1. Harold G. Kirk Brookhaven National Laboratory Quad/dipole Ring Coolers * Nufact’03 Columbia University June 6, 2003 * With contributions from A. Garren and Y. Fukui, UCLA

2. Harold G. Kirk The Process l Explore ring cooling designs l Simplify designs n Avoid solenoids where possible n Use only quads & dipoles l Obtain longitudinal cooling n Utilize beam dispersion n Maintain/reduce horizontal emittance l Linear lattice design (SYNCH) l Cooling simulation (ICOOL) Strategy

3. Harold G. Kirk The Cooling Process The basic emittance evolution equation: Heating Cooling Setting yields, Focusing Properties Material Properties

4. Harold G. Kirk 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

5. Harold G. Kirk A Quad /dipole Lattice l Compact Chasman-Green lattice l 1 m drift available for rf Low  (25 cm) at absorber l Combined function dipole simulated l Dispersion only at absorber l Allows for matching straight sections--injection/ejection l 45 0 bending cell  y max >  x max l Cell tune is ~ ¾ x y

6. Harold G. Kirk Chasman-Green Lattice Performance 10 ns  x,  y, and  z all decrease Transmission 50% Total Merit = Transmission x (  x  y  z ) initial / (  x  y  z ) final  V  R  Beam momentum 250 MeV/c 25 cm LH 2 wedges Wedge angle 20 0 Rf frequency 201.25 MHz E max = 16 MV/m

7. Harold G. Kirk A Dipole-only Lattice l 1 m drift available for rf Low  (25 cm) at absorber l Edge focusing n 22 0 entrance angle n -7 0 exit angle l Dispersion throughout cell l 45 0 bending dipoles l Very compact (9.8 m circumference) x y

8. Harold G. Kirk Dipole-only Ring Layout NSCL at Michigan State Isochronous Ring 26 0 face angles and 7 cm gaps 2 cells 90 0 bending dipoles l 9.8 m ring circumference l 4 cells l 45 0 bending dipole

9. Harold G. Kirk Dipole-only Lattice Performance 10 ns  x,  y, and  z all decrease Transmission 50% Total Merit = Transmission x (  x  y  z ) initial / (  x  y  z ) final = 100  V  R  Beam momentum 500 MeV/c 24 cm LH 2 wedges Wedge angle 10 0 Rf frequency 201.25 MHz E max = 16 MV/m

10. Harold G. Kirk Edge Effects Considerations Scott Berg – PAC03 l Uses COSY infinity fringe fields l End fields greatly affect tunes l Lattice dimensions must change l May require reducing apertures and therefore acceptances

11. Harold G. Kirk A Reverse-bend Dipole-only Lattice l Edge focusing n 30 0 / -3 0 face angles n 11 0 / 11 0 face angles l No dispersion at cell edges n Simplify adding injection/ejection sections l 45 0 and -22.5 0 bending dipoles l 28.8 m circumference without straight sections n Allow longer bunch trains x y

12. Harold G. Kirk Reverse-bend Lattice Performance 10 ns After 10 full turns Transmission 40% Merit = 80  V  R  Beam momentum 250 MeV/c 40 cm LH 2 wedges Wedge angle 18 0 Rf frequency 201.25 MHz E max = 16 MV/m

13. Harold G. Kirk The Lithium Rod Consider again the equilibrium emittance condition: Focusing Properties Material Properties But for Li rods a   of 1cm can be achieved.

14. Harold G. Kirk Lithium Rod Ring Concept The basic idea Use solenoid focusing to achieve   = 16 cm Use matching Li rods to achieve   = 1 cm l Disperse compensating rf throughout remainder of the ring l Include injection/ejection straight section Lithium rods Matching solenoids injection/ejection

15. Harold G. Kirk ICOOL Simulations The simulations to date (Y. Fukui):

16. Harold G. Kirk Li Rod Performance The transverse emittance reduces while the longitudinal emittance grows.

17. Harold G. Kirk Summary l The SYNCH + ICOOL approach works l Emittance exchange has been demonstrated With quadrupole/dipole rings and dipole-only rings, invariant phase-space density (N/   ) increases of up to to 100 have been simulated l The analysis of fringe fields of magnet ends show significant effects and must be considered l Initial studies with rings which contain Li rods point toward the possibility of further transverse emittance reduction