Transverse Beam Size Research Articles

PRODUCTION OF FEMTOSECOND PULSES AND MICRON BEAM SPOTS FOR HIGH BRIGHTNESS ELECTRON BEAM APPLICATIONS

Current and future applications of high brightness electron beams, which include advanced accelerators and beam-radiation interactions require both transverse and longitudinal beam sizes on the order of tens of microns. Ultra-high density beams may be produced at moderate energy (50 MeV) by compression and subsequent strong focusing of low emittance, photoinjector sources. We describe the implementation of this method used at the PLEIADES inverse-Compton scattering (ICS) x-ray source at LLNL in which the photoinjector-generated beam has been compressed to 300 fsec rms duration using the velocity bunching technique and focused to 20 μm rms size using an extremely high gradient, permanent magnet quadrupole focusing system.

Imaging of high-energy electron beam profile with optical diffraction radiation

Optical transition radiation (OTR) has been widely used in electron beam profile imaging. Optical diffraction radiation (ODR) has recently been used to measure the electron beam's transverse size with the angular distribution. Because of the close relationship between OTR and ODR, it is natural to ask whether ODR could be used to image the beam profile as is done with OTR. In this paper, the image formation process is investigated as a two-dimensional (2D) convolution. The image formed with ODR as a single electron passes through a circular aperture, through a rectangular slit, and beneath a semi-infinite plane is studied from first principle and taken to be the point spread function (PSF) of the imaging system. It is found that, unlike the OTR case, the PSF of ODR is space variant and largely depends on the shape of the ODR target. With this characteristic, the beam image formed with ODR differs greatly from the real beam profile, and the deconvolution process is generally needed in order to retrieve the real beam distribution from the ODR image. The possibility of using an image formed with ODR from a rectangular slit and a semi-infinite plane to determine beam profile in the direction parallel to the edge of the slit or plane and monitoring the beam's position are estimated. The theoretical prediction is compared to recently reported experimental results and a qualitative agreement is achieved.

Propagation of radially polarized elegant light beams

A radially polarized elegant beam (RPEB) in which the argument of the Laguerre part is complex is introduced and studied. The nonparaxial and paraxial propagation properties of the RPEB are demonstrated analytically and numerically in free space in terms of the vectorial Rayleigh-Sommerfeld formulas. The electric field distribution of the RPEB preserves the radial polarization at any propagation position. For the lowest-order RPEB and the lowest-order radially polarized beam cases, the general expressions for the nonparaxial propagation field are identical in free space. The exact on-axis expression of the RPEB has been provided in closed-form terms for an arbitrary transverse beam size.

Spatial coherence in the transition radiation spectrum

The formal expression of the spectral distribution of the transition radiation intensity will be here derived in the case of a relativistic three-dimensional charged beam. Charged beams with a particle density such as is typically encountered in a particle accelerator will be considered. In particular, a sufficiently high particle density will be supposed so that a continuous spatial distribution function can be reliably attributed to the charged bunch. The formula of the spectral distribution of the transition radiation intensity originated by a relativistic three-dimensional charged beam – already presented in a previous work – will be here submitted to a formal check and interpreted in the physical consequences. The present work contains an additional mathematical derivation of the radiation energy spectrum consisting in a different method to implement the continuous limit in the distribution function of the particle coordinates. In the former derivation of the formula, the average operation with respect to the continuous distribution function of the particle coordinates was applied to the radiation intensity of a N electron bunch. In the present one, it is applied to the radiation electric field of a N electron bunch. The comparison of the two alternative but in any case equivalent formal routes to the spectral distribution of the transition radiation intensity will offer the possibility to directly cross-check the mathematical self-consistency of the presented results within the limits of applicability of the continuous limit approximation. According to such results, both the flux and the angular distribution of the photons emitted at a given wavelength – even shorter than the longitudinal length of the bunch – are expected to undergo a modification as the beam transverse size is varied with respect to the observed wavelength. As a function of the beam transverse size the spatial coherence degree of the transition radiation source is thus expected to change. The physical consistency of such an effect occurring in the transition radiation emission by a charged beam can be argued on the basis of a compatibility criterion with other similar relativistic electromagnetic radiative phenomena and interpreted in the framework of the temporal causality and the Huygens–Fresnel principles. Finally, the aspect of the applicability of the continuous limit approximation to the case of a charged beam in a particle accelerator is treated in terms of a practical quantitative criterion.

