Final Cooling Options For a High- Luminosity High-Energy Lepton Collider David Neuffer FNAL Don Summers, T. Hart, … U. Miss.

Final Cooling for a Collider & Simulation High-field baseline – R. Palmer & H. Sayed Final scenario variations (IPAC15 --) –round to flat, transverse slicing, bunch recombination –quad focusing, Li lens, Parametric resonance focusing –use of wedge absorbers for final emittance exchange –MICE experiment Outline D, Neuffer2

ParameterUnitHiggs factory3 TeV design6 TeV design Beam energyTeV Number of IPs122 Circumferencem β*β* cm2.511 Tune x/y5.16/ / /40.14 Compaction E E-3 Emittance (Norm.) mm·mrad Momentum spread % Bunch length cm511 H. electrons/bunch Repetition rate Hz3015 Average luminosity10 34 cm -2 s Towards multi-TeV lepton colliders D, Neuffer3 M. Palmer, FRXC3

Final cooling baseline Baseline Final Cooling –solenoids, B  T –H 2 absorbers, –Low momentum –ε t,N : 3.0  0.3 ×10 -4 m –ε L : 1.0  70mm expensive emittance exchange D. Neuffer4 (R. Palmer et al. IPAC12 )

Detailed simulation of final cooling (H. Sayed et al. IPAC14; submitted to PRSTAB ) G4Beamline simulation of final cooling scenario –System is ~135m long –ε t,N : 3.0  m –ε L : 1.0  75mm P l :135  70 MeV/c B: 25  32 T; 325  20MHz not quite specs –Transmission ~ 50% Predominantly ε t,N / ε L emittance exchange D. Neuffer5

Variant Approaches: Keep P l, E’, f rf within ~current technology –P > 100MeV/c; f rf > ~100MHz ; B <30T (<16 for quads) –round to flat transformation –beam slicing and recombination scenarios presented at IPAC15 Most of “final cooling” is emittance exchange –How far can we get on emittance exchange alone? –Explicitly use emittance exchange in final cooling thick wedge energy loss D. Neuffer6

Variant scenario: Cool, Round-to-flat, Slice, Recombine (w/ D. Summers, T. Hart) 1.Cool –Cool until system parameters are difficult ε x,y (ε t )  ~10 -4 m, ε L  ~0.004 m –without field flips to increase angular momentum 2.Round to flat beam transform –ε t  ε x =0.0004; ε y = m ? 3.Slice transversely in large emittance –using “slow extraction-like” septum to form 16 (?) bunches ε x = ; ε y = Recombine longitudinally at high energy –bunch recombination in 20 GeV storage ring (C. Bhat) ε x = ; ε y = , ε L =0.07m D. Neuffer7

Without Round to Flat transform…. 1. Cool bunch to ~10 -4 m ε T (solenoid or quads or Li lens) –~3×10 -3 ε L 2. Transverse slice to 10 bunches: –10 -4 ε x × m ε y –Separated longitudinally 3. Accelerate as bunch train; recombine longitudinally –10 -4 m ε x × m ε y –~3×10 -2 ε L Collide as flat beams; –luminosity ~ same as ε t = ~3×10 -5 D. Neuffer8

Variant: “thick” wedge transform Use wedge to increase δp/p – increase ε L, decrease ε x If δp/p introduced by wedge >> δp/p beam ; –can get large emittance exchange exchanges x with δp (Mucool 003) – also in CERN 99-13, p.30 Example: – 100 MeV/c; δp=0.5MeV/c   = m, β 0 =1.2cm Be wedge 0.6cm, 140  wedge – obtain factor of ~5 exchange –  x  0.2 ×10 -4 m; δp=2.5 MeV/c Much simpler than equivalent final cooling section D. Neuffer9

Wedge theory (MuCool-003) Dispersion + wedge is product of two matrices  = dp/ds 2 tan[  /2]/p variables are [x, δ ], where δ =dp/p transport through wedge is transport of [x, δ] phase space ellipse, initially becoming D. Neuffer10

Results of wedge new coefficients new energy width (ε L,1 = ε L,0 (δ 1 /δ 0 )) new transverse emittance (ε x,1 = ε x,0 (δ 0 /δ 1 )) new β x, η D. Neuffer11

Evaluation of Super-wedge examples Set reference momentum at 100 MeV/c – ε x, ε y  m –β x = β y = ~1cm ~1mm beam –round numbers … Need small δp/p – δp ~0.5 MeV/c obtain by lengthening and flattening bunch ( ε L = ~0.002m) Need dense low-Z wedge –Be (ρ=1.86)  Diamond (ρ=3.6 C) dp/ds =15.1 MeV/c /cm D. Neuffer12 Evaluate in ICOOL –wedge and beam definition, match –emitcalc evaluates eigen emittances before/after –a few cm transport

