Undulator Axis Research Articles

Electric field lines of charged particle in a helical undulator

One of the devices for generating circularly polarized radiation is a helical undulator in which a relativistic charged particle moves along a helical trajectory. In this paper, the spatial distribution of the electromagnetic field produced by such a particle is analyzed using electric field lines. The equations of electric field lines, which, due to the presence of curvature and torsion in the trajectory are precisely solved. A special algorithm for erasing invisible parts of the lines has been developed to represent the lines in space. Several remarkable features of the field picture are revealed, in particular, the hard component of the radiation is concentrated in the plane orthogonal to the undulator axis and passing through the position of the particle at the current moment of time.

Linearly and circularly polarized radiation with a low on-axis heat load from an asymmetric magnet pole undulator

The heavy heat load on optical components from the normal planar undulator has become a serious problem in the synchrotron radiation light source, especially for generating the low-energy photon in a high-energy storage ring and/or a diffraction-limited storage ring. The asymmetric magnet pole undulators have different period lengths between the upper and lower magnet poles. Taking the advantage of the asymmetric magnet pole undulators in building various magnetic fields, this paper proposes a new class of undulators to obtain the specific magnetic fields which can scatter the electron velocity away from the undulator axis. It consists of four magnet arrays and has a similar structure compared to the DELTA/APPLE-X undulator; however, each couple of magnet arrays has a different period length with the period ratio of ${n}_{1}:{n}_{2}$. Taking the one-to-two and two-to-three period ratios as examples, a novel Figure 8 undulator and a novel Knot undulator are demonstrated. The polarization state can be flexibly switched from the linear polarization to the circular polarization by tuning the phase shifts of magnetic fields, with the on-axis heat load greatly suppressed. The heat-load suppressions of linear polarization at two predetermined orthogonal directions are almost the same and fully effective. Analysis and simulations of undulator designs with the corresponding radiation characteristics are reported.

Effect of the third undulator field harmonic on spontaneous and stimulated undulator radiation.

The effect of undulator field harmonics on spontaneous and stimulated undulator radiation, both on and off the undulator axis, is studied. Bessel factors for the undulators with field harmonics have been analytically calculated and numerically verified. The influence of the third undulator field harmonic on single-pass free-electron laser radiation is explored. Harmonic generation at the LCLS and SPring-8 free-electron lasers is modeled and analyzed.

Harmonic Generation in Planar Undulators in Single-Pass Free Electron Lasers

The paper presents a theoretical study of the harmonic power evolution in a single-pass free-electron laser (FEL) and a comparison with some of the experimental results. The phenomenological approach which considers the main FEL parameters (current density, the Lorentz factor, electron energy spread, and the beam geometry) provides a description of any undulator. With due regard to the real laser beam parameters, the effect from high-order harmonic radiation and the beam deviation from the undulator axis on the FEL irradiation is investigated. The Bessel coefficients are calculated for the undulator in the presence of the second periodic field. The phenomenological approach provides the free-electron laser simulation experiments at Sorgente Pulsata Auto-amplificata di Radiazione Coerente (SPARC), SPring-8 Angstrom Compact Free-Electron Laser (SACLA) and Linac Coherent Light Source (LCLS). These studies include the high-harmonic generation, a comparison of the emission power evolution with the experimentally obtained data on the harmonic generation including even and odd high-order harmonics, gain and saturation lengths and the respective power. A possible effect from the third harmonic of the planar undulator magnetic field is studied in relation to the FEL irradiation. It is shown that this effect is insignificant even at the magnetic-field harmonic amplitude equaling ~1/10 of the amplitude of the ideal magnetic field in the periodic undulator. It is found that the second-harmonic generation in FEL lasing is rather weak, that is in good agreement with the measurement results as well as the behavior of the high-order harmonics.

Area-preserving scheme for efficiency enhancement in single-pass tapered free electron lasers

Efficiency enhancement of a single-pass short-wavelength high-gain tapered free electron laser (FEL) has recently been intensively studied. The goal is to sustain the growth of radiation power in the post-saturation regime. Among the various schemes, the undulator tapering is considered an effective route to achieve higher power extraction efficiency. The tapering strategy can be of constant or varying resonant phase along the undulator axis. In this paper we propose an efficiency-enhancement scheme based on preservation of the longitudinal phase space area which ensures trapping of resonant particles in the ponderomotive bucket as long as possible along the undulator axis before significant particle depletion occurs. In the meanwhile such a scheme takes advantage of the increase of the radiation field amplitude to precipitate the particle deceleration process at the middle stage of undulator tapering. We analyze such an area-preserving scheme of undulator tapering by formulating the post-saturation FEL interaction in a one-dimensional (1-D) model via introduction of the particle trapping fraction. The output performance is evaluated through numerical iteration and confirmed with 1-D particle tracking simulations. The results show that the optimal power extraction efficiency based on the proposed scheme, together with a prebunched beam, can be greatly improved within relatively short taper length compared with other schemes before radiation diffraction effect becomes significant. Besides, the undesired sideband effects are found to be effectively suppressed. For the proposed area-preserving taper scheme, we also derive an analytical approximate formula for the resonant phase as a function of undulator axis. We expect that the analysis can shed light on the aim to further enhance the power extraction efficiency in single-pass tapered FELs.

