It is shown that the Wigner distribution provides a proper framework in which the propagation and imaging characteristics of synchrotron radiation can be analyzed, taking fully into account the effect of diffraction and electron beam emittance. The Wigner distribution can be interpreted as a phase-space density of photon flux, i.e., the brightness, and transforms through a general optical medium in the same way as in the case of collection of geometric rays. The brightness due to a collection of electrons can be calculated by a simple convolution of the brightness of a single electron with the electron phase space distribution function. Expressions for the brightness of bending magnets, wigglers and undulators are given.

Coherent x-rays have long been sought as a tool to discover microscopic details of physical and biological assemblies. Such radiation would permit biologists, chemists and physicists to probe with spatial resolutions better than 1,000 Å (perhaps 10 to 100 Å in special circumstances), and with an ability to distinguish concentrations of specific atomic elements. It has been the prevailing view that such radiation, when available, would emanate from an atomic x-ray laser. Although that is possible, we are coming to realize that to a large degree these needs will first be satisfied by coherent x-rays generated through the interaction of relativistic electron beams of very high brightness with periodic magnet structures (undulators). Within the next 2-5 years it will be possible with undulators and monochromators to generate x-rays at substantial peak and average powers, with thousands of wavelengths of longitudinal coherence, full spatial coherence, complete polarization control and broad tunability at megahertz repetition rates.

The possibility of producing vacuum ultraviolet radiation by harmonic generation on an electron beam has stimulated the study of coherent emission of light from a modulated beam. Properties of coherent emission can be easily visualized on an w-θ diagram, and considering the electron beam as a non-uniform Poisson process, coherent and incoherent radiation are described in a unified way. The case of an undulator is analyzed in detail.

As an optical source, an undulator can be described by its distribution of brilliance in phase space (angle and position in the transverse plane). This is a convolution of single-particle diffraction pattern and electron beam distribution. Approximate peak brilliance and phase space widths are given. By analogy between brilliance and Wigner function, the depth-of-field and diffraction widths are shown to be essentially the same thing. The peak brilliance is shown to have a broad maximum as a function of the beam β function (β = L/2π but is practially independent of β at short wavelengths.

When considering how to optimize undulator design, numerical tools are needed to provide precise calculations of radiation spectra and angular distributions under various conditions. Here a short description of some existing computer codes is given, which make use of different and somewhat complementary approaches. In particular, we consider: i) methods based on straightforward integration of general radiation formulae; ii) those based on the Fast Fourier Transform algorithm (FFT); iii) those based on a given analytical form of the trajectory in an ideal undulator; iv) those based on appropriate approximations of exact formulae for some special cases. In some cases, convolution of radiation spectra with the phase space distribution of both the electron beam and the detector is taken into account. Some illustrative results of each program are reported, and their respective fields of application are considered.

Properties of the radiation emitted by a plane sinusoidal undulator are calculated in the far field approximation. Software has been developed to calculate the spectral distribution and polarization of the radiated intensity I(E) at a point on (or integrated over) a cross sectional observation plane of the photon beam. Spatial distribution of monochro-matic radiation and power density contours are also calculated. Spectral broadening caused by an electron beam of finite spatial distribution is considered. Dispersive properties of the photon beam, including the dependence on deflection parameter, are analyzed. It is shown that reasonably constant intensity distribution I(E) can be obtained by properly shaping the beam acceptance aperature.

This paper presents a systematic study of the properties of spectra generated by transverse undulators in storage rings. These include far-field intensity spectra, polarization profiles, and phase-space effects. A systematic presentation of the w-e plot is made and practical formulas are given for estimating phase-space emittance effects in the far field. First, the above parameter studies are done for transverse undulators with ideal sinusoidal trajectories, then several results for actual, real-life trajectories are presented. Brief discussions of the limitations of prior undulator modelling are also given.

There are still no helical undulators that satisfy all major requirements. A new helical undulator is described that has at least some of the properties that were not obtainable until now. It can be used in a synchrotron storage ring, is completely accessible from both sides, light with both helicities can be produced, the helical field can be made quite strong, and the period length can be adjusted over a small range.-Similarly, there have been some efforts lately to develop undulators with very short periods. It is shown how a hybrid undulator with a period of the order 1 mm can be constructed.

