IBS suppression lattice in RHIC: theory in addition to experimental verification A. Fedotov

IBS suppression lattice in RHIC: theory in addition to experimental verification A. Fedotov www.phwiki.com

IBS suppression lattice in RHIC: theory in addition to experimental verification A. Fedotov

Cooper, Cord, Freelance Columnist has reference to this Academic Journal, PHwiki organized this Journal IBS suppression lattice in RHIC: theory in addition to experimental verification A. Fedotov, M. Bai, D. Bruno, P. Cameron, R. Connolly, J. Cupolo, A. Della Penna, A. Drees, W. Fischer, G. Ganetis, L. Hoff, V. Litvinenko, W. Louie, Y. Luo, N. Malitsky, G. Marr, A. Marusic, C. Montag, V. Ptitsyn, T. Satogata, S. Tepikian, D. Trbojevic, N. Tsoupas August 25-29, 2008 HB2008 Workshop, Nashville, Tennessee Collider-Accelerator Department, BNL Outline IBS in RHIC Development of IBS-suppression lattice IBS models/simulations Dedicated IBS measurements Comparison of simulations in addition to measurements RHIC per as long as mance as long as Au ions luminosity loss intensity loss 2004 run 2007 run (with longitudinal stochastic cooling in Yellow ring) Per as long as mance of RHIC collider with Au ions is limited by the process of Intra-Beam Scattering (IBS).

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IBS in RHIC ( as long as g >> gtr) 1. For energies much higher than transition energy Intra-beam Coulomb scattering (IBS) is dominated by heating of longitudinal degree of freedom. Additional heating: 2. At regions with non-zero dispersion, changes in longitudinal momentum change particle reference orbits, which additionally excites horizontal betatron motion. 3. Horizontal heating is shared between horizontal in addition to vertical planes due to x-y coupling. For the case of full coupling, transverse heating is equally shared between x in addition to y. Reducing this function allows to reduce transverse IBS rate – idea behind “IBS-suppression” lattice. Approximate longitudinal IBS diffusion rate: @g=107; gt=23 Reduction of transverse IBS RHIC lattice consists of 6 insertions (IP regions), where H-function is very low in addition to 6 arcs with regular FODO cells. As a result, dominant contribution into transverse IBS comes from the arcs. The H-function can be reduced by increasing phase advance per cell. The 2004 RHIC lattice had 82° phase advance per cell. Layout of RHIC collider: The collider is composed of 2 identical non-circular rings oriented to intersect with one another at 6 crossing points. Each arc is composed of 11 FODO cells. Lattice functions as long as arc cell RHIC Design Manual

Reduction of the IBS rate Qx/cell IBS(0.22)/ IBS(Qx) Starting (Run-4) operating point NOTE: Qx are tune advances per FODO cell Qy = (0.9 or 1 or 1.1) Qy 90o 108o 72o 126o 144o Run-8 operating point V.N. Litvinenko (2004) Future plan Stronger focusing in addition to limits When built, RHIC was already the collider with the shortest in addition to strongest focusing FODO cell of all the hadron machines. The most important consideration in this regard was Intra-beam Scattering. However, as long as the beam parameters in addition to machine per as long as mance in 2004, operational lattice with 82° phase advance appeared to be not fully optimized with respect to IBS growth in addition to thus maximum luminosity. There as long as e, it was suggested to explore RHIC per as long as mance with higher phase advance per cell. Practical range of achievable phase advances per cell is determined by existing feeding system as long as RHIC superconducting magnets which have multiple inter-connections in addition to current limits imposed by feeders in addition to power supplies. As well as interplay with other effects. It was decided to start with the test “IBS-suppression” lattice with 92° horizontal phase advance per cell. Test IBS lattice (2005) as long as APEX experiments Dispersion function as long as RHIC-4 lattice (82° phase advance) Dispersion function as long as test IBS lattice (92° phase advance) lattice development by S. Tepikian

