## Abstract

Thermionic emission cathodes are widely used in microwave tubes. In the temperature limited (TL) region, the Richardson-Dushman equation, corrected for the Schottky effect applies. In the fully space charge limited (FSCL) region, the Child-Langmuir law applies. Longo found that the following simple relation described the emission from an impregnated cathode over a wide range of voltages and temperatures: 1/J_{OP} = 1/J_{FSCL} + 1/J _{TL} (1) However, the knee of the transition curve from TL to FSCL operation described by Longo's equation is much broader than that found for most cathodes. Vaughan proposed the relation 1/J_{OP}^{n} = 1/J_{FSCL}^{n} + 1/J_{TL}^{n} (2) where n can be adjusted to provide the best fit to data. A value of 6 to 10 was given as being appropriate for good electron guns. Fortgang employed a simple model based on the cathode having a work function distribution function to fit the experimental data measured from TL to FSCL regime. He found that a single work function distribution could fit the I-V curve over a range of cathode temperatures very well. In this work, we study the space charge effects on thermionic emission via a self-consistent approach. The thermionic emission process is described by the Richardson-Dushman equation, corrected for the Schottky effect. Space charge effects are described by Poisson's equation including relativistic effects. The approach enables us to make detailed calculations over a wide range of voltages and temperatures. The knee of the transition curve from TL to FSCL operation is obtained self-consistently.

Original language | English |
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Number of pages | 1 |

Journal | IEEE International Conference on Plasma Science |

Publication status | Published - 2003 Oct 17 |

Event | 2003 IEEE International Conference on Plasma Science - Jeju, Korea, Republic of Duration: 2003 Jun 2 → 2003 Jun 5 |

## All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Electrical and Electronic Engineering