Machine:Magnets

Storage Ring Magnets

At this point all magnets have been designed, simulated and approved. A few prototype magnets (quadrupoles) have been measured mechanical and magnetically. Overall magnetic measurements with rotating coil and Hall probe systems are still pending.

Storage Ring Dipoles

Dipoles in Sirius are of three distinct families: B1, B2 and BC. The first two, B1 and B2, are electromagnetic dipoles, whereas BC is a NdFeB permanent magnet dipole made of a thin 3.2 T slice sandwiched between two low field sector dipoles.

SI Dipole Magnet Specifications

Main Parameters

Main parameters for the electromagnetic dipoles B1 and B2 are shown in Table 1, and for the permanent magnet superbend BC in Table 2.

Table 1: Storage ring dipoles B1 and B2 main parameters. A parallel face, curved dipole is assumed (constant B and dB/dx along trajectory).
	B1	B2	units
Excitation	monopolar power supply	monopolar power supply
Number of magnets	40	40
Deflection angle	2.7553	4.0964	°
Magnetic length	0.853	1.263	m
Physical length	0.807	1.21239	m
Integrated quadrupole strength¹	-0.6461	-0.9588	m^-1
Integrated sextupole strength¹	0.0	0.0	m^-2
Full central gap²	24.0	24.0	mm
Hardedge bending radius	17.7379	17.6654	m
Hardedge quadrupole strength	-0.7574	-0.7591	m^-2
Hardedge sextupole strength	0.0	0.0	m^-3
Hardedge sagitta	5.127	11.286	mm
Integrated field¹	-0.48	-0.72	T·m
Integrated quadrupole gradient ¹	6.4652	9.5946	T
Integrated sextupole gradient¹	0.0	0.0	T·m^-1
Hardedge field	-0.5642	-0.5665	T
Hardedge quadrupole gradient	7.5794	7.5967	T·m^-1
Hardedge sextupole gradient	0.0	0.0	T·m^-2
Quadrupole flexibility	10.0	10.0	%

¹ On the Runge-Kutta trajectory.

² Full gap at the horizontal central position, where Runge-Kutta beam trajectory is centered.

Table 2: Storage ring BC dipole main parameters.
	BC
Excitation	permanent NdFeB magnets
Number of magnets	20
Magnet length	0.828	m
Magnetic arc length	0.920	m
Deflection angle	4.2966	°
Peak field	3.20	T
Full gap at peak field	10.20	mm
Bending radius at peak field	3.1272	m
Critical energy at peak field	19.2	keV
Integrated field	-0.75042	T·m
Integrated gradient	6.2511	T

Electric parameters

Table 3: Storage ring dipoles B1 and B2 electric parameters
	B1	B2	units
Main coil current	394.10	394.10	A
Main coil number of turns	24	24
Stored magnetic energy	677.32	1003.66	J
Magnet inductance	8.72	12.92	mH

Multipole Errors

Table 4: Storage ring dipole multipole errors. Contribution of multipolar components relative to main dipolar field at x = 12 mm. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
Multipole error	Systematic	Random
Multipole error	Normal	Normal	Skew
B₂/B₀ (sextupole)	1.5×10^-4	1.5×10^-4	0.5×10^-4
B₃/B₀ (octupole)	-7.2×10^-5	1.5×10^-4	0.5×10^-4
B₄/B₀ (decapole)	-5.6×10^-4	1.5×10^-4	0.5×10^-4
B₅/B₀ (12-pole)	6.7×10^-5	1.5×10^-4	0.5×10^-4
B₆/B₀ (14-pole)	3.8×10^-4	-	-

Alignment and Excitation Errors

Table 5: Maximum absolute value of random alignment and excitation errors for Storage Ring Dipoles. The errors are generated with a Gaussian distribution truncated at ±1σ.
	Dipole Unit Blocks	Girders
Transverse position, $\text{[math]}$ , $\text{[math]}$	40	80	μm
Rotation around longitudinal axis	0.30	0.30	mrad
Strength error (static or low frequency)	0.05	--	%
Dipole Gradient error	0.1	--	%

SI Dipole Magnet 3D Models

BC

The BC dipoles in the Sirius storage ring is composed of a central high field slice with 1.1395 ° of deflection and two flanking low field sectors with 1.57855 °. There is a control gap in the back of the dipole that can be used to adjust the magnetic field. Additionally, the low field poles can be moved transversely to adjust the integrated field and the pole between the low and high field sectors can be rotated about the longitudinal axis to correct the integrated quadrupole gradient.

Figure 1: 3D drawing of the BC dipole model.

Figure 2: Field of the BC dipole half model.

