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Aperture studies of the BNL colliding beam accelerator with reduced superperiodicity

Description: Chromatic properties of the Brookhaven CBA (Colliding Beam Accelerator) with one low ..beta.. insertion in each of the three superperiods have been studied using the PATRICIA particle tracking program. Systematic multipoles of order 5 < n less than or equal to 10 as well as random multipoles of order 1 less than or equal to n less than or equal to 10 are, along with random closed orbit errors and sagitta effects, included when determining the aperture of the lattice. 3 references, 6 figures.
Date: January 1, 1983
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

Studies of the chromatic properties and dynamic aperture of the BNL colliding-beam accelerator. [PATRICIA particle tracking code]

Description: The PATRICIA particle tracking program has been used to study chromatic effects in the Brookhaven CBA (Colliding Beam Accelerator). The short term behavior of particles in the CBA has been followed for particle histories of 300 turns. Contributions from magnet multipoles characteristic of superconducting magnets and closed orbit errors have been included in determining the dynamic aperture of the CBA for on and off momentum particles. The width of the third integer stopband produced by the temperature dependence of magnetization induced sextupoles in the CBA cable dipoles is evaluated for helium distribution systems having periodicity of one and six. The stopband width at a tune of 68/3 is naturally zero for the system having a periodicity of six and is approx. 10/sup -4/ for the system having a periodicity of one. Results from theory are compared with results obtained with PATRICIA; the results agree within a factor of slightly more than two.
Date: January 1, 1983
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

Studies on magnet shuffling for RHIC (Relativistic Heavy Ion Collider)

Description: Shuffling of arc dipoles is performed on realistic RHIC lattices; ..delta beta../..beta.., ..delta..Xp/..sqrt beta..x, and Yp/..sqrt beta..y from random a1 and b1 multipoles are reduced to acceptable levels. Even before shuffling, the contribution from the arc dipoles is less than the contribution from the insertion magnets. In the insertions, the contribution from the random b1's is removed by the independent powering of all insertion quadrupoles; the contribution of random a1's to coupling will be corrected with skew quadrupole correction elements. 6 refs., 6 tabs.
Date: January 1, 1989
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

Tracking studies on the effects of random multipoles in the 6. 5 T lattice of the SSC Reference Designs Study

Description: The acceptance of lattice A (6.5 T) of the SSC Reference Designs Study is determined for ten different sets of random errors as various multipole orders are set to zero. On the basis of 400 turn studies it is concluded that all multipole orders in the dipoles are important. Further studies show that the beam crossing dipoles limit the acceptance - when their multipoles are scaled as r/sup -//sup (n+1)/, corresponding to an increased coil radius, the acceptance of the lattice essentially doubles.
Date: January 1, 1985
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

The acceptance of the SSC (Superconducting Supercollider) clustered lattice

Description: The physical apertures of all elements of the SSC storage lattices are considered to determine whether correction of random multipole fields in the triplet quadrupoles is necessary when betatron amplitudes there are no more than the inner radius of the beam pipe. During computer simulated beam tracking the influence of random multiple fields was included as a kick given to the test particle at the center of each quadrupole and at the ends of every dipole. The degree of multipole correction needed is shown. (LEW)
Date: January 1, 1986
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

Determination of the linear aperture of the SSC (Superconducting Supercollider) clustered lattice used for the conceptual design report

Description: A study is made of the linear aperture for the clustered lattice used for the SSC Conceptual Design Report. Random multipole errors are included in all magnetic elements including the insertion dipoles and quadrupoles. Based on the concept of smear, the linear aperture is equal to the dynamic aperture in the range -0.1 less than or equal to ..delta..P/P less than or equal to 0.03%. Strong coupling for ..delta..P/P > 0% produces large smears. A variation of the smear parameter that is insensitive to coupling is proposed. A comparison is made with results reported in the SSC Conceptual Design Report.
Date: June 23, 1986
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

Study of long term stability of betatron motion in the SSC

Description: The long term stability of betatron motion in the presence of random and systematic multipoles in the dipoles and random multipoles in the quadrupoles is reported for the collision lattice used for the SSC CDR (Conceptual Design Report). Long tracking runs of 20K and 28K show no instability. 6 refs., 3 figs., 3 tabs.
Date: January 1, 1988
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

Tracking studies on the effects of magnet multipoles on the aperture of the RHIC heavy ion collider