This work explores the effects of random undulator field errors on the output radiation. An approximate theory of these effects is summarized, along with limiting conditions on its validity, resulting in a description of the loss of radiated intensity by two universal functions. The functions' arguments are simple combinations of the basic undulator parameters. Numerical results are compared with the predictions of the universal functions. Finally, possible solutions to the problem of random errors in undulators are discussed.

Presented are the results of thermal cycling tests carried out on REC and NdFe samples, to determine the irreversible losses in room temperature open circuit magnetic moment. A stabilization prescription was developed for a REC alloy that will allow two 4day/175°C temperature cycles, which simulate two UHV bakeouts, with only a 0.35% average loss and a 0.65% loss variation in the room temperature open circuit magnetic moment after stabilization.

The problem of sorting and placement of permanent magnets in undulators is considered. First, the constraints on the electron trajectory imposed by orbital stability and optimal synchrotron radiation output are used to construct a simple 'cost function' . This function describes the deviation of the magnetic field in the device from an ideal , and is dependent upon magnet placement. The cost function is then minimized using a Simulated Annealing algorithm until the optimal arrangement of elements is found. The results of optimization of magnet placement are presented for the particular case of the SSRL Beam Line V Multiundulator 15-period device. The electron path through the device is calculated and compared with a simpler optimization strategy, and with a random (unoptimi zed) magnet arrangement. The simulated annealing optimization strategy is found to offer significant advantages - resulting in a predicted electron trajectory that is close to ideal .

We present a straightforward procedure to optimize the pole parameters of a pure SmCo permanent magnet structure with four poles per period in such a way that the magnetic field on axis is maximized for a given volume of magnet material while perturbing influences of the multipole structure on the electron beam are minimized.

A relativistic electron-beam laser designed at the Naval Research Laboratory produces circularly polarized 15 GHz radiation by means of a transverse magnetic field of which the orientation rotates continuously in the φ direction with displacement along the z axis. A field strength of about 500 Oe is presently provided by a bifilar solenoid carrying a current of 200 amperes. It is desirable to eliminate the necessity of such high currents and the attendant bulky power supplies by means of a permanent-magnet field source. This can be accomplished by a tubular magnetic structure of rectangular cross section which is twisted progressively about its z axis with the desired pitch of field rotation (2π radians in 2.5 to 6 cm). By means of a sheathing of rare earth permanent magnets oriented normally to the magnets supplying the working flux, the magnetic field can be confined to the twisted rectangular tube through which passes the cylindrical tube carrying the electron beam. Also discussed is the design of an outer permanent-magnet structure for the supply of a solenoidal focusing field of 3 kOe.

The design potential and limitations of storage rings optimized for high brilliance synchrotron radiation production are discussed. Specifically the performance expectations for insertion device radiation is emphasized. Also prospects for a spatially coherent radiation source are evaluated.

The ideal beam to be used in an undulator would be a stable high current pencil beam. Behaviour of real electron beams is much more complex. Dependence of storable currents, life times and cross-sections on the different machine parameters and modes of operation are being discussed.

This paper describes design and construction considerations of the THUNDER undulator built by Spectra, Technology, Inc. (STI) for use in free-electron laser experiments at visible wavelengths. For the parameters of these experiments, an unusually high degree of optimization of the electron-photon interaction is required and, as a result, THUNDER is built to especially high mechanical and magnetic precision. Except for its narrow magnet gap, the 5-meter THUNDER undulator is quite similar to insertion, devices under consideration. for the proposed. 6 GeV storage ring. The engineering and physics approach. adopted for this FEL, undulator design is directly applicable to insertion device development. The tolerance limits for THUNDER, established by modeling and design and achieved through careful control of mechanical and magnetic errors, are essential to the nexL generation of insertion devices.

In this paper we describe the operation of an XUV high gain FEL operating within a bypass of an electron storage ring, and discuss the implications on storage ring optimization imposed by FEL requirements. It transpires that, in the parameter regime of interest, collective effects within the beam play an important role. For example, intrabeam scattering dilutes the transverse emittance of the beam and the microwave instability increases the momentum spread. Both phenomena reduce the effectiveness of the FEL. A computer code, ZAP, has been written which, for a given lattice design, takes all such effects into consideration and produces a figure of merit for FEL operation for that machine. We show the results of ZAP for several storage ring designs, all optimized for FEL operation, and present a design example of a facility capable of producing coherent radiation at 400 Å with tens of megawatts of peak power.

