1. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 1 Use of a Quasi-Isochronous Helical Cooling Channel in the Front End of a Muon Collider Cary Yoshikawa Chuck Ankenbrandt Rol Johnson Dave Neuffer

2. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 2 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

3. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 3 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 γ 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).

4. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 4 5.0 m Bent Solenoid for Charge Separation (phase 1 ) Hg Target p 12.9 m Tapered Solenoid top view z x x’ y end view π−μ−π−μ− μ+π+μ+π+ End of Tapered Solenoid End of Bent Solenoid p(MeV/c) t(nsec)

5. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 5 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 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−π−μ− μ+π+μ+π+

6. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 6 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 = 0 κ = 1 ? Interplay Between Q-I HCC & Helical Pitch Matching

7. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 7 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. where t (nsec) p (MeV/c) Isochronous Helical Channel Basics q g

8. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 8 Transverse Stability (No RF nor material) Condition to satisfy transverse oscillation stability: where: Rewriting transverse stability conditions in q and g: Recall, isochronous condition determines dispersion factor: Note that for κ = 1, dispersion is independent of q: 12 12

9. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 9 g q stable unstable 1T2T3T4T Transverse Stability (No RF nor material) Bsol  

10. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 10 g q stable unstable 1T2T3T4T Bsol = 2T: Reference particle is not stable. p(MeV/c) t(nsec) Bsol = 3T p(MeV/c) t(nsec) Bsol = 4T

11. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 11 g q 1T2T3T4T 1T 2T 3T 4T λ = 10 m λ = 25 m λ = 20 m λ = 15 m Can find stable Q-I HCC operation with Bsol=2T & κ=1 by increasing λ (& Rref).

12. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 12 p(MeV/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

13. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 13 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

14. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 14 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.

15. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 15 Back up Slides

16. Muons, Inc. 12/1/2009Dec 1-3, 2009 MCDW at BNL Cary Y. Yoshikawa 16 p(MeV/c) t(nsec)