Uses of Quasi-Isochronous Helical Channels in the Front

Uses of Quasi-Isochronous Helical Channels in the Front

Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon Collider/Neutrino Factory Cary Yoshikawa Chuck Ankenbrandt Dave Neuffer Katsuya Yonehara 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 1 Outline Motivation Evolution of the QIHC (2 snapshots) Configuration in the Phase II proposal, which was awarded and is funding current studies. Design upstream of HCC for increased acceptance Design downstream of HCC for bunch merging Current configuration Design upstream of HCC for increased acceptance Design downstream of HCC for bunch merging Summary & Future 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 2 Motivation The Quasi-Isochronous HC aims to shorten the length of the front end of a muon collider/neutrino factory by exploiting the tunable slip factor: HC 1 2 2 1 1 2 D 2 3 1 2 3 1 1 2 2 T in the following ways:

Upstream of an HCC optimized for cooling: Affords a larger RF bucket size when operating near transition for purpose of capture and bunching after the tapered solenoid. ' 2 16 eVmax RF m c 1 sin( s ) Abucket wrf 2 HC 1 sin( s ) Having control over both T and energy of synchronous particle should enlarge phase space available for particles to be captured. The Quasi-Isochronous HC should match naturally into an HCC that is maximized for cooling (equal cooling decrements). Downstream of the HCC optimized for cooling : Allows recombination of bunches over a potentially shorter distance compared to other studies by utilizing a large slip factor after inducing different energies across the bunches: E (c ) HC z 2 m c 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 3 Configuration in the Phase II Proposal p FE Target Solenoid 5 MV/m in vacuum 4.5 m 35 MV/m in H2/Be Match

HCC(MB) 20 m 5.5 m 300 m 20 m BCP 10 m BC HCC(SB) 33 m 300 m? z(m) Subsystem Purpose 0.0 to 4.5 Capture/Tapered Solenoid Enhance pion/muon capture 4.5 to 24.5 First straight RF Buncher in vacuum 1.Initial capture of s & s into RF buckets.s & s & s into RF buckets.s into RF buckets. 2.Allow lower momenta s & s into RF buckets.s to decay into s & s into RF buckets.s. 24.5 to 44.5 Second straight RF Buncher in 100 atm H2 w/ variably thick Be windows. 1.H2 gas allows higher RF gradient. 2.Be causes higher momenta s & s into RF buckets.s to interact, enhancing useful s & s into RF buckets.s. 3.Transverse cooling. 44.5 to 50.0 Match into HCC 1.To match between straight solenoid into HCC. 2.Enhance capture by manipulating RF bucket size. 50.0 to 350

HCC(Multi-Bunch) To cool string of multiple bunches of muons in 6D phase space. 350 to 360 Bunch Combiner Preparation (BCP) To transform string of bunches at same energy into string at different energies with head bunches at higher energies than trailing bunches. 360 to 393 Bunch Combiner (BC) To combine the multiple bunches in a single one via free drift in large || channel. 393 to 693 HCC(Single-Bunch) To cool single bunch of muons in 6D phase space. 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 4 PhaseII Upstream HCC: Justification for adding H2/Be (z=24.5m) Birth of Mu-s 2m before H2/Be 35 MV/m region P vs. z Birth of Mu-s 2m into H2/Be 35 MV/m region P vs. z The rate of muons created across the transition from vacuum into the Be/H2 has increased by: ~21% (728882) 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 5 Phase II HCC Upstream: Matching Section Initial design was based on a reference with constant momentum (237 MeV/c) and T extracted in matching section via earliest arrivals over incremental longitudinal sections. Bucket Area, Reference Momenta, GammaT, Slip Factor,

Pitch (kappa), & Synch Accel Phase in Matching Section S e e le g e n d fo r u n its . 400 300 200 100 0 44.0 45.0 46.0 47.0 48.0 49.0 -200 z (m) 3/1/2011 51.0 Pmu(reference, MeV/c) 10xBucket Area(Chuck's arb) 100xGammaT 1000xSlip Factor 300xKappa 1000 x |sin(s)|s)| s)|s (degrees) -100 Note that because goes from 0 to 1, the reference sees more material as it traverses the matching section and thus |sin(s)| must increase to compensate energy loss, forcing the bucket area to decrease along z. 50.0 Abucket Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 16 wrf

