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 $\tau$ 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

Scheme for generation of fully-coherent, TW power level hard X-ray pulses from baseline undulators at the European X-ray FEL

The most promising way to increase the output power of an X-ray FEL (XFEL) is by tapering the magnetic field of the undulator. Also, significant increase in power is achievable by starting the FEL process from a monochromatic seed rather than from noise. This report proposes to make use of a cascade self-seeding scheme with wake monochromators in a tunable-gap baseline undulator at the European XFEL to create a source capable of delivering coherent radiation of unprecedented characteristics at hard X-ray wavelengths. Compared with SASE X-ray FEL parameters, the radiation from the new source has three truly unique aspects: complete longitudinal and transverse coherence, and a peak brightness three orders of magnitude higher than what is presently available at LCLS. Additionally, the new source will generate hard X-ray beam at extraordinary peak (TW) and average (kW) power level. The proposed source can thus revolutionize fields like single biomolecule imaging, inelastic scattering and nuclear resonant scattering. The self-seeding scheme with the wake monochromator is extremely compact, and takes almost no cost and time to be implemented. The upgrade proposed in this paper could take place during the commissioning stage of the European XFEL, opening a vast new range of applications from the very beginning of operations. We present feasibility study and examplifications for the SASE2 line of the European XFEL.Comment: 23 pages, 20 figure

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

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.Comment: arXiv admin note: substantial text overlap with arXiv:1407.459