Evgeni Schneidmiller

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.

Undulator radiation in a waveguide

An analytical approach is proposed to describe undulator radiation near resonance, when the presence of the vacuum-pipe affects radiation properties. This is the case of the far-infrared undulator beamline at the Free-electron LASer (FEL) in Hamburg (FLASH) that is designed to deliver pulses in the TeraHertz (THz) range and can be used for pump-probe experiments as well as for the development of novel electron-beam diagnostics techniques. Since the THz radiation diffraction size exceeds the vacuum-chamber dimensions, characterization of infrared radiation must be performed accounting for the presence of a waveguide. We developed a theory of undulator radiation in a waveguide based on paraxial and resonance approximation. We solved the field equation with a tensor Greens function technique, and extracted figures of merit describing the influence of the vacuum pipe on the radiation pulse as a function of the problem parameters. Our theory makes consistent use of dimensionless analysis and allows treatment and understanding of many asymptotes of the parameter space, together with their region of applicability.

A simple method for timing an XFEL source to high-power lasers

We propose a technique for timing an X-ray free-electron laser (XFEL) to a high-power conventional laser with femtosecond accuracy, yielding the relative jitter between pump and X-ray probe, and allowing sorting of experimental results over a certain time window. The same electron bunch is used to produce both an XFEL pulse and an ultrashort optical pulse by means of an optical radiator downstream of the X-ray undulator. Being produced by the same electron bunch, these pulses are perfectly synchronized. Cross-correlation techniques will allow to determine relative jitter between the optical pulse (and, thus, the XFEL pulse) and a pulse from an external pump-laser. Technical realization of the proposed timing scheme uses an optical-replica synthesizer setup to be installed after the final bunch-compression stage of the XFEL for electron bunch diagnostics purposes. A number of critical issues are quantitatively analyzed.

Theory of space-charge waves on gradient-profile relativistic electron beam: An analysis in propagating eigenmodes

We developed an exact analytical treatment for space-charge waves within a relativistic electron beam in terms of (self-reproducing) propagating eigenmodes. This result is of obvious theoretical relevance as it constitutes one of the few exact solution for the evolution of charged particles under the action of self-interactions. It also has clear numerical applications in particle accelerator physics where it can be used as the first self-consistent benchmark for space-charge simulation programs. Today our work is of practical relevance in FEL technology in relation with all those schemes where an optically modulated electron beam is needed and with the study of longitudinal space-charge instabilities in magnetic bunch compressors.

Quasi-optical theory of FEL amplifier with circular waveguide

Abstract A series of analytic relations for the main characteristics of a FEL amplifier with a circular electron beam, a circular waveguide and a helical undulator are obtained. An analytic solution of the self-consistent field equations at the given conditions at the input into the interaction region is obtained with the Laplace transform technique. The case is considered when the unmodulated electron beam and the radiation from the driving generator is fed into the amplifier input. An asymptotic formula for the gain taking into account the effect of the space charge and the energy spread of the particles in the beam is derived. The results of the calculation results with the analytic formulae are compared with the resu;ts obtained by direct integration on a computer of the self-consistent field equations.

Longitudinal wake field for an electron beam accelerated through an ultrahigh field gradient

Electron accelerators with higher and higher longitudinal field gradients are desirable, as they allow for the production of high-energy beams by means of compact and cheap setups. Laser-plasma acceleration technique appears to constitute the more promising breakthrough in this direction, delivering unprecedent field gradients up to TV/m. In this article we give a quantitative description of the impact of longitudinal wake fields on the electron beam. Our paper is based on the solution of Maxwells equations for the longitudinal field. Our conclusions are valid when the acceleration distance is much smaller than the overtaking length, that is the length that electrons travel as a light signal from the tail of the bunch overtakes the head of the bunch. This condition is well verified for laser-plasma devices. We calculate a closed expression for the impedance and the wake function that may be evaluated numerically. It is shown that the rate of energy loss in the bunch due to radiative interaction is equal to the energy emitted through coherent radiation in the far zone. Furthermore, an expression is found for the asymptotic limit of a large distance of the electron beam from the accelerator compared with the overtaking length. Such expression allows us to calculate analytical solutions for a Gaussian transverse and longitudinal bunch shape. We describe an application of our analytical asymptote by studying the feasibility of a table-top free-electron laser based on laser-plasma driver. Numerical estimations presented in this paper indicate that the effects of the time-dependent energy change induced by the longitudinal wake pose a serious threat to the operation of this device.

Longitudinal impedance and wake from XFEL undulators. Impact on current-enhanced SASE schemes

In this article we derive longitudinal impedance and wake function for an undulator setup with arbitrary undulator parameter, taking into account a finite transverse size of the electron bunch. Earlier studies considered a line density-distribution of electrons instead. We focus our attention on the long-wavelength asymptote (compared with resonance wavelength), at large distance of the electron bunch from the undulator entrance compared to the overtaking length, and for large vacuum-chamber size compared to the typical transverse size of the field. These restrictions define a parameter region of interest for practical applications. We calculate a closed expression for impedance and wake function that may be evaluated numerically in the most general case. Such expression allows us to derive an analytical solution for a Gaussian transverse and longitudinal bunch shape. Finally, we study the feasibility of current-enhanced SASE schemes (ESASE) recently proposed for LCLS, that fall well-within our approximations. Numerical estimations presented in this paper indicate that impedance-induced energy spread is sufficient to seriously degrade the FEL performance.

Theory of nonlinear harmonic generation in free-electron lasers with helical wigglers

Coherent Harmonic Generation (CHG), and in particular Nonlinear Harmonic Generation (NHG), is of importance for both short wavelength Free-Electron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electron-beam energy, and high-average-power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an analytical solution of Maxwells equations, derived with the help of a Greens function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) from helical wigglers vanishes on axis. Our conclusion is in open contrast with results in literature, which include a kinematical mistake in the description of the electron motion.

Tranverse Coherence Properties of X-Ray Beams in Third-Generation Light Sources

Undulator radiation is modelled as a random process, and described as an incoherent superposition of laser-like beams from single electrons. Coherence properties are quantified in terms of statistical correlation functions of the radiation field.

Transverse self-fields within an electron bunch moving in an arc of a circle

As a consequence of motions driven by external forces, self-fields (which are different from the static case) originate within an electron bunch. In the case of magnetic external forces acting on an ultrarelativistic beam, the longitudinal self-interactions are responsible for Coherent Synchrotron Radiation-related phenomena, which have been studied extensively. On the other hand, transverse self-interactions are present too. At the time being, existing theoretical analysis of transverse self-forces deal with the case of a bunch moving along a circular orbit only, without considering the situation of a bending magnet with a finite length. In this paper, we propose an electrodynamical analysis of transverse self-fields which originate, at the position of a test particle, from an ultrarelativistic electron bunch moving in an arc of a circle. The problem is first addressed within a two-particle system. We then extend our consideration to a line bunch with a stepped density distribution, a situation which can be easily generalized to the case of an arbitrary density distribution. Our approach turns out to be also useful in order to obtain a better insight in the physics involved in the case of simple circular motion.