' eVmax RF m c 2 1 sin( s ) 2 HC 1 sin( s ) 6 Phase II HCC Upstream: Matching Section P (MeV/c) z = 50.0 m (End of Match) (204.5, 236.3) ~9000 /100k POT t (nsec) 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 7 Phase II HCC Upstream: Matching Section In principle, it is possible to achieve monotonic RF bucket growth by manipulating the . phase s)|s, T (via b ), and field gradient Vmax Bucket Area, Reference Momenta, GammaT, HCC Slip Factor, Pitch(kappa), & Synch Accel Phase in Matching Section Pmu(reference, MeV/c) 100xBucket Area(eV-sec) 100xGammaT 10000xSlip Factor 300xKappa 1000 x |sin(s)|s)| s)|s (degrees) See legend for units. 550.00 450.00 350.00 250.00 150.00 50.00 -50.00 44.00 -150.00 3/1/2011 45.00

46.00 47.00 48.00 49.00 50.00 51.00 z (m) Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 8 Phase II HCC Downstream: Bunch Recombiner Preparation Before bunches out of the HCC can be combined, the string of mono-energetic bunches must be transformed into one whose head bunches (early arrivals) are at higher energies than the tail (late arrivals), since we operate above transition. This can be achieved by using an RF at off frequency. In this case, 204.08MHz for bunches with 200 MHz spacing. 300 KE(MeV) 0 L=0.002m/bunch f=204.08 MHz V = 15 MV/m 9.6m in QIHC = 0.05 -4 20 -4 20 c(m) 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 9 Phase II HCC Downstream: Bunch Recombiner Note that these simulations are 1-D only. 3-D using g4beamline is shown later.

Total length:9.6+32.5=~43m. Compare to 340m* * R. Fernow, Estimate of Front-End Magnetic Requirements, NFMCC Tech. Note 529 (2008) KE(MeV) 300 i Dr 2. 3 ft 5m in C C H QI w .43 0 = / -4 After synchrotron oscillations within a 200 MHz rf bucket. ~95% of the initial beam is captured within that bucket. 0 -4 20 3/1/2011 20 V = 12 MV/m = 0.05 -4 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 20 c(m) 10

Current HCC Upstream: End of 2nd Straight Section Pi & Mu 1.061E4 Pi+ & Mu+ 1.081E4 Mu+ Mu 9.496E3 3/1/2011 9.159E3 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 11 Current HCC Upstream: Match Emittances out of second straight: T=11 mm-rad x ||= 378 mm-rad HCC(cooling optimized) acceptance: T=20 mm-rad x ||= 40 mm-rad Need to transform a cigar shaped Tx (11 x 378) into a football shaped one (20 x 40). Want a low HCC thatll have large momentum acceptance (150 MeV/c < p <450 MeV/c) that cools longitudinally. Since we will need to operate with a nearly straight solenoid, we will need to operate below transition. Desire a low HCC with a ptransition ~ 450 MeV/c. p P(MeV/c) Bz(on z-axis) = 2.4 T Bz(on ref) = 2.3 T B(on z-axis) = 0.62200 T 450 MeV/c db/d (on z-axis) = -1.33809 T Pref = 225 MeV/c free drift for 45.2 m t 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. t(nsec)

12 Current HCC Upstream: Wedge in Match To enhance longitudinal cooling, we studied effect of adding a cylindrical wedge. Emax = 32 MV/m 1. H2:200 atm: No wedge, only H2 at 200 atm at 293 K. Pref = 225 MeV/c s~14 2. H2:100 atm: Be wedge ~1mm at reference to loose same energy as 100 atm H2. f = 201.25 MHz 3. H2: 60 atm: Max Be wedge ~1.48 mm w/ H2 at knee of breakdown. Bz(on ref) = 2.3T Bz(z-axis) = 2.4T H2:200 atm H2:100 atm H2:60 atm long (m-rad) at z = 0 m 0.13300 0.14810 0.15820 long (m-rad) at z = 30 m 0.09619 0.09843 0.09901 trans (m-rad) at z = 0 m 0.03513 0.03426 0.03374 trans (m-rad) at z = 30 m 0.01787 0.01914

