# Growth Rates in Smith-Purcell FEL

## TL;DR

This paper investigates the growth rates of Smith-Purcell free-electron lasers (SPFEL) with rectangular gratings, introducing a new calculation method and analyzing how growth rates depend on various parameters.

## Contribution

A novel method for calculating partial amplitude coefficients in SPFEL with rectangular gratings and analysis of growth rate dependencies.

## Key findings

- Growth rate dependence on harmonic number
- Growth rate dependence on beam current
- Growth rate dependence on observation angle

## Abstract

In the framework of the earlier derived dispersion equation, we study induced Smith Purcell (SP) radiation of relativistic electron beam in the absence of a resonator. We offer a new method for calculation of coefficients for partial amplitudes in the case of rectangular grating. Using this method we calculate the growth rate of the SPFEL with a rectangular grating. The growth rate dependences on harmonic number, beam current, observation angle and relativistic factor are presented.

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Source: https://tomesphere.com/paper/1702.00678