Numerical examples Wedge parameters –Diamond, w=1.75mm, θ = 100°(4.17mm thick at center) –reduces ε x by factor of 4.3, ε L increases by factor of 7.0 first half of wedge more efficient than second half … Second wedge ? –if matched to same optics (P z  100 MeV/c, σ E  0.46 MeV) ε x : 23  27μ; ε y :97  23 μ D. Neuffer13 z (cm) PzPz εx(μ)εx(μ) εyεy ε L (mm σ E MeV 6-D ε increase Pz – x plot

Parameter variations… Go to larger initial beams, larger wedge –β t =2.6cm, ε t =130μ –Diamond, w=3.0mm, θ = 85°(5.6mm thick at center) D. Neuffer14 z (cm) PzPz εx(μ)εx(μ) εyεy ε L (mm) σ E MeV 6-D ε increase Pz – x plots

Parameter variations… Go to larger initial beams, larger wedge –β t =3.6cm, ε t =200μ –Be, w=5mm, θ = 110°(14.3 mm thick at center) D. Neuffer15 z (cm) PzPz εx(μ)εx(μ) εyεy ε L (mm) σ E MeV 6-D ε increase

Compare with current final scenario last 120 m T SOLENOIDS ~1GeV rf –ε t,N : 180  m –ε L : 2.0  75mm B: 25  32 T; 325  20MHz not quite specs –Transmission ~ 50% Two Be wedges ~ 3cm –ε t,N : 200  m –ε L : 1  50mm –Transmission ~ 95+% ~30 MeV rf D. Neuffer16

Need to complete scenario Match into first wedge –long ~0.3m, δp = 0.5MeV/c –β t ~ 3cm ε t ~ 200μ beam out has dispersion η~4cm, δp ~3 MeV/c, β x ~0.5cm Match into second wedge – Accelerate centroid to 100(?) MeV/c – long ~1.5m, δp = 0.5MeV/c – β t ~ 3cm ε 1 ~ 200μ, ε 2 ~ 40μ – Dispersion match to ~0 D. Neuffer17 Biggest problem could be optical match out of wedge –Beam has small x- emittance –dispersion + smaller β x –larger δp Similar to PIC match?

Possible Final Cooling scenario 1.Intial beam from 6-D cooler – ε x = ε y = ε L = Start with ~5-6 segments of Palmer-Sayed final cooling system (or quad or PIC or Li lens) – ε x = ε y = ε L =0.003 stretch beam to σ ct  0.6m, δE=0.5MeV 3.Wedge Exchange 1 – ε x  ε y = ε L =0.015 stretch beam to σ ct  3m, δE=0.5MeV (-10 MeV Induction linac) 4.Wedge Exchange 2 – ε x  ε y  ε L =0.075 Reaccelerate – 12m long bunch  higher frequency bunch train; – recombine at higher energy D. Neuffer18

MICE Experiment to demonstrate principle Experiment at MICE parameters MICE Note 290 (Rogers et al.) –9 wedge cases Use CH 2 or Be wedge (60  cases) –w= 5 or 3.5cm select beam matched in size to wedge (σ = w/2 cm) –ε N = m, β t = 32cm ~10× final cooling case Initial small δp (2 MeV/c) –increase by ~4× –ε x reduced by ~4× D. Neuffer19

CH 2 Wedge (MICE Demo) D. Neuffer20 z (cm) PzPz ε x (m m) εyεy ε L (mm) σ E MeV 6-D ε CH 2 (polyethylene) wedge – 60 °, w=5cm, σ x = 2.5cm (β  =30cm) Increase in δp implies corresponding decrease in  X –δp: 2  8.7 MeV/c –ε x : 4.3  1.06 mm Not clear if transverse motion can be accurately tracked to see the transverse emttance decrease –transport through solenoids mixes x-y; should be separable eigen emittances PμPμ x

Disadvantages exchange per wedge limited to ~4-6 x (?) –use multiple wedges ?? (could end up with flat beam,,,,) Does not cool –beam heating by >~25%; more for larger exchange Optics matching is nontrivial D. Neuffer21

Thick Wedge parameters are so attractive it has to be part of final cooling scenario –Details depend on actual implementation values and matching solutions –how many passes possible 2  3  4 ? –how much longitudinal emittance increase is tolerable? Not optimized (100MeV/c  ???) Experiment at MICE ?? –5 cm-scale CH 2 wedge, small δE initial beam Summary D. Neuffer22

Telewedgie… D, Neuffer23

Backup slides D, Neuffer24

Round to flat transformation Light electron source ~MeV Cold source immersed in solenoid – large canonical L solenoid to skew quad triplet Changes “round” beam to flat D. Neuffer25 Heavy Electron source ~100MeV Cooled within solenoids – cools transverse P k – large canonical L (if no field flips) Can develop large difference in emittance modes D. Edwards et al., Linac2000 p.122 P.Piot et al., PRSTAB 9,

Round to flat transformation Light electron source ~MeV Cold source immersed in solenoid – large canonical L solenoid to skew quad triplet Changes “round” beam to flat D. Neuffer26 Heavy Electron source ~100MeV Cooled within solenoids – cools transverse P k – large canonical L (if no field flips) Can develop large difference in emittance modes D. Edwards et al., Linac2000 p.122 P.Piot et al., PRSTAB 9,