0.01915 6D (m^3) at z = 0 m 1.42800E-04 1.50800E-04 1.53100E-04 6D (m^3) at z = 30 m 2.30000E-05 2.85800E-05 2.78500E-05 Lowest emittance (~equilibrium) at z=30m. Highest emittance (acceptance) at z=0. Maxing out use of wedge (60 atm case) increases longitudinal acceptance by 19% over the case without any wedge. Perhaps the matching scheme should incorporate ~30m of = 0.25 QIHCC with Be wedges in H2 gas at 60 atm, followed by removal of the Be wedges to achieve the lowest equilibrium emittances. 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 13 Katsuya Yonehara Current HCC Downstream G4beamline simulation of phase rotation of bunches with 200 MHz spacing with off frequency 405 MHz. t(ns) bunch 1 bunch 1 bunch 7 bunch 13 3/1/2011 f=405 MHz V = 10 MV/m 2.5 m in QIHC

p(GeV/c) = 0.04 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. bunch 7 bunch 13 14 14 Phase II HCC Downstream: Bunch Recombiner t(ns) Initial phase rotation in G4BL result in energy spreads that are larger than 1D simulation. bunch 1 These large energy spreads translate into large time spreads at the end of the drift region. t(ns) i Dr 6. 4 ft 5m in C C H QI w .72 0 = / bunch 7 bunch 13 p(GeV/c 5 nsec f=200 MHz V = 5 MV/m in QIHC = 0.04

3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. p(GeV/c15 Conclusions and Future (upstream of HCC) Maxing out use of wedge (60 atm case) increases longitudinal acceptance by 19% over the case without any wedge. Perhaps the matching scheme should incorporate ~30m of = 0.25 QIHCC with Be wedges in H2 gas at 60 atm, followed by removal of the Be wedges to achieve the lowest equilibrium emittances. Consider use of higher RF frequencies upstream of the matching section to lower its L acceptance requirement. 201.25 325 MHz? Perhaps the matching section is better suited to follow one that has the overall longitudinal emittance be spread across several bunches with smaller emittances, ie. Daves baseline FE with phase rotation. Throughout 0 < < 1 match, design for continual RF bucket growth by . manipulating the phase s)|s, T (via b ), and field gradient Vmax Abucket 3/1/2011 16 wrf ' eVmax RF m c 2 1 sin( s ) 2 1 sin( ) s Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 16 Conclusions and Future (downstream of HCC) Initial 1D studies show promising results with 95% capture of muons merged into a single bunch over ~43 m. Initial 3D studies in G4BL have phase rotation resulting in energy spreads that are larger than 1D simulation, translating into larger time spreads at the end of the drift region. Phase rotation parameters to optimize: Off frequency, Vmax Drift parameters to optimize:

, Can also consider effect of adding RF manipulation into both phase rotation (harmonics) and drift regions. 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 17 Back up 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 18 Configuration in the Phase II Proposal FE Target p Solenoid 5 MV/m in vacuum 4.5 m 20 m 35 MV/m in H2 20 m Match 5.5 m HCC(MB) BC1 300 m 10 m BC2 HCC(SB) 33 m 300 m?

z(m) Subsystem Purpose Physical Dimensions Fields 0.0 to 4.5 Capture/Tapered Solenoid Enhance pion/muon capture L = 4.5 m R = 7.5 cm 35 cm Bsol = 20 T 4.2 T 4.5 to 24.5 First straight RF Buncher in vacuum 1. Initial capture of s & s into RF buckets.s & s & s into RF buckets.s into RF buckets. 2. Allow lower momenta s & s into RF buckets.s to decay into s & s into RF buckets.s. L = 20 m R = 35 cm Bsol = 4.2 T 160 RF Cavities: Vs & s into RF buckets.max = 5 MV/m, f= 162.5 MHz s=186: P()=150162 MeV/c 24.5 to 44.5 Second straight RF Buncher in 100 atm H2 w/ variably thick Be windows. 1. H2 gas allows higher RF gradient. 2. Be causes higher momenta s & s into RF buckets.s to interact, enhancing useful s & s into RF buckets.s. 3. Transverse cooling. L = 20 m R = 35 cm Bsol = 4.2 T 160 RF Cavities: Vs & s into RF buckets.max = 35 MV/m, f= 162.5 MHz s=208194, P()=162237 MeV/c 44.5 to

