1. V.Daniel Elvira Status Report on Cooling Simulations using GEANT4 Motivation: Explore a realistic design of a 44/88 MHz based cooling channel for a -factory to support an 88 MHz based cooling experiment. Stage 1 (a) Simple version of the 44 MHz section of the CERN cooling channel (hard edge B field, thin cavities) (b) Realistic version of (a) STUDY AGREEMENT GEANT4/PATH, ACCURACY OF APPROXIMATIONS, PERFORMANCE, ETC. Stage 2 Integrate 1 into a -factory design following consistent criteria (engineering, simulation accuracy) in both options (88/201 MHz)

2. V.Daniel Elvira Hard Edge (44 MHz) Unit Cell: 4.28 m Absorber (37 cm) r.f kicks (2 MeV gain each) + + + + - -- - Bz on axis +2 Tesla -2 Tesla Section is 47.08 m long (11 cells) 50100150 Z (cm) + + - - + + - - 100150 rf cav. are 1 cm thick (200 MV kicks) Br = -r/2 *  Bz/  z, with  z=5mm Z (cm) Br on axis 0 50 5 mm Bz = 0 when radial kicks present 0 Tesla (on absorber)

3. V.Daniel Elvira Tuning of the r.f. System (Hard Edge) Ekinetic (MeV) Z (cm) Reference particle Ekin = 200 MeV “Instantaneous” kicks (1 cm) Synch phase 90 0 (on crest)

4. V.Daniel Elvira Pseudo-Realistic: 44 (88) MHz Sections 88 cm52 cm 37 cm Unit cell: 6.04m (4.24 m) x 11 cells = 66.44 m r.f. map 52 (50) cm gaps (one every four is longer, 89 (101) cm) drift space plus effect of radial field at the absorber r.f. map from Klaus : Mag.Field from coils (B z, B r ): B z (peak) = 3.4 (2.8) T on axis (the integral under Bz versus Z is the same as in a square 2 T field) Solenoid Inner Radius = 30 (15) cm r.f. map (51cm) (50 cm 40 cm) (3.73 MeV) (16.3 cm)

5. V.Daniel Elvira CERN Channel (44 MHz) coilr.f field map absorber Unit Cell Cooling lattice (44 MHz)

6. V.Daniel Elvira Magnetic Fields For the 44 Mz section, the integral under hard edge (square 2T field) = integral under pseudo-realistic. (from coils) Unit cell absorber Shoulder comes from larger gap at absorber Z (mm)

7. V.Daniel Elvira Bx at r=10 cm (Tesla) Z (mm)

8. V.Daniel Elvira 88 MHz Section Bz (Tesla) vs Z (mm) Notice the bigger shoulders From coils with peak value taken from cern field map

9. V.Daniel Elvira Tuning of the r.f. System (Realistic) Ekinetic (MeV) Z (cm) Reference particle Ekin = 200 MeV Ekin = 275 MeV Only acceleration using the 44 MHz lattice r.f. maps from Klaus Hanke (1.4 m and 0.9 m) Synch phase 90 0 (on crest)

10. V.Daniel Elvira The Input Beam From a hard edge simulation of the target and phase rotation system (from Alessandra Lombardi) Ek = 200 MeV  x = sy = 11 cm  px = spy = 30 MeV  Ek = 14 MeV  ct = 50 cm Matched to the hard edge version of the 44 MHz section Injected immediately before the radial kick associated with the initial +2 Tesla square field

11. V.Daniel Elvira Performance (Hard Edge) Only 200 particles ! (errors very large)  T : cooling factor= 0.71  x  xp : cooling factor = 0.78 (each plane) But results on the same order as CERN simulation Transmission (11 cells) = 91%

12. V.Daniel Elvira Performance (Pseudo-Realistic) Only 1000 particles through the first two cells of the 44 MHz section Betatron resonances? Beam mis- match? Optimization Trans (2 cells!) = 48% Increase in px & transverse emittance

13. V.Daniel Elvira Quick Analysis on Betatron Resonances From MuCool Note # 98 (V. Balbekov): For a sinusoidal field, under the paraxial approximation, there is a  resonance at  = 2pc/eB 0 L = [0.2, 0.3] and a 2  resonance at  = [0.09,0.12] Were pc is the particle momentum, B 0 is B z on axis, and L is half the period of the sinusoidal field The  resonance for the 44 MHz section corresponds to Ek=[81, 147] MeV (at 170 MeV beta function is still strongly modulated). If the Bz field was a sinusoidal function, under the paraxial approximation, betatron resonancies would most probably not be a problem Need to study this issue for the real field.

14. V.Daniel Elvira Performance (Pseudo-Realistic) Only 1000 particles through the first two cells of the 44 MHz section (Field reduced by a 1.7 factor) The beam was clearly mis-matched (field is very different from the hard edge case) Trans (2 cells!) = 76% Decrease in px & transverse emittance improvement

15. V.Daniel Elvira Summary Both the hard edge (44 MHz) and the pseudo-realistic (all) versions of the CERN cooling channel were implemented. We can now read electric and magnetic field maps (interpolated or squared), and create r.f. and magnet objects within the frame of GEANT4 Hard edge results consistent with the PATH simulations by Alessandra Lombardi (need more stats) As it is, the pseudo-realistic channel does not perform well. Both the channel and beam parameters may need to be re-designed/optimized Need to improve speed of code and run on more particles