Nonparaxial propagation of radially polarized light beams

Starting from the vectorial Rayleigh-Sommerfeld formulas, the nonparaxial propagation of radially polarized light beams in free space is investigated analytically and numerically. The paraxial case can be treated as a special case of the general result. The exact expression of the radially polarized light beams, which is valid for the fields to be predicted for an arbitrary transverse beam size, has been derived in closed-form terms for any on-axis point. The validity of the analytical results is confirmed by the numerical results.

Clearing of a polydisperse water aerosol by a laser pulse in the diffusive—convective regime

The propagation of an IR laser pulse through a water aerosol layer (fog, clouds) is studied. The relative motion of the beam and medium, the diffraction spread, thermal self-action of the laser beam, absorption and scattering of radiation by particles, evaporation of particles (aerosol clearing), and the size distribution of particles were taken into account. The propagation problem was solved numerically at a macroscopic scale of the order of the beam transverse size, and the action of radiation on drops was considered at a microscopic scale of the order of the particle radius. A satisfactory agreement was obtained between theoretical and experimental results.

Longitudinal phase-space manipulation of ellipsoidal electron bunches in realistic fields

Since the recent publication of a practical recipe to create ``pancake'' electron bunches which evolve into uniformly filled ellipsoids, a number of papers have addressed both an alternative method to create such ellipsoids as well as their behavior in realistic fields. So far, the focus has been on the possibilities to preserve the initial ``thermal'' transverse emittance. This paper addresses the linear longitudinal phase space of ellipsoidal bunches. It is shown that ellipsoidal bunches allow ballistic compression at subrelativistic energies, without the detrimental effects of nonlinear space-charge forces. This in turn eliminates the need for the large correlated energy spread normally required for longitudinal compression of relativistic particle beams, while simultaneously avoiding all problems related to magnetic compression. Furthermore, the linear space-charge forces of ellipsoidal bunches can be used to reduce the remaining energy spread even further, by carefully choosing the beam transverse size, in a process that is essentially the time-reversed process of the creation of an ellipsoid at the cathode. The feasibility of compression of ellipsoidal bunches is illustrated with a relatively simple setup, consisting of a half-cell S-band photogun and a two-cell booster compressor. Detailed GPT simulations in realistic fields predict that 100 pC ellipsoidal bunches can be ballistically compressed to 100 fs, at a transverse emittance of $0.7\text{ }\ensuremath{\mu}\mathrm{m}$, with a final energy of 3.7 MeV and an energy spread of only 50 keV.

Transverse beam sizes and quasi emittances for linearly coupled optics

Two transverse eigenmode rms emittances are defined statistically in the uncoupled normalized coordinate system. They are assumed to be adiabatic invariants. With linear coupling's action-angle parameterization, the strict expression for the beam size matrix in the laboratory coordinate system is obtained. It can be expressed in matrix P defined in the action-angle parameterization or in Twiss and coupling parameters defined in Edwards–Teng's parameterization, along with the eigenmode rms emittances. Numerical simulation calculations are carried out to check the analytical expressions and to verify the adiabatic eigenmode rms emittance invariants during the skew quadrupole magnet ramping. With linear coupling's matrix perturbation approach, the strict expressions of the horizontal and vertical beam sizes in the laboratory coordinate system are approximated to give the quasi horizontal and vertical beam emittances under the weak linear difference coupling situation. The predictions of quasi horizontal and vertical beam emittances from different approximations are presented and discussed.

Huge transverse deformation in nonspecular reflection of a light beam possessing orbital angular momentum near critical incidence

We derive a general expression for the field distribution of Hermite- and Laguerre-Gaussian (LG) beams reflected at a dielectric interface. The intensity distributions of the reflected LG light beam at the beam waist are also observed experimentally in the vicinity of the critical incidence. They are greatly deformed because of the nonspecular transverse shift induced by the orbital angular momentum of the LG beam. The observed and calculated intensity distributions agree well and indicate that a large fraction of the electromagnetic energy flows as much as the transverse beam size.

Nonintercepting diagnostics for transverse beam parameters: From rings to ERLs

The characterization of particle-beam parameters in accelerators and transport lines is important to the experiment's success. The development of nonintercepting (NI) diagnostics is of growing interest in the community due to top-up operations for storage rings such as the Advanced Photon Source (APS), as well as the rapidly developing energy recovering linacs (ERLs). In both areas beam position and beam quality are relevant, and the ability to measure these in an NI manner is critical. Beam transverse size and divergence are more of a challenge, and examples of the minimally intercepting or NI measurements based on optical transition radiation (OTR), optical synchrotron radiation (OSR), X-ray synchrotron radiation (XSR), optical diffraction radiation (ODR), and undulator radiation (UR) will be presented as space permits. These are relevant to the various ERL parameter spaces and operating modes.