Probability of radiation of twisted photons by classical currents

The general formula for the probability of radiation of a twisted photon by a classical current is derived. The general theory of generation of twisted photons by undulators is developed. It is proved that the probability to record a twisted photon produced by a classical current is equal to the average number of twisted photons in a given state. The general formula for the projection of the total angular momentum of twisted photons with given the energy, the longitudinal projection of momentum, and the helicity is obtained. The symmetry property of the average number of twisted photons produced by a charged particle moving along a planar trajectory is found. The explicit formulas for the average number of twisted photons generated by undulators both in the dipole and wiggler regimes are obtained. It is established that, for the forward radiation of an ideal right-handed helical undulator, the harmonic number $n$ of the twisted photon coincides with its projection of the total angular momentum $m$. As for the ideal left-handed helical undulator, we obtain that $m=-n$. It is found that the forward radiation of twisted photons by a planar undulator obeys the selection rule that $n+m$ is an even number. It turns out that the average number of twisted photons produced by the undulator and detected off the undulator axis is a periodic function of $m$ in a certain spectral band of the quantum numbers $m$.

Electron Motion in the Three-Dimensional Field of Undulator

In this paper we consider the motion of relativistic electrons in an ideal three-dimensional magnetic field of an undulator. The ideality of the magnetic field means that, on the undulator axis, the field is directed strictly vertically upward and has a strictly sinusoidal shape. In the overwhelming majority of cases, only this leading component of the field is taken into account in calculating the electron trajectory. In this paper, in the equations of motion of an electron in the magnetic field of an undulator, all three components of the field are taken into account, so that the undulator field under consideration satisfies the stationary Maxwell equations. In this case, the differential equations of motion of the electron are solved analytically with the help of perturbation theory, and not by the method of averaging over fast oscillations of the electron, as was done in a number of previous papers. These analytic expressions for trajectories describe the behavior of particles in the focusing magnetic field of an undulator much more completely. An analysis of these expressions shows that the behavior of electrons in such a three-dimensional field of the undulator is much more complicated than what follows from the equations obtained by the averaging method. In particular, there is a cross effect when changes in the initial vertical parameters of the electron trajectory cause changes in the horizontal component of its trajectory and vice versa. A comparison of the solutions obtained analytically with the results of numerical calculations of electron trajectories using the Runge–Kutta method demonstrates their high accuracy.

Effect of an angular trajectory kick in a high-gain free-electron laser

In a free-electron laser, a transverse momentum offset (or ``kick'') results in an oscillation of the centroid of the electron beam about the undulator axis. Studying the influence of this effect on the free-electron laser (FEL) interaction is important both from a tolerance point of view and for its potential diagnostic applications. In this paper, we present a self-consistent theoretical analysis of a high-gain FEL driven by such a ``kicked'' beam. In particular, we derive a solution to the three-dimensional, linearized initial value problem of the FEL through an orthogonal expansion technique and also describe a variational method for calculating the average FEL growth rate. Our results are benchmarked with genesis simulations and provide a robust theoretical background for a comparison with previous analytical results.

Two-color operation of a free-electron laser with a tilted beam.

With the successful operation of free-electron lasers (FELs) as user facilities there has been a growing demand for experiments with two photon pulses with variable photon energy and time separation. A configuration of an undulator with variable-gap control and a delaying chicane in the middle of the beamline is proposed. An injected electron beam with a transverse tilt will only yield FEL radiation for the parts which are close to the undulator axis. This allows, after re-aligning and delaying the electron beam, a different part of the bunch to be used to produce a second FEL pulse. This method offers independent control in photon energy and delay. For the parameters of the soft X-ray beamline Athos at the SwissFEL facility the photon energy tuning range is a factor of five with an adjustable delay between the two pulses from -50 to 950 fs.

Analysis of spectral properties of harmonic undulator radiation of an electromagnet undulator

In this paper we analyze the spectral properties of undulator radiation with an electromagnet undulator for electron injected off the undulator axis. The electromagnet undulator is self bi-harmonic for locations near to the electromagnet. The electrons execute additional betatron oscillation when it injected off the undulator axis. It is observed that the electromagnet undulator can be used for harmonic lasing free electron laser operates at the cost of betatron oscillations for electron injected off the axis.

Analysis of undulator radiation with an electromagnet undulator

In this paper we discuss the theory of undulator radiation in an electromagnet undulator. We discuss the spectral properties of undulator radiation when electrons are injected off the undulator axis. This paper highlights the distinctive features of the radiation spectrum from electromagnet undulators, as compared to PPM undulators.

