Back to Search Start Over

Verifications of Schottky's Conjecture

Authors :
Kevin L. Jensen
John R. Harris
Source :
Journal of Applied Physics. 125:215306
Publication Year :
2019
Publisher :
AIP Publishing, 2019.

Abstract

Schottky's Conjecture posits that the geometric field enhancement produced by a hybrid shape formed from a small perturbation on a larger base is the product of the individual field enhancement factors of the base and perturbation in isolation. This is a powerful concept with practical applications to understanding field emitter design and operation, as actual field emitters have complicated surface shapes with structure and, therefore, contributions to field enhancement, occurring simultaneously on many length scales. Recent studies of the Conjecture imply that the degree to which it accurately predicts a hybrid structure's total field enhancement depends on the degree of self-similarity between the base and perturbation shapes. To explore these aspects of the Conjecture, we have used the zero-potential surface produced by simple charge distributions to produce compound shapes with small perturbations on larger base structures. In the limit of small perturbation strength, these simple models adequately approximate idealized compound shapes, such a hemisphere-on-hemisphere geometry. Changing the base shape and the location of the perturbation allows us to selectively degrade the self-similarity present in the problem geometry. Proofs of the Schottky Conjecture in the limit of small perturbation strength will be provided, using these techniques, for hemisphere-on-hemisphere and half-cylinder-on-half-cylinder systems—the latter being the geometry considered by Schottky and for which the Conjecture was first proposed, but not proven.

Details

ISSN :
10897550 and 00218979
Volume :
125
Database :
OpenAIRE
Journal :
Journal of Applied Physics
Accession number :
edsair.doi...........dd03573b9171f5a9d15ff02b69c4b5c5
Full Text :
https://doi.org/10.1063/1.5091712