U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Free-Electron Lasers – Theory and Practice course

Sponsoring University:

University of New Mexico


Free-Electron Lasers – Theory and Practice


Dinh C. Nguyen, Steven J. Russell and Nathan A. Moody, Los Alamos National Lab

Purpose and Audience
The purpose of this course is to introduce students to the physics and technology of free‑electron lasers (FEL) driven by radio-frequency linear accelerators (linac) with energy recovery. This course is suitable for students considering a career in FEL or workers from other fields planning to use FEL for their applications. This course also provided a broad background to engineers and technicians working on accelerator and beam technologies.

Courses in College Physics and first year Calculus.

This introductory course avoids heavy mathematical treatment and focuses on intuitive understanding of the free-electron laser and its sub-systems. The physics of wiggler/undulator radiation, bunching of electrons in a ponderomotive potential created by the radiation and the wiggler field, and rudimentary treatments of high-brightness electron beam physics will be explored. Emphasis will be placed on practical design considerations and comparisons of various FEL sub-systems such as the electron injectors (DC, normal‑conducting, and superconducting RF), cathodes (thermionic, photocathode, and field-emission), superconducting RF linac (elliptical and spoke), high-power microwave sources (klystrons, inductive output tubes, and solid-state), and power couplers (waveguides and coaxial). Upon completion of this course, the students are expected to understand the basic working relationships of the various sub-systems of an energy recovery linac FEL. They will also comprehend the basic concepts of beam dynamics (normalized rms emittance, brightness, phase-space, etc.) and will be able to analyze different FEL architectures (oscillator, amplifier, SASE, regenerative amplifier) in terms of electron beam requirements.

Instructional Method
This course includes a series of daily lectures, followed by computer lab sessions in the afternoon. The lecture handouts will be provided on the first day of the course. Daily problem sets will be assigned and it is expected that they be completed outside of scheduled class sessions, usually in the evening before the day they are due, except on the last day when final exams are given. The computer lab sessions will introduce students to FEL and beam dynamics simulations. Students will have the opportunities to model the electron’s transverse and longitudinal motions in a wiggler, FEL radiation, synchrotron motion, wiggler and optics design, and FEL efficiency calculations. Students will write a report on the simulations provided for the course lab component grade.

Course Content
Introductory materials will include electron motions in a wiggler, Lorenz transformation, relativistic Doppler shifts, wiggler radiation and FEL interaction. Fundamental concepts such as the pendulum equation, bunching, gain, and saturation will be covered. Different FEL architectures such as the oscillator, amplifier, SASE, and regenerative amplifier will be presented. Basic components of an FEL such as electron injectors, radio frequency linac, microwave systems, electron beam optics (bends, focusing quadrupoles, etc.), wiggler, cryoplant, and beam dump will be described. Different electron injectors (DC, normal-conducting and superconducting RF) and RF accelerators (superconducting elliptical and superconducting spoke) will be compared. Basic beam dynamics such as space charge effects, emittance compensation, photoemission, field emission, electron beam optics, phase space, brightness, bunch compression, coherent synchrotron radiation, and slippage will be explored. Advanced concepts such as efficiency enhancements using energy detuning and non-uniform (tapered) wigglers will be reviewed. Examples of fourth-generation light (x-rays) sources and high-power IR FELs will be analyzed.

Reading Requirements
(to be provided by the USPAS) “Theory and Practice of Free-Electron Lasers” handouts by Dinh C. Nguyen. Suggested other reference: Charle Brau, "Free Electron Lasers," Academic Press, Inc. 1990.

Credit Requirements
Students will be evaluated based on performance: final exam (30 % of final grade), homework assignments (30 % of final grade) computer lab sessions (40 % of final grade).