RF Bucket Area Introduction Intense muon beams have many potential applications, including neutrino...
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RF Bucket Area Introduction Intense muon beams have many potential applications, including neutrino factories and muon colliders. However, muons are produced as tertiary beams, resulting in diffuse phase space distributions. To make useful beams, the muons must be rapidly cooled before they decay. An idea conceived recently for the collection and cooling of muon beams is the Quasi-Isochronous Helical Cooling Channel (QIHCC), which takes advantage of the larger RF buckets for particles traveling in nearly isochronous orbits. The QIHCC also offers a natural match into the HCC, which is recognized as the most efficient cooling scheme for a neutrino factory or muon collider. Matching Section Figure 6: Design parameters in matching section. Accelerating phase φs designed to maintain constant momentum of 237 MeV/c Figure 7: Momentum (MeV/c) vs. z (mm) for μ−’s and π−’s at exit of the matching section. Muons & Pions in the Straight Solenoids Figure 2: Momentum (MeV/c; vertical) vs. time (nsec; horizontal) for μ−’s and π−’s out of tapered solenoid. Figure 3: Momentum (MeV/c) vs. time (nsec) for μ−’s and π−’s after the first straight in vacuum. Figure 4: Momentum (MeV/c) vs. z (mm) for μ−’s and π−’s at the particle’s creation. Figure 5: Momentum (MeV/c) vs. z (mm) for μ−’s and π−’s at exit of the second straight and entrance of the matching section. Future The present study started from an HCC designed without RF or material. Capture into RF buckets in the match should be greatly increased by designing it with RF and material from the start: φs: We have seen that the increase in pitch κ forces φs to increase with z, which decreases the RF bucket when other parameters are fixed. It may still be possible to have a monotonically increasing bucket area along z by adjusting the reference momenta (equivalently φs (z)), to an unrealistic degree of control (dp~ 0.01 MeV/c) as illustrated in Figure 9, motivating need for other parameters to control bucket area. η H : The slip factor, η H (or db φ /dρ), provides a degree of freedom to control bucket growth. V’max: If for some unforeseen reason the desired bucket area cannot be achieved by current containing coils, the last degree of freedom exercisable is V’max(z) at price of running sub- optimal earlier in the channel. Upstream of QIHCC, Placement and profile of material in the second straight section will be optimized for using high energy pions to create useful muons. Quantify enhanced muon rates from other particles produced at the target that interact with the material to produce useful muons. Acknowledgements This work has been supported in part by DOE STTR grant DE-SC0002739 References [1] “Cost-effective Design for a Neutrino Factory”, J. S. Berg et al., Phys. Rev. STAB 9, 011001(2006). [2] “Six-dimensional muon beam cooling...in a helical dipole channel”, Y. Derbenev and R. Johnson, Phys. Rev. STAB 8, 041002 (2005). [3] “Helical Cooling Channel Designs and Simulations for Muon Colliders”, K. Yonehara et al., IPAC2010 MOPD076. [4] G4beamline, T. Roberts, Muons, Inc. Quasi-isochronous Muon Collection Channels * Cary Y. Yoshikawa 1 , C. Ankenbrandt 1 , David V. Neuffer 2 1 Muons, Inc., Batavia, IL, 2 Fermilab, Batavia, IL * [email protected] Figure 1: Layout showing modified tapered solenoid ending with B z = 4.2 T, 20 m of RF with 5 MV/m in vacuum, 20 m of RF with 35 MV/m in H 2 gas and Be windows with varying thicknesses, the match, and HCC. Table 1: Layout Parameters ) sin( 1 ) sin( 1 2 16 2 ' max s s H RF rf bucket c m eV w A 2 2 2 3 2 1 ˆ 1 1 D H b pk pk B da dp p a D 2 2 / 3 2 2 2 2 1 ) 2 1 ( 1 ] 1 ) 1 )[( 1 ( ˆ 4.5 m 20 m FE Targe Solenoid 5 M V/m in vacuum 35 M V/m in H 2 M atch HCC 20 m 5.5 m 2 0 m p π μ π μ 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 B sol = 20 T 4.2 T 4.5 to 24.5 First straight RF Buncher in vacuum 1.Initial capture of π’s & μ’s into RF buckets. 2.Allow lower momenta π’s to decay into μ’s. L = 20 m R = 35 cm B sol = 4.2 T 160 RF Cavities: V’ max = 5 MV/m, f= 162.5 MHz φ s =186°: P(μ − )=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 for enlarged buckets. 