Investigación

 

Estimation of the space charge limited current with quadratic damping

 

D. González*, V. H. Romero** y G. González***

 

* Departamento de Matemáticas y Física, Instituto Tecnológico y de Estudios Superiores de Occidente, Periférico Sur Manuel Gómez Morón 8585 C.P. 45604, Tlaquepaque, Jal., México.

** Universidad de Guadalajara, Centro Universitario de Tonalá, Div. de Ciencias, Depto. de Ing., Tonalá Jalisco C.P. 48525, México.

*** Cátedras CONACYT, Universidad Autónoma de San Luis Potosí, San Luis Potosí, 78000 México. Coordinación para la Innovación y la Aplicación de la Ciencia y la Tecnología, Universidad Autónoma de San Luis Potosí, San Luis Potosí, 78000 México. e-mail: gabriel.gonzalez@uaslp.mx

 

Received 24 April 2015.
Accepted 29 June 2015.

 

Abstract

In this paper we analyze the motion of charged particles under the influence of a quadratic velocity dependent frictional force inside a vacuum tube diode. Our study is performed by using the adiabatic approximation that allows for exact analytic solutions for the case of weak damping. The expressions obtained for the space charge limited current reduce to the well known Child-Langmuir law under the adiabatic approximation when the dissipation parameter goes to zero.

Keywords: Child-Langmuir law; Mott-Gurney Law; space charge current.

PACS: 85.30.Fg; 52.59.Sa

 

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