1. Valery KAPIN ITEP , Moscow
Status of MADX modeling for SIS100: the effect of the new "CSLD&Q6T" magnets (OPERA-3D data)
Valery KAPIN
ITEP , Moscow
Workshop “Beam Physics for FAIR”, Hotel Bastenhaus, 5 - Jul

2. Contents* New "CSLD&Q6T" magnets Features of multipole notations
A new interface to convert “magnet-to-MAD” harmonics
DA algorithm & 2009-results for “CDLD” with MADX & MICROMAP
Benchmarking with MICROMAP on measured 29 multipoles
First results for DA-2010 and comparison with DA-2009
Random CO via small kicks in Quads (Micromap-approach)
Random CO via large kicks in Quads & CO-corrections
Conclusion: plans for further simulations.
* Work is done in collaboration with G.Franchetti (GSI)

3. Curved single layer dipole (CSLD)
one layer coil with 8 turns =>
CSLD8b with Rogovsky or Rectangular ends
Reference radius for circular multipoles [m]
0.04
semiaxes of ellipse for elliptical multipoles, a and b [m]
0.0575; 0.03
Length of “Total”, [m]
3.3656
Bending angle, [deg.];
eff. magnetic length, [m] ;
3.062
Orbit curvature radius, [m]
52.632
P. Akishin et al., “Calculated Multipoles for the SIS 100 CSLD”, the revision on 9-June-2010).

4. 6-Turn Quadrupole (Q6T) Currently a 6 turn quadrupole is foreseen
as the main quadrupole for SIS100.
Reference radius for circular multipoles [m]
0.04
semiaxes of ellipse for elliptical multipoles, a and b [m];
Useable aperture (mm)
0.0625; 0.03;
135x65
Effective field length, [m]
1.3
Max. Gradient G [T/m] 27
Length of “Total”, [m]
1.8
P. Akishin et al., “Field Representation for SIS100 6Turn Quadrupole”, 15/04/2010 (revised 23-June-2010).

5. Multipole notations x y
ion beam
z<0: “beam entry” (non-connection side)
z>0: “beam exit” (connection side)
“Centre” part
z=0: Central Slice
“Total”
CSLD z x y
ion beam
z<0: beam entry – “End”
z>0: beam exit – “End”
“Centre” section
“Total”
Q6Turn
The circular multipoles presented in the “magnetic-group”(MG) report are written in so-called “European magnet convention” as
Normalized multipole coefficients:
(used in report tables)
MAD notation the circular multipoles
Normal Skew
simply coefficient ! (not a radius of convergence).
Circular multipoles are derived from ellipical =>

6. Multipole conversions
Magnet-to-MAD conversion for dipole
Magnet-to-MAD conversion for quadrupole
V. Kapin, “Conversion of multipole data for SIS100 magnets, GSI note, 2010.
Y. Luo, “Building the RHIC tracking lattice mode”, C-A/AP/#387, 2010 by BNL, p. 3.

7. A new standard for SIS100 “magnet-to-MAD” conversions
OLD-style with “different conventions for every report”:
Cn(15-digits)->cn(3-digits) in “magnet” report
cn(3-digits or plots) converted in MAD-multipoles
New-style with “standard electronical conversion”:
P.Schizer, Fortran Library to read HDF-database with Cn(15-digits)
V.Kapin, Fortran module for conversions Cn to KNL

8. HDF-database to MAD-tfs tables

9. Algorithm for DA-calculations (Example for SIS300, 2007 at GSI)
Define boundary in (X,Y) - plane at px=py=0
via particle tracking
Transfer to emittance plane:
1) Calculate Courant-Snyder invariants for every trajectory on boundary at every turn;
(see next)

10. Transfer to emittance plane
Minimum points of invariant sums for every injection ray provide boundary
the average radius (via the area) and minimum radius are calculated:
Find cross points

11. 2009 (C2LD+Q-Dubna) : DA of SIS100 (GF-report) “comparison”
Syst. & rand. errors
RMS closed orbit – 1.5/1.0 mm
MICROMAP:
a) COD=0:
central DA=4.05 with 3-s ( )
b) COD=1.5/1.0mm:
central 3.3 with 3-s ( )
MADX:
a) COD=0:
DAave=> ( )
DAmin=> ( )
b) COD=1.5/1.0mm:
DAave => ( )
DAmin => ( )
Only with syst errors: DAave/min=4.3/4.1

