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Oct 21, 2002 S. Kahn -- Hard Edge Geant 1
Hard Edge Simulation of TETRA Ring in GEANT (again)
Steve KahnMucool/Mice Meeting
Berkeley October 21, 2002
Oct 21, 2002 S. Kahn -- Hard Edge Geant 2
Why No Progress With Realistic Fields
Need to Understand the GEANT with Hardedge Fields before Attempting Realistic Fields.
My attempts (and others) have reported large losses in using GEANT with this simulation.
Valeri Balbekov has shown that one can achieve a reasonable amount of cooling with reasonably good transmission through this TETRA ring.
Rick Fernow has similarly achieved similarly good results with a high FoM for the TETRA ring in ICOOL.
•Field maps of the solenoids have been supplied to Makino and Berz for use in their COSY model.
Oct 21, 2002 S. Kahn -- Hard Edge Geant 3
Concern whether RF is Properly Phased
Energy Gain
Es at cavity center
Correlation between Es and Energy Gain implies that the RF cavities are not correctly phased.
Oct 21, 2002 S. Kahn -- Hard Edge Geant 4
Reference Track to Phase RF Cavities
Figure shows a reference muon circulating in the ring for 20 turns.
Reference track is launched on axis with ideal Pµ and no PT.RF cavities are active.Absorbers are present.
dE/dx is turned on but no random processes are.
Track shows very little deviation from axis (shown on next transparency).
Oct 21, 2002 S. Kahn -- Hard Edge Geant 5
Phasing the RF — Looking at Path Time
The top figure shows the path time that the reference particle traverses one quadrant.
Only the gradient is varied.RED line indicates what is expected from frequency.
The lower figure shows the RMS variation of the path time for
Cavity 1 in the four quadrants of turn 1.The quadrant path time for all cavities in turn 1.
These figures indicate that the correct gradient is ~15.1 MV/m.
Quadrant Time vs Gradient
34
34.01
34.02
34.03
34.04
34.05
34.06
34.07
34.08
34.09
34.1
10 11 12 13 14 15 16 17
Gradient, MV/m
Tim
e, n
s
Cavity 1All CavitiesExpected
RMS Time Differences
0
0.05
0.1
0.15
0.2
0.25
10 11 12 13 14 15 16 17
Gradient, MV/mTi
me
devi
atio
ns, n
s
Cavity 1All Cavities
Oct 21, 2002 S. Kahn -- Hard Edge Geant 6
Phasing the RF — Looking at Energy Gain
The top figure shows the mean difference in energy gain between corresponding cavities in adjacent quadrants for the 1st turn.
Ideally this difference should be zero. All cavities in all should have the same energy gain difference.
The lower figure shows the RMS variation of the energy gain differences between corresponding cavities in adjacent quadrants.Both figures also imply that the ideal gradient should be ~15.1 MV/m.
Energy Gain vs Gradient
-0.001
0
0.001
0.002
0.003
0.004
0.005
10 11 12 13 14 15 16 17
Gradient, MV/m
Mea
n En
ergy
Gai
n, G
eV
Cavity 1All Cavities
Energy Gain vs. Gradient
0
0.001
0.002
0.003
0.004
0.005
0.006
10 11 12 13 14 15 16 17Gradie nt, MV/m
RM
S En
ergy
Dev
iatio
n, G
eV
Cavity 1All Cavities
Oct 21, 2002 S. Kahn -- Hard Edge Geant 7
Using the Optimized Gradient
Es alongReference Path
Energy along Reference Path
•The reference particle sees a more stable Esand energy variation along its path at least during the early turns.
•There is still room for improvement.
Oct 21, 2002 S. Kahn -- Hard Edge Geant 9
Typical Run
Figure shows 20 particles passed through ring with RF on and wedges in place:
σx=σy= 4 cm, σct=8 cmσPT=32 MeV/c, σE=18 MeVCorrelation between E, PT, BNo decaysNo random processes
dE/dx is mean value
Figure illustrates losses that typically occur in corner regions.
Oct 21, 2002 S. Kahn -- Hard Edge Geant 10
Emittance Calculations
The figure shows the transmission, transverse emittance. (Ignore the 6D emittance, there is a problem with it).
The transmission drops to ~10% in 12 turns.Emittance drops significantly but that is due to losses more than cooling.
Transmission
4D Emittance
Oct 21, 2002 S. Kahn -- Hard Edge Geant 11
Dispersion Plots
The figure shows the dispersion along the straight solenoid. Dx
Dy
Oct 21, 2002 S. Kahn -- Hard Edge Geant 12
Transverse Phase Space Plots
Px vs x at same position for 1st
nine turns
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