2005 predictions as long as IBS APEX experiment with the test lattice (simulations using BETACOOL code: rms unnormalized emittance growth as long as 82° in addition to 92° lattice, Cu ions @100 GeV/n) t-1rhic-4/t-192=30% reduction in transverse IBS emittance growth rate 82° lattice 92° lattice History of IBS-lattice development 2004 – IBS suppression lattice proposed. It was decided to start with incremental increase of phase advance per cell (92° as long as the first test). 2005 – development of IBS lattice as long as Cu ions during Accelerator Physics EXperiments (APEX). The progress with ramp development was marginal – the main problems were related to the tune swings during the ramp. Measurements @31GeV/n in addition to some puzzles. 2006 – no experiments, since the run was with polarized protons. 2007 – progress with tune in addition to coupling feed-back dramatically speed-up development of the ramps. Effect of IBS suppression lattice on transverse emittance growth was directly measured during APEX in June 2007. 2008 – as long as d-Au run, IBS lattice was implemented as operational lattice as long as Au ions in Yellow ring. Dedicated measurements of IBS in RHIC To ensure accurate benchmarking, collisions were turned off. In addition, h=360 rf system was used to avoid loss of particles from the bucket. Six bunches of different intensity with different initial emittance were injected, which allowed us to test expected scaling with intensity in addition to emittance. Measurements of the bunch length were done using Wall Current Monitor (WCM). Measurements of the horizontal in addition to vertical emittance in each individual bunch were done using Ionization Profile Monitor (IPM). 2004 – with Au ions 2005 – with Cu ions 2007 – Au ions with IBS-suppression lattice 2008 – Au ions with operational IBS-suppression lattice For accurate comparison of measurements with simulations, IBS studies in RHIC were per as long as med in dedicated beam mode under APEX.

IBS models in BETACOOL code (JINR, Dubna, Russia) – Gaussian distributions I. Analytic models as long as Gaussian distribution: Piwinski’s model Martini’s model (including derivatives of lattice functions) Bjorken-Mtingwa’s model (including vertical dispersion) Wei’s, Parzen’s models (high-energy approximation) Gas-relaxation model (high-energy approximation) For comparison with experimental measurements in RHIC at 100 GeV/n, we use Martini’s or Bjorken-Mtingwa’s models (which give the same results as long as RHIC parameters). IBS models in BETACOOL – non-Gaussian distributions (mostly relevant to distributions under e-cooling) II. IBS as long as non-Gaussian distributions. In situations when distribution can strongly deviate from Gaussian, as as long as example under effect of Electron Cooling, it was necessary to develop IBS models based on the amplitude dependent diffusion coefficients. Several models were developed: -“Detailed” (Burov): analytic expression as long as longitudinal coefficient as long as Gaussian distribution with longitudinal temperature much smaller than transverse in addition to smooth lattice approximation. -“bi-Gaussian” (Parzen): rms rates as long as bi-Gaussian distribution; all particles are kicked based on the rms rate expression. -“Core-tail”: different diffusion coefficients as long as particle in the core in addition to tails of the distribution. -“Kinetic model” – “Local diffusion” – algorithm is based as long as numerical evaluation of amplitude dependent diffusion coefficients in 3-D. Allows to simulate evolution of arbitrary distribution due to IBS (implemented in BETACOOL in 2007). IBS in RHIC – measurements vs. theory Example of 2005 data with Cu ions (82°/cell phase advance) Simulations (BETACOOL) – Martini’s model of IBS as long as exact designed lattice of RHIC (82°/cell), including derivatives of the lattice functions. Growth of 95% normalized emittance [mm] as long as bunch with intensity N=2.9·109 horizontal vertical Emittance measurements were done with Ionization Profile Monitor (IPM). [sec] [mm mrad]