Fieldmap Analysis

Nominally BC dipoles should deflect the beam in 4.2966 °. A 3D model of BC has been analyzed and approved. Fieldmap corresponding to one value for the control gap has been considered, namely 3.2 mm. A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

In order to take into account the s-dependent field profile of the BC dipoles a symmetric model was created with 15 segments at each side of the magnet. Their segmentation points were chosen in a way to minimize the difference between integrals of the squared profile between for the model and the field on the Runge-Kutta trajectory.

Figure 3: Field profile of segmented BC dipole model. Red curve corresponds to the field on Runge-Kutta trajectory.

Table 6: SI BC dipole segmented model.
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0010	0.018	-3.231	-0.001	-27.800
02	0.0040	0.072	-3.153	-0.005	-24.800
03	0.0050	0.080	-2.805	-0.021	-17.800
04	0.0050	0.068	-2.371	-0.027	-11.000
05	0.0050	0.058	-2.040	-0.027	-7.650
06	0.0100	0.096	-1.672	-0.026	-5.620
07	0.0100	0.074	-1.289	-0.026	-3.920
08	0.0100	0.056	-0.980	-0.025	-2.380
09	0.0100	0.044	-0.772	-0.021	-1.030
10	0.0320	0.116	-0.631	-0.023	+0.903
11	0.0320	0.097	-0.528	-0.148	+0.286
12	0.1600	0.625	-0.682	-0.888	+0.341
13	0.1600	0.628	-0.686	-0.903	+0.177
14	0.0120	0.043	-0.622	-0.874	+0.068
15	0.0140	0.033	-0.418	-0.434	-2.100
16	0.0160	0.019	-0.212	-0.107	-2.050
17	0.0350	0.020	-0.099	-0.019	-1.180

^* K=B'/(Bρ), S=B"/(2Bρ)

B1

Figure 4: 3D drawing of the B1 dipole model.

Figure 5: Field of the B1 dipole half model.

Fieldmap Analysis

Nominally B1 dipoles should deflect the beam in 2.7553 °. So far a preliminary 3D model of B1 has been analyzed and approved. Field map corresponding to the nominal excited field has been considered. The latest analyzed fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at accessed this folder.

Segmented Model

In order to take into account the s-dependent field profile of the B1 dipoles a symmetric model was created with 15 segments at each side of the magnet. Their segmentation points were chosen in a way to minimize the difference between integrals of the squared profile between for the model and the field on the Runge-Kutta trajectory.

Figure 6: Field profile of segmented B1 dipole model

Table 7: SI B1 dipole segmented model.
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0020	0.006	-0.562	-0.753	-0.297
02	0.0030	0.010	-0.562	-0.756	-0.245
03	0.0050	0.016	-0.564	-0.762	-0.117
04	0.0050	0.016	-0.566	-0.770	-0.015
05	0.0050	0.016	-0.567	-0.774	+0.004
06	0.0100	0.033	-0.568	-0.775	-0.003
07	0.0400	0.130	-0.567	-0.774	+0.019
08	0.1500	0.483	-0.563	-0.773	+0.055
09	0.1000	0.322	-0.563	-0.773	+0.076
10	0.0500	0.162	-0.565	-0.774	+0.008
11	0.0340	0.105	-0.540	-0.777	-0.159
12	0.0160	0.033	-0.363	-0.428	-2.230
13	0.0400	0.033	-0.143	-0.085	-1.960
14	0.0400	0.008	-0.034	-0.009	-0.428
15	0.0500	0.005	-0.016	-0.001	-0.102

^* K=B'/(Bρ), S=B"/(2Bρ)

B2

Figure 7: 3D drawing of the B2 dipole model.

Figure 8: Field of the B2 dipole half model.

Fieldmap Analysis

Nominally B1 dipoles should deflect the beam in 4.0964 °. So far a preliminary 3D model of B2 has been analyzed and approved. Field map corresponding to the nominal excited field has been considered. The latest analyzed fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at accessed this folder.

Segmented Model

In order to take into account the s-dependent field profile of the B2 dipoles a symmetric model was created with 17 segments at each side of the magnet. Their segmentation points were chosen in a way to minimize the difference between integrals of the squared profile between for the model and the field on the Runge-Kutta trajectory.

