# Estimates of the Maximum Lasing Frequency and of the Gain in FEL with Parabolic Potential

## TL;DR

This paper derives the resonance frequency and linear gain for odd harmonics in a free-electron laser with a parabolic potential, providing estimates for maximum lasing frequency and gain.

## Contribution

It introduces a method to calculate the resonance frequency and gain in FELs with a parabolic potential, including averaging over electron distributions.

## Key findings

- Resonance frequency of the system identified
- Linear gain for odd harmonics derived
- Estimates of maximum lasing frequency and gain provided

## Abstract

The resonance frequency of the system is found and the linear gain is derived for the odd harmonics of this frequency. Averaging of the gain is carried out over the initial distribution of electrons in a transverse cross section of the beam. Estimates are obtained of the maximum lasing frequency and of the gain at this frequency

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Source: https://tomesphere.com/paper/1701.09134