Study of beam–beam effects in eRHIC with self-consistent beam–beam simulation

Beam–beam effects in eRHIC was studied with a self-consistent (strong–strong) beam–beam simulation by using the particle-in-cell method. Beam–beam limits were examined as thresholds of the onset of coherent beam–beam instability. For the proposed luminosity, the bunch intensities optimized in consideration of the beam–beam effect were discussed. It was also found that the modulation in the beam–beam interaction on PACMAN bunches in eRHIC can induce a high-order coherent beam–beam instability with a spontaneous oscillation of transverse beam size and a chaotic oscillation of beam centroid. As the beam–beam interaction in eRHIC is traditionally considered as strong-weak or very unsymmetrical, the beam–beam problem in eRHIC represents an example of the coherent beam–beam effect in the strong-weak case of beam–beam interactions.

Six-dimensional muon beam cooling using a homogeneous absorber: Concepts, beam dynamics, cooling decrements, and equilibrium emittances in a helical dipole channel

The fast reduction of the six-dimensional phase space of muon beams is an essential requirement for muon colliders and also of great importance for neutrino factories based on accelerated muon beams. Ionization cooling, where all momentum components are degraded by an energy absorbing material and only the longitudinal momentum is restored by rf cavities, provides a means to quickly reduce transverse beam sizes. However, the beam energy spread cannot be reduced by this method unless the longitudinal emittance can be transformed or exchanged into the transverse emittance. Emittance exchange plans until now have been accomplished by using magnets to disperse the beam along the face of a wedge-shaped absorber such that higher momentum particles pass through thicker parts of the absorber and thus suffer larger ionization energy loss. In the scheme advocated in this paper, a special magnetic channel designed such that higher momentum corresponds to a longer path length, and therefore larger ionization energy loss, provides the desired emittance exchange in a homogeneous absorber without special edge shaping. Normal-conducting rf cavities imbedded in the magnetic field regenerate the energy lost in the absorber. One very attractive example of a cooling channel based on this principle uses a series of high-gradient rf cavities filled with dense hydrogen gas, where the cavities are in a magnetic channel composed of a solenoidal field with superimposed helical transverse dipole and quadrupole fields. In this scheme, the energy loss, the rf energy regeneration, the emittance exchange, and the transverse cooling happen simultaneously. The theory of this helical channel is described in some detail to support the analytical prediction of almost a factor of ${10}^{6}$ reduction in six-dimensional phase space volume in a channel about 56 m long. Equations describing the particle beam dynamics are derived and beam stability conditions are explored. Equations describing six-dimensional cooling in this channel are also derived, including explicit expressions for cooling decrements and equilibrium emittances.

Properties of self-focusing of elliptic beams

Stationary self-focusing of collimated elliptic Gaussian beams is studied numerically. It is shown that the critical self-focusing power increases with increasing the axial ratio of the initial elliptic cross section. Self-focusing is accompanied by oscillations of the beam transverse size caused by the competition between the diffraction-limited divergence and nonlinear compression. As the power of the beam with the axial ratio a/b≥3 increases, aberration self-focusing occurs, at which, after the formation and competition of several intensity maxima in the beam cross section, a global maximum appears at the beam centre, which forms a nonlinear focus. The approximation formula for the self-focusing distance is generalised to elliptic beams.

Six-dimensional muon beam cooling in a continuous, homogeneous, gaseous hydrogen absorber

The fast reduction of the six-dimensional phase space of muon beams is required for muon colliders and is also of great importance for neutrino factories based on accelerated muon beams. Ionization cooling, where all momentum components are degraded by an energy absorbing material and only the longitudinal momentum is restored by RF cavities, provides a means to quickly reduce transverse beam sizes. However, the beam momentum spread cannot be reduced by this method unless the longitudinal emittance can be transformed or exchanged into the transverse emittance. The best emittance exchange plans up to now have been accomplished by using magnets to disperse the beam along the face of a wedge-shaped absorber such that higher momentum particles pass through thicker parts of the absorber and thus suffer larger ionization energy loss. In the scheme advocated in this paper, it is noted that one can generate a magnetic channel filled with absorber where higher momentum corresponds to a longer path length and therefore larger ionization energy loss. Thus a homogeneous absorber, without any special edge shaping, can provide the desired emittance exchange. An attractive example of a cooling channel based on this principle involves the use of RF cavities filled with a continuous gaseous hydrogen absorber in a magnetic channel composed of a solenoidal field with superimposed helical transverse dipole, quadrupole, and octupole fields. The theory of this helical channel is described to support the analytical prediction of a million-fold reduction in phase space volume in a channel 150m long.

