U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

University of California, Santa Cruz

Synchrotron Radiation and Free Electron Lasers

Kwang-Je Kim and Yin-e Sun, Argonne National Lab and Zhirong Huang, SLAC

**Purpose and Audience**

This course is an introduction to the physics of high-brightness radiation beams, the performance of which have been increased remarkably recently by use of insertion devices in synchrotron radiation facilities and by the development of free electron laser (FEL) oscillators and high-gain amplifiers. Specifically, the course is designed toward students and scientists who are interested in the physics and technology of high brightness electron beams as drivers for the production of x-ray photons in the form of synchrotron radiation and FELs.

**Prerequisites**

Classical Mechanics and Electromagnetism.

**Instructional Method**

The course consists of lectures in both morning (3 hrs. per class day), and afternoon sessions (2 hrs. per class day). In addition, afternoon exercise sessions are planned to assign and explain homework and to demonstrate computer simulations.

**Course Content**

*Introduction: *coherent and incoherent radiation sources, quest for higher brightness.

*Fundamentals of electron and radiation beam propagation*: electron beam propagation in phase space, emittance and brightness, beam envelopes, phase space method of paraxial wave optics, transverse and temporal coherence, matching of radiation beam and electron beam.

*Spontaneous radiation by ultra-relativistic electrons*: retardation effects and qualitative understanding of basic properties of radiation by relativistic electron beams, radiation formulae, distinct properties of radiation from bending magnets and from periodic magnetic devices such as wigglers and undulators, magnet design, storage rings and energy recovery linacs.

*Interaction of electron and radiation beams in an undulator*: electron motion in the presence of a co-propagating radiation beam (pendulum equation), low gain amplification, Maxwell equation, interaction of electron-radiation system in 1-D, dimensionless scaling parameters, cubic equation for growth rate, effective enegy spread due to electon beam emittance, Maxwell-Klimontovich equation, solution via Laplace transformation, start-up from noise, exponential gain, quasi-linear theory for saturation, quantum effects.

*3-D free electron laser theory*: diffraction, electron beam focusing, coupled 3-D Maxwell-Klimontovitch equation, integration via unperturbed trajectories, small signal regime, Van-Kampen’s normal mode expansion, approximate solution via variational method, eigenvalue equation, dispersion relation with four scaled parameters, gain guiding and transverse coherence, fitting formulae. *(The goal in this rather mathematical section during the lecture will not be in elaborate details but to appreciate the beauty of the theoretical construction!)*

*Free electron laser oscillators*: intensity build-up and saturation in an optical cavity, gain and efficiency, optical cavity design, out-coupling of optical power, mirror technology, distributed feedback and Smith-Purcell device, FEL oscillator facilities.

*Single-pass, high-gain FELs*: linac system for high-brightness electron beams, self amplified spontaneous emission as intense, quasi-coherent x-ray sources, power and coherence properties, seeded schemes for higher temporal coherence, harmonic generation, magnet imperfection, advanced techniques including pulse slicing, undulator tapering, gain enhancement methods, pre-bunched beams, high-gain FEL projects and simulation codes.

**Reading**** Requirements**

Instructors will provide lecture notes.

**Credit Requirements**

Students will be evaluated based on homework assignments (60%), and final exam (40%).