U.S. Particle Accelerator School

U.S. Particle Accelerator School

America's National School of Accelerator Science and Technology

Michigan State University (ONLINE)

Synchrotron Radiation and Free Electron Lasers for Bright X-Rays

Ryan Lindberg, Argonne National Lab; Kwang-Je Kim, University of Chicago and Argonne National Lab; Zhirong Huang, SLAC National Accelerator Lab

This graduate-level course is an introduction to the physics of high-brightness x-ray beams, the performance of which has been significantly increased through the 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 graduate students, scientists, and engineers 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 including special relativity (e.g., at the level of

The course consists of daily lectures and guided problem and simulation laboratory sessions). The problem and simulation lab sessions will be used to: assign and explain homework, demonstrate some FEL dynamics using a provided 1D Matlab code, and to introduce the student to common 2D and 3D codes such as GENESIS and GINGER. Instructors and TAs will be available to provide help with regularly assigned problem sets.

*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 produced by relativistic electron beams, radiation formulae, polarization, distinct properties of radiation from bending magnets and from periodic magnetic devices such as wigglers and undulators. Basics of magnet design will also be covered.*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 the 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 equations:*slowly varying phase and amplitude approximation in 1-D , dimensionless scaling parameters, cubic equation for growth rate, effective energy spread due to electron beam emittance.- Klimontovich equation: introduce Klimontovich function and its evolution equation representing electrons’ phase space motion retaining the discreteness of electrons by means of delta functions.
- Perturbation scheme for coupled Maxwell-Klimontovich equations: The zeroth order for the smooth background and the first order for the EM interaction and the electrons’ discreteness, solution of the first order, linearlized equations 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 equations, integration via unperturbed trajectories, small signal regime, Van-Kampen’s normal mode expansion, approximate solution via variational methods, 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 **

*(To be provided by the USPAS) *“Synchrotron Radiation and Free-Electron Lasers: Principles of Coherent X-Ray Generation,” by Kwang-Je Kim, Zhirong Huang, and Ryan Lindberg, Cambridge University Press (2017).

**Credit Requirements **

Students will be evaluated based on daily homework assignments (60%), and a comprehensive

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