arXiv subjects

Evgeni Saldin

Publications and source records attributed to Evgeni Saldin.

At least 19 recordsLinked to original sources

arXiv2022

Effect of Aberration of Light in X-ray Free Electron Lasers

We discuss the physics of a microbunched electron beam kicked by the dipole field of a corrector magnet by describing the kinematics of coherent undulator radiation after the kick. Particle tracking shows that the electron beam direction changes after the kick, while the orientation of the microbunching wavefront stays unvaried. Therefore, electrons motion and wavefront normal have different directions. Coherent radiation emission in a downstream undulator is expected to be dramatically suppressed as soon as the kick angle becomes larger than the divergence of the output radiation. In fact, according to conventional treatments, coherent radiation is emitted along the normal to the microbunching wavefront. Here we show that kinematics predicts a surprising effect. Namely, a description of coherent undulator radiation in the laboratory frame yields the radical notion that, due light aberration, strong coherent radiation is produced along the direction of the kick. We hold a recent FEL study made at the LCLS as a direct experimental evidence that coherent undulator radiation can be kicked by an angle of about five times the rms radiation divergence without suppression. We put forward our kinematical description of this experiment.

physics.acc-ph↗

arXiv2022

Modulated Electron Bunch with Amplitude Front Tilt in an Undulator

In a previous paper we discussed the physics of a microbunched electron beam kicked by the dipole field of a corrector magnet by describing the kinematics of coherent undulator radiation after the kick. We demonstrated that the effect of aberration of light supplies the basis for understanding phenomena like the deflection of coherent undulator radiation by a dipole magnet. We illustrated this fact by examining the operation of an XFEL under the steady state assumption, that is a harmonic time dependence. We argued that in this particular case the microbunch front tilt has no objective meaning; in other words, there is no experiment that can discriminate whether an electron beam is endowed with a microbunch front tilt of not. In this paper we extend our considerations to time-dependent phenomena related with a finite electron bunch duration, or SASE mode of operation. We focus our attention on the spatiotemporal distortions of an X-ray pulse. Spatiotemporal coupling arises naturally in coherent undulator radiation behind the kick, because the deflection process involves the introduction of a tilt of the bunch profile. This tilt of the bunch profile leads to radiation pulse front tilt, which is equivalent to angular dispersion of the output radiation. We remark that our exact results can potentially be useful to developers of new generation XFEL codes for cross-checking their results.

physics.acc-ph↗

arXiv2022

Misconception Regarding Conventional Coupling of Fields and Particles in XFEL Codes

Maxwell theory is usually treated in the lab frame under the standard time order (light-signal clock synchronization). Particle tracking in the lab frame usually treats time as an independent variable. Then, the evolution of electron beams is treated according to the absolute time convention (non-standard clock synchronization). This point has never received attention in the accelerator community. There are two ways of coupling fields and particles. The first, Lorentz's way, consists in `translating' Maxwell's electrodynamics to the absolute time world-picture. The second, Einstein's way, consists in `translating' particle tracking results to the electromagnetic world-picture. Conventional particle tracking shows that the electron beam direction changes after a transverse kick, while the orientation of the microbunching fronts stays unvaried. We show that under Einstein's time order, in the ultrarelativistic asymptote the orientation of the planes of simultaneity is always perpendicular to the electron beam velocity. This allows for the production of coherent undulator radiation from a modulated electron beam in the kicked direction without suppression. We hold a recent FEL study at the LCLS as experimental evidence of microbunching wavefront readjusting after a large kick. In a previous paper we quantitatively described this result invoking the aberration of light, corresponding to Lorentz's way of coupling fields and particles. Here we give details of the Lorentz's approach used in that paper. We also demonstrate that an `inverse translation' of particle tracking results to the standard time order resolves puzzles related with the strong qualitative disagreement between simulations and experiments. Previous simulation results in ultrarelativistic electron beam physics should be reexamined in the light of the difference between particle tracking and electromagnetic world-pictures.

physics.acc-ph↗

arXiv2022

Evidence of Wigner Rotation Phenomena in the Beam Splitting Experiment at the LCLS

