1. NuFACT06 Summer School -Factory Front End and Cooling David Neuffer f Fermilab

2. 2 0utline  Lecture I –Front End  General introduction –Study 2A ν-Factory –variations  Capture and decay from target  Bunching and φ-E rotation  Lecture II – Cooling  Ionization cooling concepts  Cooling for a ν-Factory –MICE experiment  µ + -µ - collider cooling

3. 3 References  “Cost-effective design for a neutrino factory”, J. Berg et al., PRSTAB 9, 011001(2006)  “Recent progress in neutrino factory …”, M. Alsharo’a et al., PRSTAB 6, 081001 (2003)  “Beams for European Neutrino Experiments (BENE) CERN- 2006-005  S. Ozaki et al., Feasibility Study 2, BNL-52623(2001).  N. Holtkamp and D. Finley, eds., Study 1, Fermilab-Pub- 00/108-E (2000).  The Study of a European neutrino factory complex, CERN/PS/2002-080.  R. Palmer- NuFACT05 Summer School lecture notes

4. 4 Neutrino Factory - Study 2A  Proton driver  Produces proton bunches  8 or 24 GeV, ~10 15 p/s, ~50Hz bunches  Target and drift  (> 0.2  /p)  Buncher, bunch rotation, cool  Accelerate  to 20 GeV or more  Linac, RLA and FFAGs  Store at 20 GeV (0.4ms)  e +  + e *  Long baseline Detector  >10 20 /year

5. 5 Target for π production  Typical beam: 10 GeV protons up to 4 MW  1m long bunches up to 4×10 13 /bunch, 60Hz  Options:  Solid targets –C (graphite targets) (NUMI) –Solid metal ( p- source) – rotating Cu-Ni target  Liquid Metal targets –SNS – type (confined flow) –MERIT – Hg jet in free space –Best for 4MW ??

6. 6 The Fundamental Problem with Solid Targets What do we need in materials to get us to multi-MW Power Levels?  low elasticity modulus (limit  Stress = EαΔT/(1-2ν)  low thermal expansion  high heat capacity  good diffusivity to move heat away from hot spots  high strength  resilience to shock/fracture strength  resilience to irradiation damage That ’ s All !

7. 7 Liquid Targets  Contained liquid flow (~SNS)  Damage to containment vessel possible  Shock of short pulse  Liquid Jet target  Hg jet ~  Jet is disrupted by beam –δT = 50  s ?  Need target material capture and recirculation system

8. 8 MERIT experiment at CERN  Target date: November 2006!  i.e. ready to receive and install the solenoid and Hg-loop Beam parameters:  Nominal momentum 24 GeV/c  Intensity/bunch – baseline: harmonic 16 (i.e. 16 buckets in PS,  t=125ns)  2-2.5  10 12 protons / bunch  total maximum ~30  10 12 protons/pulse Next steps:  MD time in 2006 assigned  To address the most critical configurations – priorities should be defined  Set-up time at the beginning of 2007 may be required to achieve the highest intensities Magnet tested at 15T Hg jets

9. 9 π capture from target  Protons on target produce large number of π’s  Broad energy range (0 to 10+GeV)  More at lower energies  Transverse momentum (up to ~0.3GeV/c)  Capture beam from target  Options:  Li lens  Magnetic horn  Magnetic Solenoid

10. 10 Li Lens properties  Current-carrying conducting cylinder  Focusing Field:  Fermilab values:  R 0 =1 cm, I=0.5MA, L=15 cm, B(R 0 )=10T  Focuses 9GeV/c p with p  < 0.45 GeV/c  Problems  Pulsed at <1Hz, need liquid for 10 + Hz  Absorbs particles (π,p-bar)  Forward capture  Captures only one sign Focusing angle: Θ=(0.3B(r) L)/P

11. 11 Magnetic Horn after target  Baseline capture for superbeams/NUMI  Magnetic field from I on wall  Lenses can be tuned to obtain narrow band or broad-band acceptance  Pulsed current, thin conductors  Breakage over many pulses  Beam lost on material  focuses + or - particles NUMI beam line

