Evgeni Saldin

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.

A novel self-seeding scheme for hard X-ray FELs

Typical SASE XFEL pulses exhibit poor longitudinal coherence, a characteristic inherited from the start-up from shot noise. Self-seeding schemes are an answer to the call for improved longitudinal coherence. If applied to already working or designed XFELs, these schemes are subject to constraints, including minimal change to the baseline design, and possibility to recover the baseline mode of operation. In this work we propose a novel single-bunch self-seeding method, based on a particular kind of monochromator that satisfies these constraints. We will limit ourselves to the analysis of the simplest possible configuration, consisting of an input undulator and an output undulator, separated by our novel monochromatization stage. Such a stage consists of a weak few-meter long chicane, acting as a tunable delay stage, washing out the electron beam microbunching, and creating a transverse offset for the monochromator. In essence, the monochromator consists of a single crystal in Bragg-transmission geometry, which operates as a bandstop filter for the transmitted X-ray SASE radiation pulse. When the incident angle and the spectral contents of the incoming beam satisfy the Bragg diffraction condition, the temporal waveform of the transmitted radiation pulse shows a long monochromatic tail, whose duration is inversely proportional to the bandwidth of the absorption line in the transmittance spectrum. The magnetic chicane is tuned to shift the electron bunch on top of the monochromatic wake created by the bandstop filter thus selecting (temporal windowing) a part of the wake. By this, the electron bunch is seeded with a radiation pulse characterized by a bandwidth much narrower than the natural FEL bandwidth. The output power from our setup can be further increased by tapering the magnetic field of the undulator, yielding a tremendous increase in peak brightness with respect to the baseline mode of operation. In this work we present a feasibility study and exemplifications for the LCLS, and we discuss advantages of our method compared to other self-seeding techniques.

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.

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.

Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources

Abstract This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert–Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical (geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 up to 10 3 A ). Sometimes, the so-called Gaussian–Schell model, that is widely used in statistical optics in the description of partially coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the cross-spectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.

On a linear theory of an FEL amplifier with an axisymmetric electron beam

Abstract The paper touches upon the questions of the linear theory of an FEL amplifier with an axisymmetric electron beam. An FEL model is discussed wherein diffraction effects, space charge fields and energy spread of electrons in the beam are taken into account. The rigorous solutions of the eigenvalue problem have been found for the stepped and bounded parabolic electron beam profiles. The multilayer approximation method has been used to solve the eigenvalue problem for the beams with an arbitrary gradient profile of current density. For the stepped electron beam profile the initial problem is solved analytically with the Laplace transform technique and in the case of the arbitrary gradient profile with the numerical solution of the self-consistent field equations. The optimum conditions of the external radiation field focusing on the electron beam have been obtained.

Terawatt-scale sub-10-fs laser technology ¿ key to generation of GW-level attosecond pulses in X-ray free electron laser

We propose a technique for the production of attosecond X-ray pulses which is based on the use of X-ray SASE FEL combined with a femtosecond laser system. A few-cycle optical pulse from a Ti:sapphire laser interacts with the electron beam in a 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 X-ray undulator and produces SASE radiation. Due to energy modulation the frequency is correlated to the longitudinal position within the few-cycle-driven slice of 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. The selection of single-spike pulses is achieved by using a crystal monochromator after the X-ray undulator. Our studies show that the proposed technique is capable to produce 300-as long single pulses with GW-level output power in the 0.1 nm wavelength range, and is applicable to the European X-Ray Laser Project XFEL and the Linac Coherent Light Source at SLAC.

Diffraction effects in the self-amplified spontaneous emission FEL

In this paper we present a systematic approach for analytical description of SASE FEL (SASE: self-amplified spontaneous emission) in the linear mode. We calculate the average radiation power, radiation spectrum envelope, angular distribution of the radiation intensity in far zone, longitudinal and transverse correlation functions, degree of transverse coherence etc. Using the results of analytical calculations presented in reduced form, we analyze various features of the SASE FEL in the linear mode. The general result is applied to the special case of an electron beam having Gaussian profile and Gaussian energy distribution. These analytical results can serve as a primary standard for testing the codes. In this paper we present numerical study of the process of amplification in the SASE FEL using three-dimension time-dependent code FAST. Comparison with analytical results shows that in the high-gain linear limit there is good agreement between the numerical and analytical results. It has been found that even after finishing the transverse mode selection process the degree of transverse coherence of the radiation from SASE FEL visibly differs from unity. This is consequence of the interdependence of the longitudinal and transverse coherence. The SASE FEL has poor longitudinal coherence which develops slowly with the undulator length thus preventing a full transverse coherence.