A result from particle tracking states that, after a microbunched electron beam is kicked, its trajectory changes while the orientation of the microbunching wavefront remains as before. Experiments at the LCLS showed that radiation in the kicked direction is produced practically without suppression. This could be explained if the orientation of the microbunching wavefront is readjusted along the kicked direction. In previous papers we showed that when the evolution of the electron beam modulation is treated according to relativistic kinematics, the orientation of the microbunching wavefront in the ultrarelativistic asymptotic is always perpendicular to the electron beam velocity. There we refrained from using advanced theoretical concepts to explain or analyze the wavefront rotation. For example, we only hinted to the relation of this phenomenon with the concept of Wigner rotation. This more abstract view of wavefront rotation underlines its elementary nature. The Wigner rotation is known as a fundamental effect in elementary particle physics. The composition of non collinear boosts does not result in a simple boost but, rather, in a Lorentz transformation involving a boost and a rotation, the Wigner rotation. Here we show that during the LCLS experiments, a Wigner rotation was actually directly recorded for the first time with a ultrarelativistic, macroscopic object: an ultrarelativistic electron bunch in an XFEL modulated at nm-scale of the size of about 10 microns. Here we point out the role of Wigner rotation in the analysis and interpretation of experiments with ultrarelativistic, microbunched electron beams in FELs. After the beam splitting experiment at the LCLS it became clear that, in the ultrarelativistic asymptotic, the projection of the microbunching wave vector onto the beam velocity is a Lorentz invariant, similar to the helicity in particle physics.

physics.acc-ph↗

arXiv2019

Wigner Rotation: Theory and Application to Practical Relativistic Engineering Problems

The standard expression for the Wigner rotation leads to incorrect result for the wavefront rotation. The results for the Wigner rotation in the Lorentz lab frame obtained by many experts on special relativity such as Moeller and Jackson, are incorrect. They overestimate the angle of the Wigner rotation by a factor $γ$ compared to its real value, and the direction of the rotation is also determined incorrectly. In 1959, Bargman, Michel, and Telegdi (BMT) proposed a consistent relativistic theory for the dynamics of the spin as observed in the lab frame, which was successfully tested in experiments. The BMT equation naturally involves the Wigner rotation as the purely kinematic addition to the Larmor rotation which, in turn, is a consequence of interaction of the intrinsic magnetic moment with the external magnetic field. It is commonly believed that the BMT equation contains the standard (and incorrect) result for the Wigner rotation in the Lorentz lab frame. The existing textbooks then suggest that the experimental test of the BMT equation is a direct proof of validity for the standard expression for Wigner rotation. Here we focus on the analysis of the reason why authors of textbooks obtained an incorrect expression for the Wigner rotation. We demonstrate that the notion that the standard (incorrect) result for the Wigner rotation as an integral part of the BMT equation in most texts is based, in turn, on an incorrect physical argument. The aim of the present paper is to analyze the complicated situation relating to the use of the theory of relativity and, in particular, Wigner rotation theory, in accelerator physics.

physics.acc-ph↗

arXiv2018

Effects of energy spread on Brightness and Coherence of undulator sources

The (spectral) brightness for partially transverse coherent sources as Synchrotron Radiation (SR) and Free-Electron Laser (FEL) sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single-electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction-limited rings with ultralow emittance coming on-line. Here we discuss the effects of energy spread on the brightness of undulator radiation at resonance, as well as relevant relations with coherence properties.

physics.acc-ph↗

arXiv2017

Relativity and Accelerator Engineering

From a geometrical viewpoint, according to the theory of relativity, space and time constitute a four-dimensional continuum with pseudo-Euclidean structure. This has recently begun to be a practically important statement in accelerator physics. An X-ray Free Electron Laser (XFEL) is in fact the best, exciting example of an engineering system where improvements in accelerator technology makes it possible to develop ultrarelativistic macroscopic objects with an internal fine structure, and the theory of relativity plays an essential role in their description. An ultrarelativistic electron bunch modulated at nanometer-scale in XFELs has indeed a macroscopic finite-size of order of 10 $μ$m. Its internal, collective structure is characterized in terms of a wave number vector. Here we will show that a four-dimensional geometrical approach, unusual in accelerator physics, is needed to solve problems involving the emission of radiation from an ultrarelativistic modulated electron beam accelerating along a curved trajectory. We will see that relativistic kinematics enters XFEL physics in a most fundamental way through the so-called Wigner rotation of the modulation wave number vector, which is closely associated to the relativity of simultaneity. If not taken into account, relativistic kinematics effects would lead to a strong qualitative disagreement between theory and experiments. In this paper, several examples of relativistic kinematics effects, which are important for current and future XFEL operation, are studied. The theory of relativity is applied by providing details of the clock synchronization procedure within the laboratory frame. This approach, exploited here but unusual in literature, is rather "practical", and should be acceptable to accelerator physicists.

