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Title: Minimum current principle and variational method in theory of space charge limited flow

In spirit of the principle of least action, which means that when a perturbation is applied to a physical system, its reaction is such that it modifies its state to “agree” with the perturbation by “minimal” change of its initial state. In particular, the electron field emission should produce the minimum current consistent with boundary conditions. It can be found theoretically by solving corresponding equations using different techniques. We apply here the variational method for the current calculation, which can be quite effective even when involving a short set of trial functions. The approach to a better result can be monitored by the total current that should decrease when we on the right track. Here, we present only an illustration for simple geometries of devices with the electron flow. The development of these methods can be useful when the emitter and/or anode shapes make difficult the use of standard approaches. Though direct numerical calculations including particle-in-cell technique are very effective, but theoretical calculations can provide an important insight for understanding general features of flow formation and even sometimes be realized by simpler routines.
Authors:
 [1]
  1. Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019 (United States)
Publication Date:
OSTI Identifier:
22492816
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 118; Journal Issue: 15; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANODES; BOUNDARY CONDITIONS; DISTURBANCES; EQUATIONS; FIELD EMISSION; GEOMETRY; SHAPE; SPACE CHARGE; VARIATIONAL METHODS