SNS Ring Collimation system

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Electron Cooling Dynamics
for RHIC A.
Fedotov, I. Ben-Zvi, Yu. Eidelman, V. Litvinenko
(BNL) I. Meshkov. A. Sidorin,
A. Smirnov, G. Trubnikov (JINR) D. Bruhwiler
et al. (Tech-X)
(October 21, 2004)
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Special features of high-energy cooling at RHIC

• Cooling with up to 55 MeV electrons well beyond
  typical low-energy coolers.
• The electron accelerator cannot be an
  electrostatic machine.
• First cooling with bunched electron beam.
• High temperature of electron beam cooling with
  hot electrons compared to conventional coolers.
• Magnetized beam transport with discontinuous
  solenoidal field.
• Acceleration of an average current of 100 mA and
  above.
• Energy recovery of a high current.
• Very high precision of high-field superconducting
  solenoid.
• Accurate cooling times estimates and detailed
  evolution of ion beam distribution function.
• Finding and achieving optimum parameters for
  cooling beam.
• Impact of cooling on dynamics of cooled ion
  beam
• A comprehensive analysis, simulations and
  experiments are required to demonstrate
  feasibility of such high-energy cooling for a
  collider.

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Major RD items
BNLs Electron Cooler team I. Ben-Zvi, M.
Blaskiewicz, J. Brennan, A. Burrill, R. Calaga,
P. Cameron, X. Chang, G. Citver, Yu. Eidelman, H.
Hahn, M. Harrison, A. Hershcovitch, A. Jain, V.
Litvinenko, N. Malitsky, C. Montag, A. Fedotov,
D. Kairan, J. Kewisch, W. Mackay, G. McIntyre, A.
Nicolleti, D. Pate, G. Parzen, S. Peggs, J. Rank,
T. Roser, J. Scaduto, T. Srinivasan-Rao, D.
Trbojevic, J. Wei, A. Zaltsman, Y. Zhao and
others

• An RD of several items is presently
  underway
• The photoinjector (including its laser and
  photocathode deposition system) up to 20 nC,
  100-300 mA CW rf photo-cathode electron gun
• Energy Recovery Linac (ERL) with high-current
  cavities large bore 700 MHz cavity with ferrite
  HOM dampers and high beam breakup threshold

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RD items (continued)
3. Magnetized beam transport beam transport has
to obey certain rules in order to preserve the
magnetization of the beam with a discontinuous
magnetic field. 4. Superconducting
solenoid prototype is designed for 2-5 T
magnetic field. The solenoid must meet very
stringent field quality requirement with a
solenoid field-error below 1x10-5
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Cooling dynamics

• 5. Cooling theory and simulations
• 1) VORPAL code (Tech-X, Colorado)
• D. Bruhwiler et al.
• 2) BETACOOL code (JINR, Dubna, Russia)
• I. Meshkov et al.
• 3) SIMCOOL code (BNLs version)
• Yu. Eidelman et al.
• 4) UAL (BNL)
• N. Malitsky et al.

usage 1. Benchmarking of
available formulas for Cooling force. 2. Study
dependence of Cooling force on various
parameters.
usage Cooling dynamics studies.
usage Impact of cooling on ion beam
dynamics
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Cooling theory, simulations and experimental
benchmarking collaboration

• BNL A. Fedotov, I. Ben-Zvi, Yu. Eidelman, J.
  Kewisch, V. Litvinenko,
• N. Malitsky, G. Parzen
• JINR, Russia I. Meshkov, A. Sidorin, A.
  Smirnov, G. Trubnikov
• BINP, Russia V. Parkhomchuk, A. Skrinsky, others
• Tech-X, Colorado D. Bruhwiler, D. Abell, R.
  Busby, J. Cary, others
• FNAL A. Burov
• JLAB Ya. Derbenev
• INTAS collaborationGSI (Darmstadt), ITEP
  (Russia), JINR (Russia), FZ (Julich), TEMF
  (Darmstadt), TSL (Uppsala), U. of Kiev (Ukraine)
  O. Boine-Frankenheim et al.