physics.class-ph↗

arXiv2017

On Radiation Emission from a Microbunched Beam with Wavefront Tilt and Its Experimental Observation

In this paper we compare experimental observations and theory of radiation emission from a microbunched beam with microbunching wavefront tilt with respect to the direction of motion. The theory refers to the work [1], which predicts, in this case, exponential suppression of coherent radiation along the kicked direction. The observations refer to a recent experiment performed at the LCLS [2,3], where a microbunched beam was kicked by a bend and sent to a radiator undulator. The experiment resulted in the emission of strong coherent radiation that had its maximum along the kicked direction of motion, when the undulator parameter was detuned to a value larger than the nominal one. We first analyze the theory in detail, and we confirm the correctness of its derivation according to the conventional theory of radiation emission from charged particles. Subsequently, we look for possible peculiarities in the experiment, which may not be modeled by the theory. We show that only spurious effects are not accounted for. We conclude that the experiment defies explanation in terms of the conventional theory of radiation emission.

physics.acc-ph↗

arXiv2017

Opportunities for Two-color Experiments at the SASE3 undulator line of the European XFEL

X-ray Free Electron Lasers (XFELs) have been proven to generate short and powerful radiation pulses allowing for a wide class of novel experiments. If an XFEL facility supports the generation of two X-ray pulses with different wavelengths and controllable delay, the range of possible experiments is broadened even further to include X-ray-pump/X-ray-probe applications. In this work we discuss the possibility of applying a simple and cost-effective method for producing two-color pulses at the SASE3 soft X-ray beamline of the European XFEL. The technique is based on the installation of a magnetic chicane in the baseline undulator and can be accomplished in several steps. We discuss the scientific interest of this upgrade for the Small Quantum Systems (SQS) instrument, in connection with the high-repetition rate of the European XFEL, and we provide start-to-end simulations up to the radiation focus on the sample, proving the feasibility of our concept.

physics.acc-ph↗

arXiv2017

Radiation by Moving Charges

It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz transformations. The electrodynamics problem can then be treated within a "single inertial frame" description. To evaluate radiation fields from moving charged particles we need their velocities and positions as a function of the lab frame time t. The relativistic motion of a particle in the lab frame is described by Newton's second law corrected for the relativistic dependence of the particle momentum on the velocity. In all standard derivations the trajectories in the source part of the usual Maxwell's equations are identified with the trajectories $\vec{x}(t)$ calculated by using the "corrected" Newton's second law. This way of coupling fields and particles is considered correct. We argue that this procedure needs to be changed by demonstrating a counterintuitive: the results of conventional theory of radiation by relativistically moving charges are not consistent with the principle of relativity. The trajectory of a particle in the lab frame consistent with the usual Maxwell's equations, is found by solving the dynamics equation in manifestly covariant form, with the proper time $τ$ used to parameterize the particle world-line in space-time. We find a difference between the "true" particle trajectory $\vec{x}(t)$ calculated or measured in the conventional way, and the covariant particle trajectory $\vec{x}_{cov}(t)$ calculated by projecting the world-line to the lab frame and using t to parameterize the trajectory curve. The difference is due to a choice of convention, but only $\vec{x}_{cov}(t)$ is consistent with the usual Maxwell's equations: therefore, a correction of the conventional synchrotron-cyclotron radiation theory is required.

