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)

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 m long (11 cells) Z (cm) rf cav. are 1 cm thick (200 MV kicks) Br = -r/2 *  Bz/  z, with  z=5mm Z (cm) Br on axis mm Bz = 0 when radial kicks present 0 Tesla (on absorber)

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)

V.Daniel Elvira Pseudo-Realistic: 44 (88) MHz Sections 88 cm52 cm 37 cm Unit cell: 6.04m (4.24 m) x 11 cells = 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)

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

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)

V.Daniel Elvira |Br| at r=10 cm (Tesla) Z (mm) Note the oscillation in |Br| amplitude due to the extra gap (absorber) To inject the same input beam at a location different from zero is equivalent to change the beam correlations. We will test the effect of correlations in performance by injecting the beam both at zero and a the location of the green bar.

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

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)

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 =  y = 11 cm  px =  py = 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

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%

V.Daniel Elvira Performance (Pseudo-Realistic) Only 1000 particles through the first two cells of the 44 MHz section Betatron resonances? Beam mis-match? RF implementation? Trans (2 cells!) = 48% Increase in px & transverse emittance If we inject the beam at the location of the green bar (see a few slides above), which would be equivalent to a change in the input beam correlations, transmission increases to 68% The beam is not the optimum for this channel

V.Daniel Elvira Typical particle which is lost…. Notice r.f. acceleration, dE/dx in LH2, and death at a coil boundary Particle trajectory ends when it hits the magnet (r=30 cm) P(GeV) vs Z (cm) R (cm) vs Z (cm)

V.Daniel Elvira Particles are not lost due to r.f. mis-tuning E - vs ct (with r.f. & abs.) Initial, and after 1 st and 2 nd cells No r.f. or absorbers ! but same lattice Transmission is almost identical as before

V.Daniel Elvira Typical particle which is lost….( again but now for a system with no r.f. or absorbers) The track is virtually identical as before (with r.f. and absorbers) P(GeV) vs Z (cm) R (cm) vs Z (cm) Notice there is no acceleration or dE/dx until it hits the magnet

V.Daniel Elvira What happens if I also remove the space occupied by the absorber in the lattice ? The shoulder (second frequency) disappears from Bz, and the amplitude of |Br| does not oscillate Transmission increases to 56% (from 48%) The modulation in the field due to the extra gap for the absorber does have an effect on performance Bz (T) at r=10 cm vs Z (mm)Br (T) at r=10 cm vs Z (mm)

V.Daniel Elvira Now I change the size of the inter-magnet gap around the nominal 52 cm value Bz (T) at r=10 cm vs Z (mm)Br (T) at r=10 cm vs Z (mm) Optimal transmission value found at a gap of 20 cm Note that Bz is more sine-like and |Br| more delta-like (the double peak disappeared) Transmission increased to 73% (from 48%) If the beam is injected at the location of the green bar (instead of zero), the transmission goes up to 92% (equiv. to a change in beam correlations) A change in correlations and the size of the gap improves performance

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 But the real beam through the real field is does not follow this approximation.

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 to test beam matching) 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

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. The large difference in performance with respect to the hard edged simulation may be explained by the different magnetic fields. (The input beam is not matched anymore either)