12. Benchmarking 2010: MICROMAP & MADX measured 29 multipoles
29 multipoles localized in 3 region, entrance, body, and exit of the magnet.
For large order multipoles =>
Reasonable doubts on the capability
of codes to deal properly with large numbers. => the effect on the particle dynamics should be tested
Fig. The stability at s = 0m in SIS100.
MICROMAP - black (grey) dots
MADX – red line - the border of stability for 1000 turns.
each point represents the initial particle coordinate with x′ = y′ = 0.
G. Franchetti & V. Kapin, “Particle stability code benchmarking in a highly nonlinear system”, GSI note, 27-May-2010

13. DA with syst. & random errors
DAave/
DAmin
5.39/4.82 10
4.434.65 /
3.454.29 20
3.964.25 /
3.283.68 30
3.804.02 /
3.103.65
30% (2009) /

14. DA syst. & rand. Errors+C.O.
1) C.O. (small 1.6e-5 kicks in quads) no correction
DAave=3.553.91, DAmin=3.00 (2009: / )
Where
xco,max, mm
yco,max, mm
xco,rms, mm
yco,rms, mm
all elements
1.7÷8.6; rms=5.0
1.6÷3.5; rms=2.9
0.7÷4.0; rms=2.1
0.5÷1.3; rms=1.0
pickup monitors
1.6÷8.0; rms=4.8
1.2÷3.1; rms=2.4
0.8÷4.6; rms=2.5
0.5÷1.1; rms=0.9
collim. in dipoles
1.5÷7.2; rms=4.3
1.5÷3.0; rms=2.5
0.6÷3.6; rms=2.0
0.5÷1.2; rms=1.0
collim. in quads
1.6÷8.5; rms=4.7
1.4÷3.4; rms=2.5
0.6÷4.4; rms=2.3
0.6÷1.3; rms=1.0
2) C.O. (20x1.6e-5 kicks in quads) CO-corrected* (Exclude 3 not corrected)
DAave=3.443.95, DAmin=3.143.64.
Where
xco,max, mm
yco,max, mm
xco,rms, mm
yco,rms, mm
all elements
3.0÷9.8; rms=6.1
2.1÷5.7; rms=3.8
0.7÷4.4; rms=2.6
0.6÷2.3; rms=1.2
pickup monitors
1.4÷9.5; rms=5.6
0.6÷3.7; rms=1.9
0.5÷5.2; rms=3.1
0.3÷1.9; rms=0.9
collim. in dipoles
2.8÷9.0; rms=5.4
1.8÷5.2; rms=3.4
0.7÷4.2; rms=2.4
0.6÷2.2; rms=1.1
collim. in quads
1.6÷9.7; rms=5.8
2.0÷5.7; rms=3.4
0.5÷4.7; rms=2.8
0.7÷2.6; rms=1.3
*CO-correction is done with support by S.Sorge (GSI)

15. DA syst. & rand. Errors+C.O: seed examples
Example: seed 2001 for “small” kick
Where
xco,max, mm
yco,max, mm
xco,rms, mm
yco,rms, mm
all elements
5.3
2.9
2.3
1.0
pickup monitors
5.1
2.2
2.7
0.9
collim. in dipoles
4.8
2.5
2.1
collim. in quads
4.5
1.8
0.8
Example: seed 2020 for “large” corrected kick
Where
xco,max, mm
yco,max, mm
xco,rms, mm
yco,rms, mm
all elements
5.6
2.1
2.5
0.7
pickup monitors
5.4
1.2
2.9
0.5
collim. in dipoles
5.1
1.8
2.2
0.6
collim. in quads
2.0
2.6

16. DA syst. & rand. Errors+C.O: “small” kicks vs “large”-corrected kicks

17. Preliminary conclusions:
Random errors of 10-30% essentially reduce DA to 20-40% with spread of ~10%
C.O. provides additional reduction up to 10%.
C.O. simulations with small kicks are approx. equivalent to “large” kicks with corrected C.0.
Need for estimation of fabrication errors (with both feeddown formulae and report on 2D simulations).
Calculation of beam losses after definition of errors level