• K. Goldammer, A. Meseck
  BESSY GmbH, Berlin

In the FEL process, bunching and coherent radiation is produced at the fundamental frequency as well as its higher harmonics. BESSY proposes a linac-based cascaded High-Gain Harmonic-Generation (HGHG) free electron laser (FEL) multi-user facility. The BESSY soft X-ray FEL will be seeded by three lasers spanning the spectral range of 230nm to 460nm. Two to four HGHG stages downconvert the seed wavelength to the desired radiation range of 1.24nm to 51nm using higher harmonic bunching. As a surplus, higher harmonic radiation is intrinsically produced in each FEL stage. Radiation on a higher harmonic of the FEL frequency is of high interest because it yields the possibility to reduce the number of FEL stages. This paper details extensive studies of the higher harmonic content of the BESSY FEL radiation. Important aspects of FEL interaction on higher harmonics as resulting from theory and from numerical simulations are discussed. For the case of the BESSY FEL, methods for improving the harmonic content are presented. These methods are examined as to their influence on FEL output power, pulse duration and spectral bandwidth. Focus is laid on the application of higher harmonic radiation to seeding.

Funded by the Bundesministerium für Bildung und Forschung, the state of Berlin and the Zukunftsfonds Berlin

• B.C. Kuske, M. Abo-Bakr, A. Meseck
  BESSY GmbH, Berlin

Funding: Bundesministerium für Bildung und Forschung, the state of Berlin and the Zukunftsfonds Berlin

In present FEL designs, undulators are usually optimized for an electron bunch with properties constant along the bunch length. The central energy, emittance and other parameters are assumed not to vary from slice to slice. Unavoidable timing jitter of the photo cathode laser, and phase and amplitude errors of the RF fields in the injector and the linac result in variations in emittance, energy spread and beam dimensions along the bunch, causing a jitter in the arrival time of the electron bunch. Due to the passage through bunch compressors, the bunch shows a considerable residual energy chirp. Even assuming a perfect and on-time seed laser pulse, the changing properties along the bunch in combination with the arrival time jitter cause varying conditions for the interaction of the electron bunch with the seed laser radiation. This paper talks about how far the BESSY-FEL radiation is affected by the expected time jitter and the realistic bunch profile, and investigates counter measures. The studies are confined to the low energy FEL line generating output at l = 10nm.

• B.C. Kuske, M. Abo-Bakr, K. Goldammer, A. Meseck
  BESSY GmbH, Berlin

Funding: Bundesministerium für Bildung und Forschung, the state of Berlin and the Zukunftsfonds Berlin

Contrary to storage rings, where the electron bunch properties are damped to equilibrium values due to the repeated passages through identical structures, every bunch in a single pass FEL will show individual imprints of it's passage through the linac. Based on ASTRA and ELEGANT tracking studies, realistic bunches were tracked through the BESSY-FEL undulators; the effect of timing errors of the photo cathode laser, and phase and amplitude errors of the RF fields in the injector and the linac on the FEL radiation were studied. The fluctuations of the bunch parameter due to these errors are of the order of magnitude of their variation over the bunch length, reflecting the initial electron distribution and the impact of the passed optics. The unavoidable residual energy chirp in connection with the timing jitter is of concern. The expected shot to shot variations in the FEL output are discussed.

• J.T. Donohue
  CENBG, Gradignan
• J. Gardelle
  CESTA, Le Barp

A simulation of the generation of Smith-Purcell (S-P) radiation at terahertz frequencies is performed using the two-dimensional particle-in-cell code MAGIC. The simulation supposes that a continuous, thin (but infinitely wide), mono-energetic electron beam passes over a diffraction grating, while a strong axial magnetic field constrains the electrons to essentially one-dimensional motion. We simulate two configurations, one similar to the Dartmouth S-P FEL [1], with a low energy continuous beam, and the other similar to the recent MIT experiment which uses a pre-bunched 15 MeV beam [2].

[1] A Bakhtyari, J. E. Walsh, and J. H. Brownell, Phys. Rev. Lett. E 65, 066503 (2002). [2] S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, Phys. Rev. Lett. 94, 054803 (2005)

• R. Bonifacio
  INFN-Milano, Milano
• N. Piovella
  Universita' degli Studi di Milano, MILANO

We formulate a quantum linear theory of the N-particle free-electron laser Hamiltonian model, quantizing both the radiation field and the electron motion, in the steady state regime. Quantum effects such as frequency shift, line narrowing, quantum limitation for bunching and energy spread and minimum uncertainty states are described. Using a second quantization formalism we demonstrate quantum entanglement between the recoiling electrons and the radiation field.

• R. Bonifacio
  INFN-Milano, Milano

We derive a simple analytical solution for the non linear regime in the quasi steady state situation of the high gain Free Electron Laser (FEL) and Collective Atomic Recoil Lasing (CARL) model which up to now have been described only numerically. We show that the system can be described by an exact reduced Hamiltonian which does not contain the field explicitly. We give simple analytical expressions for the field amplitude, frequency shift, bunching factor, particle average momentum and momentum spread, as well as the period of oscillations around the quasi steady state solution, in very good agreement with the numerical values.

• J. Wu, P. Emma, Z. Huang
  SLAC, Menlo Park, California

Funding: Work supported by the U.S. Department of Energy under Contract No. DE-AC02-76SF00515.

Longitudinal space charge (LSC) force can be a main effect driving the microbunching instability in the linac for an x-ray free-electron laser (FEL). In this paper, the LSC-induced beam modulation is studied using an integral equation approach that takes into account the transverse (radial) variation of LSC field. Changes of beam energy and the transverse beam size can be also incorporated. We discuss the validity of this approach and compare it with other analyses as well as numerical simulations. We apply this approach to study the LSC effect in the LCLS accelerator

• A. Gover
  University of Tel-Aviv, Faculty of Engineering, Tel-Aviv

A unified analysis for Superradiant emission from bunched electron beams in various kinds of radiation scheme is presented. Radiation schemes that can be described by the formulation include Pre-bunched FEL (PB-FEL), Coherent Synchrotron Radiation (CSR), Smith-Purcell Radiation, Cerenkov-Radiation, Transition-Radiation and more. The theory is based on mode excitation formulation - either discrete or continuous (the latter - in open structures). The discrete mode formulation permits simple evaluation of the spatially coherent power and spectral power of the source. These figures of merit of the radiation source are useful for characterizing and comparing the performance of different radiation schemes. When the bunched electron beam emits superradiantly, these parameters scale like the square of the number of electrons, orders of magnitude more than spontaneous emission. The formulation applies to emission from single electron bunches, periodically bunched beams, or emission from a finite number of bunches in a macro-pulse. We have recently employed the formulation to calculate a ne kind of coherent radiation from electron beam: enhanced Electron Spin Resonance Emission from a polarized electron beam. Estimates of the characteristics and possible applications of this effect will be presented.