Simulations vs. Measurements; Cu ions, APEX 2005 (82°/cell phase advance lattice; 100 GeV/n) FWHM [ns] bunch length growth as long as intensities N=2.9·109 in addition to 1.4·109. Growth of 95% normalized horizontal emittance [mm] as long as two bunch intensities N=2.9·109 (upper curve) in addition to 1.4·109. Dash lines – simulations; solid lines – measurements. Two bunches with different intensity. N=2.9109 N=1.4109 [ns] [sec] [sec] [mm] IPM measurements of transverse emittance (June 2007, APEX data as long as Au ions @100 GeV/nucleon) Au ions at 100 GeV/n (June 2007, APEX data) (Blue ring: normal lattice with 82° phase advance per cell; Yellow ring: IBS lattice with 92° phase advance) in Yellow in Blue in Blue in Yellow bunch intensities bunch length emittance in Blue in Yellow We had 6 bunches in each ring. Only 3 bunches per ring are shown.

IBS suppression lattice APEX experiment – June 2007 (V. Litvinenko et al.) Conclusions Transverse IBS emittance growth is suppressed by 30±10% January 9, 2008 APEX measurements, using operational Run-8 IBS lattice (95° phase advance) in Yellow ring Goal of the experiment: To underst in addition to what portion of vertical emittance growth comes from x-y coupling. Quantitative underst in addition to ing of emittance growth in horizontal in addition to vertical planes should help us to conclude whether single-plane transverse stochastic cooling will be sufficient to counteract both horizontal in addition to vertical emittance growth. Measurements (at g=107): 1. Decoupled case: dQmin=0.001, tunes were separated by 0.018 2. Fully coupled case: dQmin=0.018, tunes were separated by 0.018 Model & measured dispersion

Au ions at 100 GeV/n (January 2008, APEX data) (Yellow ring: operational IBS lattice with 95° phase advance) coupled case data Longitudinal bunch length growth due to IBS (simulations vs. measurement, bucket 121) red – measurement blue – simulation 95°/cell phase advance lattice Fully coupled case (January 9, 2008 APEX data): Horizontal emittance growth (simulation vs. measurement, bucket 121) red – Horizontal emittance (measurement) blue – expected (simulation) with Run-7 lattice (82°/cell) green – expected (simulation) as long as Run-8 “IBS-suppression” lattice (95°/cell) For simulations with 82° in addition to 95° lattice, longitudinal beam parameters (momentum spread in addition to bunch length) were chosen the same. Reduction in horizontal IBS emittance growth rate, as predicted.

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IBS lattice summary Clear advantages: reduced transverse emittance growth – confirmed by dedicated beam experiments increased RF bucket area, due to higher gt (by 13%) –better rebucketing shorter bunch length – better vertex luminosity Additional advantages: – helps to achieve lower b due to slower emittance growth – more relaxed PS current at the beta squeeze Concerns: – new lattice, more time as long as development – no problem in Run-8. – higher main quad current (reliability issue) – seems not a problem in Run-8. – nonlinear characteristics of the lattice, the dynamic aperture in addition to its possible effects on beam lifetime – to be explored in simulations Conclusions, future plans Already developed lattice (95° phase advanced per cell) has expected 30% reduction in transverse IBS emittance growth rate. Significant improvement in integrated & vertex luminosity is expected. Use 95° lattice in both Blue in addition to Yellow rings during next RHIC run with Au-Au. Push b down to 0.5m with 95° lattices. Develop lattice even with higher phase advance per cell. The lattice with 107° is presently under development. Test/develop this new lattice during next APEX experiments with heavy ions. Acknowledgements Development in addition to implementation of RHIC lattice with higher phase advance per cell became possible as a result of dedicated work of large group of people at Collider-Accelerator Department. We are grateful to I. Ben-Zvi, D. Kayran, G. Parzen, T. Roser in addition to J. Wei as long as many useful discussions on this subject. We used BETACOOL code developed at JINR, Dubna, Russia. Thank you

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