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)