Figure 9: Field profile of segmented B2 dipole model

Table 8: SI B2 dipole segmented model.
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.1250	0.405	-0.566	-0.774	+0.045
02	0.0550	0.179	-0.569	-0.774	+0.028
03	0.0100	0.033	-0.570	-0.774	+0.018
04	0.0050	0.016	-0.568	-0.767	-0.019
05	0.0050	0.016	-0.566	-0.759	-0.150
06	0.0050	0.016	-0.565	-0.753	-0.268
07	0.0050	0.016	-0.566	-0.756	-0.195
08	0.0100	0.033	-0.568	-0.768	-0.011
09	0.0100	0.033	-0.570	-0.774	+0.022
10	0.1750	0.568	-0.567	-0.773	+0.081
11	0.1750	0.567	-0.566	-0.773	+0.107
12	0.0200	0.063	-0.553	-0.791	-0.030
13	0.0100	0.028	-0.480	-0.682	-0.204
14	0.0150	0.030	-0.345	-0.361	-2.440
15	0.0200	0.022	-0.192	-0.108	-2.480
16	0.0300	0.014	-0.084	-0.026	-1.220
17	0.0320	0.005	-0.029	-0.005	-0.359
18	0.0325	0.004	-0.022	-0.001	-0.149

^* K=B'/(Bρ), S=B"/(2Bρ)

SI Dipole Magnet Measurements

A summary of magnet field measurements of SI BC dipole. The Hall probe measurement files can be found at this folder.

BC

Analysis of BC hallprobe measurements. The analysis results can be found at this folder with subfolders x0-0p0079mm which contains results based on Runge-Kutta trajectory and x0-0p0079mm-reftraj holds the results based on reference trajectory. The initial x coordinate used was + 79um. The reference point is 7.703087 mm for reference trajectory.

Summary

rx position of reference point:     +7.703087 mm
initial rx position of trajectory:  +0.079092 mm
         /---------------------------------------------------------------------------------------\
         |       DeflectionAngle[deg]   |            KL[1/m]          |         SL[1/m²]         |
         |       Avg ± Std       MaxMin |      Avg ± Std      MaxMin  |     Avg ± Std     MaxMin |
/--------|------------------------------|-----------------------------|--------------------------|
| BC     |  +2.14829 ± 0.00016  0.00060 |  -0.3127 ± 0.0002   0.0008  |   -0.35 ± 0.074   0.24   |
| Diff[%]|  -0.00048 ± 0.00743  0.02801 |  -0.0554 ± 0.0595   0.2446  |   21.05 ± 16.75  54.60   |
\------------------------------------------------------------------------------------------------/

The values used to calculate the difference to model were:

Deflection angle: 2.1483 deg

KL: - 0.31267 1/m

SL: -0.35037 1/m²

Deflection Angle

Figure 10: Deflection angle calculated with reference trajectory, initial point at x = +79 um and the reference point is 7.703087mm.

Integrated Quadrupole

Figure 11: Integrated quadrupole calculated with reference trajectory, initial point at x = +79 um and the reference point is 7.703087mm.

Integrated Sextupole

Figure 12: Integrated sextupole calculated with reference trajectory, initial point at x = +79 um and the reference point is 7.703087mm.

B1

Analysis of B1 hallprobe measurements. The analysis results can be found at this folder with subfolders x0-8p527mm which contains results based on Runge-Kutta trajectory and x0-8p527mm-reftraj holds the results based on reference trajectory. The initial point of reference trajectory is 8.5270 mm and reference point is 13.6929 mm.

Summary

rx position of reference point:     +13.692930 mm
initial rx position of trajectory:  +8.527000 mm
         /---------------------------------------------------------------------------------------\
         |       DeflectionAngle[deg]   |            KL[1/m]          |         SL[1/m²]         |
         |       Avg ± Std       MaxMin |      Avg ± Std      MaxMin  |      Avg ± Std    MaxMin |
/--------|------------------------------|-----------------------------|--------------------------|
| B1     |  +1.37760 ± 0.00029  0.00103 |  -0.3228 ± 0.0002   0.0007  |   -0.096 ± 0.015   0.056 |
| Diff[%]|  -0.00354 ± 0.02085  0.07471 |  +0.0393 ± 0.0623   0.2133  |   +11.08 ± 13.95   52.17 |
\------------------------------------------------------------------------------------------------/

The values used to calculate the difference to model were:

Deflection angle: 1.37765 deg

KL: -0.32289 1/m

SL: -0.10763 1/m²

Deflection Angle

Figure 13: Deflection angle at current 403.6 A calculated with reference trajectory, initial point at x = 8.527 mm and reference point is 13.6929 mm.

Integrated Quadrupole

Figure 14: Integrated gradient at current 403.6 A calculated with reference trajectory, initial point at x = 8.527 mm and reference point is 13.6929 mm.

Integrated Sextupole

Figure 15: Integrated sextupole at current 403.6 A calculated with reference trajectory, initial point at x = 8.527 mm and reference point is 13.6929 mm.

