Betatron Oscillation Amplitude Research Articles

Nonlinear field effects in the collector ring due to large-amplitude particle oscillations

In the frame of the FAIR project, the Collector Ring (CR) is planned to be built for efficient cooling of antiprotons and rare isotope beams [1]. In order to accept hot beam from separators large acceptances are required. This paper examines the effects which can influence the beam dynamics due to large betatron oscillation amplitude and momentum spread. Using analytic expressions, the amplitude-dependent tune shifts driven by sextupole magnets, the fringe field of quadrupole magnets, and kinematics effects have been calculated. The obtained results have been compared with numerical simulations by means of precise multi-turn particle tracing. The tracking analysis for the CR has been performed considering the real shape of the magnetic field of the wide aperture quadrupole. We report on quantitative studies of the effects on the dynamic aperture of the rings.

Widening and distortion of the particle energy distribution by chromaticity in quasi-isochronous rings

This paper reports the observation of beam energy widening and distortion from Gaussian due to a nonvanishing horizontal chromaticity at a quasi-isochronous storage ring. The result originates from an average path-length dependence on the betatron oscillation amplitudes, which is intimately correlated to the transverse chromaticities. It is the first experimental validation of the impact of such a nonlinear transverse-longitudinal coupling effect on the equilibrium beam characteristics in a storage ring. The results could be important for quasi-isochronous rings, steady-state microbunching, nonscaling fixed-field alternate gradient accelerators, etc., where very small momentum compaction or large chromaticity is required.

Trace-space reconstruction of low-emittance electron beams through betatron radiation in laser-plasma accelerators

A new methodology able to model and reconstruct the transverse trace space of low-emittance electron beams accelerated in the bubble regime of laser-plasma interaction is presented. The single-shot measurement of both the electron energy spectrum and the betatron radiation spectrum is shown to allow a complete measurement of the transverse emittance, including the correlation term. A novel technique to directly measure the betatron oscillation amplitude distribution is described and tested at the SPARC-LAB test facility through the interaction of the ultrashort ultraintense Ti:Sa laser FLAME with a He gas-jet target. Via the exposed technique the beam transverse profile is also retrieved. From the study of the electron transverse dynamics inside the plasma bubble, the nonlinear correlation between the betatron amplitude and the divergence, i.e. the angle with respect the acceleration axis, is found. The angular distribution of the electron beam inside the bubble is retrieved. The knowledge of the trace-space density allows a more accurate measurement of the transverse emittance with respect to previous paradigms.

Enhanced x-rays from resonant betatron oscillations in laser wakefield with external wigglers

Generation of ultra-short betatron x-rays by laser-accelerated electron beams is of great research interest as it has many applications. In this paper, we propose a scheme for obtaining bright betatron x-rays by applying external wiggler magnetic field in the laser wakefield to resonantly drive the betatron oscillations of the accelerated electrons therein. This results in a significant enhancement of the betatron oscillation amplitude and generation of bright x-rays with high photon energy. The scheme is demonstrated using two-dimensional particle-in-cell simulation and discussed using a simple analytical model.

Enhanced betatron radiation in strongly magnetized plasma

Betatron radiation in strongly magnetized plasma is investigated by two dimensional (2D) particle-in-cell (PIC) simulations. The results show that the betatron radiation in magnetized plasmas is strongly enhanced and is more collimated compared to that in unmagnetized plasma. Single particle model analysis shows that the frequency and the amplitude of the electrons's betatron oscillation are strongly influenced by the axial external magnetic field and the axial self-generated magnetic field. And the 2D PIC simulation shows that the axial magnetic field is actually induced by the external magnetic field and tends to increase the betatron frequency. By disturbing the perturbation of the plasma density in the laser-produced channel, the hosing instability is also suppressed, which results in a better angular distribution and a better symmetry of the betatron radiation.

Amplitude-dependent orbital period in alternating gradient accelerators

Orbital period in a ring accelerator and time of flight in a linear accelerator depend on the amplitude of betatron oscillations. The variation is negligible in ordinary particle accelerators with relatively small beam emittance. In an accelerator for large emittance beams like muons and unstable nuclei, however, this effect cannot be ignored. We measured orbital period in a linear non-scaling fixed field alternating gradient (FFAG) accelerator, which is a candidate for muon acceleration, and compared with the theoretical prediction. The good agreement between them gives important ground for the design of particle accelerators for a new generation of particle and nuclear physics experiments.

