Improvement of the crossed undulator design for effective circular polarization control in X-ray FELs

The production of X-ray radiation with a high degree of circular polarization constitutes an important goal at XFEL facilities. A simple scheme to obtain circular polarization control with crossed undulators has been proposed so far. In its simplest configuration the crossed undulators consist of pair of short planar undulators in crossed position separated by an electromagnetic phase shifter. An advantage of this configuration is a fast helicity switching. A drawback is that a high degree of circular polarization (over 90%) can only be achieved for lengths of the insertion devices significantly shorter than the gain length, i.e. at output power significantly lower than the saturation power level. The obvious and technically possible extension considered in this paper, is to use a setup with two or more crossed undulators separated by phase shifters. This cascade crossed undulator scheme is distinguished, in performance, by a fast helicity switching, a high degree of circular polarization (over 95%) and a high output power level, comparable with the saturation power level in the baseline undulator at fundamental wavelength. We present feasibility study and exemplifications for the LCLS baseline in the soft X-ray regime

Extension of self-seeding scheme with single crystal monochromator to lower energy < 5 keV as a way to generate multi-TW scale pulses at the European XFEL

We propose a use of the self-seeding scheme with single crystal monochromator to produce high power, fully-coherent pulses for applications at a dedicated bio-imaging beamline at the European X-ray FEL in the photon energy range between 3.5 keV and 5 keV. We exploit the C(111) Bragg reflection (pi-polarization) in diamond crystals with a thickness of 0.1 mm, and we show that, by tapering the 40 cells of the SASE3 type undulator the FEL power can reach up to 2 TW in the entire photon energy range. The present design assumes the use of a nominal electron bunch with charge 0.1 nC at nominal electron beam energy 17.5 GeV. The main application of the scheme proposed in this work is for single shot imaging of individual protein molecules

On quantum effects in spontaneous emission by a relativistic electron beam in an undulator

Robb and Bonifacio (2011) claimed that a previously neglected quantum effect results in noticeable changes in the evolution of the energy distribution associated with spontaneous emission in long undulators. They revisited theoretical models used to describe the emission of radiation by relativistic electrons as a continuous diffusive process, and claimed that in the asymptotic limit for a large number of undulator periods the evolution of the electron energy distribution occurs as discrete energy groups according to Poisson distribution. We show that these novel results have no physical sense, because they are based on a one-dimensional model of spontaneous emission and assume that electrons are sheets of charge. However, electrons are point-like particles and, as is well-known, the bandwidth of the angular-integrated spectrum of undulator radiation is independent of the number of undulator periods. If we determine the evolution of the energy distribution using a three-dimensional theory we find the well-known results consistent with a continuous diffusive process. The additional pedagogical purpose of this paper is to review how quantum diffusion of electron energy in an undulator with small undulator parameter can be simply analyzed using the Thomson cross-section expression, unlike the conventional treatment based on the expression for the Lienard-Wiechert fields

Theoretical computation of the polarization characteristics of an X-ray Free-Electron Laser with planar undulator

We show that radiation pulses from an X-ray Free-Electron Laser (XFEL) with a planar undulator, which are mainly polarized in the horizontal direction, exhibit a suppression of the vertical polarization component of the power at least by a factor $\lambda_w^2/(4 \pi L_g)^2$, where $\lambda_w$ is the length of the undulator period and $L_g$ is the FEL field gain length. We illustrate this fact by examining the XFEL operation under the steady state assumption. In our calculations we considered only resonance terms: in fact, non resonance terms are suppressed by a factor $\lambda_w^3/(4 \pi L_g)^3$ and can be neglected. While finding a situation for making quantitative comparison between analytical and experimental results may not be straightforward, the qualitative aspects of the suppression of the vertical polarization rate at XFELs should be easy to observe. We remark that our exact results can potentially be useful to developers of new generation FEL codes for cross-checking their results

Scheme to increase the output average spectral flux of the European XFEL at 14.414.4 keV

Techniques like inelastic X-ray scattering (IXS) and nuclear resonance scattering (NRS) are currently limited by the photon flux available at X-ray sources. At $14.4$ keV, third generation synchrotron radiation sources produce a maximum of $10^{10}$ photons per second in a meV bandwidth. In this work we discuss about the possibility of increasing this flux a thousand-fold by exploiting high repetition rate self-seeded pulses at the European XFEL. Here we report on a feasibility study for an optimized configuration of the SASE2 beamline at the European XFEL which combines self-seeding and undulator tapering techniques in order to increase the average spectral flux at $14.4$ keV. In particular, we propose to perform monochromatization at $7.2$ keV with the help of self-seeding, and amplify the seed in the first part of output undulator. The amplification process can be stopped at a position well before saturation, where the electron beam gets considerable bunching at the 2nd harmonic of the coherent radiation. A second part of the output undulator follows, tuned to the 2nd harmonic frequency, i.e. at $14.4$ keV and is used to obtain saturation at this energy. One can further prolong the exchange of energy between the photon and the electron beam by tapering the last part of the output undulator. We performed start-to-end simulations and demonstrate that self-seeding, combined with undulator tapering, allows one to achieve more than a hundred-fold increase in average spectral flux compared with the nominal SASE regime at saturation, resulting in a maximum flux of order $10^{13}$ photons per second in a meV bandwidth

Brightness of Synchrotron radiation from Undulators and Bending Magnets

We consider the maximum of the Wigner distribution (WD) of synchrotron radiation (SR) fields as a possible definition of SR source brightness. Such figure of merit was originally introduced in the SR community by Kim. The brightness defined in this way is always positive and, in the geometrical optics limit, can be interpreted as maximum density of photon flux in phase space. For undulator and bending magnet radiation from a single electron, the WD function can be explicitly calculated. In the case of an electron beam with a finite emittance the brightness is given by the maximum of the convolution of a single electron WD function and the probability distribution of the electrons in phase space. In the particular case when both electron beam size and electron beam divergence dominate over the diffraction size and the diffraction angle, one can use a geometrical optics approach. However, there are intermediate regimes when only the electron beam size or the electron beam divergence dominate. In this asymptotic cases the geometrical optics approach is still applicable, and the brightness definition used here yields back once more the maximum photon flux density in phase space. In these intermediate regimes we find a significant numerical disagreement between exact calculations and the approximation for undulator brightness currently used in literature. We extend the WD formalism to a satisfactory theory for the brightness of a bending magnet. We find that in the intermediate regimes the usually accepted approximation for bending magnet brightness turns out to be inconsistent even parametrically.Comment: 72 pages plus cover, 4 figure