U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

Massachusetts Institute of Technology (MIT)

Synchrotron Radiation and Free Electron Lasers for Bright X-Rays

Kwang-Je Kim and Ryan Lindberg, Argonne National Lab; Zhirong Huang, SLAC; Daniel Ratner, Stanford University

**Purpose and Audience**

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

**Prerequisites**

Upper division undergraduate courses in classical mechanics and in electromagnetism (at the level of "Introduction to Electrodynamics" by David J. Griffiths).

*It is the responsibility of the student to ensure that they meet the course prerequisites or have equivalent experience. *

**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, relativity.*Spontaneous radiation by an ultra-relativistic electron:*retardation effects and qualitative understanding of basic properties of radiation by relativistic electron beams, radiation formulae, polarization, distinct properties of radiation from bending magnets and from periodic magnetic devices such as wigglers and undulators, magnet design.*Electron beam basics:*electron beam propagation in phase space, emittance and brightness, beam envelopes, storage rings, linacs, energy recovery linacs. Phase space method of paraxial wave optics: brightness, transverse and temporal coherence, matching of radiation beam and electron beam.*Electron motion in an undulator in the presence of a co-propagating radiation beam:*pendulum equation, low gain amplification, intensity build-up and saturation in an FEL oscillator, gain and efficiency.*Maxwell equation:*slowly varying phase and amplitude approximation in 1-D , dimensionless scaling parameters, cubic equation for growth rate, effective energy spread due to electon beam emittance, Maxwell-Vlasov equation, solution via Laplace transformation, start-up from noise, exponential gain, quasi-linear theory for saturation, quantum effects.*Generation of harmonics:*nonlinear harmonic generation, harmonics in FEL oscillators, high-gain harmonic generation, effects of energy spread.*3-D free electron laser theory:*diffraction, electron beam focusing, coupled 3-D Maxwell-Vlasov 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.*Numerical methods:*simulation methods, available simulation codes, fitting formulae.*Self-amplified spontaneous emission for quasi-coherent x-rays:*linac system for high-brightness electron beams, self amplified spontaneous emission as intense, quasi-coherent x-ray sources, power and coherence properties, tapering, gain enhancement scheme, operating facilities.*Seeded harmonic generation for coherent soft x-rays:*harmonic generation, various degrading effects, advanced techniques including echo-assisted scheme. enhancement methods, pre-bunched beams, high-gain FEL projects and simulation codes.*Free electron laser oscillators for hard x-rays:*optical cavity design, out-coupling of optical power, mirror technology, distributed feedback and Smith-Purcell device, FEL oscillator facilities.

**Reading Requirements**

Instructors will provide lecture notes.

**Credit Requirements**

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

**IU/USPAS course number P571**