50.0 Match into HCC 1. To match between straight solenoid into HCC. 2. Enhance capture due to transition occurring in match. L = 5.5 m (5.5 s & s into RF buckets.s) R = 35 cm Bsol = 6.3 T 4.2 T 44 RF Cavities: Vs & s into RF buckets.max = 35 MV/m, f= 162.5 MHz s varied to maintain P()=237 MeV/c 50.0 to 350 HCC(Multi-Bunch) To cool string of multiple bunches of muons in 6D phase space. L = 300 m =1m R = 35 cm Bsol = 4.2 T Vs & s into RF buckets.max = 16 MV/m, f= 200,400,800 MHz 350 to 360 Bunch Combiner Preparation (BCP) To transform string of bunches at same energy into string at different energies with head bunches at higher energies than trailing bunches. L = 10 m =1m R = 35 cm Bsol = 4.2 T Vs & s into RF buckets.max = 15 MV/m f= 204.08 MHz for 201.25 MHz spacing. 360 to 393 Bunch Combiner (BC) To combine the multiple bunches in a single one via free drift in large || channel. L = 33 m =1m R = 35 cm Bsol = 4.2 T Vs & s into RF buckets.max = 0

393 to 693 HCC(Single-Bunch) To cool single bunch of muons in 6D phase space. L = 300 m =1m R = 35 cm Bsol = 4.2 T Vs & s into RF buckets.max = 16 MV/m, f= 200,400,800 MHz 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 19 Reference Momenta and Bucket Area Momenta (MeV/c) or Bucket Area (arb. units) 350 300 Pmu(reference) Bucket Area 250 200 150 100 35 MV/m H2 100 atm @ 273K {variable Be windows} = I()/2 5 MV/m Vacuum 50 0 0 5 10 15 20 25 30 35

40 45 50 z (m) 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 20 Phase II HCC Upstream: Matching Section z = 50.0 m (End of Match) Mu+ P vs t MuP vs t Pi+ P vs t PiP vs t (204.5, 236.3) 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 21 Current HCC Upstream: Two Straights FE Target p Solenoid 5 MV/m in vacuum 4.5 m 20 m 35 MV/m in H2 20 m Match

5.5 m HCC(MB) 300 m BC1 10 m BC2 HCC(SB) 33 m 300 m? T ra n s v e rs e E m itta n c e (m -ra d ) Transverse Emittances of Mu- in the 2 Straight Sections 0.022 0.020 T(acceptance) < 20 mm 0.018 0.016 0.014 eperp-3sig (m-rad) eperp-6sig (m-rad) 0.012 0.010 0.008 162.5 MHz H2, 35 MV/m Vacuum, 5 MV/m 0.006 0.004 0.002 0.000 0 10 20 30 40 50 z (m)

3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 22 L o n g itu d in a l E m itta n c e (m -ra d ) Current HCC Upstream Longitudinal Emittances of Mu- in the 2 Straight Sections 0.400 0.350 0.300 0.250 elong-3sig (m-rad) elong-6sig (m-rad) 0.200 162.5 MHz Vacuum, 5 MV/m H2, 35 MV/m 0.150 0.100 0.050 0.000 0 L(acceptance) < 40 mm 10 20 30 40 50 z (m) Emittances out of second straight are 11 mm-rad transverse by 378 mm-rad longitudinal. o Transverse is fine. o Longitudinal is ~10xs too large. Need to transform a cigar shaped Tx (11 x 378) into a football shaped one (20 x 40). 3/1/2011 Muons, MAP Winter Meeting at JLAB

Cary Y. Yoshikawa Inc. 23 Current HCC Upstream To transform a cigar Tx into a football, we strive to have emittance exchange from longitudinal to transverse at a rate that can be cooled transversely, netting zero emittance growth transversely and cooling longitudinally. So, we look into the following for different cooling decrement schemes in the HCC at various kappa, with particular attention to low kappa values. Transverse stability Transverse equilibrium emittance Momentum acceptance Linear extrapolation Note at low kappa, we expect less transverse/longitudinal coupling, so the hope is that the momentum acceptance mostly applies to the transverse component and the RF holds onto the muons hot longitudinally. 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 24 Current HCC Upstream Transverse stability requires: 0 < G < R2 or equivalently 0 < G/R2 < 1 where 1 q2 R 1 2 1 2 1.0 0.9 0.8 0.7 G/R^2 2q 2

1 D 1 G D 1 2 Transverse Stability G/R2 (Equal) G/R2 (Trans) G/R2 (Long) 0.6 0.5 0.4 0.3 0.2 2 3/ 2 2 1 2 q 1 D 1 1 2 pk 2 0.1 B 1 2 q z 1 pk b a 0.0 0 0.1 0.2 0.3 0.4 0.5 0.6

