Verifications of Schottky's Conjecture
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 05, 2019
- Source ID
- 10.1063/1.5091712
Entities
People
- J. R. Harris
- Kevin L. Jensen
Organizations
- Air Force Office of Scientific Research
- Air Force Research Laboratory
- United States Naval Research Laboratory