B2

Analysis of B2 hallprobe measurements. The analysis results can be found at this folder with subfolders x0-8p153mm which contains results based on Runge-Kutta trajectory and x0-8p153mm-reftraj holds the results based on reference trajectory. The initial point of reference trajectory is 8.1530 mm and reference point is 19.4278 mm.

Summary

rx position of reference point:     +19.427847 mm
initial rx position of trajectory:  +8.153000 mm
         /---------------------------------------------------------------------------------------\
         |       DeflectionAngle[deg]   |            KL[1/m]          |         SL[1/m²]         |
         |       Avg ± Std       MaxMin |      Avg ± Std      MaxMin  |      Avg ± Std    MaxMin |
/--------|------------------------------|-----------------------------|--------------------------|
| B2     |  +2.04820 ± 0.00045  0.00146 |  -0.4794 ± 0.0003   0.0011  |   -0.096 ± 0.011   0.058 |
| Diff[%]|  -0.00011 ± 0.02175  0.07151 |  +0.0841 ± 0.0596   0.2288  |   +2.388 ± 11.45   58.42 |
\------------------------------------------------------------------------------------------------/

The values used to calculate the difference to model were:

Deflection angle: 2.0482 deg

KL: -0.47982 1/m

SL: -0.09868 1/m²

Deflection Angle

Figure 16: Deflection angle at current 401.8 A calculated with reference trajectory and initial point at x = 8.153 mm and reference point is 19.4278 mm.

Integrated Quadrupole

Figure 17: Integrated gradient at current 401.8 A calculated with reference trajectory and initial point at x = 8.153 mm and reference point is 19.4278 mm.

Integrated Sextupole

Figure 18: Integrated sextupole at current 401.8 A calculated with reference trajectory and initial point at x = 8.153 mm and reference point is 19.4278 mm.

SI Dipole Magnet Sorting

B1 Installation Order

Table 9: Storage Ring Dipoles B1 Installation.
Not Used
Magnet Name	Magnet Serial ID
SI-01C1:MA-B1	B1-025
SI-01C4:MA-B1	B1-040
SI-02C1:MA-B1	B1-003
SI-02C4:MA-B1	B1-031
SI-03C1:MA-B1	B1-029
SI-03C4:MA-B1	B1-038
SI-04C1:MA-B1	B1-004
SI-04C4:MA-B1	B1-005
SI-05C1:MA-B1	B1-024
SI-05C4:MA-B1	B1-016
SI-06C1:MA-B1	B1-012
SI-06C4:MA-B1	B1-030
SI-07C1:MA-B1	B1-018
SI-07C4:MA-B1	B1-011
SI-08C1:MA-B1	B1-033
SI-08C4:MA-B1	B1-013
SI-09C1:MA-B1	B1-015
SI-09C4:MA-B1	B1-042
SI-10C1:MA-B1	B1-021
SI-10C4:MA-B1	B1-019
SI-11C1:MA-B1	B1-043
SI-11C4:MA-B1	B1-009
SI-12C1:MA-B1	B1-036
SI-12C4:MA-B1	B1-034
SI-13C1:MA-B1	B1-020
SI-13C4:MA-B1	B1-010
SI-14C1:MA-B1	B1-027
SI-14C4:MA-B1	B1-002
SI-15C1:MA-B1	B1-023
SI-15C4:MA-B1	B1-014
SI-16C1:MA-B1	B1-035
SI-16C4:MA-B1	B1-032
SI-17C1:MA-B1	B1-039
SI-17C4:MA-B1	B1-017
SI-18C1:MA-B1	B1-028
SI-18C4:MA-B1	B1-037
SI-19C1:MA-B1	B1-006
SI-19C4:MA-B1	B1-046
SI-20C1:MA-B1	B1-041
SI-20C4:MA-B1	B1-026
Magnet Name	Magnet Serial ID
---	B1-022

