F E L

Preface

This booklet is just a collection of formulae for the design of a FEL device and a "quick" evaluation of its performance. These formulae, developed over the last thirty years, have been the workhorses allowing a substantive assistance in understanding the FEL Physics. They have provided us with a concrete tool for analysis when more serious and complete computations were not available or demanded long computational times. We decided to present this synopsis for various reasons, some of which are listed below:

1. Over the years we contributed to most of the formulae typically exploited in the analysis of FEL devices
2. We have been involved in the design and the construction of different types of FEL, ranging from Storage Ring to Self Amplified Spontaneous Emission (SASE) devices. We can therefore confirm the usefulness of these formulae as a design tool
3. we are often contacted by young researchers (and not only) asking for help in finding empirical formulae on gain, saturation.. which they heard about, but have found difficult to locate in the vast amount of FEL literature
4. these formulae are often rediscovered and they are not always used correctly.

The above reasons compelled us to collect the formulae which are in our notes often consulted in our daily work. We have reduced the discussion to a minimum and, indeed, we report the formulae and their range of validity without great detailed explanation. It will also be evident that we are essentially referring to "home-made" work and that we do not refer to other contributions, except for the Ming Xie formula, which played a significant role in the development of high gain FEL devices.

As already remarked, the booklet summarizes about thirty years of work in the field, and we owe our gratitude to an almost infinite number of colleagues, who helped us indirectly contributing to the work or giving their criticisms. It is therefore quite impossible to make a complete list, notwithstanding we have the pleasure of recognizing: W. B. Colson - his clear and careful work has strongly influenced our researches, Our Friends and Younger co-workers L. Giannessi, M. Migliorati, A. Renieri, E. Sabia, A. Segreto, and finally it is a pleasure to thank S. G. Biedron and H. P. Freund for suggestions during the early stages of the work. We have forgotten many others, this is our fault only and we sincerely apologize.