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Need for accurate predictions of cooling times

• Cooling times for relativistic energies are
  much longer than for typical coolers
• standard (order of magnitude) estimate of cooling
  times for Au ion at RHIC storage energy of 100
  GeV gives t of the order of 1000 sec, compared to
  a typical cooling time of the order of 0.1 sec
  in existing coolers
• while an order of magnitude estimate was
  sufficient for typical coolers it becomes
  unacceptable for RHIC with a store time of a few
  hours and fast emittance degradation due to Intra
  Beam Scattering (IBS)
• We need computer simulations which will give
  us cooling times estimates with an accuracy much
  better than an order of magnitude.

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Cooling Simulations outstanding issues

• The task of getting accurate estimates for
  cooling times is further complicated by many
  unexplored effects for high-energy cooling
• 1. Cooling with bunched electron beam.
• 2. Cooling with hot electrons
  RHIC Typical
  coolers
• transverse electron temperature
  1000 eV 0.1-1 eV
• longitudinal electron temperature
  50 meV 0.1 meV
• 3. Do we have sufficient magnetized cooling
  (suppressed transverse temperature)?
• 4. Understanding of cooling force for RHIC
  regime.
• 5. What are the optimum parameters for bunched
  electron beam?
• 6. Cooling in a collider brings special
  treatments of various effects for example, IBS.
• 7. Dynamics of cooled ion beam
• - impact on threshold of collective
  instabilities,
• - beam-beam parameters, luminosity, etc.

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Cooling Force studies

• Cooling
  Force studies
• 1. Benchmarking of available formulas vs
  VORPAL code (direct simulation of friction force
  N-body simulations) for various regimes.
• 2. Experimental benchmarking of typical cooling
  parameters
• (planned CELSIUS, December 2004)
• Experimental tests of some issues relevant to
  high-energy cooling
• (planned CELSIUS)
• 4. Application to RHIC regime.

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1. Benchmarking with formulas
Derbenev-Skrinsky (D-S) - analytic
Derbenev-Skrinsky-Meshkov (D-S-M) - analytic
Factor 2/3 without ln offsets defect of
adiabatic collisions by contributions with large
impact parameters so that integral momentum
transfer is no longer zero in long. direction
when V_tr0
V. Parkhomchuck (VP) - empiric
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Calculated Fcool based on VP formula for test
parameters used in VORPAL simulations
Fcool in normalized units
test region
Vion m/sec
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Example comparison of dv_parallel (longitudinal
friction force coefficient) between VP formula
and direct numerical calculations using VORPAL
code.
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Comparison of D-S vs VP formulas in
experiments(longitudinal friction force
measurements)
Y-N. Rao et al. CELSIUS, Sweden2001
D-S
VP
D-S overestimates cooling force, VP agrees
reasonably well requires detailed benchmarking
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Example of VORPAL code for two different
longitudinal temperatures of electron beam
VORPAL (dots) vs VP formula (curves) studies of
cooling force maximum (2003)
Fc
V
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Cooling force studies preliminary conclusions

• Some benchmarking of analytic formulas for
  magnetized cooling vs VORPAL were performed
• - good agreement with VP formula in tested
  parameter-regions
• - agrees with D-S formula in some regions
  and deviates in others
• more detailed benchmarking is planned
  (sweeps over parameter range on parallel
  computer cluster).
• 3. Preliminary simulations using VORPAL code
  with scaled RHIC parameters were performed to
  study dependence on longitudinal and transverse
  temperature of electron beam
• 4. Benchmarking with experiments is planned.

D. Bruhwiler talk
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IBS studies

• IBS
  studies
• Benchmarking of various IBS models.
• Experimental benchmarking in RHIC.

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IBS models
BetaCool code
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RHIC IBS experiment 4789, bunches 121 and 301
(with accurate initial bunch length)
en95 mm mrad
N0.6109 model experiment
N0.3109 model experiment
J. Wei talk
time sec
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Development of cooling dynamics codes

• IBS
  Cooling
• Cooling dynamics codes SimCool BetaCool
• To study requirements
• - e-cooler (strength of magnetic field, effects
  of solenoid errors, etc.)
• - e-beam (emittance, energy spread, etc.)

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BetaCool/SimCool codes rapid cooling of beam
core for almost unchanged rms parameters
effective increase in luminosity
Transverse profile
Luminosity increase
Longitudinal profile
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IBS treatment under cooling

• Cooling in a collider most important parameter
  is luminosity which directly depends on detailed
  beam distributions.
• Standard treatment of IBS based on rms parameter
  is no longer satisfactory we can see that
  distribution may be very sharp/collapsed while
  rms parameters are approximately unchanged.
• Applying rms based IBS rates for beam core
  significantly underestimate core diffusion.