0.7 0.8 0.9 1 Kappa or pitch Linear Approx for Momentum Acceptance in R=35cm HCC 20 1600 18 16 1400 Delta P about Ref 225 MeV/c Equilibrium Transverse Emittance (mm-rad) Equilibrium Transverse Emittances +(Equal) -(Equal) +(Trans) -(Trans) 14 12 10 8 6 4 2 0 -2 0 0.2 0.4 0.6 Kappa(pitch) 3/1/2011 0.8 1 a dp p

D 1 a D 1 p p da a p=-1pa/a(Equal)p=-1pp=-1pa/a(Equal)a/a(Equal) 1200 p=-1pa/a(Equal)p=-1pp=-1pa/a(Equal)a/a(Trans) 1000 p=-1pa/a(Equal)p=-1pp=-1pa/a(Equal)a/a(Long) 800 600 400 200 0 0 0.1 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Kappa 25 1 Current HCC Upstream Emittances out of second straight: unstable Transverse Stability 1.0 T=11 mm-rad x ||= 378 mm-rad

0.9 0.8 HCC(cooling optimized) acceptance: stable Need to transform a cigar shaped Tx (11 x 378) into a football shaped one (20 x 40). Look into cooling at low . G/R^2 T=20 mm-rad x ||= 40 mm-rad 0.7 G/R2 (Equal) G/R2 (Trans) G/R2 (Long) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Kappa or pitch Linear Approx for Momentum Acceptance in R=35cm HCC 20 1600 18

16 1400 Delta P about Ref 225 MeV/c Equilibrium Transverse Emittance (mm-rad) Equilibrium Transverse Emittances +(Equal) -(Equal) +(Trans) -(Trans) 14 12 10 8 6 4 2 0 -2 0 0.2 0.4 0.6 Kappa(pitch) 3/1/2011 0.8 1 a dp p D 1 a D 1 p p da a p=-1pa/a(Equal)p=-1pp=-1pa/a(Equal)a/a(Equal) 1200 p=-1pa/a(Equal)p=-1pp=-1pa/a(Equal)a/a(Trans) 1000 p=-1pa/a(Equal)p=-1pp=-1pa/a(Equal)a/a(Long) 800 600 400 200

0 0 0.1 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Kappa 26 1 Equal Cooling = 0.1 Equal Cooling = 0.2 Equal Cooling = 0.3 3/1/2011 Transverse Only Cooling = 0.1 Transverse Only Cooling = 0.2 Transverse Only Cooling = 0.3 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 27

Neither equal cooling decrements nor transverse only cooling provides the desired acceptance. Prior experience with Quasi Iso HCC work suggests the following possibilities to increase acceptance. 1. Enlarging Rref as well as Raperture. Will use Rref = Raperture = 30 cm (front end baseline). Previously, used Rref = 16 cm & Raperture = 35 cm (HCC baseline). 2. Increasing B fields. Equal cooling and transverse only fix B fields, which turn out to be rather low. Quasi-Iso allows Bsol to be a degree of freedom. 3. Try to simultaneously design for ptransition 450 MeV/c and pref = 225 MeV/c. This attempt is not totally consistent. The pseudo-p transition mentioned on slides going forward effectively defines the dispersion for a muon with p=ptransition on the reference orbit. But, only a muon with p=p ref will be on the reference orbit. Despite the skewed accounting scheme for the dispersion, the exercise proved useful. Recall: 1 2 T2 3/1/2011 D 1 2 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 28 P~transition = 450 MeV/c Bsol = 2 T P~transition = 750 MeV/c Bsol = 2 T P~transition = 850 MeV/c Bsol = 2 T P~transition = 850 MeV/c G/R2 = 0.224 3/1/2011

G/R2 = 0.322 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. Bsol = 2.3 T 29 P~transition = 1050 MeV/c P~transition = 875 MeV/c Bsol = 3.2 T Bsol = 2.4 T Ptransition (MeV/c) Bsol (T) -1 bd (T) bq (T/m) b2 (T) 450 0.25 2 1.126 0.19778 0.83897 0.12585 0.412 100-300 271 550 0.25 2

1.653 0.27054 0.36016 0.05402 0.507 100-345 300 650 0.25 2 2.285 0.35786 0.21441 0.03216 0.539 100-402 338 750 0.25 2 3.023 0.45972 0.88475 0.13271 0.462 100-455 395 850 0.25

2 3.866 0.57613 1.65084 0.24763 0.224 100-326 > 326 0.58700 1.26141 0.18921 0.322 100-504 406 0.62200 1.33809 0.20071 0.294 100-521 424 850 875 0.25 0.25 3/1/2011 900 0.25 2.3 2.4 3.866 4.093 at JLAB Muons, MAP Winter Meeting