12. 12 NUMI target, beam  Target  segmented graphite, water cooled  954mm long; 47 20mm segments  Movable: can be positioned up to 2.5m upstream of horn to tune beam energy  Parabolic horns  Pulsed at up to 200kA; 3T peak field  Focus π‘s into decay tunnel

13. 13 Solenoid lens capture  Target is immersed in high field solenoid  Particles are trapped in Larmor orbits  Produced with p = p ‖, p   Spiral with radius r = p  /(0.3 B sol )  Particles with p  < 0.3 B sol R sol /2 are trapped  p ,max < 0.225 GeV/c for B=20T, R sol = 0.075m  Focuses both + and - particles

14. 14 Solenoid transport  Magnetic field adiabatically decreases along the transport  Transverse momentum decreases  Busch’s theorem: B r orbit 2 is constant  B=20T → 2T (r=3.75cm →= 12cm)  P  = 0.225→0.07GeV/c  Emittance = ~ σ x σ px / 105.66  ~8cm×25 MeV/c / 105.66 ≅ 0.02m  P remains constant (P ‖ increases)  Transport designed to maximize π →  acceptance

15. 15 Homework problems: targetry  How many 24 GeV protons per second are in a 4 MW beam? With 60Hz bunches, how many protons/bunch?  a beam of 24GeV protons produces, on average, one pion pair per proton with mean momentum of 250 MeV/c (per pion). What percentage of the proton beam kinetic energy is converted to pions?  If the target is surrounded by a 20T solenoid with a 5cm radius, what maximum transverse momentum of pions is accepted?  If B is adiabatically reduced to 1T what is the resulting transverse momentum and beam size?  Estimated normalized emittance?

16. 16 π→μν decay in transport  π-lifetime is 2.60×10 -8  s  L = 7.8 β  m  For π  μ+ν, is 23.4 MeV/c, E  =0.6 to 1.0E π  Capture relatively low-energy π  μ  100 – 300 MeV/c  Beam is initially short in length  Bunch on target is 1 to 3 ns rms length  As Beam drifts down beam transport, energy-position (time) correlation develops: L=0m L=36m 0 0.4 GeV -20m 100m

17. 17 Phase-energy rotation  To maximize number of ~monoenergetic μ’s, neutrino factory designs use phase-energy rotation  Requires:  “short” initial p-bunch  Drift space  Acceleration (induction linac or rf) –at least ±100 MV  Goal:  Accelerate “low-energy tail”  Decelerate “high-energy head:  Obtain long bunch –with smaller energy spread L=1m L=112m rf 0 0.5GeV/c -50m50m LL

18. 18 Phase Energy rotation options  Single bunch capture  Low-frequency rf (~30MHz)  Best for collider (?) (but only  + or  - )  Induction Linac  Nondistortion capture possible  Very expensive technology, low gradient  Captures only  + or  -  “High Frequency” buncher and phase rotation  Captures into string of bunches (~200MHz)  Captures both  + and  -

19. 19 Phase/energy rotation  Low-frequency rf; capture into single long bunch  25MHz – 3MV/m  +25% 50MHz  10m from target to 50m  But:  Low-frequency rf is very expensive  Continuation into cooling and acceleration a problem (200MHz?) 12 m Only captures one sign …

20. 20 Induction Linac for φ-E Rotation  Induction Linac can provide long pulse for φ-E rotation  Arbitrary voltage waveform possible  Limited to < ~1MV/m  need > ~200MV, > 200m  Very expensive, large power requirements  Only captures one sign

21. 21 Nondistortion φ-E rotation  Cancellation with single induction linac gives distortion  (Head has larger δE than tail)  Sequence of 2 (or more) linacs can spread beam out evenly  Goal is to spread beam out evenly mapping Kinetic Energy to length (Δcτ); all at same final energy  (0.25 to 0.225MeV) to (0 to 80m)

22. 22 Study 2 system  Drift to develop Energy- phase correlation  Accelerate tail; decelerate head of beam, non- distortion (280m induction linacs (!))  Bunch at 200 MHz  ~0.2  /p  Inject into 200 MHz cooling system  Cools transversely (to  t = ~0.002m

