The limits of the validity of the theory of a spherical diode and the problem of calculation of dense electron beams with substantially different scales

Belkin, V. M.; Zavyalov, M. A.; Syrovoi, V. A.

doi:10.1134/s1064226909040135

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Cited by 5 publications

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“…Zhang et al 7 and Chen et al 8 treat the relativistic cylindrical diode, but not the spherical diode. For a relativistic treatment of the spherical diode, reference may be made to Chetvertkov 9 and Belkin et al 10 None of the above references include a convenient formula for the relativistic spherical or cylindrical diode. In addition, Pierce's classical converging gun design was based on the tabulated solution of the non-relativistic spherical diode by Langmuir and Blodgett; 4 here we present a novel, simple scaling law for spherical diodes which is valid up to 10 MV in diode voltage.…”

Section: Introductionmentioning

confidence: 99%

On relativistic space charge limited current in planar, cylindrical, and spherical diodes

et al. 2016

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This paper revisits the relativistic limiting current in planar, cylindrical, and spherical diodes, with alternative analytic and numerical treatments which are easy to implement. Convenient, approximate expressions for the limited current are presented for gap voltages up to 10 MV. They are accurate to within 1% for planar diode, and to within 4% for both cylindrical and spherical diode in the range 10 À5 < r c =r a < 500, where r a and r c are, respectively, the anode and cathode radius.

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Section: Introductionmentioning

confidence: 99%