skip to main content

Title: Time evolution of electron flow in a model diode: Non-perturbative analysis

Using a combination of Eulerian and Lagrangian variables we study the time evolution of the electron flow from a no-current state to a final state with the stationary current in a planar one-dimensional diode. The electrons can be injected externally or generated by the cathode via field emission governed by a current-field law. The initial zero current regime is replaced suddenly by injection or, in the case of field emission, by jumping the anode voltage from zero to a constant positive value. The case of equipotential electrodes and fixed injection is studied along with a positive anode potential. When the current is fixed externally, the approach to the stationary state goes without oscillations if the initial electron velocity is high enough and the anode can absorb the injected flow. Otherwise the accumulated space charge creates a potential barrier which reflects the flow and leads to its oscillations, but our method of analysis is invalid in such conditions. In the field emission case the flow goes to its stationary state through a train of decaying oscillations whose period is of the order of the electron transit time, in agreement with earlier studies based on perturbation techniques. Our approximate method does notmore » permit very high cathode emissivity although the method works when the stationary current density is only about 10% smaller than the Child-Langmuir limit.« less
Authors:
;  [1]
  1. Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019 (United States)
Publication Date:
OSTI Identifier:
22266118
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 114; Journal Issue: 23; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ANODES; CATHODES; CURRENT DENSITY; ELECTRIC POTENTIAL; ELECTRONS; EMISSIVITY; FIELD EMISSION; LAGRANGIAN FUNCTION; ONE-DIMENSIONAL CALCULATIONS; OSCILLATIONS; PERTURBATION THEORY; SPACE CHARGE