FEL simulation code FAST Free-Electron Laser at the TESLA Test Facility Generic name FAST stands for a set of codes for ``full physics'' analysis of FEL amplifier: Eigenvalue problem (analysis of beam radiation modes) Linear simulation code (initial-value problem) Nonlinear simulation code E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov Workshop on Start-to-End Simulations of X-RAY FELs Zeuthen, August 21, 2003 Analysis of beam radiation modes

Free-Electron Laser at the TESLA Test Facility FAST code: physical model Calculation of the fields is based on the integral solution of Maxwell's equations (paraxial approximation): A high accuracy of calculations is achieved due to use of exact integral solution. There are no problems with an effect of artificial boundary conditions which is unavoidable in algorithms solving partial derivative equations. Motion of particles - approximation of parallel beam. Applicability region: L f /(2  ). min(1, /(2  ); L g. , or B. 1. U c is space charge term,   is individual betatron shift of the detuning, and C  (r) is offset-correlated one. Linear simulation code solves equations for the first harmonic of the beam bunchig:

Free-Electron Laser at the TESLA Test Facility FAST code: Main features The code allows one to simulate: FEL amplifier driven by electron bunch of any length with slice parameters changing along the bunch. Start-up from shot noise. Simultaneously external seed with superimposed noise in the electron beam. High-efficiency FEL amplifier with tapered undulator. Harmonic generation. Post-processor codes calculate: field distribution in the near and far diffraction zone, spectrum, time, space and spectral correlation functions, probability distributions of the radiation power and the radiation energy.

Free-Electron Laser at the TESLA Test Facility FAST code: Testing in SASE mode with analytical solutions

Free-Electron Laser at the TESLA Test Facility FAST code: Testing in SASE mode with analytical solutions

Free-Electron Laser at the TESLA Test Facility FAST code: Testing in SASE mode with analytical solutions

Free-Electron Laser at the TESLA Test Facility FAST code: Testing in SASE mode with analytical solutions

Free-Electron Laser at the TESLA Test Facility FAST code: Testing in SASE mode with analytical solutions

Free-Electron Laser at the TESLA Test Facility Undulator period: w Undulator field: H w Radiation wavelength: Energy of the electron: E 0 Electron beam current: I Energy spread in the beam:  E Emittance of the electron beam:  Focusing beta function:  Diffraction parameter: B = 2   r 2  /c Energy spread parameter:  T 2 =  _E 0 2 /(E 0 2  2 ) Parameter of betatron oscillations: k  = 1/(   ) Space charge parameter:  p 2 = 2c 2 /(  s  r  ) 2 Efficiency parameter:  = c  2z  /  Detuning parameter: C = [k w -  /(2c  z 2 )]/  Gain parameter:  = [ I  2  s 2 /(I A c 2  z 2  ) ] 1/2 Dimensional parameters of FEL amplifier: Parameters of FEL physics: Application of similarity techniques for analysis of simulation results is a powerful tool for deep insight into the FEL physics. Examples: limits for minimum wavelength in classical FEL amplifier and XFEL /NIM A374(1996)401/:

Free-Electron Laser at the TESLA Test Facility Conclusion

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Free-Electron Laser at the TESLA Test Facility FAST code: Testing in SASE mode with analytical solutions

Free-Electron Laser at the TESLA Test Facility FAST code: Testing in SASE mode with analytical solutions

Free-Electron Laser at the TESLA Test Facility FAST code: Main features Physical model incorporates 3-D description of the radiation field, space charge, energy spread, emittance, shot noise. A set of simulation codes consists of two parts: steady-state and time- dependent. Each part contains linear and nonlinear (macroparticle) code. All codes use the same field solver. Special technique has been developed for fast calculations of the retarded fields. Linear codes are very fast, typically by 2 orders of magnitude faster than nonlinear codes. The code allows one to simulate: - The radiation from the electron bunch of any longitudinal bunch shape (temporal, spatial and spectral characteristics, correlation functions, etc). - Simultaneously external seed with superimposed noise in the electron beam. - High-gain, high-efficiency FEL amplifier with tapered undulator. - Harmonic generation. Electron bunch of any length and any longitudinal profile can be simulated. The accuracy of the simulations with the code FAST can be well controlled, and it has been tested thoroughly with analytical solutions in steady-state and SASE modes.

Free-Electron Laser at the TESLA Test Facility FAST code: output parameters The output of the code are the arrays for the field values in the Fresnel diffraction zone. Post-processor programs are used for calculation of: -- field distribution in the far diffraction zone, -- spectrum, -- time, space and spectral correlation functions, -- probability distributions of the radiation power and the radiation energy.

Analysis of beam radiation modes