physics.acc-ph↗

arXiv2016

On the Coupling of Fields and Particles in Accelerator and Plasma Physics

In accelerator and plasma physics it is accepted that there is no need to solve the dynamical equations for particles in covariant form, i.e. by using the coordinate-independent proper time to parameterize particle world-lines in space-time: to describe dynamics in the laboratory frame, there is no need to use the laws of relativistic kinematics. It is sufficient to account for the relativistic dependence of particles momenta on the velocity in the second Newton's law. Then, the coupling of fields and particles is based on the use of result from particle dynamics treated according to Newton's laws in terms of the relativistic three-momentum and on the use of Maxwell's equations in standard form. Previously, we argued that this is a misconception. Here we describe in detail how to calculate the coupling between fields and particles in a correct way and how to develop a new algorithm for a particle tracking code in agreement with the use of Maxwell's equations in their standard form. Advanced textbooks on classical electrodynamics correctly tell us that Maxwell's equations in standard form in the laboratory frame and charged particles are coupled by introducing particles trajectories as projections of particles world-lines onto coordinates of the laboratory frame and then by using the laboratory time to parameterize the trajectory curves. We show a difference between conventional and covariant particle tracking results in the laboratory frame. This essential point has never received attention in the physical community. Only the solution of the dynamical equations in covariant form gives the correct coupling between field equations in standard form and particles trajectories in the laboratory frame. Previous theoretical and simulation results in accelerator and plasma physics should be re-examined in the light of the pointed difference between conventional and covariant particle tracking.

physics.acc-ph↗

arXiv2016

Circular polarization opportunities at the SASE3 undulator line of the European XFEL

XFELs provide X-ray pulses with unprecedented peak brightness and ultrashort duration. They are usually driven by planar undulators, meaning that the output radiation is linearly polarized. For many experimental applications, however, polarization control is critical: besides the ability to produce linearly polarized radiation, one often needs the possibility of generating circularly polarized radiation with a high, stable degree of polarization. This may be achieved by using a first part of the XFEL undulator to produce bunching and then, by propagating the the bunched beam through an "afterburner" - a short undulator with tunable polarization, where only limited gain takes place. One of the issues that one needs to consider in this case is the separation of the circularly polarized radiation obtained in the radiator from the linearly polarized background produced in the first part of the FEL. In this article we review several methods to do so, including the inverse tapering technique. In particular, we use the Genesis FEL code to simulate a case study pertaining to the SASE3 FEL line at the European XFEL with up-to-date parameters and we confirm that a high degree of circular polarization is expected. Moreover, we propose to further improve the effectiveness of the inverse tapering technique either via angular separation of the linearly polarized radiation or strongly defocusing it at the sample position. In this way we exploit the unique flexibility of the European XFEL from both the electron beam and the photon beam optics side.

physics.acc-ph↗

arXiv2016

A Critical Experimental Test of Synchrotron Radiation Theory with 3rd Generation Light Source

A recent "beam splitting" experiment at LCLS apparently demonstrated that after a microbunched electron beam is kicked on a large angle compared to the divergence of the FEL radiation, the microbunching wave front is readjusted along the new direction of motion of the kicked beam. Therefore, coherent radiation from an undulator placed after the kicker is emitted along the kicked direction without suppression. This strong emission of coherent undulator radiation in the kicked direction cannot be explained in the framework of conventional synchrotron radiation theory. In a previous paper we explained this puzzle. We demonstrated that, in accelerator physics, the coupling of fields and particles is based, on the one hand, on the use of results from particle dynamics treated according to the absolute time convention and, on the other hand, on the use of Maxwell equations treated according to the standard (Einstein) synchronization convention. Here lies the misconception which led to the strong qualitative disagreement between theory and experiment. After the "beam splitting" experiment at LCLS, it became clear that the conventional theory of synchrotron radiation cannot ensure the correct description of coherent and spontaneous emission from a kicked electron beam, nor the emission from a beam with finite angular divergence, in an undulator or a bending magnet. However, this result requires further experimental confirmation. In this publication we propose an uncomplicated and inexpensive experiment to test synchrotron radiation theory at 3rd generation light sources.

physics.acc-ph↗

arXiv2015

Scheme to increase the output average spectral flux of the European XFEL at $14.4$ 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.

physics.acc-ph↗

arXiv2015

Novel opportunities for sub-meV inelastic X-ray scattering at high-repetition rate self-seeded X-ray free-electron lasers