The dependence of electron beam lifetime on vertical aperture is measured for the storage ring BESSY providing quantitative information necessary for estimating the usable gap sizes of the variable vacuum gap undulator presently being built. The data allow one to distinguish between different lifetime limiting mechanisms thus yielding useful storage ring diagnostics. General agreement with available particle loss models is observed.

In this paper we describe the different goals of the Orsay optical Klystron : free electron laser, coherent harmonic generation, tool for beam diagnostics, source for spin polarized photoemission of solids, optical experiments on clusters and holography.

Operation of a high gain VUV/Soft X-Ray Free Electron Laser (FEL) oscillator on the Stanford X-Ray Center (SXRC) storage ring is investigated. Laser energy and emittance acceptance in the high gain regime for XUV light are examined using the FEL amplifier simulation code FRED. Assuming 50% mirror reflectivity, oscillation is shown to be feasible down to 220 Å with a realizable wiggler magnet placed in the 27 meter straight section of the 1 GeV SXRC ring. Laser output power and time structure are determined for a 960 Å oscillator operating in both "cw" and slow pulsed modes.

We have built a compact tunable hybrid undulator for use in a small free-electron laser. The design and adjustment procedures, as well as the results of measurements on the wiggler and lasing performance are summarized here.

In this communication it is illustrated the technique used for the dipole moment measurement of a set of SmCo permanent magnets. These magnets have been used for the realization of a linear undulator for the ENEA-Frascati free electron laser device. The main results of the measurements are summarized. Some criteria for the assembling of the undulator are analyzed in order to minimize the effects of the differences between the magnets. The evaluation of experimental error measurement is included. Finally it is described the computer code that suggested the best configuration according to the above criteria.

A NdFe-steel hybrid configured permanent magnet wiggler is being developed for insertion in the SPEAR ring at the Stanford Synchrotron Radiation Laboratory, SSRL. Featuring 15 complete periods, a 12.9-cm magnetic period length, and a peak magnetic field range of 0.01-1.4 Tesla, the wiggler was designed to provide an intense radiation source for the National Laboratory/University of California participating research team (PRT) facility on Beam Line VIII-W. A new permanent magnet material, neodymium-iron (NdFe), is being used in the magnetic structure instead of rare-earth cobalt, REC, used previously in the 27-period wiggler now on Beam Line VI. NdFe advantages include a 16% higher coercive force (10.6-kOe vs. 9.0-kOe) and lower cost. The wiggler design features a thin walled, rigid vacuum chamber with pole pockets on opposing surfaces allowing a 2.1-cm minimum magnetic gap with a 1.8-cm beam vertical aperture. At 3 GeV the wiggler at peak field is expected to radiate approximately two kilowatts in a 5-mrad horizontal fan with a 7.8 keV critical energy. Calculations are in progress to model the wiggler radiation spatial and spectral radiation emission.

The design constraints and expected performance of insertion devices in the proposed European Synchrotron Radiation Facility are presented. The phase space distribution of the radiation from the multipole wigglers and wavelength shifter is described. The peak flux and brilliance obtainable from undulator sources are examined and the tunability of specific devices is discussed.

The design and optimization of short period (λu ⪅ 20 mm) undulators is discussed. It is shown that such undulators are preferably realized by permanent magnet arrays in the hybrid configuration. Evaluation of the magnetic field of the hybrid configuration by the scalar potential method is reviewed and useful approximations for the short period region are derived.

The characteristics of the Soft X-ray Undulator to be installed on the x-ray ring of the National Synchrotron Light Source are presented. The output of the undulator in the presence of finite electron beam emittance is estimated. The coherence e prop of the radiation are described, leading to an expected partially coherent flux of 102 photons per second. Numerical methods for estimating the irradiance of undulator radiation are presented. The methods use the exact solution for radiation from a single electron and combine the radiation pattern with the electron beam distribution, allowing us to examine cases such as even harmonic radiation on the undulator axis, as well as the red-shift of harmonic peaks due to electron beam emittance. Finally, the effects of electron beam energy spread are briefly considered.

A high field wiggler to be inserted in the European Syncrotron Radiation Facility (ESRF), as designed at the Joint Research Centre at Ispra, is presented. A peak field in excess of 3.0 Tesla is obtained by means of two superconducting racetrack windings made up with Nb-Ti copper stabilized wires. Current grading is foreseen. With the use of high current densities and a small magnetic gap, half period length of ~ 8 cm is obtained. In order to null the field integral along the beam path through the magnet, two small conventional magnets, to be installed outside the LHe cryostat, are foreseen. The magnetic field for the chosen configuration is calculated by 2-D and 3-D codes. A code has been developed to evaluate the behaviour of the magnet in case of a quench. The X-ray source characteristics have been analysed.

