M.V. Yurkov

The physics of free electron lasers

Introduction.- One-Dimensional Theory of the FEL Amplifier.- One-Dimensional Theory of the FEL Oscillator.- Diffraction Effects in the FEL Amplifier.- Waveguide FEL.- FEL Amplifier Starting from Shot Noise.- Appendices.- References.- Index

Possible application of X-ray optical elements for reducing the spectral bandwidth of an X-ray SASE FEL

Abstract A new design for a single pass X-ray Self-Amplified Spontaneous Emission (SASE) FEL is proposed. The scheme consists of two undulators and an X-ray monochromator located between them. The first stage of the FEL amplifier operates in the SASE linear regime. After the exit of the first undulator the electron bunch is guided through a non-isochronous bypass and the X-ray beam enters the monochromator. The main function of the bypass is to suppress the modulation of the electron beam induced in the first undulator. This is possible because of the finite value of the natural energy spread in the beam. At the entrance to the second undulator the radiation power from the monochromator dominates significantly over the shot noise and the residual electron bunching. As a result the second stage of the FEL amplifier operates in the steady-state regime when the input signal bandwidth is small with respect to that of the FEL amplifier. Integral losses of the radiation power in the monochromator are relatively small because grazing incidence optics can be used. The proposed scheme is illustrated for the example of the 6 nm option SASE FEL at the TESLA Test Facility under construction at DESY. As shown in this paper the spectral bandwidth of such a two-stage SASE FEL (Δλ/λ⋍ 5 × 10 −5 ) is close to the limit defined by the finite duration of the radiation pulse. The average brilliance is equal to 7 × 10 24 photons/(s × mrad 2 × mm 2 × 0.1% bandw.) which is by two orders of magnitude higher than the value which could be reached by the conventional SASE FEL. The monochromatization of the radiation is performed at a low level of radiation power (about 500 times less than the saturation level) which allows one to use conventional X-ray optical elements (grazing incidence grating and mirrors) for the monochromator design.

Statistical properties of radiation from VUV and X-ray free electron laser

The paper presents a comprehensive analysis of the statistical properties of the radiation from a self-amplified spontaneous emission (SASE) free electron laser operating in linear and nonlinear mode. The investigation has been performed in a one-dimensional approximation assuming the electron pulse length to be much larger than a coherence length of the radiation. The following statistical properties of the SASE FEL radiation have been studied in detail: time and spectral field correlations, distribution of the fluctuations of the instantaneous radiation power, distribution of the energy in the electron bunch, distribution of the radiation energy after the monochromator installed at the FEL amplifier exit and radiation spectrum. The linear high gain limit is studied analytically. It is shown that the radiation from a SASE FEL operating in the linear regime possesses all the features corresponding to completely chaotic polarized radiation. A detailed study of statistical properties of the radiation from a SASE FEL operating in linear and nonlinear regime has been performed by means of time-dependent simulation codes. All numerical results presented in the paper have been calculated for the 70 nm SASE FEL at the TESLA Test Facility being under construction at DESY.

FAST: a three-dimensional time-dependent FEL simulation code

In this report we briefly describe the three-dimensional, time-dependent FEL simulation code FAST. The equations of motion of the particles and Maxwells equations are solved simultaneously taking into account the slippage effect. Radiation fields are calculated using an integral solution of Maxwells equations. A special technique has been developed for fast calculations of the radiation field, drastically reducing the required CPU time. As a result, the developed code allows one to use a personal computer for time-dependent simulations. The code allows one to simulate the radiation from the electron bunch of any transverse and longitudinal bunch shape; to simulate simultaneously an external seed with superimposed noise in the electron beam; to take into account energy spread in the electron beam and the space charge fields; and to simulate a high-gain, high-efficiency FEL amplifier with a tapered undulator. It is important to note that there are no significant memory limitations in the developed code and an electron bunch of any length can be simulated.

On the coherent radiation of an electron bunch moving in an arc of a circle

Abstract Existing theories of coherent synchrotron radiation (CSR) are developed for the motion of an electron bunch on a circular orbit and do not describe the case of finite magnet length. In this paper we present the CSR theory for a bunch of any length moving in an arc of a finite angle. The radiative interaction of the electrons in the bunch is analyzed for a line charge distribution using an ultrarelativistic approximation. It is shown in particular that this interaction is important not only inside the magnet but also on the straight part of the trajectory after the magnet. Detailed analytical study of the CSR effects in the electron bunch with a stepped distribution of the charge density has been performed. The simple analytical technique of the radiative force calculation has been developed. The analytical solutions in the form of elementary functions are obtained for the radiative interaction force, for the energy loss distribution along the bunch and for the total energy loss of the bunch. The latter result is confirmed with calculation of the energy of coherent radiation in the far zone. The criterium for the applicable region of the existing theories to the case of a finite magnet length is obtained.