2.Be causes higher momenta π’s to interact, enhancing useful μ’s. L = 20 m R = 35 cm B sol = 4.2 T 160 RF Cavities: V’ max = 35 MV/m, f= 162.5 MHz φ s =208194°, P(μ − )=162237 MeV/c 44.5 to 50.0 Match into HCC 1.To match between straight solenoid into HCC. 2.Enhance μ capture due to transition occurring in match. L = 5.5 m (5.5 λ’s) R = 35 cm B sol = 6.3 T 4.2 T 44 RF Cavities: V’ max = 35 MV/m, f= 162.5 MHz φ s varied to maintain P(μ − )=237 MeV/c 50.0 to 70.0 HCC To cool muons. L = 20 m (20 B sol = 4.2 T 160 RF Cavities: Pi-& M u-JustA fterTapered S olenoid E nding w /Bz=4.2T Pi- P vs.t M u- P vs.t A tend of5 M V/m Straightin Vacuum (z=24.5m) (105,162 ) M u- P vs.t Pi- P vs.t B irth ofParticles Pi- P vs.z M u- P vs.z A tEnd of35 M V/m Straightw /H 2 @ 100 atm 273K (z=44.5m ) (181,237) M u- P vs.t Pi- P vs.t BucketArea,Reference M om enta,G am m aT,H C C Slip Factor, Pitch(kappa),& Synch AccelPhase in M atching Section -200 -100 0 100 200 300 400 44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 z (m ) See legend for units. Pmu(reference,MeV/c) 50xBucketArea(eV-sec) 100xGam m aT 10000xSlip Factor 300xK appa 1000 x |sin(φs)| φs (degrees) M u- P vs t Pi- P vs t (204.5,236.3) A tEnd ofM atching Secton (z = 50.0 m ) Optimization with Only φ s Figure9: Example of design parameters in matching section that uses same γT of established HCC match, but manipulates reference momenta to allow monotonic growth of bucket area. B ucketA rea,R eference M om enta,G am m aT,H C C Slip Factor, Pitch(kappa),& Synch A ccelPhase in M atching Section -150.00 -50.00 50.00 150.00 250.00 350.00 450.00 550.00 44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 z (m ) See legend forunits. Pmu(reference,MeV/c) 100xB ucketA rea(eV-sec) 100xGam m aT 10000xS lip Factor 300xKappa 1000 x |sin(φs)| φs (degrees) Summary We have made a preliminary design of a system upstream of the HCC to enhance the number of muons in its acceptance. An innovation has been introduced to use the high energy pions to create useful muons by incorporating material at strategic locations. We have added RF with H 2 gas into an HCC matching section and performed an initial study that involves crossing transition.
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Transcript of RF Bucket Area Introduction Intense muon beams have many potential applications, including neutrino...
RF Bucket Area
Introduction
Intense muon beams have many potential applications, including neutrino factories and muon colliders. However, muons are produced as tertiary beams, resulting in diffuse phase space distributions. To make useful beams, the muons must be rapidly cooled before they decay. An idea conceived recently for the collection and cooling of muon beams is the Quasi-Isochronous Helical Cooling Channel (QIHCC), which takes advantage of the larger RF buckets for particles traveling in nearly isochronous orbits. The QIHCC also offers a natural match into the HCC, which is recognized as the most efficient cooling scheme for a neutrino factory or muon collider.
Matching Section
Figure 6: Design parameters in matching section. Accelerating phase φs designed to maintain constant momentum of 237 MeV/c
Figure 7: Momentum (MeV/c) vs. z (mm) for μ−’s and π−’s at exit of the matching section.
Muons & Pions in the Straight Solenoids
Figure 2: Momentum (MeV/c; vertical) vs. time (nsec; horizontal) for μ−’s and π−’s out of tapered solenoid.
Figure 3: Momentum (MeV/c) vs. time (nsec) for μ−’s and π−’s after the first straight in vacuum.
Figure 4: Momentum (MeV/c) vs. z (mm) for μ−’s and π−’s at the particle’s creation.
Figure 5: Momentum (MeV/c) vs. z (mm) for μ−’s and π−’s at exit of the second straight and entrance of the matching section.
FutureThe present study started from an HCC designed without RF or
material. Capture into RF buckets in the match should be greatly
increased by designing it with RF and material from the start: φs: We have seen that the increase in pitch κ forces φs to
increase with z, which decreases the RF bucket when other parameters are fixed. It may still be possible to have a monotonically increasing bucket area along z by adjusting the reference momenta (equivalently φs (z)), to an unrealistic degree of control (dp~ 0.01 MeV/c) as illustrated in Figure 9, motivating need for other parameters to control bucket area.
ηH: The slip factor, ηH(or dbφ/dρ), provides a degree of freedom to control bucket growth.
V’max: If for some unforeseen reason the desired bucket area cannot be achieved by current containing coils, the last degree of freedom exercisable is V’max(z) at price of running sub-optimal earlier in the channel.
Upstream of QIHCC, Placement and profile of material in the second straight
section will be optimized for using high energy pions to create useful muons.
Quantify enhanced muon rates from other particles produced at the target that interact with the material to produce useful muons.