Enhanced betatron oscillations in laser wakefield acceleration by off-axis laser alignment to a capillary plasma waveguide

The generation of betatron radiations by laser-accelerated electron beams is of great interest in the scientific community as it has many applications. In this paper, we propose a new method for the generation of short wavelength betatron radiations. In the new scheme, a high power laser pulse is sent into a capillary plasma waveguide at an off-axis position to intentionally enhance the betatron oscillation amplitude, which can lead to the production of shorter wavelength radiations. We demonstrated that the idea works by 2D particle-in-cell simulations and we also developed a theory to explain the phenomena. In this paper, details of the results are described.

Reconstruction of lattice parameters and beam momentum distribution from turn-by-turn beam position monitor readings in circular accelerators

In high chromaticity circular accelerators, rapid decoherence of the betatron motion of a particle beam can make the measurement of lattice and bunch values, such as Courant-Snyder parameters and betatron amplitude, difficult. A method for reconstructing the momentum distribution of a beam from beam position measurements is presented. Further analysis of the same beam position monitor data allows estimates to be made of the Courant-Snyder parameters and the amplitude of coherent betatron oscillation of the beam. The methods are tested through application to data taken on the linear nonscaling fixed field alternating gradient accelerator, EMMA.

Optimization of the crystal assisted collimation of the SPS beam

The possibility for optimization of crystal assisted collimation has been studied at the CERN SPS for stored beams of protons and Pb ions with 270 GeV/c per unit charge. A bent silicon crystal used as a primary collimator deflects halo particles in the channeling regime, directing them into a tungsten absorber. In channeling conditions a strong reduction of off-momentum particle numbers produced in the crystal and absorber, which form collimation leakage, has been observed in the first high dispersion (HD) area downstream. The present study shows that the collimation leakage is minimal for some values of the absorber offset relative to the crystal. The optimal offset value is larger for Pb ions because of their considerably larger ionization losses in the crystal, which cause large increases of particle betatron oscillation amplitudes. The optimal absorber offset allows obtaining maximal efficiency of crystal-assisted collimation.

Beam diffusion measurements using collimator scans in the LHC

The time evolution of beam losses during a collimator scan provides information on halo diffusion and population. This is an essential input for machine performance characterization and for the design of collimation systems. Beam halo measurements in the CERN Large Hadron Collider were conducted through collimator scrapings in a dedicated beam study for the first time at 4 TeV. Four scans were performed with two collimators, in the vertical plane for beam 1 and horizontally for beam 2, before and after bringing the beams into collisions. Inward and outward steps were performed. A diffusion model was used to interpret the observed loss rate evolution in response to the collimator steps. With this technique, diffusion coefficients were estimated as a function of betatron oscillation amplitude from approximately 3 to 7 standard deviations of the transverse beam distribution. A comparison of halo diffusion and core emittance growth rates is also presented.

Generation of maximum photon flux at the optimum plasma density in the laser-driven betatron oscillation

The plasma density effect on x-ray characteristics from betatron oscillation in a laser wakefield accelerator was studied via two-dimensional particle-in-cell simulations. Inside an ion cavity, accelerated electrons with betatron oscillatory motion produce synchrotron radiation. As the plasma density increases, both bunch charge and betatron oscillation amplitude increase in the laser unmodulated regime and decrease again in the laser modulated regime. The multicavitation and weaker field from the laser modulation result in a smaller bunch charge and a decrease in oscillation amplitude in the modulated regime. The photon flux and critical energy in the wiggler regime, where the ion cavity acts as a wiggler, can be optimized and controlled through plasma density. In this work, the mechanism of the optimum ratio of laser pulse duration to plasma wavelength for maximum photon flux was investigated.

New injection scheme using a pulsed quadrupole magnet in electron storage rings

We demonstrated a new injection scheme using a single pulsed quadrupole magnet (PQM) with no pulsed local bump at the Photon Factory Advanced Ring (PF-AR) in High Energy Accelerator Research Organization (KEK). The scheme employs the basic property of a quadrupole magnet, that the field at the center is zero, and nonzero elsewhere. The amplitude of coherent betatron oscillation of the injected beam is effectively reduced by the PQM; then, the injected beam is captured into the ring without largely affecting the already stored beam. In order to investigate the performance of the scheme with a real beam, we built the PQM providing a higher field gradient over $3\text{ }\text{ }\mathrm{T}/\mathrm{m}$ and a shorter pulse width of $2.4\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$, which is twice the revolution period of the PF-AR. After the field measurements confirmed the PQM specifications, we installed it into the ring. Then, we conducted the experiment using a real beam and consequently succeeded in storing the beam current of more than 60 mA at the PF-AR. This is the first successful beam injection using a single PQM in electron storage rings.

Analytical description of stripping foil extraction from isochronous cyclotrons.