Self-amplified spontaneous emission FEL with energy-chirped electron beam and its application for generation of attosecond x-ray pulses

Influence of a linear energy chirp in the electron beam on a SASE FEL operation is studied analytically and numerically using 1-D model. Explicit expressions for Greens functions and for output power of a SASE FEL are obtained for high-gain linear regime in the limits of small and large energy chirp parameter. Saturation length and power versus energy chirp parameter are calculated numerically. It is shown that the effect of linear energy chirp on FEL gain is equivalent to the linear undulator tapering (or linear energy variation along the undulator). A consequence of this fact is a possibility to perfectly compensate FEL gain degradation, caused by the energy chirp, by means of the undulator tapering independently of the value of the energy chirp parameter. An application of this effect for generation of attosecond pulses from a hard X-ray FEL is proposed. Strong energy modulation within a short slice of an electron bunch is produced by few-cycle optical laser pulse in a short undulator, placed in front of the main undulator. Gain degradation within this slice is compensated by an appropriate undulator taper while the rest of the bunch suffers from this taper and does not lase. Three-dimensional simulations predict that short (200 attoseconds) high-power (up to 100 GW) pulses can be produced in Angstroem wavelength range with a high degree of contrast. A possibility to reduce pulse duration to sub-100 attosecond scale is discussed.

Coherence properties of the European XFEL

The European x-ray free-electron laser (XFEL) provides x-ray self-amplified spontaneous emission (SASE) FEL radiation in the wavelength range from 0.1 to 3 nm using three undulator systems. The SASE mode of operation at the European XFEL defines specific behavior of longitudinal and transverse coherence properties. In this paper, we describe the evolution of the temporal and transverse correlation functions along the undulator length, and we extract the corresponding evolution of coherence time and degree of transverse coherence as typical figures of merit. Generation of coherent radiation inside the FEL undulators is followed by beam transport to the experiments. During transport, the total number of coherent modes is preserved, but the wavefront can be disturbed, and we analyze the conditions under which this occurs. It is emphasized that the development of experimental observables for the degree of coherence and wavefront properties will be important for experiments using coherent x-ray radiation.

Study of a noise degradation of amplification process in a multistage HGHG FEL

Recent advances in free-electron laser (FEL) physics and accelerator techniques led to the possibility of generating coherent X-ray radiation with self-amplified spontaneous emission (SASE) FEL. Despite the fact that the SASE FEL is capable of providing much higher peak brilliance than spontaneous synchrotron radiation sources, there is a great potential for improvements. The brilliance of the output radiation from the SASE FEL is mainly limited by the poor longitudinal coherence of the radiation. One of the approaches to obtain fully coherent X-ray radiation uses frequency multiplication, a scheme known as the high-gain harmonic generation (HGHG) FEL. In the HGHG FEL the radiation output is derived from a coherent subharmonic laser seed pulse. Consequently, the optical properties of the HGHG FEL are expected to reflect the characteristics of the high-quality seed laser. This paper is devoted to the investigation of the physical processes in the HGHG FEL. Our studies have shown that the frequency multiplication process produces noise degradation proportional at least to the square of the frequency multiplication factor. This prevents operation of HGHG FEL at a very short wavelength range.

A new technique to generate 100 GW-level attosecond X-ray pulses from the X-ray SASE FELs

Abstract We propose a scheme for generation of single 100 GW 300-as pulse in the X-ray free electron laser with the use of a few cycles optical pulse from Ti:sapphire laser system. Femtosecond optical pulse interacts with the electron beam in the two-period undulator resonant to 800 nm wavelength and produces energy modulation within a slice of the electron bunch. Following the energy modulator the electron beam enters the first part of the baseline gap-adjustable X-ray undulator and produces SASE radiation with 100 MW-level power. Due to energy modulation the frequency is correlated to the longitudinal position within the few-cycle-driven slice of the SASE radiation pulse. The largest frequency offset corresponds to a single-spike pulse in the time domain which is confined to one half-oscillation period near the central peak electron energy. After the first undulator the electron beam is guided through a magnetic delay which we use to position the X-ray spike with the largest frequency offset at the “fresh” part of the electron bunch. After the chicane the electron beam and the radiation produced in the first undulator enter the second undulator which is resonant with the offset frequency. In the second undulator the seed radiation at reference frequency plays no role, and only a single (300 as duration) spike grows rapidly. The final part of the undulator is a tapered section allowing to achieve maximum output power 100–150 GW in 0.15 nm wavelength range. Attosecond X-ray pulse is naturally synchronized with its fs optical pulse which reveals unique perspective for pump–probe experiments with sub-femtosecond resolution.

Klystron instability of a relativistic electron beam in a bunch compressor

In this paper, we consider a klystron-like mechanism of amplification of parasitic density modulations in an electron bunch passing a magnetic bunch compressor. Analytical expressions are derived for the small-signal gain. The effect of wakefields in front of the bunch compressor is analyzed by using a model of linear compression which assumes linear correlated energy chirp and linear dependence of a path length on energy deviation. Analysis of the density modulation growth due to coherent synchrotron radiation inside bends of the magnetic bunch compressor is done for the simplified case of no correlated energy chirp (no compression). Analytical results of this paper can be used for benchmarking numerical simulation codes.