Quasi-linear analysis of a Smith-Purcell free electron amplifier

Mordechai Botton*, Amiram Ron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present an analysis of a Smith-Purcell free electron amplifier. The study is based on a scheme known as the quasi-linear theory which enables us to consider nonlinear effects. The model consists of a nonrelativistic electron beam which moves above a corrugated periodic structure. An electromagnetic wave is incident on the combined system. The wave is reflected from the structure and a manifold of radiating and evanescent waves are generated. One evanescent mode which is synchronous with the velocity of the beam, interacts with the electrons and can be amplified. The amplified wave is scattered from the structure, thus the radiating waves are also amplified. Expressions for the gain of the device and the form of the radiating waves are obtained. The interaction with the waves alters the characteristics of the beam. We find a nonlinear diffusion equation to describe these changes, and analyze their effects on the gain of the device. It is shown that in the nonlinear regime the gain depends both on the first and second derivatives of the velocity distribution function.

Original languageAmerican English
Pages (from-to)258-261
Number of pages4
JournalNuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Issue number1-2
StatePublished - 10 Dec 1989
Externally publishedYes

Bibliographical note

Funding Information:
One of us (A.R.) acknowledges the support of the fund for Encouragement of Research at the Technion .


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