Analytical expressions are derived describing beam parameters on a stripping foil (SF) as a function of radial amplitude of betatron oscillations and of energy gain. The results computed from these expressions are in good agreement with those from numerical calculations. These results indicate the existence of a parametric relationship between radial emittance and energy spread, via the amplitude of radial betatron oscillations. This relationship enables one to generate the working diagram of expected beam parameters on a SF. Such a diagram can be particularly useful for designers of extraction systems, since it gives the relationship between quantities used as extraction system input parameters. The derived analytical expressions can make the design of cyclotrons easier and significantly reduce the need of numerical simulations.

Nonlinear dynamics in a SPEAR wiggler

BL11, the most recently installed wiggler in the SPEAR storage ring at the Stanford Synchrotron Radiation Laboratory, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and closed orbit shifts were used to characterize the nonlinear fields. Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different from the magnetic measurements made along a straight line with a stretched wire. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Because of the relatively large dispersion (1.2 m) at BL11, the nonlinearities particularly reduced the off-energy dynamic aperture. Because of the nature of these nonlinear fields, it is impossible, even theoretically, to cancel them completely with short multipole correctors. Magic finger corrector magnets were built, however, that partially correct the nonlinear perturbation, greatly improving the storage ring performance.

Observation of a hybrid spin resonance

A new type of spin depolarization resonance has been observed at the Brookhaven Alternating Gradient Synchrotron (AGS). This spin resonance is identified as a strong closed-orbit sideband around the dominant intrinsic spin resonance. The strength of the resonance was proportional to the 9th harmonic component of the horizontal closed orbit and proportional to the vertical betatron oscillation amplitude. This "hybrid" spin resonance cannot be overcome by the partial snake at the AGS, but it can be corrected by the harmonic orbit correctors.

Perturbation Analysis of Octupoles in Circular Accelerators

The octupole effects in a circular accelerator are analyzed using a first-order canonical perturbation theory. It is shown that, to the first order, the nonlinear amplitude-dependent tune shifts due to an octupole are composed of two types: terms of second order and terms of fourth order in betatron-oscillation amplitudes. The fourth-order part of tune shifts is expressed in terms of distortion functions. Distortion functions are also expanded in harmonics to express the higher-order tune shifts in harmonically expanded form. Finally, the results are applied to an accelerator and compared with the results of numerical tracking of particles. Laskar's algorithm for numerical analysis of the fundamental frequency is used to determine tunes from the tracking data, in which the error becomes inversely proportional to the cube of the number of data points.

Features of operation of a FEL with reversed guide field

Features of the nonlinear regime of a FEL with reversed guide field operating in the millimeter wavelength range have been studied numerically by particle techniques. The FEL efficiency for both conventional and reversed guide fields for the case in which the simulating particles were on a steady state trajectory at the entrance to the interaction region was rather high. Taking into account a significant spread of the transverse electron impulses which exists in the experiment due to, for example, a nonadiabatic wiggler field increase at the entrance to the FEL interaction region results in a significant decrease of efficiency for the FEL with conventional guide field orientation while it remains practically unchanged for the FEL with reversed guide field.For the FEL parameters close to the experimental ones an analysis of electron motion shows that for reversed guide field the period and amplitude of betatron oscillations are significantly less than for the conventional guide field case. Most likely, that is the reason which leads to the substantial changing of the interaction in the two cases.

Development of a focusing wiggler with trapezoid-shaped permanent magnets

A focusing wiggler with trapezoid-shaped permanent magnets has been developed for the infrared free electron laser. A numerical trajectory analysis using a measured magnetic field shows that a betatron oscillation amplitude of the electron beam with 1π mm mrad emittance can be restrained within 1 mm and the FEL's gain is higher than with the conventional wiggler. The magnetic field error can be easily reduced to 0.1% by precisely adjusting each magnet gap.

Hamiltonian Formulation for Synchrobetatron Resonance Driven by Dispersion in RF Cavities

Synchrobetatron resonance driven by dispersion in RF cavities is studied by using the Hamiltonian formalism. Explicit expressions are given for the growth rate of betatron and synchrotron oscillation amplitudes on resonance and on fast-crossing of the resonance. The effect of distributed RF cavities is also studied, and it is shown that the resonance can be suppressed by proper arrangement of RF cavities. The theory is shown to agree fairly well with the computer simulation for PETRA and some numerical examples are given for the booster of the TRIUMF Kaon Factory project. This paper is an abridged version of Ref. (1), and readers are referred to Ref. (1) for more details.

A Programmable High Power Beam Damper for the Tevatron

A bunch-by-bunch beam damper has been developed for the Fermilab Tevatron. The system reduces betatron oscillation amplitudes and incorporates some useful machine diagnostics. The device is programmable via look-up tables so the output is an arbitrary function, on a bunch-by-bunch basis, of the beam displacement. We are presently using this feature to measure the betatron tune throughout the acceleration cycle.