Orbit Distortion Research Articles

Control of Emittance Growth in a Bunch Compressor for the International Linear Collider

We present a short two-stage bunch compressor system that has been selected as an alternative design in the ILC (International Linear Collider). The designed bunch compressor system has two rf sections and two chicanes in which each chicane consists of four bending magnets. Each bunch compressor stage includes a 34 m lattice of bending magnets that is relatively short compared to the baseline design with a 150 m lattice in the ILC. Beams with bunch length of 6 mm rms and 9 mm rms can be compressed to 0.15 mm rms and 0.3 mm rms in the bunch compressor system, respectively. We show the optimized parameters of the bunch compressor system and results of transverse and longitudinal beam trackings in the compressor system. We examined the influences of coherent and incoherent synchrotron radiations in the chicanes on the transverse emittance. Control of the emittance growth due to machine errors is an important issue in the performance of the bunch compressor. Thus, we performed the lattice corrections such as corrections of orbit distortion, dispersion function and skew component to control the emittance growths due to several machine errors in the bunch compressor system. It is shown that the system is error tolerant and the lattice corrections are very effective to suppress growth of the emittance in the bunch compressor system.

Studies of closed orbit correction and slow orbit feedback for the SSRF storage ring

Details of the active ways to suppress Closed Orbit Distortion (COD), including bending magnet sorting and survey and alignment of the magnets, are discussed based on the studies of affections to the COD by the bending magnet field error and the misalignment of quadrupoles. The closed orbit correction and the Slow Orbit Feed Back (SOFB) system for the SSRF storage ring are presented in this paper. With these available methods, better results were obtained during the commissioning period with 3 GeV beam energy.

COD correction for laser cooling at S-LSR

A closed orbit is corrected for single-turn injection to perform laser cooling experiments of 40 keV 24 Mg + beam at the small laser-equipped storage ring (S-LSR). Closed orbit distortion (COD) corrections have been carried out using a downhill simplex method, and CODs of less than ± 0.5 mm have been achieved throughout the whole circumference. The injection orbit and the CODs are optimized to pass through the two aperture holes in the alignment targets located in the laser cooling section with an algorithm to maximize beam lifetime. The CODs at the aperture holes are reduced to be less than ± 0.2 mm , assuring an overlap between the laser and the 24 Mg + ion beam.

Calculations of electronic structure of the UF6 molecule and the UO2 crystal with a relativistic pseudopotential

The influence of relativistic effects on the properties of uranium hexafluoride was considered. Detailed comparison of the spectrum of one-electron energies obtained in the nonrelativistic (by the Hartree-Fock method), relativistic (by the Dirac-Fock method), and scalar-relativistic (using a relativistic potential of the uranium atom core) calculations was carried out. The methods of optimization of atomic basis in the LCAO calculations of molecules and crystals are discussed which make it possible to consider distortion of atomic orbitals upon the formation chemical bonds. The influence of the atomic basis optimization on the results of scalar-relativistic calculations of the molecule UF6 properties is analyzed. Calculations of the electronic structure and properties of UO2 crystals with relativistic and nonrelativistic pseudopotentials are fulfilled.

RHIC polarized proton status and plan

The Relativistic Heavy Ion Collider (RHIC) as the first high energy polarized proton collider has been providing collisions at a beam energy of 100 GeV since 2001. Equipped with two full Siberian snakes in each ring, polarization is preserved during the acceleration from injection to 100 GeV with careful control of the betatron tunes and the vertical orbit distortions. In the latest RHIC polarized proton run in 2006, a peak luminosity of 28 × 1030cm−2 s−1 with 60% average polarization at store was achieved. During the run, RHIC also demonstrated its capability in providing a combination of polarized proton collisions with longitudinal polarization and radial polarization were provided to the STAR experiment and PHENIX experiment with the local spin rotators installed on either side of the STAR detector and PHENIX detector. Polarized protons were also first accelerated to 250 GeV at the end of RHIC 2006 run with a 46% polarization measured at this new store energy in one of the RHIC accelerators. Currently, the luminosity in RHIC is limited by the beam-beam effect. The plan is to triple the luminosity. Plans to achieve polarized proton collision at 250 GeV are also reported.

Study of closed orbit response to magnet vibrations at the SSRF storage ring**Supported by SSRF Project

This paper presents the analytical and simulation responses of the closed orbit distortion in the SSRF storage ring to random and plane wave like magnet vibrations respectively. It is shown that the use of girder is very beneficial in the view of suppressing this response function. Effect of the independently supported gradient bending magnets to the closed orbit response is given. An analytic formula is written to give a rough estimate of the closed orbit distortion due to ground motion, taking into account the closed orbit response function and girder transfer function. As an example, the result of SSRF case is given.

