LowEnergy Ionization Cooling

1
Low-Energy Ionization Cooling

• David Neuffer
• Fermilab

2
Outline

• Low-energy cooling-protons
• ions and beta-beams
• Low-energy cooling muons
• emittance exchange

3
Combining Cooling and Heating

• Low-Z absorbers (H2, Li, Be, ) to reduce
  multiple scattering
• High Gradient RF
• To cool before ?-decay (2.2? ?s)
• To keep beam bunched
• Strong-Focusing at absorbers
• To keep multiple scattering
• less than beam divergence
• ? Quad focusing ?
• ? Li lens focusing ?
• ? Solenoid focusing?

4
Low-energy cooling of ions

• Ionization cooling of protons/ ions has been
  unattractive because nuclear reaction rate is
  competitive with energy-loss cooling rate
• And other cooling methods are available
• But can have some value if the goal is beam
  storage to obtain nuclear reactions
• Absorber is also nuclear interaction medium
• Y. Mori neutron beam source
• NIM paper
• C. Rubbia, Ferrari, Kadi, Vlachoudis source of
  ions for ß-beams

5
Cooling/Heating equations

• Cooling equations are same as used for muons
• mass a mp, charge z e
• Some formulae may be inaccurate for small ßv/c
• Add heating through nuclear interactions
• Ionization/recombination should be included
• For small ß, longitudinal dE/dx heating is large
• At ß 0.1, gL -1.64, ?g 0.36
• Coupling only with x cannot obtain damping in
  both x and z

0.0
1.0
3.0
5.0
bg
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µ Cooling Regimes

• Efficient cooling requires
• Frictional Cooling (lt1MeV/c) Sg3
• Ionization Cooling (0.3GeV/c) Sg2
• Radiative Cooling (gt1TeV/c) Sg4
• Low-et cooling Sg2ß2
• (longitudinal heating)

7
Miscellaneous Cooling equations
For small ß
Better for larger mass?
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Example

• ERIT-P-storage ring to obtain directed neutron
  beam (Mori-Okabe, FFAG05)
• 10 MeV protons
• 9Be target for neutrons
• s 0.5 barns
• ß v/c 0.145
• Large dE heating
• Baseline Absorber
• 5µ Be absorber
• dEp36 keV/turn
• Design Intensity
• 1000Hz, 6.51010p/cycle
• 100W primary beam
• lt 1.5 kW on foil
• 0.4 kW at nturns 1000

9
ERIT results

• With only production reaction, lifetime is 30000
  turns
• With baseline parameters, cannot cool both x and
  E
• Optimal x-E exchange increases storage time from
  1000 to 3000 turns (3850 turns 1ms)
• With x-y-E coupling, can cool 3-D with gi 0.12
• Cooling time would be 5000 turns
• With ß?0.2m, ?dErms 0.4MeV, ??,N 0.0004m
  (xrms2.3cm)
• xrms 7.3cm at ß?2m (would need r 20cm arc
  apertures)
• (but 1ms refill time would make this
  unnecessary)

10
3-D mixing lattice

• For 3-D cooling, need to mix with both x and y
• Possible is Moebius lattice (R. Talman)
• Single turn includes x-y exchange transport
• solenoid(s) or skew quads
• in zero dispersion region for simplicity
• Solenoid BL p B?
• For 10 MeV p BL 1.44T-m
• Complete period is 2 turns

11
Emittance exchange parameters

• with gL,0 -1.63, ? 0.5m,
• need G 3.5 to get gL0.12
• (LW 0.3m)

12
Wedge for thin foil

• Obtain variable thickness by bent foil (Mori et
  al.)
• Choose x00.15m, LW0.3, do5µ
• then a0.15, dR2.5
• for gL,0 -1.63, ? 0.5m
• Barely Compatible with ß 0.2m
• Beam energy loss not too large?
• lt1kW Power on foil

Beam
a0.15
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Other heating terms

• Mixing of transverse heating with longitudinal
  could be larger effect (Wang Kim)

At ERIT parameters ßx 1.0m, ßz 16m, ?0.6m, Be
absorber, dd2/ds 0.00032, d?2/ds 0.0133 only
5, 1.5 changes At ßx 0.2m, 25 change
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Beta beams for neutrinos (Zuchelli)

