Abstract
A procedure exploiting the conventional perturbation theory and the transformation of space variable x through\(x = {\int _0^\xi v(\xi') d\xi'} \) is applied to investigate a case of the electron flow in a Pierce diode. The introduction of such variable ζ simplifies the basic set of equations describing the system, which makes an analytic evaluation of electrode spacing as well as the perturbed electric field, due to electron motion, straightforward.
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References
El-Labany, S. K. and Rowlands, G.: 1989,Astrophys. Space Sci. 161, 247.
Godfrey, B. B.: 1982,Bull. Am. Phys. Soc. 27, 955.
Godfrey, B. B.: 1987,Phys. Fluids 30, 1553.
Kuhn, S.: 1984,Phys. Fluids 27, 1834.
Pierce, J. R.: 1944,J. Appl. Phys. 15, 721.
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El-Labany, S.K. A linear theory of electron flow in A Pierce. Astrophys Space Sci 166, 337–342 (1990). https://doi.org/10.1007/BF01094905
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DOI: https://doi.org/10.1007/BF01094905