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 (H 2, 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 β-beams
5 Cooling/Heating equations Cooling equations are same as used for muons mass = a m p, charge = z e Some formulae may be inaccurate for small β=v/c Add heating through nuclear interactions Ionization/recombination should be included For small β, longitudinal dE/dx heating is large At β =0.1, g L = -1.64, ∑ g = 0.36 Coupling only with x cannot obtain damping in both x and z
6 μ Cooling Regimes Efficient cooling requires: Frictional Cooling (<1MeV/c) Σ g =~3 Ionization Cooling (~0.3GeV/c) Σ g =~2 Radiative Cooling (>1TeV/c) Σ g =~4 Low-ε t cooling Σ g =~2β 2 (longitudinal heating)
7 Miscellaneous Cooling equations For small β: Better for larger mass?
8 Example ERIT-P-storage ring to obtain directed neutron beam (Mori-Okabe, FFAG05) 10 MeV protons 9 Be target for neutrons σ ≈ 0.5 barns β = v/c =0.145 Large δE heating Baseline Absorber 5µ Be absorber δE p =~36 keV/turn Design Intensity 1000Hz, 6.5×10 10 p/cycle 100W primary beam < 1.5 kW on foil –0.4 kW at n turns =1000
9 ERIT results With only production reaction, lifetime is 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 g i = 0.12 Cooling time would be ~5000 turns With β =0.2m, δE rms = 0.4MeV, ,N = m (x rms =2.3cm) x rms = 7.3cm at β =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 = π Bρ –For 10 MeV p : BL = 1.44T-m Complete period is 2 turns
11 Emittance exchange parameters with g L,0 = -1.63, η = 0.5m, need G = 3.5 to get g L =0.12 –(L W =0.3m) Beam Center Geometry of wedge absorber L W =1/G
12 “Wedge” for thin foil Obtain variable thickness by bent foil (Mori et al.) Choose x 0 =0.15m, L W =0.3, δ o =5µ then a=0.15, δ R =2.5 for g L,0 = -1.63, η = 0.5m Barely Compatible with β * = 0.2m Beam energy loss not too large? <1kW Power on foil a=0.15 Beam
13 Other heating terms: Mixing of transverse heating with longitudinal could be larger effect: (Wang & Kim) At ERIT parameters: β x = 1.0m, β z = 16m, η=0.6m, Be absorber, dδ 2 /ds= , d θ 2 /ds= only 5%, 1.5% changes … At β x = 0.2m, ~25% change …
14 Beta beams for neutrinos (Zuchelli) ν-sources v-sources Number of possible sources is limited (v sources easier) Want: lifetime ~1s large ν-energy ν and ν* easily extracted atoms Noble gases easier to extract 6 He 2 “easiest” E ν* =1.94MeV 18 Ne 10 for ν E ν =1.52MeV Noble gas ( 8 B, 8 Li) have E ν,ν * =~7MeV Want ν and ν* / year…
15 β-beam Scenario Neutrino Source Decay Ring Ion production: Target - Ion Conversion Ring Ion Driver 25MeV Li ? Decay ring B = 400 Tm B = 5 T C = 3300 m L ss = 1100 m 8 B: = 80 8 Li: = 50 Acceleration to medium energy RCS 8z GeV/c Acceleration to final energy Fermilab Main Injector Experiment Ion acceleration Linac Beam preparation ECR pulsed Ion productionAccelerationNeutrino source
16 β-beam Scenario (Rubbia et al.) Produce Li and inject at 25 MeV Charge exchange injection nuclear interaction at gas jet target produces 8 Li or 8 B Multiturn with cooling maximizes ion production 8 Li or 8 B is caught on stopper(W) heated to reemit as gas 8 Li or 8 B gas is ion source for β- beam accelerate Accelerate to Bρ = 400 T-m Fermilab main injector Stack in storage ring for: 8 B 8 Be + e + +ν or 8 Li 8 Be + e - + ν* neutrino source
17 Cooling for β -beams (Rubbia et al.) β-beam requires ions with appropriate nuclear decay 8 B 8 Be + e + + ν 8 Li 8 Be + e - + ν* Ions are produced by nuclear interactions 6 Li + 3 He 8 B + n 7 Li + 2 H 8 Li + 1 H 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 β-beams example: 6 Li + 3 He 8 B + n Beam: 25MeV 6 Li +++ P Li =529.9 MeV/c Bρ = 0.59 T-m; v/c= Absorber: 3 He Z=2, A=3, I=31eV, z=3, a=6 dE/ds = MeV/cm, L R =756cm –at (ρ He-3 = gm/cm 3 ) Liquid, (ρ He-3 = 0.134∙10 -3 P gm/cm3/atm in gas) dE/ds= 1180 MeV/gm/cm 2, L R = 70.9 gm/cm 2 If g x = (Σ g = 0.37), β ┴ =0.3m at absorber ε N,eq = ~ m-rad σ x,rms = 1.2 cm at β ┴ =0.3m, σ x,rms = 3.14 cm at β ┴ =2.0m σ E,eq is ~ 0.4 MeV ln[ ]=5.68, energy straggling underestimated?
