1. Dynamic Aperture Studies with Acceleraticum
XIV SuperB General Meeting, 27 September – 1 Octomber 2010,
LNF-INFN, Frascati
Dynamic Aperture Studies with Acceleraticum
E.Levichev and P.Piminov
Budker Institute of Nuclear Physics
Novosibirsk, Russia
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

2. For simulation we use home-made tracking code named Acceleraticum
Simulation Code
For simulation we use home-made tracking code named Acceleraticum
Converter from/to MAD or SAD lattice standard
Symplectic 4D/6D Tracking
Uncoupled and Coupled Optics Calculation
Linear Parameters Calculation (chromaticity, radiation integrals, etc)
Many Tools Facilitating Nonlinear Dynamics Study
Several Routines for Dynamic Aperture Optimization (Best Sextupole Pair, gradient search, etc)
Recently, Dieter Einfeld’s group cross-checked several accelerator codes and Acceleraticum shown good results. See Einfeld talk at
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

3. Lattice Parameters Lattice V12 by Pantaleo Raimondi Parameters LER HER
Units
Circumference, L
1.258 km
Energy, E
4.18
6.70
GeV
Compaction factor, α
4.04·10 -4
4.35·10 -4
Betatron coupling, κ
0.25 %
Horizontal emmitance, εx
1.827
1.979
nm·rad
Energy spread, σE
6.68·10 -4
6.31·10 -4
Damping times, τx / τz
40.6/20.3
26.7/13.3
Betatron tunes, νx / νz
42.575/18.595
40.575/17.595
Synchrotron tune, νs
0.0129
0.0135
Natural chromaticity, ξx / ξz
-137/-449
-134/-447
Beta IP, βx / βz
2.6/0.0274 cm
Beam IP, σx / σz
7.16/0.037
6.88/0.035 um
Bunch length, σs
0.408
0.420
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

4. On Energy Dynamic Aperture
Nonlinear Perturbations
Sextupoles
Octupoles
Quadrupole Fringe Fields
Kinematics Terms
Ideal Lattice
DA in R.M.S. Beam Size
1000 turns
CRAB Sextupoles is Switched Off
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

5. On Energy Dynamic Aperture
Parameters of Crab Sexts
LER
HER
Units
Length, L 35 m
Strength, K2
±33.34
m-3
Horizontal beta, βx
14.6
Vertical beta, βz
200
CRAB Sextupoles are Switched On
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

6. Nonlinear Chromaticity
Tune Dependence on Energy Deviation (RF is off)
CRAB OFF
Qx=0.5
CRAB ON
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

7. Off Energy Dynamic Aperture
RF On
CRAB OFF
CRAB ON
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

8. Tune-Amplitude Dependence
Nonlinearities from
LER
HER
Acceleraticum
Cxx
Cxz
Czz
Units
Sextupoles
247
-510
-8520
253
-402
-6510
cm-2
Octupoles
-120
112
384
-124
142
365
Quadrupole fringe fields
240
1440
5750
1510
5830
Kinematic term
0.6 35
5090
4440
Total
370
1205
3380
375
1320
3390
Nonlinearities from
LER
HER
MADX-PTC
Cxx
Cxz
Czz
Units
Sextupoles
252
-481
-7482
256
-408
-7459
cm-2
Octupoles
-118
107
405
-116
124
392
Quadrupole fringe fields
254
1616
6372
253
1614
6369
Kinematic term
100
149
6967
Total
488
1390
6262
493
1479
6270
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

9. Crab Sextupole Influence
Pictures show the horizontal and vertical envelope of
the last stable horizontal trajectory vs azimuth of the storage ring.
blue is crab off red is crab on
Crab sextupoles interact with IR sextupoles
and produce strong nonlinear coupling
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”

10. Summary
Dynamic aperture of the lattice without crab sextupoles seems to be sufficient
The quadrupole fringe field and the kinematics term are not strong. They can be compensated by weak octupoles
Crab sexupoles produce strong nonlinear coupling and limit dynamic aperture
E.Levichev and P.Piminov, “Dynamic Aperture Studies with Acceleraticum”