Description: Tracking studies including the effects of random multipoles resulting from construction errors have been made for RHIC with two independent tracking programs at three different tunes. The studies were made using ten different sets of random errors for each of the programs. The aperture was defined as the worst case, and the results of the two programs are in good agreement. A second set of studies was made for which the number of dipoles was doubled to determine whether doubling the number of independent random errors results in a reduction of the effects or random multipoles. The results for the two cases, one dipole per half cell and two dipoles per half cell, indicate there is little difference in dynamic aperture. 3 refs., 3 figs.
Date: January 1, 1985
Creator: Dell, G.F. & Parzen, G.
Partner: UNT Libraries Government Documents Department

Tracking studies on a RHIC lattice configuration for crossing the transition energy

Description: Particle tracking has been performed on RHIC when special quadrupoles in the arcs are used to produce a jump in the transition gamma. Studies include: worst case (full powering of the special quadrupoles) to determine the stability limit of the motion, and tracking of a particle throughout the ..gamma..t pulse to test if the motion is stable for the required 47,000 turns. 4 refs., 7 figs.
Date: January 1, 1988
Creator: Dell, G.F. & Parzen, G.
Partner: UNT Libraries Government Documents Department

Aperture studies on RHIC for 30 and 100 GeV/nucleon operation with random and systematic magnet errors

Description: Tracking studies on RHIC for the emittances and momentum spreads necessary for operation at 30 and 100 GeV/nucleon have been made when the effects of random and systematic magnet errors are included. All test particles are stable for the emittances required. Tune shifts from systematic b/sub 2/ are compensated by the chromaticity correcting sextupoles of the arcs. Tune shifts from systematic b/sub 3/ and b/sub 4/ are compensated by correction coils placed adjacent to the arc quadrupoles. The emittances required for operation are significantly smaller than the emittance corresponding to the dynamic aperture.
Date: January 1, 1987
Creator: Dell, G.F. & Hahn, H.
Partner: UNT Libraries Government Documents Department

Aperture studies with Patricia and Racetrack on simple lattices containing SSC dipoles

Description: The PATRICIA and RACETRACK particle tracking programs have been compared by tracking on a simple lattice. The dynamic aperture was found to decrease as the number of passes through the lattice per run increased from 20 to approx. 300, and it remained constant for longer runs. The dynamic apertures found by the two programs are consistent. The dependence of the dynamic aperture on horizontal tune near a decapole resonance was investigated. RACETRACK and PATRICIA showed decreases in the aperture on opposite sides of the resonance. A second set of studies was made with PATRICIA in which the dynamic apertures of lattices consisting of cells of the types used for the Reference Designs Study were determined when random multipole errors of the dipoles were included. The dependence of aperture on the number of cells in the lattice was determined. Finally, a comparison of magnet types suggested for the SSC was made by determining the aperture of lattices containing these magnets.
Date: June 23, 1984
Creator: Dell, G.F.; Leemann, B. & Willeke, F.
Partner: UNT Libraries Government Documents Department

Comparison of aperture determinations on RHIC for single particles tracked 10{sup 6} turns and 100 particles, having randomly generated initial coordinates, tracked for 1000 turns

Description: Aperture determinations from 100 particles tracked for 1000 turns using randomly selected initial coordinates are compared with results from 10{sup 6} turn runs when initial coordinates are defined by {epsilon}{sub x} = {epsilon}{sub y} and X{sub i}{prime} = Y{sub i}{prime} = 0. Measurements were made with ten distributions of magnetic field errors. The results from tracking 100 particles for 10{sup 3} turns are equivalent to those from 10{sup 6} turn runs, have a distribution of considerably less width, and require only one tenth the computer time.
Date: June 1, 1993
Creator: Dell, G. F.
Partner: UNT Libraries Government Documents Department

Aperture determination of RHIC92 from randomly generated initial coordinates

Description: Results obtained by tracking 100 particles for 1,000 turns when initial coordinates are selected randomly, with the requirement that the total emittance be constant, are compared to results from 1,000-turn and 10{sup 6}-turn runs when initial coordinates satisfy {epsilon}{sub x}(i) = {epsilon}{sub y}(i) and X{sub i}{prime} = Y{sub i}{prime} = 0. For studies of ten distributions of magnetic field errors, the 100-particle results given apertures equivalent to those from 10{sup 6}-turn runs, have an aperture distribution of considerably less width, and yet require only one tenth the computer time.
Date: December 31, 1992
Creator: Dell, G. F.
Partner: UNT Libraries Government Documents Department

Comparison of aperture determinations on RHIC for single particles tracked 10[sup 6] turns and 100 particles, having randomly generated initial coordinates, tracked for 1000 turns

