Multiparticle time-domain analysis of coherent undulator radiation

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

Undulator radiation (UR) in an undulator with field harmonics in two orthogonal planes is theoretically studied taking nonperiodic magnetic components and off-axis effects into account. New analytical expressions for the UR spectrum and UR intensity are written explicitly in terms of the generalized Bessel function and Airy function. In limiting cases, they describe the radiation of a two-frequency planar undulator, a helical undulator, and an elliptical undulator. The influence of the finite size of the electron beam, the emittance, electron beam deflection from the axis, the spread of the electron energy, and the influence of the constant components of the magnetic field are taken into account analytically. The expressions make it possible to distinguish the contributions of each field component and characteristics of the beam and undulator to the generation of UR harmonics. The phenomenological FEL model is used to study the evolution of harmonic power in the FEL experiments of LCLS and LEUTL. The influence of the beam parameters and undulator parameters on the harmonic generation is analyzed. The theoretical results of the power and radiation spectrum of the FEL are in agreement with experiments. It is shown that the second harmonic in the X-ray FEL of LCLS can be due to the beam deflection from the axis by $${\sim}12$$ $$\mu$$ m, and the second harmonic in the UV-A FEL of LEUTL is due to wide ( $${\sim}0.2$$ mm) beams of electrons and photons.

Coherent radiation emitted from a compressed electron bunch as it traverses the sharp edge regions of a magnetic chicane has been investigated at the Brookhaven National Laboratory Accelerator Test Facility. Electron beam measurements using coherent transition radiation interferometry indicate a 100 fs rms bunch accompanied by distinct distortions in energy spectrum due to strong self-fields. These self-fields are manifested in emitted high power THz radiation, which displays signatures of the phenomenon known as coherent edge radiation. Radiation characterization studies undertaken include spectral analysis, far-field intensity distribution, polarization, and dependence on the electron bunch length. The observed aspects of the beam and radiation allow detailed comparisons with start-to-end simulations.

Laser-Compton scattering (LCS) experiments were carried out at the Idaho Accelerator Center (ICA) using the 5 ns (FWHM) and 22 MeV electron beam. The electron beam was brought to an approximate head-on collision with a 7 ns (FWHM), 10 Hz, 29 MW peak power Nd:YAG laser. We observed clear and narrow X-ray peaks resulting from the interaction of relativistic electrons with the 532 nm Nd:YAG laser second harmonic line on top of a very low bremsstrahlung background. We have developed a method of using LCS as a non-intercepting electron beam monitor. Unlike the method used by Leemans et al. (1996), our method focused on the variation of the shape of the LCS spectrum rather than the LCS intensity as a function of the observation angle in order to extract the electron beam parameters at the interaction region. The electron beam parameters were determined by making simultaneous fits to spectra taken across the LCS X-ray cone. We also used the variation of LCS X-ray peak energy and spectral width as a function of the detector angles to determine the electron beam angular spread, and direction and compared the results to the previous method. Experimental data show that in addition to being viewed as potential bright, tunable and monochromatic X-ray source, LCS can provide important information on electron beam pulse length, direction, energy, angular, and energy spread. Since the quality of LCS X-ray peaks, such as degree of monochromaticity, peak energy and flux, depends strongly on the electron beam parameters, LCS can therefore be viewed as an important non-destructive means for electron beam diagnostics.

The theory of absorption and emission of electromagnetic radiation by an oscillator consisting of the atomic nucleus and one electrically charged particle is deduced using classical electrodynamics. In the steady state of an atom, emission and absorption of electromagnetic radiation are equal, so the atom is stable. In order to include reactive effects of electromagnetic radiation in the motion equations, the Newton equation is modified by adding the radiative reaction force. This paper is an introduction to the derivation of the basic assumptions of quantum mechanics.

We present particle-in-cell (PIC) simulations of electron bunches with nm scale longitudinal modulation produced using a compact 2-20 MeV LINAC. The modulation is initially imparted in the transverse dimension of the electron bunch with a nano-patterned photo-emitter in an X-band RF gun with 2 MeV exit energy. The electron bunch passes through a 1 m standing wave X-band LINAC which can raise the beam energy up to 20 MeV. The transverse modulation is exchanged into the longitudinal dimension using a double dog-leg emittance exchange setup wit ha5c ell RF deflector cavity. The modulation pitch can be tuned by adjusting the spacing of the nano-patterned photo-emitter or magnification of the transverse pitch with electron optics. The electron beam parameters are optimized to produce coherent XFEL radiation upon interacting with a laser undulator.