23. 23 High-frequency Buncher +  Rotation  Drift (110m)  Allows  beam to decay; beam develops  correlation  Buncher (~333  230MHz)  Bunching rf with E 0 = 125 MeV,  1  = 0.01 { L   1  =~1.5m at L tot = 150m}  V rf increases gradually from 0 to ~6 MV/m  Rotation (~233  200MHz)  Adiabatic rotation  V rf =~10 MV/m  Cooler (~100m long) (~200 MHz)  fixed frequency transverse cooling system Replaces Induction Linacs with medium- frequency rf (~200MHz) !  Captures both μ + and μ - !!

24. 24 Adiabatic Buncher overview  Want rf phase to be zero for reference energies as beam travels down buncher  Spacing must be N rf  rf increases (rf frequency decreases)  Match to rf = ~1.5m at end:  Gradually increase rf gradient (linear or quadratic ramp): Example: rf : 0.90  1.5m

25. 25 Adiabatic Buncher example  Adiabatic buncher (z=90 →150m)  Set T 0,  :  125 MeV/c, 0.01  In buncher:  Match to rf =1.5m at end:  zero-phase with 1/  at integer intervals of  :  Adiabatically increase rf gradient: rf : 0.90  1.5m

26. 26  Rotation  At end of buncher, change rf to decelerate high-energy bunches, accelerate low energy bunches  Reference bunch at zero phase, set rf less than bunch spacing (increase rf frequency)  Place low/high energy bunches at accelerating/decelerating phases  Can use fixed frequency (requires fast rotation) or  Change frequency along channel to maintain phasing “Vernier” rotation –A. Van Ginneken

27. 27 Fast “Vernier”  Rotation  At end of buncher, choose:  Fixed-energy particle T 0  Second reference bunch T N  Vernier offset   Example:  T 0 = 125 MeV  Choose N= 10,  =0.1 –T 10 starts at 77.28 MeV  Along rotator, keep reference particles at (N +  ) rf spacing  10 = 36° at  =0.1  Bunch centroids change:  Use E rf = 10MV/m; L Rt =8.74m  High gradient not needed …  Bunches rotate to ~equal energies. rf : 1.485  1.517m in rotation; rf =  ct/10 at end ( rf  1.532m) Nonlinearities cancel: T(1/  ) ; Sin(  )

28. 28 “ICOOL” Adiabatic  Rotation  At end of buncher, choose:  reference particle T 0  Reference bunch T N (N bunches from 0)  V ’ rf gradient, offset   Example:  T 0 = 125 MeV  Choose N= 10,  =0.1 –T 10 starts at 77.28 MeV  In ICOOL  T 0 = T 0 + E 0 'z…  T N =T N + E N ' z  Rotate until T 0 ≅ T N  Along rotator, keep reference particles at (N +  ) rf spacing  E N ' ≅eV' sin(2π  )  λ rf ~1.4 to 1.5 m over buncher ~Adiabatic Particles remain in bunches as bunch centroids align Match into 201.25 MHz Cooling System

29. 29 Initial Study 2A(12/03)  Drift (110.7m)  Buncher (51m)  P 1 =280, P 2 =154 MeV/c, N B =18  V rf = 3 L/51 + 9 (L/51) 2 MV/m  Vernier Phase Rotator (54m)  N V = 18.05, V rf =12 MV/m  Cooler (up to 100m)  Alternating solenoid 2.7T, 0.75m cells  2cm LiH/cell  16MV/m rf (30°) 5000 particle simulation

30. 30 ICOOL results-Study 2A (12/03)  ~0.23 μ/p within reference acceptance at end of 80m cooling channel (ε ⊥ <0.03m)  ~0.11 μ/p within restricted acceptance (ε ⊥ <0.015m)  At end of φ-E Rotator: A~0.10 μ/p and 0.05 μ/p  Rms emittance cooled from ε ⊥ = 0.0185 to ε ⊥ = ~0.008m  Longitudinal rms emittance ≅0.070m (per bunch)