• Number of possible sources is limited (v sources
  easier)
• Want
• lifetime 1s
• large ?-energy
• ? and ?
• easily extracted atoms
• Noble gases easier to extract
• 6He2 easiest E? 1.94MeV
• 18Ne10 for ? E? 1.52MeV
• Noble gas
• (8B, 8Li) have E ? ,? 7MeV
• Want 1020 ? and ? / year

v-sources
?-sources
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ß-beam Scenario
Ion production
Acceleration
Neutrino source
Experiment
Ion Driver 25MeV Li ?
Acceleration to final energy Fermilab Main
Injector
Ion production Target - Ion Conversion Ring
Neutrino Source Decay Ring
Beam preparation ECR pulsed
Decay ring Br 400 Tm B 5 T C 3300
m Lss 1100 m 8B g 80 8Li g 50
Ion acceleration Linac
8z GeV/c
Acceleration to medium energy RCS
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ß-beam Scenario (Rubbia et al.)

• Produce Li and inject at 25 MeV
• Charge exchange injection
• nuclear interaction at gas jet target produces
  8Li or 8B
• Multiturn with cooling maximizes ion production
• 8Li or 8B is caught on stopper(W)
• heated to reemit as gas
• 8Li or 8B gas is ion source for ß-beam accelerate
• Accelerate to B? 400 T-m
• Fermilab main injector
• Stack in storage ring for
• 8B?8Be e? or 8Li?8Be e- ? neutrino
  source

17
Cooling for ß-beams (Rubbia et al.)

• ß-beam requires ions with appropriate nuclear
  decay
• 8B?8Be e ?
• 8Li?8Be e- ?
• Ions are produced by nuclear interactions
• 6Li 3He ? 8B n
• 7Li 2H ? 8Li 1H
• Secondary ions must be collected and
  reaccelerated
• Either heavy or light ion could be beam or target
• Ref. 1 prefers heavy ion beam ions are produced
  more forward (reverse kinematics)
• Parameters can be chosen such that target cools
  beam
• (losses and heating from nuclear interactions,
  however)

18
ß-beams example 6Li 3He ? 8B n

• Beam 25MeV 6Li
• PLi 529.9 MeV/c B? 0.59 T-m v/c0.09415
• Absorber3He
• Z2, A3, I31eV, z3, a6
• dE/ds 110.6 MeV/cm, LR756cm
• at (?He-3 0.09375 gm/cm3)Liquid, (?He-3
  0.13410-3P gm/cm3/atm in gas)
• dE/ds 1180 MeV/gm/cm2, LR 70.9 gm/cm2
• If gx 0.123 (Sg 0.37), ß- 0.3m at
  absorber
• eN,eq 0.000046 m-rad
• sx,rms 1.2 cm at ß- 0.3m,
• sx,rms 3.14 cm at ß- 2.0m
• sE,eq is 0.4 MeV
• ln 5.68,
• energy straggling
• underestimated?

19
Cooling time/power 6Li 3He ? 8B n

• Nuclear cross section for beam loss is 1 barn
  (10-24 cm2) or more
• s 10-24cm2,corresponds to 5gm/cm2 of 3He
• 10 3-D cooling e-foldings
• Cross-section for 8B production is 10 mbarn
• At best, 10-2 of 6Li is converted
• Goal is 1013/s of 8B production
• then at least 1015 Li6/s needed
• Space charge limit is 1012 6Li/ring
• Cycle time is lt10-3 s
• If C10m, t 355 ns, 2820 turns/ms
• 5/28201.77310-3 gm/cm2 (0.019 cm _at_ liquid
  density )
• 2.1 MeV/turn energy loss and regain required
  (0.7MV rf)
• 0.944 MW cooling rf power

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ß-beams example 7Li 2H ? 8Li 1H

• Beam 25MeV 7Li
• PLi 572 MeV/c B? 0.66 T-m v/c0.0872
• Absorber2H
• Z1, A2, I19eV, z3, a7
• dE/ds 184.7 MeV/cm, LR724cm
• at (?H-2 0.169 gm/cm3)Liquid, (?H-2 0.17910-3P
  gm/cm3/atm in gas)
• dE/ds 1090 MeV/gm/cm2, LR 70.9 gm/cm2
• If gx 0.123 (Sg 0.37), ß- 0.3m at
  absorber
• eN,eq 0.000027 m-rad
• sx,rms 1.0 cm at ß- 0.3m,
• sx,rms 2.5 cm at ß- 2.0m
• sE,eq is 0.36 MeV
• ln 6.0,
• Easier than 8B example ?