19 Cooling time/power : 6 Li + 3 He 8 B + n Nuclear cross section for beam loss is 1 barn ( cm 2 ) or more σ = cm 2, corresponds to ~5gm/cm 2 of 3 He ~10 3-D cooling e-foldings … Cross-section for 8 B production is ~10 mbarn At best, of 6 Li is converted Goal is /s of 8 B production then at least Li 6 /s needed Space charge limit is ~ Li/ring Cycle time is <10 -3 s If C=10m, τ =355 ns, 2820 turns/ms 5/2820=1.773*10 -3 gm/cm 2 (0.019 liquid density …) 2.1 MeV/turn energy loss and regain required …(0.7MV rf) MW cooling rf power…
20 β-beams example: 7 Li + 2 H 8 Li + 1 H Beam: 25MeV 7 Li +++ P Li =572 MeV/c Bρ = 0.66 T-m; v/c= Absorber: 2 H Z=1, A=2, I=19eV, z=3, a=7 dE/ds = MeV/cm, L R =724cm –at (ρ H-2 = gm/cm 3 ) Liquid, (ρ H-2 = 0.179∙10 -3 P gm/cm3/atm in gas) dE/ds= 1090 MeV/gm/cm 2, L R = 70.9 gm/cm 2 If g x = (Σ g = 0.37), β ┴ =0.3m at absorber ε N,eq = ~ m-rad σ x,rms = 1.0 cm at β ┴ =0.3m, σ x,rms = 2.5 cm at β ┴ =2.0m σ E,eq is ~ 0.36 MeV ln[ ]=6.0, Easier than 8 B example ?
21 Cooling time/power- 7 Li + 2 H 8 Li + 1 H Nuclear cross section for beam loss is 1 barn ( cm 2 ) or more σ = cm 2, corresponds to ~3.3gm/cm 2 of 2 H ~9 3-D cooling e-foldings … Cross-section for 8 Li production is ~100 mbarn of 7 Li is converted ?? 10 × better than 8 B neutrinos Goal is /s of 8 Li production then at least Li 7 /s needed Space charge limit is ~ Li/ring Cycle time can be up to s, but use s If C=10m, τ =355 ns, 2820 turns 3.3/2820=1.2*10 -3 gm/cm 2 (0.007 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 = 10 12, B F =0.2, β = 0.094, z=3, a=6, ε N,rms = : δν ≈ 0.2 tolerable ?? Space charge sets limit on number of particles in beam
23 Inverse vs. Direct Kinematics 6 Li 3 beam + 3 He 2 target 25 MeV Li gas-jet target tapered nozzle for wedge? product is ~ 8 B 8 to 23 MeV Stop in Tantalum absorber penetrates more (5 to 12μ) <14.5° Beam divergence ~6° (2.5σ) Boil out to vapor neutralize to vapor, extract, ionize, accelerate 100% efficiency … 3 He 2 beam + 6 Li 3 target 12.5 MeV He beam Li foil target (or liquid waterfall?) fold to get wedge … product is ~ 8 B ~1 to 8 MeV Stop in Tantalum absorber penetrates less (2 to 5μ) <30° Beam divergence is ~10° (2.5σ) Boil out to vapor
24 X-sections, kinematics
25 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 z 2 factor in dE/dx but not in multiple scattering, …
26 Low-Energy “cooling”-emittance exchange dP μ /ds varies as ~1/β 3 “Cooling” distance becomes very short: for liquid H at P μ = 10MeV/c Focusing can get quite strong: Solenoid: β =0.002m at 30T, 10MeV/c ε N,eq = 1.5×10 -4 cm at 10MeV/c Small enough for “low-emittance” collider PµPµ L cool 200 MeV/c cm 100 cm
27 Emittance exchange: solenoid focusing Solenoid focusing(30T) 0.002m Momentum (30→10 MeV/c) L ≈ 5cm R < 1cm Liquid Hydrogen (or gas) PµPµ L cool 200 MeV/c cm Use gas H 2 if cooling length too short ε N,eq = 1.0×10 -4 cm at 10MeV/c, 50T -Will need rf to change p to z
28 Gas absorbers With gas absorbers can adjust energy loss rate avoid beam loss
29 Collider Parameters
30 Summary
31 β-beams alternate: 6 Li + 3 He 8 B + n Beam: 12.5MeV 3 He ++ P Li =264 MeV/c Bρ = 0.44 T-m; v/c=0.094 Absorber: 6 Li Z=3, A=6, I=43eV, z=2, a=3 dE/ds = 170 MeV/cm, L R =155cm –at (ρ Li-6 = 0.46 gm/cm 3 ) Space charge 2 smaller If g x = (Σ g = 0.37), β ┴ =0.3m at absorber ε N,eq = ~ m-rad σ x,rms = 2.0 cm at β ┴ =0.3m, σ x,rms = 5.3 cm at β ┴ =2.0m σ E,eq is ~ 0.3 MeV ln[ ]=5.34