Electron dynamics inside a vacuum tube diode through linear differential equations

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 charg...

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Bibliographic Details
Published in:Journal of plasma physics 2014-04, Vol.80 (2), p.247-254
Main Authors: González, Gabriel, Orozco, Fco. Javier González
Format: Article
Language:English
Subjects:
Charge density
Current density
Differential equations
Diodes
Dynamics
Electrodes
Nonlinearity
Plasma physics
Vacuum tubes
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Summary: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.
ISSN:0022-3778
1469-7807
DOI:10.1017/S0022377813001256