21
Cooling time/power- 7Li 2H ? 8Li 1H

• Nuclear cross section for beam loss is 1 barn
  (10-24 cm2) or more
• s 10-24cm2,corresponds to 3.3gm/cm2 of 2H
• 9 3-D cooling e-foldings
• Cross-section for 8Li production is 100 mbarn
• 10-1 of 7Li is converted ?? 10 better than
  8B neutrinos
• Goal is 1013/s of 8Li production
• then at least 1014 Li7/s needed
• Space charge limit is 1012 7Li/ring
• Cycle time can be up to 10-2 s, but use 10-3s
• If C10m, t 355 ns, 2820 turns
• 3.3/28201.210-3 gm/cm2 (0.007 cm _at_ liquid
  density )
• 1.3 MeV/turn energy loss and regain required
  (0.43MV rf)
• 0.06 MW cooling rf power

22
Space charge limitation

• At N 1012, BF 0.2, ß0.094, z3, a6, eN,rms
  0.000046
• d? 0.2
• tolerable ??
• Space charge sets limit on number of particles in
  beam

23
Inverse vs. Direct Kinematics

• 6Li3 beam 3He2 target
• 25 MeV Li
• gas-jet target
• tapered nozzle for wedge?
• product is 8B
• 8 to 23 MeV
• Stop in Tantalum absorber
• penetrates more (5 to 12µ)
• ? lt14.5
• Beam divergence 6 (2.5s)
• Boil out to vapor
• neutralize to vapor, extract, ionize, accelerate
• 100 efficiency

• 3He2 beam 6Li3 target
• 12.5 MeV He beam
• Li foil target (or liquid waterfall?)
• fold to get wedge
• product is 8B
• 1 to 8 MeV
• Stop in Tantalum absorber
• penetrates less (2 to 5µ)
• ? lt30
• Beam divergence is 10 (2.5s)
• Boil out to vapor

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X-sections, kinematics
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Rubbia et al. contains errors

• Longitudinal emittance growth 2 larger than his
  
• synchrotron oscillations reduce energy spread
  growth rate but not emittance growth rate
• Emittance exchange with only x does not give 3-D
  cooling need x-y coupling and balancing of
  cooling rates
• Increases equilibrium emittance, beam size
• increase needed for space charge, however
• Includes z2 factor in dE/dx but not in multiple
  scattering,

26
Low-Energy cooling-emittance exchange

• dPµ/ds varies as 1/ß3
• Cooling distance becomes very short
• for liquid H at
  Pµ10MeV/c
• Focusing can get quite strong
• Solenoid
• ß?0.002m at 30T, 10MeV/c
• eN,eq 1.510-4 cm at 10MeV/c
• Small enough for low-emittance collider

100 cm
Lcool
0.1 cm
200 MeV/c
10
Pµ
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Emittance exchange solenoid focusing

• Solenoid focusing(30T)
• ??? 0.002m
• Momentum (30?10 MeV/c)
• L 5cm
• R lt 1cm
• Liquid Hydrogen (or gas)

Lcool

• eN,eq 1.010-4 cm at 10MeV/c, 50T

0.1cm
Use gas H2 if cooling length too short
-Will need rf to change ?p to ?z
200 MeV/c
10
Pµ
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Gas absorbers

• With gas absorbers can adjust energy loss rate
• avoid beam loss

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????? Collider Parameters
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Summary
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ß-beams alternate 6Li 3He ? 8B n

• Beam 12.5MeV 3He
• PLi 264 MeV/c B? 0.44 T-m v/c0.094
• Absorber 6Li
• Z3, A6, I43eV, z2, a3
• dE/ds 170 MeV/cm, LR155cm
• at (?Li-6 0.46 gm/cm3)
• Space charge 2? smaller
• If gx 0.123 (Sg 0.37), ß- 0.3m at
  absorber
• eN,eq 0.000133m-rad
• sx,rms 2.0 cm at ß- 0.3m,
• sx,rms 5.3 cm at ß- 2.0m
• sE,eq is 0.3 MeV
• ln 5.34