Description: Aperture determinations from 100 particles tracked for 1000 turns using randomly selected initial coordinates are compared with results from 10[sup 6] turn runs when initial coordinates are defined by [epsilon][sub x] = [epsilon][sub y] and X[sub i][prime] = Y[sub i][prime] = 0. Measurements were made with ten distributions of magnetic field errors. The results from tracking 100 particles for 10[sup 3] turns are equivalent to those from 10[sup 6] turn runs, have a distribution of considerably less width, and require only one tenth the computer time.
Date: January 1, 1993
Creator: Dell, G.F.
Partner: UNT Libraries Government Documents Department

Skew chromaticity in large accelerators

Description: The 2-D ``skew chromaticity`` vector k is introduced when the standard on-momentum description of linear coupling is extended to include off-momentum particles. A lattice that is well decoupled on-momentum may be badly decoupled off-momentum, inside the natural momentum spread of the beam. There are two general areas of concern: (1) the free space in the tune plane is decreased; (2) collective phenomena may be destabilized. Two strong new criteria for head-tail stability in the presence of off-momentum coupling are derived, which are consistent with experimental and operational observations at the Tevatron, and with tracking data from RHIC.
Date: May 1, 1995
Creator: Peggs, S. & Dell, G.F.
Partner: UNT Libraries Government Documents Department

Simulation of the space charge effect in RHIC

Description: Space charge forces, representing the weak-strong case, are simulated by kicks from a line charge having a 2D-Gaussian transverse charge distribution. A series of particles having initial coordinates consistent with the dimensions of the injected beam are tracked sequentially, and tunes are obtained from analysis of the coordinates, x, x{prime}, y, and y{prime}, at the end of each turn. Stability is tested using 30K turn tracking runs during which the momentum error {delta} varies as {delta} = {delta}sin(2{pi}Q{sub s}t).
Date: May 1, 1995
Creator: Dell, G.F. & Peggs, S.
Partner: UNT Libraries Government Documents Department

Skew chromaticity

Description: The on-momentum description of linear coupling between horizontal and vertical betatron motion is extended to include off-momentum particles, introducing a vector quantity called the ``skew chromaticity``. This vector tends to be long in large superconducting storage rings, where it restricts the available working space in the tune plane, and modifies collective effect stability criteria. Skew chromaticity measurements at the Cornell Electron Storage Ring (CESR) and at the Fermilab Tevatron are reported, as well as tracking results from the Relativistic Heavy Ion Collider (RHIC). The observation of anomalous head-tail beam Iowa new the tune diagonal in the Tevatron are explained in terms of the extended theory, including modified criteria for headtail stability. These results are confirmed in head-tail simulations. Sources of skew chromaticity are investigated.
Date: December 31, 1994
Creator: Peggs, S. & Dell, G.F.
Partner: UNT Libraries Government Documents Department

Aperture determination by long term and multiparticle tracking

Description: Apertures determined by long term tracking for 10{sup 6} turns at {beta}{sup {asterisk}} {equals} 2m and 6m and tracking of 100 particles for 1000 turns at {beta}{sup {asterisk}} {equals} 2m are reported. The multiparticle results are consistent with aperture determined from 10{sup 6} turn runs. Finally, the 10{sup 6} turn results are extrapolated to 3 {times} 10{sup 9} turns to obtain an estimate of the aperture for which particles survive for 10 hours in RHIC. 2 refs., 5 figs., 1 tab.
Date: January 1, 1991
Creator: Dell, G.F. & Parzen, G.
Partner: UNT Libraries Government Documents Department

The chromatic correction in RHIC (Relativistic Heavy Ion Collider)

Description: The scheme for the correction of chromatic effects in the Relativistic Heavy Ion Collider at BNL is discussed. This scheme uses six families of sextupoles excited by four independent power supplies, and provides adequate control of linear and quadratic terms in the tune vs momentum dependence and reduces the variation of the betatron amplitude, vs momentum.
Date: January 1, 1987
Creator: Lee, S.Y.; Dell, G.F.; Hahn, H. & Parzen, G.
Partner: UNT Libraries Government Documents Department

RHIC tracking studies with real magnets in real places

Description: Results from RHIC tracking studies in which measured magnetic field errors are used in all arc magnets are reported. the dependence of betatron tunes on initial amplitudes, aspect ratio, and momentum are reported and are not significantly different from measured tune dependences when randomly generated magnetic field errors are used in all magnets. Survival plots at injection and storage are also consistent with previous determinations.
Date: July 1, 1996
Creator: Dell, G.F.; Peggs, S. & Pilat, F.
Partner: UNT Libraries Government Documents Department