Rev. 75, 1851. (1949); 75, 1869 (1949); 79, 992 (1950).
A. Vlasov, J. Phy. (U.S.S.R.) 9, 25 (1945).
L. Landau, J. Phy. (U.S.S.R.) 10, 25 (1946).
D. A. Watkins, J.A.P. 23, 568 (1952).
D. Pines and D. Bohm, Phy. Rev. 85, 339 (1952).
W. C. Hahn, G.E. Rev. 42, 258 (1939).
S. Ramo, Phy. Rev. 56, 256 (1939).
J. R. Pierce, Proc. I.R.E. 40, 1675 (1952).
S. V. Yadavalli, Tech. Report Ser. No. 1, Issue No. 64, Electronics Research Laboratory, University of California, Berkeley.
I. Fredholm, Acta Math. 27, 365 (1903).
D. R. Hamilton, J. K. Knipp and J. B. H. Kuper, Klystrons and microwave triodes, Vol. 7, M.I.T. Rad. Lab. Series, McGraw-Hill, 1948, p. 136.
F. B. Llewellyn and L. C. Peterson, Proc. I.R.E. 32, 144 (1944).
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Article copyright:
© Copyright 1954
American Mathematical Society