B2 Installation Order

Table 10: Storage Ring Dipoles B2 Installation.
Not Used
Magnet Name	Magnet Serial ID
SI-01C2:MA-B2	B2-002
SI-01C3:MA-B2	B2-001
SI-02C2:MA-B2	B2-010
SI-02C3:MA-B2	B2-011
SI-03C2:MA-B2	B2-017
SI-03C3:MA-B2	B2-014
SI-04C2:MA-B2	B2-032
SI-04C3:MA-B2	B2-043
SI-05C2:MA-B2	B2-022
SI-05C3:MA-B2	B2-045
SI-06C2:MA-B2	B2-004
SI-06C3:MA-B2	B2-015
SI-07C2:MA-B2	B2-023
SI-07C3:MA-B2	B2-037
SI-08C2:MA-B2	B2-008
SI-08C3:MA-B2	B2-013
SI-09C2:MA-B2	B2-019
SI-09C3:MA-B2	B2-030
SI-10C2:MA-B2	B2-033
SI-10C3:MA-B2	B2-007
SI-11C2:MA-B2	B2-042
SI-11C3:MA-B2	B2-016
SI-12C2:MA-B2	B2-034
SI-12C3:MA-B2	B2-018
SI-13C2:MA-B2	B2-036
SI-13C3:MA-B2	B2-038
SI-14C2:MA-B2	B2-021
SI-14C3:MA-B2	B2-005
SI-15C2:MA-B2	B2-006
SI-15C3:MA-B2	B2-029
SI-16C2:MA-B2	B2-003
SI-16C3:MA-B2	B2-027
SI-17C2:MA-B2	B2-040
SI-17C3:MA-B2	B2-044
SI-18C2:MA-B2	B2-031
SI-18C3:MA-B2	B2-028
SI-19C2:MA-B2	B2-026
SI-19C3:MA-B2	B2-025
SI-20C2:MA-B2	B2-046
SI-20C3:MA-B2	B2-009
Magnet Name	Magnet Serial ID
---	B2-024

Storage Ring Quadrupoles

There will be three types of quadrupole magnets in the Sirius lattice: Q14, Q20 and Q30, labeled as such according to their hard-edge lengths in simulations. Magnets from families QDA, QDB1, QDB2, QDP1 and QDP2 will be of type Q14; magnets from families QFA, Q1, Q2, Q3 and Q4 will be of type Q20; and magnets from families QFB and QFP will be of type Q30.

SI Quadrupole Magnet Specifications

Main Parameters

Table 11 lists main specifications for the quadrupoles.

Table 11: Storage ring quadrupole magnets specification
	Q14	Q20	Q30	units
Number of magnets	70	170	30
Magnetic length ¹	0.140	0.200	0.300	m
Maximum strength ¹	3.72	4.54	4.54	m^-2
Bore diameter	28	28	28	mm
Field flexibility for individual quadrupole ²	± 10	± 5	± 5	%
Maximum integrated strength ³	0.5208	0.908	1.362	m^-1
Maximum integrated field gradient ³	5.21	9.09	13.63	T
Maximum field gradient ³	37.23	45.43	45.43	T·m^-1
Maximum field at pole tip ³	0.52	0.64	0.64	T

¹ Maximum values required for excitation with the main coils only.

² Obtained with trim coils.

³ Derived parameters from base specification parameters.

Electric parameters

Table 12: Storage ring quadrupole electric parameters
	Q14	Q20	Q30	units
Main coil current	146.60	154.66	153.80	A
Main coil number of turns	20.00	23.25	23.25
Maximum trim coil current	10.00	10.00	10.00	A
Trim coil number of turns	28.00	18.00	18.00
Stored magnetic energy	72.45	140.33	211.01	J
Magnet inductance	6.74	11.73	17.84	mH

Multipole Errors

Table 13: Storage ring quadrupole multipole errors. Contribution of multipolar components relative to main quadrupolar field at x = 12 mm. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
Multipole error	Q14 Systematic Normal	Q20 Systematic Normal	Q30 Systematic Normal	Random
Multipole error	Q14 Systematic Normal	Q20 Systematic Normal	Q30 Systematic Normal	Normal	Skew
B₂/B₁ (sextupole)				1.5×10^-4	0.5×10^-4
B₃/B₁ (octupole)				1.5×10^-4	0.5×10^-4
B₄/B₁ (decapole)				1.5×10^-4	0.5×10^-4
B₅/B₁ (12-pole)	-3.9×10^-4	-4.1×10^-4	-4.3×10^-4	1.5×10^-4	0.5×10^-4
B₉/B₁ (20-pole)	+1.7×10^-3	+1.7×10^-3	+1.8×10^-3
B₁₃/B₁ (20-pole)	-8.0×10^-4	-7.7×10^-4	-8.1×10^-4
B₁₇/B₁ (20-pole)	+8.5×10^-5	+5.9×10^-5	+7.2×10^-5

Alignment and Excitation Errors

Table 14: Maximum absolute value of random alignment and excitation errors for the Storage Ring Quadrupoles. The errors are generated with a Gaussian distribution truncated at ±1σ.
	Quadrupoles
Transverse position, $\text{[math]}$ , $\text{[math]}$	40	μm
Rotation around longitudinal axis	0.30	mrad
Strength error (static or low frequency)	0.05	%

SI Quadrupole Magnet 3D Models

All three types of quadrupoles models, namely Q14, Q20 and Q30 quadrupoles, have been designed, analyzed and approved.