Electron cooling experiments at the ESR

The properties of electron cooled beams of highly charged ions have been studied at the ESR. New experiments using a beam scraper to determine the transverse beam size provide the beam parameters in the intrabeam scattering dominated intensity regime, but also at very low intensity when the ion beam enters into an ultra-cold state. Extremely low values of longitudinal and transverse beam temperature on the order of meV were achieved for less than 1000 stored ions. An experiment with bunched ultra-cold beam showed a limit of the line density which agrees with the one observed for coasting beams. Cooling of decelerated ions at a minimum energy of 3MeV/u has been demonstrated recently.

On the brightness of diluted photon source in synchrotron light facilities

The undulator radiation spectral brightness in storage ring is studied taking into account the effects of the electron beam oscillating trajectory and the beam transverse size variation along the undulator. The modified optimal beta function at the source point to reach maximum brightness is obtained that is in direct relation with the emitted photons wavelength. It is shown that the maximum spectral brightness in long wavelength range is achieved with low beta lattice, while in short wavelength range with larger beta.

Novel scheme of the long wavelength FEL amplifier with a transverse electron current

A novel scheme of the long wavelength FEL amplifier with a transverse electron current has been discussed. In this scheme an amplified signal propagates across the electron beam and the operating wavelength is equal to the undulator period. A specific feature of the transverse current amplifier is the absence of saturation, i.e. under special optimization of the undulator field, the output power grows proportionally to interaction distance, which is defined by the beam transverse size. The X-band amplifier should be based on the U-2 accelerator at the Budker Institute of Nuclear Physics and produce 500 kV, 1 kA/cm sheet electron beam with transverse size amounts 140 cm (J. Appl. Phys. 72 (1992) 1657). It has been observed that a gain of ∼38 dB corresponding to a 6.5 GW output power and 10% efficiency could be achieved for a 2 kOe undulator field and a 1 MW seed signal. Additional optimization of guiding and undulator fields provides the possibility of increasing the output power up to 18 GW with an efficiency of 27%.

Muon beam ionization cooling in a linear quadrupole channel

In a scenario for either a Neutrino Factory or Muon Collider, the anticipated transverse beam emittance subsequent to capture and phase rotation is so large that it permits a relaxation of the requirements on beam spot size in the early stages relative to the final stages of ionization cooling. Staging the cooling process according to initial emittances, coupled with modest cooling factors, permits more optimal and efficient cooling channel designs and avoids much of the difficulty encountered with channels which attempt to maintain strong focusing (large, 300–500 mrad, divergences) across ultra-large momentum ranges (⩾±20% δ p/ p). Relaxation of spot size at the absorber, especially in the “precooling” stage, allowed development of an efficient transverse cooling channel based simply on a quadrupole FODO cell. This work describes the design of such a cooling channel and its application as an upstream stage of beam cooling. Being a linear channel with no bends, it serves to reduce the large transverse beam size delivered from muon-beam capture and bunching before entering more restricted optical structures such as transverse plus longitudinal cooling channels or accelerators.

Erratum: Nonlinearities and effects of transverse beam size in beam position monitors [Phys. Rev. ST Accel. Beams4, 092801 (2001)

1 MoreReceived 12 February 2003DOI:https://doi.org/10.1103/PhysRevSTAB.6.039902This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Crystallisation of ion beams in the rf quadrupole storage ring PALLAS

The crystallisation of laser-cooled Mg+ ion beams circulating in the table-top rf quadrupole storage ring PALLAS at a velocity of the order of 2800 m/s (beam energy 1 eV) is reviewed. Emphasis is given to the description of the experimental techniques that were required for this first realisation of crystalline beams. The equivalence of the equations of motion for rf electric and magnetic confinement and thus for PALLAS and high-energy storage rings is pointed out. The phase transition is indicated by the detection of a sudden collapse of the transverse beam size, by the low velocity spread, and by the exceptional stability of the crystalline state, persisting for more than3000 revolutions or 106 focusing periods without any cooling.