A model superconducting helical undulator fabricated using a small filament, tube-type, multifilamentary Nb3Sn wire

A model helical undulator 250 mm in length, designed and fabricated with a period of 14 mm, was tested in a liquid helium bath. The helical coil was wound with a multifilamentary, tube-type Nb3Sn strand with 217 sub-elements. The coil Ic and the magnetic field in the bore were measured at 4.2 K in a liquid helium bath using a Hall probe. Ic was found to be 842 A, and the bore field reached the design specification of 0.8 T. The transverse bore field was also measured as a function of position along the length of the undulator axis and was seen to exhibit the expected sinusoidal behavior. The measured Ic was compared with that obtained from a crossing of a load line (determined from FEM modeling) with the Ic(B) curve of a short sample Nb3Sn strand. The coil exhibited the same critical current as the short sample.

In situcorrection of field errors induced by temperature gradient in cryogenic undulators

A new technique of undulator field correction for cryogenic permanent magnet undulators (CPMUs) is proposed to correct the phase error induced by temperature gradient. This technique takes advantage of two important instruments: one is the in-vacuum self-aligned field analyzer with laser instrumentation system to precisely measure the distribution of the magnetic field generated by the permanent magnet arrays placed in vacuum, and the other is the differential adjuster to correct the local variation of the magnet gap. The details of the two instruments are described together with the method of how to analyze the field measurement data and deduce the gap variation along the undulator axis. The correction technique was applied to the CPMU with a length of 1.7 m and a magnetic period of 14 mm. It was found that the phase error induced during the cooling process was attributable to local gap variations of around $30\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, which were then corrected by the differential adjuster.

Wire scanner system for FLASH at DESY

The design and implementation of a new kind of wire scanner for the Free Electron Laser at Hamburg (FLASH) is presented. In the undulator section of FLASH a set of seven wire scanner stations determine the relative position and the profile of the electron beam with a spatial resolution of a few μm. They allow the measurement of the absolute beam position related to the undulator axis with a precision better than 50μm. Monte Carlo calculations are performed in order to get an optimal position for the scintillators, which are used to detect the secondary particles scattered by the wire. Results of beam trajectory and beam size measurements along the undulator section are presented.

Betatron harmonic radiation from harmonic undulators

Abstract In this paper we discuss the spectral properties of undulator radiation with a harmonic undulator field to include the off-axis field structure in the analysis. The analysis is aimed to clarify the role of betatron oscillation in a harmonic undulator which arise when the electrons are emitted off the undulator axis.

Betatron harmonic radiation from harmonic undulators

In this paper we discuss the spectral properties of undulator radiation with a harmonic undulator field to include the off-axis field structure in the analysis. The analysis is aimed to clarify the role of betatron oscillation in a harmonic undulator which arise when the electrons are emitted off the undulator axis.

Damping of betatron oscillations in undulator magnets with the aid of an axial magnetic field

In this paper we consider the calculation of the linearly polarised undulator brightness with the inclusion of the sextupolar magnetic field contributions and an axial magnetic field. The analysis is aimed at the damping of the betatron oscillations which arise when the electrons are injected off the undulator axis.

Consideration on an undulator magnetic structure for polarization control

A magnetic structure composed of electromagnets and permanent magnets is proposed as an undulator to control the polarization state of synchrotron radiation. The horizontal field is produced by the permanent magnets and tuned by moving them along the undulator axis, while the vertical field is produced by the electromagnets and tuned by changing the coil current. The proposed device has two important degrees of freedom. One is that of the periodic length of the electromagnets and the other is that of the relative phase between the vertical and horizontal fields. Thanks to them, the proposed device works as various types of undulator to realize polarization control.

Statistical correlations and intensity spiking in the SASE FEL

In the linear regime before saturation, we describe the statistical correlations in the narrow band chaotic output of the self-amplified spontaneous emission free-electron laser. At a fixed position along the undulator axis, we derive joint probability distributions for the intensity in the output pulse to have values I 1 and I 2 at times t 1 and t 2, and for the spectral intensity to have values I ̃ 1 and I ̃ 2 at frequencies ω 1 and ω 2. Probability distributions for the peak values of intensity in the time and frequency domains are also determined.

Initial gain measurements of an 800 nm SASE FEL, VISA

The Visible to Infrared SASE Amplifier (VISA) FEL is designed to obtain high gain at a radiation wavelength of 800 nm. The FEL uses the high brightness electron beam of the Accelerator Test Facility (ATF), with energy of 72 MeV. VISA uses a novel, 4 m long, strong focusing undulator with a gap of 6 mm and a period of 1.8 cm. To obtain large gain the beam and undulator axis have to be aligned to better than 5 μm. Results from initial measurements on the alignment, gain, and spectrum will be presented and compared to theoretical calculations and simulations.