Figure 19: 3D drawing of the Q14 quadrupole model.

Figure 20: Field of the Q14 quadrupole model.

Figure 21: 3D drawing of the Q20 quadrupole model.

Figure 22: Field of the Q20 quadrupole model.

Figure 23: 3D drawing of the Q30 quadrupole model.

Figure 24: Field of the Q30 quadrupole model.

Fieldmap Analysis

Q14

The 3D magnetic model of Q14 has been analyzed and approved, corresponding to maximum quadrupole strength, both family and trim coils excited. Analysis data for the latest model fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at this folder.

Q20

The 3D magnetic model of Q20 has been analyzed and approved, corresponding to maximum quadrupole strength, both family and trim coils excited. Analysis data for the latest model fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at this folder.

Q30

The 3D magnetic model of Q30 has been analyzed and approved, corresponding to maximum quadrupole strength, both family and trim coils excited. Analysis data for the latest model fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at this folder.

Table 15 brings the main fieldmap analysis results.

Table 15: Storage ring quadrupole magnet 3D-model parameters
	Q14	Q20	Q30	units
Physical length ¹	0.1255	0.1865	0.2890	m
Magnetic length ²	0.1401	0.2001	0.3003	m
Maximum main coil current	160 / 3040	150 / 3600	150 / 3600	A / A.turns
Maximum trim coil current	10 / 180	10 / 180	10 / 180	A / A.turns
Maximum integrated field gradient	5.730	9.611	14.44	T
Relative multipole (n=5) ³	-2.7×10^-4	-3.2×10^-4	-4.4×10^-4
Relative multipole (n=9) ³	+1.5×10^-3	+1.7×10^-3	+1.8×10^-3
Relative multipole (n=13) ³	-6.3×10^-4	-6.5×10^-4	-6.7×10^-4

¹ with end plates but without coils.

² integrated gradient divided by gradient at longitudinal center.

³ normal integrated multipoles divided by integrated quadrupole at x = 11.7 mm.

Segmented Model

Currently the hard-edge approximation is being used to model all quadrupoles for beam dynamics calculations purposes.

Figure 25: Quadrupole strength profile of Q14. Red curve corresponds to the strength on Runge-Kutta trajectory.

Table 16: SI quadrupole Q14 half segmented model (maximum strength).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0700	0.000	-0.000e+00	-4.090e+00	-0.000e+00

^* K=B'/(Bρ), S=B"/(2Bρ)

Figure 26: Quadrupole strength profile of Q20. Red curve corresponds to the strength on Runge-Kutta trajectory.

Table 17: SI quadrupole Q20 half segmented model (maximum strength).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.1000	0.000	-0.000e+00	-4.800e+00	-0.000e+00

^* K=B'/(Bρ), S=B"/(2Bρ)

Figure 27: Quadrupole strength profile of Q30. Red curve corresponds to the strength on Runge-Kutta trajectory.

Table 18: SI quadrupole Q30 half segmented model (maximum strength).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.1500	0.000	-0.000e+00	-4.810e+00	-0.000e+00

^* K=B'/(Bρ), S=B"/(2Bρ)

SI Quadrupole Magnet Measurements

A summary of magnet field measurements of SI quadrupoles.

Q14

Summary

         /-------------------------------------------------------------------------------------------------\
         |          IntQuad[T]        |       XCenter[um]    |        YCenter[um]    |    RollError[mrad]  |
         |      Avg ± Std     MaxMin  |   Avg ± Std  MaxMin  |    Avg ± Std  MaxMin  |   Avg ± Std  MaxMin |
/--------|----------------------------|----------------------|-----------------------|---------------------|
| QDA    |  +5.2405 ± 0.0024  0.0074  |  -0.1 ± 5.4   20.3   |   +5.6 ± 4.3   13.4   |  -0.4 ± 0.1   0.2   |
| QDB1   |  +5.2373 ± 0.0030  0.0125  |  +2.0 ± 5.7   24.9   |   +3.5 ± 5.2   24.6   |  -0.3 ± 0.1   0.4   |
| QDB2   |  +5.2338 ± 0.0013  0.0044  |  +0.1 ± 7.3   28.0   |   +3.4 ± 4.2   15.6   |  -0.3 ± 0.1   0.6   |
| QDP1   |  +5.2365 ± 0.0021  0.0070  |  +4.7 ± 5.5   17.8   |   +3.6 ± 3.2   11.4   |  -0.4 ± 0.1   0.2   |
| QDP2   |  +5.2365 ± 0.0012  0.0042  |  -2.1 ± 5.4   15.6   |   +4.5 ± 5.3   17.9   |  -0.4 ± 0.1   0.3   |
\----------------------------------------------------------------------------------------------------------/

Integrated Quadrupole

Figure 28: Integrated quadrupole strengths of Q14 magnets.