Transverse beam profile
after 4 hours
after 30 minutes
initial
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Models for IBS treatment of cooled beam

• Several models are under study
• Detailed IBS (A. Burov, FNAL) analytical
  expression for diffusion coefficient which keeps
  dependence of individual particle actions.
• bi-Gaussian rms IBS rates distribution (G.Parzen,
  BNL)
• Core-tail model (BNL)
• 3.1 Cooled ion distribution is divided into
  2 regions.
• 3.2 Particles in the core are kicked
  according to diffusion coefficient for the core,
  particles in the tails are kicked according to
  rms parameters of full distribution.
• 3.3. Fitting procedure with bi-Gaussian was
  implemented which improved accuracy of
  core-tail model.

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Example of difference between core cooling
Transverse profile
luminosity
rms based IBS
factor 20
core-tail model
factor 2
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Detailed simulation of cooling dynamics

• RHIC-II cooling
  simulations
• Cooling dynamics under various effects
• Tolerance to magnetic field errors
• Cooling optimization
• Cooling at full energy
• Pre-cooling at low energy
• Cooling at various collision energies
• etc.

Details in RHIC-II E-Cooling Design Report (ZDR)
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RHIC-II Luminosity with and without
cooling(Au 100 GeV)
with cooling
ltLgt71027
E-cooling factor of 10 increase in
average luminosity per store
no cooling
no cooling
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Beam-beam parameter
Operation near the beam-beam limit is expected
Beam-beam parameter per IP without additional
optimization with e-beam
Beam-beam parameter per IP with additional
optimization of e-beam
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Cooling in a collider

• Electron cooling in collider provides
• control of beam heating due to IBS, noise,
  beam-beam reduces beam emittances to a required
  level.
• rapid cooling of beam core rapid luminosity
  increase.
• bunch shortening which can lead to a very low
  beta-star with a subsequent luminosity increase.
• more effective cooling - using two-stage cooling
  by first pre-cooling at low energy with a
  subsequent cooling at higher energy.

especially for protons
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Example of two-stage cooling for proton in RHIC
pre-cooling at low energy
Pre-cooling protons at 27 GeV, Np1x1011
Ne1x1011
Ne5x1010 and 1x1011
Subsequent emittance growth at 250 GeV of
initially pre-cooled protons
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Impact of cooled beam on ion dynamics

• IBS Cooling
  beam-beam
• Negative impacts of good cooling (rapidly cooled
  core)
• - beam-beam parameter may be exceeded
• - too much luminosity rapid beam
  disintegration in IP
• 2. Possible positive impacts
• - may help to improve beam-beam limit (as
  in electron machines with radiation damping)
• - noise, etc. results in a coherent kick
  at IP goes into incoherent motion (with
  subsequent emittance growth) cooling can damp
  such coherent oscillations
• 3. Instabilities of cooled ions beams
• 
  
  UAL

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Beam experiments towards high-energy cooling

• In present coolers (CELSIUS, ESR, etc.)
• Measure cooling force and benchmark codes.
• Benchmark new models of IBS required to treat
  distribution shrinking under cooling.
• 3. Study stability of cooled distribution.
• Create condition expected in RHIC cooler and
  study some issues like magnetized cooling with
  small cooling logarithm, effect of solenoid
  errors, etc.
• Experiments will begin starting December, 2004 at
  Celsius (Uppsala).

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Future study topics

• 1. Continue simulations of cooling dynamics
• - Friction force studies with VORPAL
• a) need confirmation of observed effects b)
  study many remaining topics
• c) detailed simulations for expected RHIC
  parameters
• - Detailed benchmarking of dynamics codes
  SIMCOOL and BETACOOL
• - Further development and improved
  treatment of various effects
• 2. Optimize parameters for electron beam
• Optimize parameters for electron cooler.
• RHIC E-Cooling Design Report
  (ZDR) first iteration is available
• 4. Evaluate full dynamics of cooled ion beam
• - beam-beam, luminosities, instabilities of
  cooled beam, etc.
• - detailed study of ion beam dynamics with
  UAL
• - cures of instabilities control of
  cooling, etc.
• RHIC E-Cooling R D issues
  to be resolved in 2-3 years.