For the 0.8 GeV storage ring BESSY in Berlin an insertion device to be used as undulator and wiggler (0 ≤ K ≤ 6) is currently under construction. The pure permanent magnet structure consists of 35 periods with 7 cm period length. The influence of operating this structure with the small emittance optic METRO was studied quantitatively in linear synchrotron theory by modelling the multipole structure by hard edge dipole magnets. Working point, betatron functions etc. were studied as function of the K parameter. It turns out that vertical focussing can be compensated sufficiently well for fields ≤12 kG by detuning the two adjacent quadrupoles. The model calculations were checked by calculating trajectories through the full three dimensional magnetic field by solving the equations of motion. As expected, vertical focussing is overestimated in the hard edge model by about 20 %.

Certain types of insertion devices for angiography can produce extraordinarily large heat fluxes on critical components of a synchrotron beam line and its optics. The shutters, beam splitters, filters, and the first-stage monochromators all are subjected to large fluxes of radiation. The cooling requirements of such beam line components are approached in a comprehensive manner to identify the governing parameters from first principles. Analytical techniques have been used to study various methods of handling the heat loads using both liquid metal and water coolants for various potential heated geometries. It is found that when properly designed, liquid metal cooling can be much more efficient. In addition, composites and low Z surfaces have been considered. Also investigated are the heat transfer problems of the optical stages and rotating monochromators.

This paper presents an overview of optical, thermal, and mechanical problems encountered with optical elements in beams of synchrotron-radiation (SR) emitted by electron "sidewinders" such as wigglers, undulators, and free-electron lasers (FELs). Perhaps the most challenging problem is the management of the high-power densities from wigglers without degradation of the optical quality of the beam. Another challenging problem is the reduction of near-specular scattering by surfce microroughness on the mirrors. Near-specular scattering becomes more important as the degree of coherence and collimation to be maintained increases from bend-magnet SR to undulator and FEL radiation. It is emphasized that the surface autocovariance length of the mirror is the determiner of the angular distribution of scattering, and that very long autocovariance lengths are required for highly coherent SR beams.

Insertion devices as radiation sources on storage rings offer potential for substantial gains in beam brightness and flux delivered to a sample. Achieving these gains, however, requires several new aspects of beam line design. New aspects of beam line design arise from the high beam power, the complex spectral and geometrical characteristics, and the need for a wide spectral range. We discuss these aspects of insertion device soft X-ray synchrotron radiation beam lines with examples drawn from our project creating Beam Line Wunder at the Stanford Synchrotron Radiation Laboratory. The major research use envisioned for this beam line is for spectroscopic experiments which require the highest possible intensity and resolution for a tunable constant deviation source. We summarize the current status of each of the beam line major components: the Multi-undulator, the transport system, the Locust Monochromator, the computer control system, and the experimental area.

Free electron lasers place demands on optics which require extensions of the state of the art in both substrates and coatings. Further effort is needed to counteract the sources of energy deposition into the optics, and to deal effectively with the resulting thermal effects. In this paper I review the scaling and possible mechanisms of single photon damage, and discuss the thermal phenomena expected in FEL optics.

High power and high power densities due to absorbed radiation are significant design considerations which can limit performance of mirrors receiving highly collimated synchrotron radiation from insertion devices and bending magnet sources. Although the grazing incidence angles needed for x-ray optics spread the thermal load, localized, non-uniform heating can cause distortions which exceed allowable surface figure errors and limit focusing resolution. This paper discusses the suitability of numerical approximations using finite element methods for heat transfer, deformation, and stress analysis of optical elements. The primary analysis objectives are (1) to estimate optical surface figure under maximum heat loads, (2) to correctly predict thermal stresses in order to select suitable materials and mechanical design configurations, and (3) to minimize fabrication costs by specifying appropriate tolerances for surface figure. Important factors which determine accuracy of results include finite element model mesh refinement, accuracy of boundary condition modeling, and reliability of material property data. Some methods to verify accuracy are suggested. Design analysis for an x-ray mirror is presented. Some specific configurations for internal water-cooling are evaluated in order to determine design sensitivity with respect to structural geometry, material properties, fabrication tolerances, absorbed heat magnitude and distribution, and heat transfer approximations. Estimated accuracy of these results is discussed.