Horizontal Magnetic Center

Figure 29: Horizontal magnet center of Q14 magnets.

Vertical Magnetic Center

Figure 30: Vertical magnet center of Q14 magnets.

Roll-Angle Error

Figure 31: Roll angle error of Q14 magnets.

Q20

Summary

          .--------------------------------------------------------------------------------------------------.
          |          IntQuad[T]        |       XCenter[um]     |        YCenter[um]    |    RollError[mrad]  |
          |      Avg ± Std     MaxMin  |   Avg ± Std  MaxMin   |    Avg ± Std  MaxMin  |   Avg ± Std  MaxMin |
. --------|----------------------------|-----------------------|-----------------------|---------------------|
| QFA     |  -9.0805 ± 0.0047  0.0173  |  +8.4 ± 3.0   10.2    |   +6.8 ± 5.6   16.0   |  +0.0 ± 0.1   0.4   |
| Q1      |  -9.0995 ± 0.0071  0.0278  |  +5.7 ± 6.6   30.4    |   +3.8 ± 5.0   22.4   |  +0.1 ± 0.1   0.5   |
| Q2      |  -9.0855 ± 0.0042  0.0160  |  +7.1 ± 5.1   22.0    |   +4.0 ± 5.5   28.5   |  +0.1 ± 0.1   0.4   |
| Q3      |  -9.0883 ± 0.0057  0.0235  |  +6.5 ± 5.9   25.5    |   +4.0 ± 6.6   31.4   |  +0.0 ± 0.1   0.3   |
| Q4      |  -9.0790 ± 0.0059  0.0236  |  +7.8 ± 5.5   26.2    |   +3.5 ± 4.4   20.8   |  +0.1 ± 0.1   0.4   |
.------------------------------------------------------------------------------------------------------------.

Integrated Quadrupole

Figure 32: Integrated quadrupole strengths of Q20 magnets.

Horizontal Magnetic Center

Figure 33: Horizontal magnet center of Q20 magnets.

Vertical Magnetic Center

Figure 34: Vertical magnet center of Q20 magnets.

Roll-Angle Error

Figure 35: Roll angle error of Q20 magnets.

Q30

Summary

          .-----------------------------------------------------------------------------------------------------.
          |          IntQuad[T]        |       XCenter[um]     |       YCenter[um]      |    RollError[mrad]    |
          |      Avg ± Std     MaxMin  |   Avg ± Std   MaxMin  |    Avg ± Std   MaxMin  |   Avg ± Std  MaxMin   |
. --------|----------------------------|-----------------------|------------------------|-----------------------|
| QFB     | -13.6385 ± 0.0050  0.0215  |  +0.6 ± 7.1    28.9   |   -1.8 ± 4.5    18.0   |  -0.3 ± 0.05  0.2     |
| QFP     | -13.6295 ± 0.0038  0.0127  |  -4.2 ± 5.1    18.8   |   -2.8 ± 4.0    13.2   |  -0.2 ± 0.1   0.3     |
.---------------------------------------------------------------------------------------------------------------.

Integrated Quadrupole

Figure 36: Integrated quadrupole strengths of Q30 magnets.

Horizontal Magnetic Center

Figure 37: Horizontal magnet center of Q30 magnets.

Vertical Magnetic Center

Figure 38: Vertical magnet center of Q30 magnets.

Roll-Angle Error

Figure 39: Roll angle error of Q30 magnets.