Local correction schemes to counteract insertion device effects

Insertion devices (IDs) of various types provide light of high brilliance to experimenters at the Swiss Light Source (SLS) beamlines. However, changes in the photon energy and polarization by movement of the ID gap and phase shift cause orbit distortions that result in a displacement of the photon beam in both angle and position at the beamline. A feed-forward correction scheme has been developed to quantify and precisely correct these effects using designated correctors local to the photon source. The settings for these correctors are determined using an orbit configuration consisting of 73 digital beam position monitors (DBPMs) and associated correctors; recently commissioned X-ray beam position monitors (XBPMs) located at the beamline front-end are also included in the correction algorithm to further constrain the photon beam to its specified position. The feed-forward correction procedure is finally implemented at the local processor level and applied at a rate of 10Hz. A photon pointing stability at the sub-microradian level is achieved. The entire gap scan, feed-forward generation and subsequent verification can be completed from within a few minutes to several hours depending on the complexity of the ID. The methodology of the procedure is described and the results from several ID analyses are presented. The effect of the ID on the betatron tune is also discussed. Both feed-forward and feedback procedures have been implemented to maintain the horizontal and vertical components of the tune at the desired working points.

The structure of betaxolol from single crystal X-ray diffraction and natural bond orbital analysis

The structure of betaxolol obtained from ethanol:water solution was studied by X-ray diffraction. The geometrical parameters needed to define the structure are tabulated. The X-ray data show the existence of two conformers in the unit cell differing only in the conformation of the cyclopropylmethoxy fragment. Differences in the bond lengths angles and dihedral between both conformations are observed. The cyclopropyl groups lie in approximately perpendicular planes. The two molecular geometries identified by single crystal X-ray diffraction were optimized at the B3LYP/6-31G(d,p) level of theory. Both isolated molecules are retained as distinct conformers upon geometry optimization, despite some dihedral relaxation. The electronic structure of the most important molecular fragments was described in terms of Natural Bond Orbitals. The energetic and spatial features of the occupied and vacant orbitals were studied. The different structures observed in the solid state were explained by the specific interactions involving the oxygen lone pairs in cyclopropylmethoxy. It was observed some orbital and geometry distortion in cyclopropyl caused by the crystal packing.

Lone pair versus bonding pair electrons: The mechanism of electronic polarization of water in the presence of positive ions

It is commonly accepted that the water molecules in the first solvation shell of a positive ion are strongly polarized because of an elongation of the oxygen lone pair orbitals along the ion-oxygen direction and this is commonly considered the dominant effect. Recent experimental and theoretical works have instead suggested that this is not the dominant aspect and that the problem is by far more complicated. Consistent with the picture given above, here we show that, in particular, an equally important role into the polarization process is played by the bonding pair electrons located along the internal oxygen-hydrogen bond. We also provide some arguments which suggest that the main reason of such a behavior is due to the distortion of the molecular orbitals caused by the interaction between non-hydrogen-bonded water molecules in the first solvation shell of the ion.

Sorting of bending magnets for the SSRF booster**Supported by SSRF Project

The Shanghai Synchrotron Radiation Facility (SSRF)booster ring, a full energy injector for the storage ring, is deigned to accelerate the electron beam energy from 150 MeV to 3.5 GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping. Closed orbit distortion (COD) caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting. Considering the affections of random errors in measurement, both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5 is given as the final installation sequence of the booster bending magnets in this paper.

Field interference studies between bump magnets with different coil structures at Chinese Spallation Neutron Source

For magnets arranged so closely that the distance between them is comparable to the magnet apertures, the field interference becomes important. This is the case in the injection region at the China Spallation Neutron Source (CSNS) where several bump magnets are used to create fixed and dynamic local orbit bumps for the beam injection using the H(-) stripping and the phase space painting method. The reduction in the field integral due to the field interference will cause an orbit distortion, and the orbit bumps will be no longer localized. It is found that the end coil structure plays an important role in reducing the fringe field of a magnet. This has been analyzed by using both the image current method and three-dimensional magnetic field calculations. The saddle end coil instead of the compact end coil has been adopted at the CSNS. The relative reduction in the field integration after the optimization can meet the design requirement of about 1% or less.

Identification of longitudinal coherent oscillations induced by path-length fluctuations

This paper explains an analytical formula for longitudinal coherent oscillations in an electron storage ring, including path-length oscillations. A path-length oscillation produced by closed orbit distortion was experimentally identified in the NewSUBARU electron storage ring and found to be harmful to normal operations. Such oscillations are also a potential problem in other advanced light sources especially in a quasi-isochronous operation.

