G. Parzen

The RHIC design overview

The salient performance objectives for the Relativistic Heavy Ion Collider (RHIC) are presented and the rationale for the design choices of the major collider systems is conveyed. RHIC provides collisions of heavy ions covering the entire mass range from protons to gold. For the prototypical case of Au-on-Au, one obtains energies up to 100 GeV/n per beam and luminosities of B2 � 10 26 cm � 2 s � 1 , averaged over a 10-h storage time. Operation with polarized protons is also possible. The overall accelerator complex used for gold ions consists of the Tandem Van de Graaff, the Booster, the AGS, and the Collider itself, and the scenario for the beam transfer between machines is described. The two separate collider rings cross at six interaction points, where the lattice design provides low-beta insertions for maximum luminosity. The interaction diamond length of o20 cm rms is achieved by bunched beam operation and holding the 56 bunches in a 197 MHz radio-frequency (RF) system after their acceleration in a 28 MHz RF system. The rings are constructed with superconducting magnets, which have a cold bore aperture of 6.9 cm in the arcs. The RHIC specific design challenges posed by intrabeam scattering of heavy ions, passage through transition energy with slow-ramping superconducting magnets, and control of magnetic errors in the low-beta triplet quadrupoles are addressed. r 2002 Elsevier Science B.V. All rights reserved.

Intrabeam scattering at high energies

Abstract The growth of a beam of charged particles due to intrabeam scattering is studied in the high energy limit. The variation of the β-functions and the dispersion around the accelerator are included. In the high γ limit, analytical results are found for the horizontal, vertical and longitudinal growth rates. For a lattice consisting only of regular cells, with no insertions, a time invariant is found and the longitudinal and transverse growth rates are simply related. The dependence of the final state of the beam on the final energy is also studied.

Space charge limits in proton synchrotrons

Abstract A simulation program has been written to study the effects of space charge and to compute the space charge limit in circular accelerators. This program tracks particles through the elements of the accelerator lattice, representing the space charge force as a kick at the exit and entrance of each element. The results of the simulation study indicate that the intrinsic space charge limit appears to play a dominant role in determining the space charge limit. The intrinsic space charge limit is the space charge limit in the absence of magnetic field errors, and is the limit due to forces generated by the beam itself. The intrinsic limit appears to provide an upper bound for the space charge limit which is not far from what is actually achieved by three operating accelerators. The presence of resonances due to magnetic field errors becomes important only when the beam intensity gets close to the intrinsic limit, and can prevent the accelerator from achieving the intrinsic limit. The results of the simulation study are compared with measured results for three existing accelerators. Results are also given for the proposed AGS booster.

Superconducting Magnet Models for Isabelle

The development program for the superconducting magnets of the Intersecting Storage Accelerators is described. The dipole magnet design is of the cos ? type and employs wide ribbon conductor. Magnetic measurements are compared with calculations which include the effects of conductor magnetization and iron saturation. Calculations of the harmonics due to the magnet ends will also be presented along with estimates of the effect of the shape of the outer boundary of the iron shield on the field and the degree of interaction between the magnets in the two rings. The conductor is a metal-filled braid woven from 186 wires each containing 400 filaments. A precision molding technique has been developed which assures accurate placement of the turns and could be used for semi-mass production. The iron cores are laminated and assembled in a special way to eliminate the axial differential expansion between the coil and the core. Correction coils for the 3? and 5? terms are built into the bore tubes. These coils are necessary to correct the small (10-3) harmonics produced by conductor magnetization at low field and iron saturation at high fields.

Linear orbit parameters for the exact equations of motion

This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The /spl beta/, /spl alpha/ and /spl psi/ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for /spl eta/=x//spl beta//sup 1/2 / is found. New relationships between /spl alpha/, /spl beta/, /spl psi/ and /spl nu/ are derived.

Intrinsic and resonance space charge limits

The space charge limit in circular program accelerators has been studied using a simulation program. Results from the simulation study indicate a different model for the space charge limit than the often-presented models which emphasize resonances due to magnetic field errors. In studies of three operating accelerators, which include the Alternating Gradient Synchrotron, the Proton Synchrotron Booster, and the Fermilab Booster, it was found that the computed intrinsic space charge limit was fairly close to the experimentally observed space charge limit. This result and studies of the effects of resonances due to magnetic field errors suggest that the intrinsic space charge limit provides an upper bound for the space charge limit which is not far from what is actually achieved by operating accelerators. The resonances present due to magnetic field errors, if strong enough, can prevent the accelerator from achieving the intrinsic space charge limit. However, the effects of these resonances were found to be appreciable only when the beam intensity gets close to the intrinsic space charge limit. Well below the intrinsic space charge limit, there is little beam growth due to magnetic field error driven resonances, and the space charge forces tend to stabilize these resonances.<<ETX>>

Superconducting Magnet System for the AGS High Energy Unseparated Beam

A beam line to the Multi-Particle Spectrometer capable of handling 30 GeV/c secondary beams will consist of four large identical superconducting dipoles and a number of room temperature quadrupoles. The total bending angle is 20°, 5° per magnet, and the room temperature aperture required in the dipoles is 20 cm. The four dipoles will be of the cos ¿ type and will have an overall length of 2.5 m and nominal maximum field of 4.0 T at 2800 A. The conductor will be a thin, wide metal-impregnated braid. The circular aperture is surrounded by coils which are a six-block approximation to a single-layer cos ¿ current sheet, and a coaxial cylinder of laminated iron at helium temperature. Each magnet will weigh about 10 tons. The design of the dewar including its heat load is discussed. The system is planned to be operational in Fall 1975.

Particle motion inside and near a linear half-integer stopband

This paper studies the motion of a particle whose tune is inside and near a linear half-integer stopband. Results are found for the tune and beta functions in the stable region close to an edge of the stopband. It is shown that the eigenvalues and the eigenfunctions of the transfer matrix are real inside the stopband. All the results found are also valid for small accelerators where the large accelerator approximation is not used.

Beta functions in the presence of linear coupling

One effect of random a/sub 1/, the skew quadrupole field error, is to perturb the beta -functions. This effect may be large in proton accelerators using superconducting magnets, because of the relatively large random a/sub 1/ expected in these magnets. This effect has been studied in the RHIC accelerator (the Relativistic Heavy Ion Collider proposed at Brookhaven National Laboratory). An analytic result has been found for the changes in the beta functions caused by the random a/sub 1/. This result indicates that the important harmonics of a/sub 1/ that need to be controlled are the harmonics near nu /sub x/+ nu /sub y/. This has been verified in computer studies.<<ETX>>

Tune splitting in the presence of linear coupling

For RHIC (Relativistic Heavy Ion Collider), a tune splitting as large as 0.2 was found in one case. A correction system has been developed for correcting this large tune splitting which uses two families of skew quadrupole correctors. It has been found that this correction system corrects most of the large tune splitting, but a residual tune splitting that is still appreciable remains. The residual tune splitting appears to be due to higher-order effects of the random a/sub 1/ multipole. Loosely speaking, one may say that the residual tune splitting is associated with the nearby linear sum resonance, nu /sub x/+ nu /sub y/=integer. A skew quadrupole correction system that appears capable of correcting a large part of the residual tune splitting has been developed.<<ETX>>