status report on cooling simulations using geant4
DESCRIPTION
Status Report on Cooling Simulations using GEANT4. Motivation: Explore a realistic design of a 44/88 MHz based cooling channel for a n -factory to support an 88 MHz based cooling experiment. - PowerPoint PPT PresentationTRANSCRIPT
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 a
xis
+2 Tesla
-2 Tesla
Section is 47.08 m long (11 cells)
50 100 150
Z (cm)
+
+-
-
+
+-
-
100 150150150
rf cav. are 1 cm thick (200 MV kicks)
Br = -r/2 * Bz/z, with z=5mm
Z (cm)
Br
on a
xis
0
505 mm
Bz = 0 when radial kicks present
0 Tesla (on absorber)
V.Daniel Elvira
Tuning of the r.f. System (Hard Edge)Eki
neti
c (M
eV
)
Z (cm)
Reference particle
Ekin = 200 MeV
“Instantaneous” kicks (1 cm)
Synch phase 900 (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 = 66.44 m
r.f. map
r.f. map r.f. map
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 (Bz, Br): Bz(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
MeV2.870)dz(rEz MeV2.70)dzdt(rEz
cm3.270)dz(rE
0)dz(rEz
z
z
r.f. map
(51cm)
(50 cm 40 cm)
(3.73 MeV)(16.3 cm)
V.Daniel Elvira
CERN Channel (44 MHz)
coil r.f field mapabsorber
Unit Cell
Cooling lattice (44 MHz)
V.Daniel Elvira
Magnetic FieldsFor 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 absorberZ (mm)
V.Daniel Elvira
Bx at r=10 cm (Tesla)
Z (mm)
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)Eki
neti
c (M
eV
)
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 900 (on crest)
V.Daniel Elvira
The Input BeamFrom 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
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?
Optimization
Trans (2 cells!) = 48%
Increase in px & transverse emittance
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/eB0L = [0.2, 0.3]
and a 2 resonance at = [0.09,0.12]
Were pc is the particle momentum, B0 is Bz 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.
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
V.Daniel Elvira
SummaryBoth 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