Compact Storage Ring for Far-Infrared Coherent Synchrotron Radiation Source

We present the results of design studies for a compact storage ring that may produce coherent synchrotron radiation in the far-infrared frequency range. The momentum compaction factor in the ring is easily varied by controlling dispersion function and thus a short bunch length of a few picoseconds can be achieved. We have performed a detailed analysis of beam dynamics for a short bunch length in the ring. Within the controllable range of the second-order momentum compaction factor in the ring, it was shown that the alpha bucket and the rf bucket were created. It is shown that the compact ring with conservative machine errors has a sufficient dynamic aperture after the correction of closed orbit distortion. Multi-particle tracking simulations are performed to investigate longitudinal beam instability due to the broadband impedance in the ring. We investigated the effects of coherent synchrotron radiation wake in the ring on longitudinal beam distribution. From these studies, it is shown that the designed compact ring may provide stable electron beams of approximately around 2 ps rms.

Transverse emittance dilution due to coupler kicks in linear accelerators

One of the main concerns in the design of low emittance linear accelerators (linacs) is the preservation of beam emittance. Here we discuss one possible source of emittance dilution, the coupler kick, due to transverse electromagnetic fields in the accelerating cavities of the linac caused by the power coupler geometry. In addition to emittance growth, the coupler kick also produces orbit distortions. It is common wisdom that emittance growth from coupler kicks can be strongly reduced by using two couplers per cavity mounted opposite each other or by having the couplers of successive cavities alternate from above to below the beam pipe so as to cancel each individual kick. While this is correct, including two couplers per cavity or alternating the coupler location requires large technical changes and increased cost for superconducting cryomodules where cryogenic pipes are arranged parallel to a string of several cavities. We therefore analyze consequences of alternate coupler placements. We show here that alternating the coupler location from above to below compensates the emittance growth as well as the orbit distortions. For sufficiently large $Q$ values, alternating the coupler location from before to after the cavity leads to a cancellation of the orbit distortion but not of the emittance growth, whereas alternating the coupler location from before and above to behind and below the cavity cancels the emittance growth but not the orbit distortion. We show that cancellations hold for sufficiently large $Q$ values. These compensations hold even when each cavity is individually detuned, e.g., by microphonics. Another effective method for reducing coupler kicks that is studied is the optimization of the phase of the coupler kick so as to minimize the effects on emittance from each coupler. This technique is independent of the coupler geometry but relies on operating on crest. A final technique studied is symmetrization of the cavity geometry in the coupler region with the addition of a stub opposite the coupler. This technique works by reducing the amplitude of the off axis fields and is thus effective for off-crest acceleration as well. We show applications of these techniques to the energy recovery linac (ERL) planned at Cornell University.

Orbit and optics distortion in fixed field alternating gradient muon accelerators

In a linear nonscaling fixed field alternating gradient (FFAG) accelerator, betatron tunes vary over a wide range and a beam has to cross integer and half-integer tunes several times. Although it is plausible to say that integer and half-integer resonances are not harmful if the crossing speed is fast, no quantitative argument exists. With tracking simulation, we studied orbit and optics distortion due to alignment and magnet errors. It was found that the concept of integer and half-integer resonance crossing is irrelevant to explain beam behavior in a nonscaling FFAG when acceleration is fast and betatron tunes change quickly. In a muon FFAG accelerator, it takes 17 turns for acceleration and the betatron tunes change more than 10, for example. Instead, the orbit and optics distortion is excited by random dipole and quadrupole kicks. The latter causes beam size growth because the beam starts tumbling in phase space, but not necessarily with emittance growth.

The collision-induced polarizability of a pair of hydrogen molecules

Collision-induced light scattering, impulsive stimulated scattering, and subpicosecond-induced birefringence all depend on the transient changes Deltaalpha in molecular polarizabilities that occur when molecules collide. Ab initio results for Deltaalpha are needed to permit comparisons with accurate experimental results for these spectra and for refractive index virial coefficients and dielectric virial coefficients. In this work, we provide results for Deltaalpha for a pair of hydrogen molecules, treated at CCSD(T) level, with an aug-cc-pV5Z (spdf) basis set. Our values replace the best previous ab initio results for the variation of Deltaalpha with intermolecular separation, the self-consistent-field results obtained by Bounds [Mol. Phys. 38, 2099 (1979)] with a relatively small (3s2p) basis set for H2. For the six geometrical configurations studied by Bounds, the inclusion of correlation and improvements in the basis tend to increase both the trace Deltaalpha(0)0 and the anisotropy Deltaalpha2m of the pair polarizability. The change in the anisotropy is relatively small, but our values for the trace differ by factors of 2 or more from Bounds' results. For use in computing experimental line shapes, intensities, and virial coefficients, we have calculated Deltaalpha for 18 different relative orientations of a pair of H2 molecules, with the intermolecular separation R ranging from 2 a.u. (3 a.u. for a linear pair) to 10 a.u. The H2 bond length is fixed at the vibrationally averaged internuclear separation in the ground state r=1.449 a.u. Our results agree well with the CCSD(T) results for Deltaalpha obtained by Maroulis [J. Phys. Chem. A 104, 4772 (2000)] for two pair configurations of H2...H2 (linear and T-shaped) at a fixed internuclear distance of R=6.5 a.u. in a [6s4p1d] basis. As the intermolecular distance increases (for R>or=8 a.u.), the spherical-tensor components of Deltaalpha converge to the results from a long-range model that includes dipole-induced-dipole (DID) interactions, higher-multipole induction, nonuniformity of the local field, hyperpolarization, and van der Waals dispersion. Deviations from the first-order DID model are still evident for R between 8 and 10 a.u. in most orientations of the pair. At shorter range, overlap damping, exchange, and orbital distortion reduce both Deltaalpha0(0) and Deltaalpha(2)0 below their long-range limiting forms.