A crystalline undulator consists of a crystal with a periodic deformation in which channeled particles undergo oscillations and emit coherent undulator radiation. Patterning by an alternate series of tensile Si3N4 strips on a Si crystal is shown to be a tractable method to construct a crystalline undulator. The method allows periodic deformation of the crystal with the parameters suitable for implementation of a crystalline undulator. The resulting periodic deformation is present in the bulk of the Si crystal with an essentially uniform amplitude, making the entire volume of the crystal available for channeling and in turn for emission of undulator radiation.

The parameters of a high-current electron beam extracted from the self-focusing zone through a hole in the anode into a vacuum chamber are investigated. The beam parameters were determined from the measurement of the spatial distribution of destruction and glow arising in polymethyl methacrylate samples installed at different distances from the anode (electron beam autographs). The formation of two electron beams --- a self-focused with a high energy density, propagating along the axis of the cone facing the base to the anode with an apex angle of ~ 7o and a high-energy beam of low density, propagating in a hollow truncated cone and surrounding self-focused, was found. The oscillograms of the current and the energy of the electron beams were measured. Keywords: vacuum diode, electron beam, filamentation, self-focusing, polymethyl methacrylate, destruction, glow, high current pulsed electron beam

PurposeThe physics design of the High Energy Photon Source (HEPS) was finished after many times of iteration. Hereby, the typical equilibrium electron beam parameters corresponding to the proposed two baseline operation modes in the baseline design of HEPS are presented.MethodsTo compute the equilibrium parameters of the electron beam, the lattice parameters, RF parameters, and the parameters of the insertion devices (IDs) were determined first. Furthermore, it is more precise to use the full-current electron beam parameters in the estimations of the performance of the synchrotron light. Therefore, not only the single-particle dynamics but also the current-dependent collective effects need to be considered in the computations of the full-current, equilibrium parameters of the electron beam. Both analytic computations and multi-particle tracking simulations were carried out.ResultsThe full-current, equilibrium parameters of the electron beams in the HEPS storage ring are presented in this paper. Moreover, the main beam parameters in the injector (the booster and the LINAC), corresponding to the two baseline operation modes of the storage ring, are also presented.ConclusionThe typical electron beam parameters corresponding to the two baseline operation modes are given in detail in this paper.

The usage of dosimetry of small fields in radiotherapy to measure radiation dose is difficult because of high-dose gradients, lateral electronic disequilibrium, and detector volume effects. In this study, three dosimeters namely, Markus, Semiflex 3D, and Diode E were tested using the Elekta-accelerator electron beams. The electron beam parameters, penumbra, and output factor were determined using these dosimetersfor each field size and energy. According to the results, Diode E and Advanced Markus exhibited the greatest difference in Rq among the electron beam parameters. Furthermore, the greatest difference in penumbrawas observed between Diode E and Advanced Markus for the field size of 3cm2 at 10MeV. In terms of output factor, three dosimeters exhibited the greatest differencebetween Diode E and Advanced Markus for the field size of 3cm2 at 10MeV. The findings indicate that the Semiflex 3D can be regarded as an appropriate dosimeter for electron small-field dosimetry.

The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form. In state space order reduction methods, the equations of motion are expressed as a set of first order equations and transformed using the Lyapunov–Floquet (L–F) transformation such that the linear parts of new set of equations are time invariant. At this stage, four order reduction methodologies, namely linear, nonlinear projection via singular perturbation, post-processing approach and invariant manifold technique, are suggested. The invariant manifold technique yields a unique ‘reducibility condition’ that provides the conditions under which an accurate nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An alternate approach of deriving reduced order models in direct second order form is also presented. Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L–F and other canonical transformations. Then a master-slave separation of degrees of freedom is used and a nonlinear relation between the slave coordinates and the master coordinates is constructed. This method yields the same ‘reducibility conditions’ obtained by invariant manifold approach in state space. Some examples are given to show potential applications to real problems using above mentioned methodologies. Order reduction possibilities and results for various cases including ‘parametric’, ‘internal’, ‘true internal’ and ‘true combination resonances’ are discussed. A generalization of these ideas to periodic-quasiperiodic systems is included and demonstrated by means of an example.

The basic problem of order reduction of linear and nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via Time Periodic Center Manifold Theory. A ‘reducibility condition’ is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show applications to real problems. Order reduction possibilities and results for various cases including ‘parametric’, ‘internal’, ‘true internal’ and ‘combination’ resonances are discussed.

A non-destructive electron beam diagnostic for a SASE FEL using coherent off-axis undulator radiation

Design formulas for short-wavelength FELs

Electron beam induced current (EBIC) investigations of GaAs-MESFET