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Electron dynamics inside a vacuum tube diode through linear differential equations

Published online by Cambridge University Press:  13 December 2013

Gabriel González and
Fco. Javier González Orozco
Gabriel González*
Affiliation:
Departamento de Matemáticas y Física, Instituto Tecnológico y de Estudios Superiores de Occidente, Periférico Sur Manuel Gómez Morín 8585 C.P. 45604, Tlaquepaque, Jal., Mexico
Fco. Javier González Orozco
Affiliation:
Departamento de Matemáticas y Física, Instituto Tecnológico y de Estudios Superiores de Occidente, Periférico Sur Manuel Gómez Morín 8585 C.P. 45604, Tlaquepaque, Jal., Mexico
*
†Email address for correspondence: gabrielglez@iteso.mx
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Abstract

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In this paper we analyze the motion of charged particles in a vacuum tube diode by solving linear differential equations. Our analysis is based on expressing the volume charge density as a function of the current density and coordinates only, i.e. ρ=ρ(J,z), while in the usual scheme the volume charge density is expressed as a function of the current density and electrostatic potential, i.e. ρ=ρ(J,V). We show that, in the case of slow varying charge density, the space-charge-limited current is reduced up to 50%. Our approach gives the well-known behavior of the classical current density proportional to the three-halves power of the bias potential and inversely proportional to the square of the gap distance between electrodes, and does not require the solution of the nonlinear differential equation normally associated with the Child–Langmuir formulation.

Information

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 2 , April 2014, pp. 247 - 254
Copyright
Copyright © Cambridge University Press 2013 

References

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