31. 31 Study2A June 2004 scenario  Drift –110.7m  Bunch -51m  V  (1/  ) =0.0079  12 rf freq., 110MV  330 MHz  230MHz  -E Rotate – 54m – (416MV total)  15 rf freq. 230  202 MHz  P 1 = 280, P 2 = 154  N V = 18.032  Match and cool (80m)  0.75 m cells, 0.02m LiH  “Realistic” fields, components  Captures both μ + and μ -

32. 32 Features/Flaws of Study 2A Front End  Fairly long section – ~300m long  Study 2 was induction linac 1MV/m, 450m long  Produces long bunch trains of ~200 MHz bunches  ~80m long (~50 bunches)  Transverse cooling is ~2½ in x and y  No cooling or more cooling ?  Method works better than it should …  Requires rf within magnetic fields  12 MV/m at B = 1.75T

33. 33 Another example: ~88 MHz  Drift – 90m  Buncher-60m  Rf gradient 0 to 4 MV/m  Rf frequency: 166→100 MHz  Total rf voltage 120MV  Rotator-60m  Rf gradient 7 MV/m – 100→87 MHz  420MV total  Acceptance ~ study 2A (but no cooling yet)  Less adiabatic 0 GeV/c 0.5 GeV/c

34. 34 rf in Rotation/Cooling Channels:  Can cavities hold rf gradient in magnetic fields??  MUCOOL 800 MHz result :  V' goes from 45MV/m to 12MV/m (as B -> 4T)  Vacuum rf cavity  Worse at 200MHz ??

35. 35 Use gas-filled rf cavities?  Muons, Inc. tests:  Higher gas density permits higher gradient  Magnetic field does not decrease maximum allowable gradient  Gas filled cavities may be needed for cooling with focusing magnetic fields  Density > ~60 atm H 2 (7.5% liq.)  Energy loss for µ’s is >~ 2MV/m  Can use energy loss for cooling Mo electrode, B=3T, E=66 MV/m Mo B=0 E=64MV/m Cu E=52MV/m Be E= 50MV/m 800 MHz rf tests

36. 36 Gas-filled rf cavites (Muons, Inc.) Cool here  Add gas + higher gradient to obtain cooling within rotator  ~300MeV energy loss in cooling region  Rotator is 54m;  Need ~4.5MeV/m H 2 Energy  133atm equivalent 295ºK gas  ~250 MeV energy loss  Alternating Solenoid lattice in rotator  20MV/m rf cavities  Gas-filled cavities may enable higher gradient (Muons, Inc.)

37. 37 High-gradient rf with gas-filled cavities Transverse emittance Acceptance (per 24GeV p)  Pressure at 150Atm  Rf voltage at 24 MV/m  Transverse rms emittance cools 0.019 to ~0.008m  Acceptance ~0.22  /p at ε T < 0.03m  ~0.12  /p at ε T < 0.015m  About equal to Study 2A

38. 38 Simulation results 50m -50m 0 0.5 GeV/c

39. 39 Cost impact of Gas cavities  Removes 80m cooling section (-185 M$)  Increase V rf ' from 12.5 to 20 or 24 MV/m  Power supply cost  V' 2 (?)  44 M$  107M$ or 155M$  Magnets: 2T  2.5T Alternating Solenoids  23 M$  26.2 M$  Costs due to vacuum  gas-filled cavities (??)  Total change:  Cost decreases by 110 M$ to 62 M$ (???)

40. 40 Cost estimates:  Costs of a neutrino factory (MuCOOL-322, Palmer and Zisman): Study 2Study 2A “Study 2A front end reduces cost by ~ 350MP$

41. 41 Summary  Buncher and  E Rotator (ν-Factory) Variations  Gas-filled rf cavities can be used in Buncher-Rotator  Gas cavities can have high gradient in large B (3T or more?)  Variations that meet Study 2A performance can be found  Shorter systems – possibly much cheaper??  Gas-filled rf cavities To do:  Optimizations, Best Scenario, cost/performance …  More realistic systems

42. 42 Postdoc availability – Front end SBIR with Muons, Inc. – capture,  -  rotation and cooling with gas-filled rf cavities