The first crystal of the Brown-Hower x-ray monochromator of the LBL-EXXON 54 pole wiggler beamline at Stanford Synchrotron Radiation Laboratory (SSRL) is subjected to intense synchrotron radiation. To provide an accurate thermal/structural analysis of the existing monochromator design, a finite element analysis (FEA) was performed. A very high and extremely localized heat flux is incident on the Si (220) crystal. The crystal, which possesses pronouncedly temperature-dependent orthotropic properties, in combination with the localized heat load, make the analysis ideally suited for finite element techniques. Characterization of the incident synchrotron radiation is discussed, followed by a review of the techniques employed in modeling the monochromator and its thermal/structural boundary conditions. The results of the finite element analysis, three-dimensional temperature distributions, surface displacements and slopes, and stresses, in the area of interest, are presented. Lastly, the effects these results have on monochromator output flux and resolution are examined.

An ellipsoidal copper mirror has been diamond turned at the Lawrence Livermore National Laboratory to provide strong demagnification of synchrotron light. its surface curvature varies too rapidly over its extent for conventional polishing techniques to be applicable. Surface smoothing has been attempted in this case by applying lacquer to the surface and then metallizing it for operation in the soft x-ray range. This paper describes the results obtained with this mirror in focussing 1 keV undulator light, surface damage to the lacquer, and the results of some diagnostics done on the mirror surface in the visible regime.

The first generation of insertion devices having reached maturity (or almost), it is appropriate to survey directions along which new developments are expected. These include: Beam cooling with undulators, elementary particle physics with wigglers and undulators, microwigglers, dynamic (i.e. electromagnetic) insertion devices, bunched electron beam wigglers, time compression of photon pulses, the confinement and compression of radiation, optimized insertion devices, damage resistant optics, photon bunch contouring, and the rebunching of electron beams by phase switching. A theorem will be mentioned which limits the number of photons emitted by a relativistic electron (e.g. one passing through an insertion device).

In this paper we consider the main reasons why a quantum theory of the free-electron laser is of interest, and summarize and compare a number of different approaches, and their main results. Recent results concerning the intrinsic linewidth and photon statistics of the free-electron laser are also presented.

There are a variety of methods for generating radiation in the range from infrared to gamma rays, and four different techniques using charged particle beams will be presented. The first three are considered as spontaneous emissions sources, and the last as a stimulated source. None of the approaches are likely to be suitable for insertion in a storage ring, since they all involve a significant alteration in particle trajectories.

Experimental study of a microwave undulator which uses the transverse field of micro-wave has been performed successfully at the Photon Factory electron linac. When the S-band microwave power of 300 kW was fed into the undulator cavity, the equivalent magnetic field of 0.45 kG has been obtained. The undulator radiation in the visible region was observed and its spectrum was measured.

A variational approach to isolating optimum particle trajectories in insertion devices is presented in this paper. The method is based on assigning performance functions to insertion devices which are functionals of the particle trajectory, and then extremizing the performance functions by varying the particle trajectory. A concrete example of general interest is solved, and an outline of extending the method to general cases is given.

Operation of free-electron lasers at long optical wavelengths (≥600 nm) has now been successfully demonstrated at several laboratories. To operate a free-electron laser at shorter wavelengths imposes constraints on the brightness of the electron beam which are difficult to achieve. Until recently, it was perceived that only an electron storage ring could satisfy these beam requirements. However, our previous 1-D theoretical calculations revealed that modest improvements in the emittance available from rf-linear accelerators would be sufficient to allow operation of an FEL in the XUV spectral range. We shall present new theoretical results for the design of a linac-driven XUV FEL derived from an improved simulation model. The model is fully three-dimensional in its treatment of the undulator magnetic field, the optical radiation field, and the motion of electrons in a finite-emittance beam. Furthermore, the model computes self-consistently the motion of the electrons and the amplification, diffraction, and the refraction of the light within the undulator magnet. Propagation of the optical beam and reflection at the mirrors of the optical resonator are incorporated in the model so that a complete laser oscillator solution can be generated. The computed performance parameters of a particular XUV FEL oscillator design will be compared with the output of synchrotron radiation sources.

The process by which the radiation intensity grows and correlation in the electron distribution develops, as the beam passes through a long undulator, is described.