Eur. Phys. J. D 42, 441-454 (2007)
https://doi.org/10.1140/epjd/e2007-00132-7

A fluid model of the current-voltage characteristics of an electron emitting electrode immersed in a two electron temperature plasma

¹ University of Ljubljana, Faculty of Electrical Engineering, Tržaška 25, 1000 Ljubljana, Slovenia
² Jožef Stefan Institute, Jamova 39, POB 100, 1000 Ljubljana, Slovenia
³ University of Maribor, Faculty of Civil Engineering, Smetanova 17, 2000 Maribor, Slovenia

Corresponding author: ^a tomaz.gyergyek@fe.uni-lj.si

Received: 24 May 2006
Revised: 29 September 2006
Published online: 23 March 2007

Abstract

The current voltage characteristics of a negatively biased electron emitting electrode immersed in a two-electron temperature plasma are analyzed by a simple one dimensional fluid model. Based on the assumption that the electron density in the pre-sheath region obeys the Boltzmann law the Bohm criterion is derived in the form of a transcendental equation for the Mach number, which can have up to 3 solutions. According to these solutions the ion velocity at the sheath edge can be determined either by the hot or by the cool electron temperature. When it is determined by the cool electron temperature and the hot electron temperature is high enough the critical electron emission current from the collector can have a very pronounced local maximum and a minimum when regarded as a function of the electrode potential. Because of that the current voltage characteristics of the electrode may exhibit up to 3 different floating potentials. This result is in good agreement with the experimental observations reported in [J. Appl. Phys. 63, 5674 (1988)].