muons, inc. 12/1/2009dec 1-3, 2009 mcdw at bnl cary y. yoshikawa 1 use of a quasi-isochronous...
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12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
1Muons,Inc.
Use of a Quasi-Isochronous Helical Cooling Channel in the Front End of a
Muon Collider
Cary Yoshikawa
Chuck Ankenbrandt
Rol Johnson
Dave Neuffer
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
2Muons,Inc.
Outline
• Motivation
• Bent Solenoid for Charge Separation
• Isochronous Helical Channel Basics
• Transverse Stability (No RF nor material)
• Demonstrates a level of consistency between analytic calculations and simulations.
• Schedule of Tasks
• Summary & Future
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
3Muons,Inc.
Motivation
• A Quasi-Isochronous HCC aims to take advantage of a larger RF bucket size when operating near transition for purpose of capture and bunching after the tapered solenoid.
• We expect cooled particles with initial energy above separatrices to fall into buckets. Particles in buckets migrate toward center.
• Having control over both γT and energy of synchronous particle should enlarge phase space available for particles to be captured.
• The Quasi-Isochronous HCC should match naturally into an HCC maximized for cooling (equal cooling decrements).
2
1
0 22
16
h
eVE
hA ss
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
4Muons,Inc.
5.0 m
Bent Solenoid for Charge Separation (phase 1 )
Hg
Tar
get
p
12.9 m
TaperedSolenoid
top view
z
xx’
x’
yend view
π−
μ−
μ+
π+
End of Tapered Solenoid
End of Bent Solenoid
p(M
eV/c
)
t(nsec)
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
5Muons,Inc.
Bent Solenoid ExitImmediately after the bent solenoid, a wedge may be implemented to flatten the momentum spread (emittance exchange).
• The larger transverse angles could be well suited for cooling if material is introduced early in Q-I HCC where κ (pitch angle) is small. We anticipate κ starting at 0 to match out of bent solenoid (with wedge?) and ending at 1 to match into an HCC with equal cooling decrements.
p(MeV/c)
y(mm
)
π−
μ−
μ+
π+
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
6Muons,Inc.
Q-I HCC HCC
p
…
Bent
Solenoid
Tapered
Solenoid
The degree of integration between designs of the Quasi-Isochronous HCC aspect and helical pitch matching will be determined during our SBIR phase I.
• Implementing a Q-I HCC starting at large κ may require too large an aperture. This could be alleviated by starting at lower κ and cooling muons before arriving at large κ.
• Design of helical pitch matching should incorporate titled coils and is likely to complicate Q-I HCC design.
• If needed, probably ignore tilts in first pass of Q-I HCC design, but return to tilts in iterative process.
Use large RF buckets for capture and also pre-cool.
Equal cooling decrements will maximize rate of cooling.
κ = 0κ = 1
?
Interplay Between Q-I HCC & Helical Pitch Matching
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
7Muons,Inc.
• The helical channel can be configured to run isochronous at a chosen momentum. The well known Derbenev/Johnson Phys. Rev. STAB paper derives a slip factor from which parameters to operate at transition gamma are defined.
01ˆ
1
122
2
3
2
TT
D
b
pk
pkB
da
dp
p
aD
2
2/3
2
2221
)21(
1
]1)1)[(1(ˆ
where
t (nsec)
p (MeV/c)
Isochronous Helical Channel Basics
qg
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
8Muons,Inc.
Transverse Stability (No RF nor material)
20 RG
1ˆ DgqG
2
2
11
2
1
q
R
Condition to satisfy transverse oscillation stability:
where:
Rewriting transverse stability conditions in q and g:
qg 2
2
2
11
4
ˆ
qD
qg
Recall, isochronous condition determines dispersion factor:
22
2 11ˆ
D
Note that for κ = 1, dispersion is independent of q:
g
qD
2
221
1
1ˆ
1 2
1 2
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
9Muons,Inc.
g
q
stable
unstable
unstable
1T 2T 3T 4T
Transverse Stability (No RF nor material)
11 2
pk
Bq sol
Bsol 1
2
22ˆ
1
)1(
D
qg
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
10Muons,Inc.
g
q
stable
unstable
unstable1T 2T 3T 4T
Bsol = 2T:
Reference particle is not stable.
p(M
eV/c
)
t(nsec)
Bsol = 3T
p(M
eV/c
)
t(nsec)
Bsol = 4T
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
11Muons,Inc.
g
q
1T 2T 3T 4T
1T1T
1T
2T 2T
2T
3T 3T
3T
4T 4T
4T
λ = 10 m
λ = 25 mλ = 20 m
λ = 15 m
Can find stable Q-I HCC operation with Bsol=2T & κ=1 by increasing λ (& Rref).
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
12Muons,Inc.
p(M
eV/c
)
t(nsec)
λ = 10 m
Bsol = 2 T
λ = 20 m
Bsol = 2 T
λ = 25 m
Bsol = 2 T
λ = 15 m
Bsol = 2 T
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
13Muons,Inc.
Phase I Performance Schedule (Tasks and Milestones) 3 months after start of funding:
• All pre-requisites are simulated. a. Pion Production and tapered solenoid simulations (currently
ready for use). b. Bent solenoid and accompanying dipoles to separate
opposite signed pions/muons.
6 months after start of funding: • Design, simulation, and optimization of HCC with RF operating near
γt underway.• Study effect of higher order terms in Q-I HCC.• Determine degree of integration between designs of the Quasi-Isochronous
HCC aspect and helical pitch matching.
9 months after start of funding: • Design, simulation, and optimization of HCC with RF operating near
γt completed. • Phase II proposal written to propose experiments to verify viability
of concepts developed in phase I.
Schedule of Tasks
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
14Muons,Inc.
Summary & Future• We believe there is great potential to be realized by utilizing the large RF
buckets that operate near transition at the front end of a muon collider.
• A Quasi-Isochronous HCC will provide a natural match into an equal cooling decrement HCC that cools muons in the shortest distance.
• Consistency between analytic calculations for transverse stability and simulations have been demonstrated.
• The degree of integration between designs of the Quasi-Isochronous HCC aspect and helical pitch matching will be determined during our SBIR phase I.
• We have presented a schedule, driven by our SBIR phase I.
• The end of the phase I is the phase II submission, which is around April 2010.
• We will present our findings at the 2010 LEMC.
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
15Muons,Inc.
Back up Slides
12/1/2009 Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa
16Muons,Inc.
p(M
eV/c)
t(nsec)