1. Harold G. Kirk Brookhaven National Laboratory Progress in Quad Ring Coolers Ring Cooler Workshop UCLA March 7-8, 2002

2. Harold G. Kirk Snowmass 01 l Explore Ring Cooling Designs l Use only Quads & Dipoles l Obtain Longitudinal Cooling l Maintain/Reduce Transverse Emittance l Linear Lattice Design (SYNCH) l Cooling Simulation (ICOOL) Strategy

3. Harold G. Kirk The Snowmass Lattice l 4 m drift available for rf Low  (25 cm) at absorber l Pseudo-combined function dipole l Allows for matching straight sections l 45 0 bending cell  x max >  y max l Cell tune is ~ 3/4 x y

4. Harold G. Kirk Single Particle Dynamic No Stochastic Processes 10 ns Longitudinal phase space damping increases with degree of wedge angle  Horizontal phase space reduces for wedge angles 15 0 Vertical phase space reduces at a rate independent of wedge angles  V  R 

5. Harold G. Kirk Snowmass Lattice Performance 10 ns initial  y > initial  x  y and  z decreases  x increases Transmission 40% Total Merit = Transmission x (  x  y  z ) initial / (  x  y  z ) final  V  R  Beam momentum 500 MeV/c 25 cm LH 2 wedges Wedge angle 10 0 Rf frequency 201.25 MHz E max = 10 MV/m

6. Harold G. Kirk Equilibrium Emittances Problem is noted with the equilibrium horizontal emittance, which is much higher than expected Horizontal equilibrium emittance persists even for 0 0 wedges. Higher order dispersion effects?

7. Harold G. Kirk The Berkeley Lattice l 4 m drift available for rf Low  (25 cm) at absorber l Pseudo-combined function dipole l Allows for matching straight sections l 22.5 0 bending cell  y max >  x max l Cell tune is ~ 3/4 x y

8. Harold G. Kirk Berkeley Lattice Equilibrium Emittances Horizontal equilibrium emittance increases with wedge angle but 0 0 wedge angle behaves as expected Longitudinal equilibrium emittance declines with increasing wedge angle

9. Harold G. Kirk Berkeley Lattice Performance 10 ns  y and  z decreases  x nearly constant Transmission 60% Total Merit = Transmission x (  x  y  z ) initial / (  x  y  z ) final  V  R  Beam momentum 500 MeV/c 25 cm LH 2 wedges Wedge angle 20 0 Rf frequency 201.25 MHz E max = 8 MV/m

10. Harold G. Kirk Consider Decay Losses Ratio ( initial InitialAfter 8 Turns After 16 Turns  x, mm 2.50.930.87  y, mm 2.62.332.65  z, mm 29.22.834.02 Transmission1.00.670.55 Decay survival 1.00.650.43 Total merit peaks near 8 full turns. 20 0 to 30 0 wedges are best. final )

11. Harold G. Kirk What has been accomplished l The SYNCH + ICOOL approach works well l Emittance exchange has been demonstrated l This quad ring design does not replace Study II front end but can follow it l Transmission losses are still high l Need to consider realistic quads (L = 20cm ; R = 20 cm) l Horizontal - vertical coupling should be considered n Skew quads n Solenoids l Need to incorporate soft edges