Nature of the Aqueous Hydroxide Ion Probed by X-ray Absorption Spectroscopy

X-ray absorption spectra of aqueous 4 and 6 M potassium hydroxide solutions have been measured near the oxygen K edge. Upon addition of KOH to water, a new spectral feature (532.5 eV) emerges at energies well below the liquid water pre-edge feature (535 eV) and is attributed to OH- ions. In addition to spectral changes explicitly due to absorption by solvated OH- ions, calculated XA spectra indicate that first-solvation-shell water molecules exhibit an absorption spectrum that is unique from that of bulk liquid water. It is suggested that this spectral change results primarily from direct electronic perturbation of the unoccupied molecular orbitals of first-shell water molecules and only secondarily from geometric distortion of the local hydrogen bond network within the first hydration shell. Both the experimental and the calculated XA spectra indicate that the nature of the interaction between the OH- ion and the solvating water molecules is fundamentally different than the corresponding interactions of aqueous halide anions with respect to this direct orbital distortion. Analysis of the Mulliken charge populations suggests that the origin of this difference is a disparity in the charge asymmetry between the hydrogen atoms of the solvating water molecules. The charge asymmetry is induced both by electric field effects due to the presence of the anion and by charge transfer from the respective ions. The computational results also indicate that the OH- ion exists with a predominately "hyper-coordinated" solvation shell and that the OH- ion does not readily donate hydrogen bonds to the surrounding water molecules.

Study of the mass resolving power in the CR storage ring operated as a TOF spectrometer

In this paper we focus on the study of the mass resolving power in the Collector Ring (CR). In one of the modes of operation it is planned to be used as a Time-Of-Flight (TOF) mass spectrometer by making it isochronous, i.e., with a revolution time independent of particle velocity. The dependence of the TOF in the storage ring on the acceptance, closed orbit distortion, nonlinear imperfection of magnet field is analyzed. A kinetic simulation code is used to study the beam dynamics in the isochronous ring. The results of a 6D tracking code give us confidence that the isochronous mode of the CR can be used for mass measurements with a high precision, however, with the restrictions on the acceptance.

Beam-based measurement of skew-quadrupole field distribution along the longitudinal direction in a long undulator

The skew-quadrupole field errors in an undulator were determined from the response of the stored beam. This method used was to measure the change of the horizontal closed orbit distortion produced by two types of vertical local bump orbit in the undulator. In this method, the unknown distribution of the skew-quadrupole field along the longitudinal direction in the undulator was expressed quantitatively by the multipole moments. Therefore, the reliable result is obtained. In addition, this method is faster than the global modelling of a ring, which uses the response matrix of the whole ring, and is not sensitive to skew-quadrupole field errors in sections other than the target section. Therefore, this method is suitable for measuring the gap dependence.

Design of a low-emittance 2.5-GeV pohang light source lattice

The Pohang Light Source (PLS) storage ring is a synchrotron light source with the emittance of 18.9 nm at 2.5 GeV. We designed a new lattice with an achromat of the emittance of 13 nm that may provide more brilliant synchrotron radiation. We investigated dependence of the dynamic aperture on the betatron tune to search for large dynamic aperture in the low-emittance lattice by a simulation method. We examined the dynamic apertures by a tune survey within a specified tune space without and with machine errors. It is also shown that how large is the dynamic aperture in the storage ring after correction of a closed orbit distortion. The operating tune for the low-emittance lattice can be chosen on the view point of dynamic apertures obtained from a tune survey. The low-emittance lattice with the achromat shows the reduced horizontal and vertical beam sizes by 10% and 29% in the positions of insertion devices and by 31% and 52% in the bending magnets than the present lattice, respectively. It is also shown that the low-emittance lattice with 13 nm may provide sufficient dynamic aperture without changing of configuration of magnets in the storage ring.