Cary Y. Yoshikawa 2.5 Inc. 4.327 0.65790 1.42075 0.21311 G/R2 Plow Phigh PEarliest Arrival (MeV/c) 30 0.269 100-539 445 Current HCC Upstream: Wedge in Match To enhance longitudinal cooling, we investigated effect of adding a wedge: 1. Baseline is the 200 atm of H2 at 293 K as studied before. (200 atm) 2. Channel contains 100 atm of H2 at 293 K plus a cylindrical Be wedge 1.051 mm thick at the reference (r=30cm) between RF cavities 10 cm apart. (100 atm) 3. 3/1/2011 Wedge has zero thickness on the z-axis and twice as thick at r=60 cm. Energy loss in Be equals that in H2. Channel contains 60 atm of H2 at 293 K plus a cylindrical Be wedge 1.481 mm thick at the reference (r=30cm) between RF cavities 10 cm apart. (60 atm) Wedge has zero thickness on the z-axis and twice as thick at r=60 cm. Total energy loss is same as in both cases above.

H2 density is at knee of breakdown curve. Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 31 Current HCC Upstream: Wedge in Match Longitudinal Emittance of Mu+'s Traversing a Kappa=0.25 QIHCC (2nd pass stoch on) H2:200 atm, 3 H2:100 atm, 3 H2:60 atm, 3 Long. Emittance (m-rad) 0.18 0.16 0.14 0.12 0.10 0.08 HCC 0.06 0.04 0.02 0.00 0 5 10 15 20 25 30 35 40 45 50 z (m) 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa

Inc. 32 Current HCC Upstream: Wedge in Match Transverse Emittance of Mu+'s Traversing a Kappa=0.25 QIHCC (2nd pass stoch on) 0.040 H2:200 atm, 3 H2:100 atm, 3 H2:60 atm, 3 Trans. Emittance (m-rad) 0.035 0.030 0.025 0.020 0.015 HCC 0.010 0.005 0.000 0 5 10 15 20 25 30 35 40 45 50 z (m) 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 33 Current HCC Upstream: Wedge in Match

6-D Emittance of Mu+'s Traversing a Kappa=0.25 QIHCC (2nd pass stoch on) 6-D Emittance (m^3) 1.8E-04 1.6E-04 H2:200 atm, 3 H2:100 atm, 3 1.4E-04 H2:60 atm, 3 1.2E-04 1.0E-04 8.0E-05 6.0E-05 4.0E-05 2.0E-05 0.0E+00 0 3/1/2011 5 10 15 20 25 z (m) Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 30 35 40 45 50 34 Current HCC Downstream Katsuya Yonehara ToF(ns) bunched beam

Phase rotation bunch 1 bunch 1 bunch 7 bunch 7 P(GeV) bunch 13 bunch 13 Test with 3 bunches (ToF = -30, 0, 30 ns) = 0.405 GHz, E = 10 MV/m synchrotron oscillation at z = 2.5 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 35 35 Current HCC Downstream Katsuya Yonehara bunched beam cont. bunch 7 bunch 13 7 13 7 bun ch ch n bu bu nc h h1 c n bu bunch 1 bun ch

1 Phase slipping in HS magnet 13 h c bun = 0.72 Particles are aligned in timing at z = 49 Note that t is too large to be in 200 MHz RF buckett is too large to be in 200 MHz RF bucket 3/1/2011 Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. 36 36 Current HCC Downstream Katsuya Yonehara bunched beam cont. =0.2 GHz, E=5 MV/m =0.04 bun ch 1 3 7 bun ch bu nc h1 bun ch 1 3 bun c h7 bu nc h1 Merging in isochronous HS magnet 3/1/2011

Muons, MAP Winter Meeting at JLAB Cary Y. Yoshikawa Inc. bunch 13 bunch 7 bunch 1 bunch 13 bunch 7 bunch 1 5 nsec 37 37 Current HCC Downstream Katsuya Yonehara single particle =0.408 GHz, E=5 MV/m =0.04 of synchrotron oscillation at z=4.2 = 0.72 Particles are aligned in timing at z = 33 Phase rotation in HS magnet 3/1/2011 8/20/10 Phase rotation in Bessel field magnet Meeting at JLAB Muons, MAP Winter meeting CaryMI, Y.Friday Yoshikawa Inc. 38 38

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