U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

University of New Mexico

The Physics of Free Electron Lasers

Dinh Nguyen and Quinn R. Marksteiner, Los Alamos National Lab

**Purpose and Audience**

This introductory course explores the physics of high-brightness radiation generated by relativistic electrons in free electron lasers (FEL) based on various configurations including low-gain oscillators, high-gain self-amplified spontaneous emission, seeded amplifiers, regenerative amplifiers, high-gain harmonic generation, and echo-enhanced harmonic generation.

* It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience. *

**Objectives**

The purpose of this course is to introduce students, scientists and technologists to the physics of free‑electron lasers (FEL) driven by radio-frequency linear accelerators. Upon completion of this course, the students are expected to understand the basic concepts of how an FEL works. These basic concepts include (but not limited to) bunched beam radiation, energy and density modulations, gain, FEL saturation and synchrotron oscillations. They will be able to analyze the various FEL architectures (oscillator, self-amplified spontaneous emission, seeded amplifiers, regenerative amplifier, high-gain harmonic generation) in terms of electron beam requirements and FEL performance. They will also learn the quasi-coherent nature of the radiation produced by today’s SASE FEL and the contemporary techniques to improve the radiation coherence.

The course consists of lectures in both morning (theory and experiments) and afternoon sessions (simulations). Some of the afternoon sessions involve FEL simulation work. Optional evening sessions can be held to explain homework assignments.

__Introduction__: properties of radiation, special relativity, basic features of FEL, fourth-generation light sources, brightness, pulse format.__Synchrotron radiation:__radiation from bending magnets, wigglers and undulators, harmonics, spectral brightness.__Radiation from ensembles of electrons:__superposition of wave trains, incoherent synchrotron radiation, coherent radiation from bunched beams, bunching factor.__Motions in an undulator:__transverse motion, transverse and longitudinal velocities, ponderomotive wave, pendulum equation, motion in phase-space, energy and density modulations.__One-dimensional FEL theory:__slowly varying envelope approximation, 1-D wave equation, Pierce parameter, 3rd order differential equation, solutions to cubic equation, growth rate.__Low-gain oscillators__: optical resonators, small-signal gain, gain saturation, cavity length detuning, gain and efficiency.__Self-amplified spontaneous emission:__start-up noise, exponential gain, saturation, spectral and coherence properties, 3-D effects, X-ray FELs.__Seeded high-gain amplifier:__optical guiding, group velocity reduction, regenerative amplifier, self-seeding, pre-bunching__Harmonic generation:__nonlinear harmonics, high-gain harmonic generation, echo-enhanced HGHG.__FEL simulations:__1-D simulations (using MATLAB) and a 3-D FEL code (Genesis).

*(to be provided by USPAS) “*Free-Electron Lasers in the Ultraviolet and X-Ray Regime” 2nd edition (Springer 2014) by Peter Schmüser, Martin Dohlus and Jörg Rossbach. Instructors will also provide lecture notes.

Students will be evaluated based on performance as follows: final exam (40% of final grade), homework assignments (30%) and computer class (30%).

**IU/USPAS course number P671**