R. Helm

Evaluation of Synchrotron Radiation Integrals

Many of the important properties of the stored beam in an electron storage ring are determined by integrals, ’ taken around the whole ring, of various characteristic functions of the guide fielci. Some of the integrals are handled easily, but a few are usually estimated graphically - particularly for alternating-gradient guide fields. This report describes a convenient method for evaluating numerically these recalcitrant integrals. In the usual linear approximation, the integrals we wish to consider are most conveniently expressed in terms of four (somewhat redundant) functions of the azimuthal coordinates: p(s) the radius of curvature of the design orbit, n the field index, F(s) the radial betatro; function andT(s) the off-energy (or “dispersion”) function. The Integrals We restrict our attention to guide fields made up of a number of magnetic segments - magnets or straight sections The functions p and n are assumed to have constant values within a given magnet, but vary abruptly at the entrance and erit boundaries. The integrals of interest are given by:

Third-order corrections to the SLC final focus

The minimum /spl beta/ achievable at the interaction point (/spl beta/*) with the current design of the SLC final focus is limited to /spl sim/5 mm by third order optical aberrations, most notably the U/sub 1266/ and U/sub 3466/ terms (using the notation of K. Brown). A new lattice is presented which effectively zeros these terms. The remaining third order terms which accrue from the interleaved sextupole pairs in the chromatic correction section (CCS) can be cancelled by the inclusion of five octupoles (two in the CCS, and three in the final telescope). The resulting final focus system is corrected to third order for any usable range of /spl beta/* (given the constraints on the beam divergence at the interaction point). The potential luminosity obtainable from such a system is also presented.<<ETX>>

Standard wiggler magnets

Abstract Interest in wiggler magnets (a close sequence of transverse fields with alternating polarity) to extend and enhance the spectrum of synchrotron radiation from electron storage rings has increased significantly during the past few years. In this paper we consider standard wigglers i.e. wigglers in which interference effects on the spectrum of synchrotron radiation are not important. In standard wigglers the spectrum of synchrotron radiation has the same general shape as the spectrum from ring bending magnets. However, the critical energy of the wiggler spectrum may be different. The critical energy of the wiggler spectrum is given by: e CW = ϵ CB B W B B , where ϵCB is the critical energy from the bending magnets and BW and BB are the magnetic field strengths of the wiggler magnet and bending magnets respectively. Since most electron storage rings operate with relatively low bending magnet fields (BB≲12 kG), even a modest wiggler magnet field (≈ 18 kG) can significantly increase the critical energy. Such magnets are planned for ADONE and SPEAR. Higher field ≈ 45 kG) superconducting magnets are planned at Daresbury and Brookhaven to produce due to the superposition of the radiation from the individual poles. Wiggler designs are discussed the spectrum is produced due to the superposition of the radiation from the individual poles. Wiggler designs are discussed as well as the effect of wigglers on the synchrotron radiation spectrum and on the operation of storage rings.

Localized chromaticity correction of low-beta insertions in storage rings

The correction of the chromaticity of low-beta insertions in the storage rings is usually made with sextupole lenses in the rings arcs. When decreasing the beta functions at the insertion point (IP), this technique becomes fairly ineffective, since it fails to properly correct the higher order chromatic aberrations. Here we consider the approach where the chromatic effects of the quadrupole lenses generating low beta functions at the IP are corrected locally with two families of sextupoles, one family for each plane. Each family has two pairs of sextupoles which are located symmetrically on both sides of the IP. The sextupole-like aberrations of individual sextupoles are eliminated by utilizing optics forming a -I transformation between sextupoles in the pair. The optics also includes bending magnets which preserve equal dispersion functions at the two sextupoles in each pair. At sextupoles in one family, the vertical beta function is made large and the horizontal is made small. The situation is reversed in the sextupoles of the other family. The betatron phase advances from the IP to the sextupoles are chosen to eliminate a second order chromatic aberration. The application of the localized chromatic correction is demonstrated using as an example the lattice design for the Low Energy Ring of the SLAC/LBL/LLNL PEP-II B Factory.<<ETX>>

Beam-based magnetic alignment of the Final Focus Test Beam

In order to optimize tunability and backgrounds in linear collider final focus systems, it is necessary to align strong quadrupole and sextupole magnets with beam-based measurements. Algorithms for alignment have been used successfully on the Final Focus Test Beam (FFTB) beamline at SLAC. Quadrupole magnets were aligned using a shunt technique, with resolutions from 50 microns down to 700 nanometers. Sextupole magnets were aligned by moving the magnets transverse to the beam and observing the kick on downstream beam position monitors. This procedure resulted in sextupole misalignment resolutions of 5 to 20 microns. All magnets were then moved into aligned positions via remote-controlled stages capable of sub-micron resolution. Details of the fitting algorithms, results of the measurement, and potential improvements in the system are discussed.

Emittance Calculations for the Stanford Linear Collider Injector

A computer code has been implemented for on-line acquisition and analysis of data for emittance measurements of the SLC injector beam. The beam emittances have been determined experimentally using this code; measured beam emittance values have been found to be within expectations. When the system operates in the automatic mode, an emittance measurement takes less than two minutes. This emittance measurement method has been thoroughly tested and has been extended to other regions of the SLC system. Resultant beam sigma matrices are used in the lattice design models to calculate the strengths of quadrupoles required for the optical matching of the CID beam into the SLC Linac.

A final focus system for the Next Linear Collider

The final focus of the Next Linear Collider (NLC) demagnifies electron and positron beams of 250-750 GeV energy down to a transverse size of about 2.5/spl times/350 nm/sup 2/ at the interaction point (IP). The basic layout, momentum bandwidth, vibration tolerances, wakefield effects, and the tunability of the proposed final focus design are discussed. Also a perspective is given on the crab cavity and on effects of the solenoid field in the interaction region.

Low Energy Ring lattice of the PEP-II asymmetric B-factory

Developing a lattice that contains a very low beta value at the interaction point (IP) and has adequate dynamic aperture is one of the major challenges in designing the PEP-II asymmetric B-factory. For the Low Energy Ring (LER) we have studied several different chromatic correction schemes since the conceptual design report (CDR). Based on these studies, a hybrid solution with local and semi-local chromatic sextupoles has been selected as the new baseline lattice to replace the local scheme in the CDR. The new design simplifies the interaction region (IR) and reduces the number of sextupoles in the arcs. Arc sextupoles are paired at /spl pi/ phase difference and are not interleaved. In this paper we describe the baseline lattice with the emphasis on the lattice changes made since the CDR.

Optimization of the NLC final focus system

An optimization scheme for final focus systems is discussed and applied to the NLC design. The optical functions at the defocusing sextupoles, the sextupole strength, and the length of the system must obey eight conditions that are imposed by the spot size increase due to higher-order aberrations, the effects of synchrotron radiation in the bending magnets, power supply ripple, magnet vibration tolerances, and the estimated orbit stability at the sextupoles. These eight conditions determine the minimum optimum length of the system. The NLC final focus design was shortened to this optimum.

The optics of the Final Focus Test Beam

Strategies for tuning and correcting aberrations that arise as the real Final Focus Test Beam (FFTB) lattice departs from the design lattice are presented. The following beam-based tuning and alignment strategies are examined: quadrupole alignment, quadrupole tuning, sextupole pair alignment and tuning, and stability of CCX, CCY, and final doublet. The tuning of the incoming beam is considered with regard to alpha and beta matching, incoming dispersion, and incoming coupling.<<ETX>>