Use of a Quasi-Isochronous Helical Cooling Channel in the Front End of a Muon Collider

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Use of a Quasi-Isochronous Helical Cooling
Channel in the Front End of a Muon Collider Cary
Yoshikawa Chuck Ankenbrandt Rol Johnson Dave
Neuffer
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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

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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 ?T 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).

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Bent Solenoid for Charge Separation (phase 1 )
x
x
top view
p- µ-
z
p
Hg Target
µ p
Tapered Solenoid
5.0 m
12.9 m
End of Bent Solenoid
End of Tapered Solenoid
p(MeV/c)
t(nsec)
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Bent Solenoid Exit

• Immediately 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 ? (pitch angle) is small. We
  anticipate ? 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- µ-
y(mm)
µ p
p(MeV/c)
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Interplay Between Q-I HCC Helical Pitch
Matching

• 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 ? may
  require too large an aperture. This could be
  alleviated by starting at lower ? and cooling
  muons before arriving at large ?.
• 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.

?
? 0
? 1
Q-I HCC
HCC
Bent Solenoid
Tapered Solenoid
Use large RF buckets for capture and also
pre-cool.
Equal cooling decrements will maximize rate of
cooling.
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Isochronous Helical Channel Basics

• 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.

g
q
where
p (MeV/c)
t (nsec)
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Transverse Stability (No RF nor material)
Condition to satisfy transverse oscillation
stability
1
2
where
Rewriting transverse stability conditions in q
and g
1
2
Recall, isochronous condition determines
dispersion factor
Note that for ? 1, dispersion is independent of
q
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Transverse Stability (No RF nor material)
g
q
Bsol ?
?
10
Bsol 2T Reference particle is not stable.
g
q
p(MeV/c)
Bsol 3T
p(MeV/c)
Bsol 4T
t(nsec)
t(nsec)
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Can find stable Q-I HCC operation with Bsol2T
?1 by increasing ? ( Rref).
1T
2T
3T
4T
1T
2T
3T
4T
? 10 m
? 15 m
g
1T
1T
2T
2T
3T
3T
4T
4T
? 25 m
? 20 m
q
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? 10 m Bsol 2 T
? 15 m Bsol 2 T
? 25 m Bsol 2 T
? 20 m Bsol 2 T
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Schedule of Tasks

• 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 ?t 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 ?t completed.
• Phase II proposal written to propose experiments
  to verify viability of concepts developed in
  phase I.

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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.

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Back up Slides
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p(MeV/c)
t(nsec)