Inelastic X-ray scattering (IXS) is an important tool for studies of equilibrium dynamics in condensed matter. A new spectrometer recently proposed for ultra-high-resolution IXS (UHRIX) has achieved 0.6~meV and 0.25~nm$^{-1}$ spectral and momentum transfer resolutions, respectively. However, further improvements down to 0.1~meV and 0.02~nm$^{-1}$ are required to close the gap in energy-momentum space between high and low frequency probes. We show that this goal can be achieved by further optimizing the X-ray optics and by increasing the spectral flux of the incident X-ray pulses. UHRIX performs best at energies from 5 to 10 keV, where a combination of self-seeding and undulator tapering at the SASE-2 beamline of the European XFEL promises up to a hundred-fold increase in average spectral flux compared with nominal SASE pulses at saturation, or three orders of magnitude more than possible with storage-ring based radiation sources. Wave-optics propagation shows that about $7\times 10^{12}$~ph/s in a $90$-$μ$eV bandwidth can be achieved on the sample. This will provide unique new possibilities for dynamics studies by IXS.

physics.acc-ph↗

arXiv2015

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 $λ_w^2/(4 πL_g)^2$, where $λ_w$ 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 $λ_w^3/(4 πL_g)^3$ 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.

physics.acc-ph↗

arXiv2014

Brightness of synchrotron radiation from wigglers

According to literature, while calculating the brightness of synchrotron radiation from wigglers, one needs to account for the so called `depth-of-field' effects. In fact, the particle beam cross section varies along the wiggler. It is usually stated that the effective photon source size increases accordingly, while the brightness is reduced. Here we claim that this is a misconception originating from an analysis of the wiggler source based on geometrical arguments, regarded as almost self-evident. According to electrodynamics, depth-of-field effects do not exist: we demonstrate this statement both theoretically and numerically, using a well-known first-principle computer code. This fact shows that under the usually accepted approximations, the description of the wiggler brightness turns out to be inconsistent even qualitatively. Therefore, there is a need for a well-defined procedure for computing the brightness from a wiggler source. We accomplish this task based on the use of a Wigner function formalism. In the geometrical optics limit computations can be performed analytically. Within this limit, we restrict ourselves to the case of the beam size-dominated regime, which is typical for synchrotron radiation facilities in the X-ray wavelength range. We give a direct demonstration of the fact that the apparent horizontal source size is broadened in proportion to the beamline opening angle and to the length of the wiggler. While this effect is well-understood, a direct proof appears not to have been given elsewhere. We consider the problem of the calculation of the wiggler source size by means of numerical simulations alone, which play the same role of an experiment. We report a significant numerical disagreement between exact calculations and approximations currently used in literature.

physics.acc-ph↗

arXiv2014

Perspectives of Imaging of Single Protein Molecules with the Present Design of the European XFEL. - Part I - X-ray Source, Beamlime Optics and Instrument Simulations

The Single Particles, Clusters and Biomolecules (SPB) instrument at the European XFEL is located behind the SASE1 undulator, and aims to support imaging and structure determination of biological specimen between about 0.1 micrometer and 1 micrometer size. The instrument is designed to work at photon energies from 3 keV up to 16 keV. This wide operation range is a cause for challenges to the focusing optics. In particular, a long propagation distance of about 900 m between x-ray source and sample leads to a large lateral photon beam size at the optics. The beam divergence is the most important parameter for the optical system, and is largest for the lowest photon energies and for the shortest pulse duration (corresponding to the lowest charge). Due to the large divergence of nominal X-ray pulses with duration shorter than 10 fs, one suffers diffraction from mirror aperture, leading to a 100-fold decrease in fluence at photon energies around 4 keV, which are ideal for imaging of single biomolecules. The nominal SASE1 output power is about 50 GW. This is very far from the level required for single biomolecule imaging, even assuming perfect beamline and focusing efficiency. Here we demonstrate that the parameters of the accelerator complex and of the SASE1 undulator offer an opportunity to optimize the SPB beamline for single biomolecule imaging with minimal additional costs and time. Start to end simulations from the electron injector at the beginning of the accelerator complex up to the generation of diffraction data indicate that one can achieve diffraction without diffraction with about 0.5 photons per Shannon pixel at near-atomic resolution with 1e13 photons in a 4 fs pulse at 4 keV photon energy and in a 100 nm focus, corresponding to a fluence of 1e23 ph/cm^2. This result is exemplified using the RNA Pol II molecule as a case study.

physics.acc-ph↗