1. 1 Advances for a Solenoid/Dipole 6D Cooling Ring X. Ding, UCLA Muon Accelerator Program-Winter Meeting Jefferson Lab 3/1/11

2. 2 Collaborators D. Cline (UCLA) Al. Garren (PBL) H. Kirk (BNL) J. S. Berg (BNL) X.Ding3/1/11

3. 3 Outline 1. Evolution of the Solenoid/Dipole Ring Cooler Design 2. Analysis of lattices (Beam Dynamics) 3. 6D Cooling 4. Summary X.Ding3/1/11

4. Evolution of the Solenoid/Dipole Ring Cooler (Racetrack Lattice) 4X.Ding3/1/11

5. Evolution of the Solenoid/Dipole Ring Cooler (Problem with the Racetrack Lattice) Excessive losses in lattice Low working momentum (145 MeV/c): large dispersion Very limited energy acceptance Strong transverse/longitudinal couping Non-robust cooling rate 3/1/11X.Ding5

6. 6 Dipole Solenoid Evolution of the Solenoid/Dipole Ring Cooler (Four-sided Lattice) X.Ding3/1/11

7. Evolution of the Solenoid/Dipole Ring Cooler (Switch from racetrack to 4-sided) Reduce dispersion High energy operation: XZ partition numbers improved Improve dynamic aperture Achieve robust 6D cooling 3/1/11X.Ding7

8. 8 Racetrack ring4 sided ring (modified) Momentum145 MeV/c Superperiods244 Arc length6 m7 m6 m Straight section length5.85 m5 m Superperiod length & xytunes 11.85 m, 1.74812 m, 1.7511 m, 1.75 Circumference23.7 m48 m44 m Evolution of the Solenoid/Dipole Ring Cooler (Specifications) X.Ding3/1/11

9. Analysis of Lattices (Racetrack: Left, 4-sided: Right) Dispersion is reduced in the 4-sided cooling ring 3/1/11X.Ding9

10. 10 Analysis of Lattices X.Ding3/1/11 Time of Flight minimum for the 4-sided lattice moves to higher energy and it can increase lattice energy

11. 11 Analysis of Lattices Dynamic Aperture (4-sided Lattice) X.Ding3/1/11

12. 6D Cooling (4 sided ring) Layout of RF Cavity & LH 2 Absorber in a 4- sided ring quadrant B SOL+ SOL- SOLS+ SOLS- o o 2oo o o oo +os 2os oosoos 2os oo+os o o 2 oo o o 2oo SOLS+ SOLS- SOL- SOL+ LH 2 RF LH 2 RF 12X.Ding3/1/11 Accelerating gradient, RF phase and frequency 15 MV/m, 30 degree, 201.25 MHz Length and energy loss rate in the LH 2 wedge absorber 19.5cm, 0.3 MeV/cm

13. 13 6D Cooling (4 sided ring) Cold Beam -- Equilibrium (LH 2 -Wedge/23 deg, with Stochastics) X.Ding3/1/11

14. 14 6D Cooling (4 sided ring) Damping without Stochastics (LH 2 -Wedge/23 deg) X.Ding3/1/11

15. 15 6D Cooling (4 sided ring) 6D Cooling with Stochastics (LH 2 -Wedge/23 deg) X.Ding3/1/11

16. 16 6D Cooling (4 sided ring) 6D Cooling with Stochastics (LH 2 -Wedge/23 deg) Number of turns015Reduction Normalizes Horizontal emittance (mm)6.974.9551.4067 Normalized Vertical emittance (mm)10.624.3192.459 Normalized Longitudinal emittance (mm)20.126.7492.981 6D emittance (mm 3 )1489.3144.410.3 Transmission (%)10039.0 X.Ding3/1/11

17. 6D Cooling (Modified 4-sided Lattice) 3/1/11X.Ding17 4 sided lattice Modified 4 sided lattice

18. 6D Cooling (Modified 4-sided Lattice) Cold Beam -- Equilibrium (LH 2 -Wedge/23 deg, with Stochastics) 3/1/11X.Ding18 Transmission is much improved

19. 6D Cooling (Modified 4 sided ring) 6D Cooling with Stochastics (LH 2 -Wedge/23 deg) 3/1/11X.Ding19 6D cooling is much improved and transmission is higher for the modified 4 –sided lattice

20. 6D Cooling (Modified 4 sided ring) 6D Cooling with Stochastics (LH 2 -Wedge/23 deg) 3/1/11X.Ding20 Number of turns015Reduction Normalizes Horizontal emittance (mm)12.595.3382.36 Normalized Vertical emittance (mm)14.983.9113.83 Normalized Longitudinal emittance (mm)21.778.4892.56 6D emittance (mm 3 )1489.3144.423.2 Transmission (%)10065.8

21. Summary The achromat lattices of the Dipole/Solenoid Ring Coolers are designed. The analysis of the lattices for their linear parameters and dynamic aperture are performed. The simulation demonstrates that our modified four sided ring cooler has a robust 6D cooling. 3/1/11X.Ding21