AcknowledgementsThis work has been supported in part by DOE STTR grant DE-SC0002739
References[1] “Cost-effective Design for a Neutrino Factory”, J. S. Berg et
al., Phys. Rev. STAB 9, 011001(2006).[2] “Six-dimensional muon beam cooling...in a helical dipole
channel”, Y. Derbenev and R. Johnson, Phys. Rev. STAB 8, 041002 (2005).
[3] “Helical Cooling Channel Designs and Simulations for Muon Colliders”, K. Yonehara et al., IPAC2010 MOPD076.
[4] G4beamline, T. Roberts, http://www.muonsinc.com[5] MERIT: http://cern.ch/merit/
Muons, Inc.
Quasi-isochronous Muon Collection Channels*
Cary Y. Yoshikawa1, C. Ankenbrandt1, David V. Neuffer2
1Muons, Inc., Batavia, IL, 2Fermilab, Batavia, IL*[email protected]
Figure 1: Layout showing modified tapered solenoid ending with Bz = 4.2 T, 20 m of RF with 5 MV/m in vacuum, 20 m of RF with 35 MV/m in H2 gas and Be windows with varying thicknesses, the match, and HCC.
Table 1: Layout Parameters
)sin(1
)sin(1
2
162'
max
s
s
H
RF
rfbucket
cmeV
wA
22
2
3
2 1ˆ1
1
DH
b
pk
pkB
da
dp
p
aD
2
2/3
2
2221
)21(
1
]1)1)[(1(ˆ
4.5 m 20 m F
E T
arg
et
Solenoid 5 MV/m in vacuum 35 MV/m in H2 Match HCC
20 m 5.5 m 20 m
p πμ
πμ
z(m) Subsystem Purpose Physical Dimensions
Fields
0.0 to 4.5 Capture/Tapered Solenoid
Enhance pion/muon capture L = 4.5 mR = 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 π’s & μ’s into RF buckets.2.Allow lower momenta π’s to decay into μ’s.
L = 20 mR = 35 cm
Bsol = 4.2 T160 RF Cavities: V’max = 5 MV/m, f= 162.5 MHz
φs=186°: P(μ−)=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 for enlarged buckets.2.Be causes higher momenta π’s to interact, enhancing useful μ’s.
L = 20 mR = 35 cm
Bsol = 4.2 T160 RF Cavities: V’max = 35 MV/m, f= 162.5 MHz
φs=208194°, P(μ−)=162237 MeV/c
44.5 to 50.0 Match into HCC 1.To match between straight solenoid into HCC.2.Enhance μ capture due to transition occurring in match.
L = 5.5 m (5.5 λ’s)R = 35 cm
Bsol = 6.3 T 4.2 T44 RF Cavities: V’max = 35 MV/m, f= 162.5 MHz
φs varied to maintain P(μ−)=237 MeV/c
50.0 to 70.0 HCC To cool muons. L = 20 m (20 λ’s)R = 35 cm
Bsol = 4.2 T160 RF Cavities: V’max = 35 MV/m, f= 162.5 MHz
φs=-12.6° to maintain P(μ−)=237 MeV/c
Pi- & Mu- Just After Tapered Solenoid Ending w/ Bz=4.2T
Pi- P vs. t
Mu- P vs. t
At end of 5 MV/m Straight in Vacuum (z=24.5m)
(105, 162)
Mu- P vs. t
Pi- P vs. t
Birth of Particles
Pi- P vs. z
Mu- P vs. z
At End of 35 MV/m Straight w/ H2 @ 100 atm 273K (z=44.5m)
(181, 237)
Mu- P vs. t
Pi- P vs. t
Bucket Area, Reference Momenta, GammaT, HCC Slip Factor, Pitch(kappa), & Synch Accel Phase in Matching Section
-200
-100
0
100
200
300
400
44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00
z (m)
See l
egen
d for
units
.
Pmu(reference, MeV/c)50xBucket Area(eV-sec)100xGammaT10000xSlip Factor300xKappa1000 x |sin(φs)|φs (degrees)
Mu- P vs t
Pi- P vs t
(204.5, 236.3)
At End of Matching Secton (z = 50.0 m)
Optimization with Only φs
Figure9: Example of design parameters in matching section that uses same γT of established HCC match, but manipulates reference momenta to allow monotonic growth of bucket area.
Bucket Area, Reference Momenta, GammaT, HCC Slip Factor, Pitch(kappa), & Synch Accel Phase in Matching Section
-150.00
-50.00
50.00
150.00
250.00
350.00
450.00
550.00
44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00
z (m)
See
lege
nd fo
r uni
ts.
Pmu(reference, MeV/c)100xBucket Area(eV-sec)100xGammaT10000xSlip Factor300xKappa1000 x |sin(φs)|φs (degrees)
Summary We have made a preliminary design of a system upstream of
the HCC to enhance the number of muons in its acceptance. An innovation has been introduced to use the high energy
pions to create useful muons by incorporating material at strategic locations.
We have added RF with H2 gas into an HCC matching section and performed an initial study that involves crossing transition.