SI Quadrupole Magnet Sorting

Q14 Installation Order

Table 19: Storage Ring Quadrupoles Q14 Installation.
QDA
Magnet Name	Magnet Serial ID
SI-01M2:MA-QDA	Q14-081
SI-05M1:MA-QDA	Q14-077
SI-05M2:MA-QDA	Q14-028
SI-09M1:MA-QDA	Q14-059
SI-09M2:MA-QDA	Q14-062
SI-13M1:MA-QDA	Q14-058
SI-13M2:MA-QDA	Q14-040
SI-17M1:MA-QDA	Q14-034
SI-17M2:MA-QDA	Q14-068
SI-01M1:MA-QDA	Q14-018
QDB1
Magnet Name	Magnet Serial ID
SI-02M1:MA-QDB1	Q14-010
SI-02M2:MA-QDB1	Q14-017
SI-04M1:MA-QDB1	Q14-011
SI-04M2:MA-QDB1	Q14-008
SI-06M1:MA-QDB1	Q14-023
SI-06M2:MA-QDB1	Q14-035
SI-08M1:MA-QDB1	Q14-048
SI-08M2:MA-QDB1	Q14-075
SI-10M1:MA-QDB1	Q14-021
SI-10M2:MA-QDB1	Q14-055
SI-12M1:MA-QDB1	Q14-014
SI-12M2:MA-QDB1	Q14-033
SI-14M1:MA-QDB1	Q14-026
SI-14M2:MA-QDB1	Q14-067
SI-16M1:MA-QDB1	Q14-057
SI-16M2:MA-QDB1	Q14-027
SI-18M1:MA-QDB1	Q14-079
SI-18M2:MA-QDB1	Q14-009
SI-20M1:MA-QDB1	Q14-025
SI-20M2:MA-QDB1	Q14-053
QDB2
Magnet Name	Magnet Serial ID
SI-02M1:MA-QDB2	Q14-039
SI-02M2:MA-QDB2	Q14-050
SI-04M1:MA-QDB2	Q14-038
SI-04M2:MA-QDB2	Q14-020
SI-06M1:MA-QDB2	Q14-045
SI-06M2:MA-QDB2	Q14-047
SI-08M1:MA-QDB2	Q14-064
SI-08M2:MA-QDB2	Q14-046
SI-10M1:MA-QDB2	Q14-032
SI-10M2:MA-QDB2	Q14-030
SI-12M1:MA-QDB2	Q14-065
SI-12M2:MA-QDB2	Q14-056
SI-14M1:MA-QDB2	Q14-049
SI-14M2:MA-QDB2	Q14-054
SI-16M1:MA-QDB2	Q14-063
SI-16M2:MA-QDB2	Q14-004
SI-18M1:MA-QDB2	Q14-015
SI-18M2:MA-QDB2	Q14-066
SI-20M1:MA-QDB2	Q14-060
SI-20M2:MA-QDB2	Q14-052
QDP1
Magnet Name	Magnet Serial ID
SI-03M1:MA-QDP1	Q14-069
SI-03M2:MA-QDP1	Q14-072
SI-07M1:MA-QDP1	Q14-019
SI-07M2:MA-QDP1	Q14-031
SI-11M1:MA-QDP1	Q14-041
SI-11M2:MA-QDP1	Q14-070
SI-15M1:MA-QDP1	Q14-051
SI-15M2:MA-QDP1	Q14-042
SI-19M1:MA-QDP1	Q14-029
SI-19M2:MA-QDP1	Q14-061
QDP2
Magnet Name	Magnet Serial ID
SI-03M1:MA-QDP2	Q14-012
SI-03M2:MA-QDP2	Q14-005
SI-07M1:MA-QDP2	Q14-078
SI-07M2:MA-QDP2	Q14-071
SI-11M1:MA-QDP2	Q14-007
SI-11M2:MA-QDP2	Q14-006
SI-15M1:MA-QDP2	Q14-073
SI-15M2:MA-QDP2	Q14-016
SI-19M1:MA-QDP2	Q14-037
SI-19M2:MA-QDP2	Q14-002
Not Used
Magnet Name	Magnet Serial ID
---	Q14-044
---	Q14-074
---	Q14-043
---	Q14-013
---	Q14-024
---	Q14-076
---	Q14-080
---	Q14-036

Q20 Installation Order

Table 20: Storage Ring Quadrupoles Q20 Installation.
QFA
Magnet Name	Magnet Serial ID
SI-01M2:MA-QFA	Q20-076
SI-05M1:MA-QFA	Q20-079
SI-05M2:MA-QFA	Q20-176
SI-09M1:MA-QFA	Q20-074
SI-09M2:MA-QFA	Q20-101
SI-13M1:MA-QFA	Q20-162
SI-13M2:MA-QFA	Q20-155
SI-17M1:MA-QFA	Q20-095
SI-17M2:MA-QFA	Q20-071
SI-01M1:MA-QFA	Q20-049
Q1
Magnet Name	Magnet Serial ID
SI-01C1:MA-Q1	Q20-030
SI-01C4:MA-Q1	Q20-132
SI-02C1:MA-Q1	Q20-013
SI-02C4:MA-Q1	Q20-014
SI-03C1:MA-Q1	Q20-027
SI-03C4:MA-Q1	Q20-008
SI-04C1:MA-Q1	Q20-029
SI-04C4:MA-Q1	Q20-023
SI-05C1:MA-Q1	Q20-149
SI-05C4:MA-Q1	Q20-028
SI-06C1:MA-Q1	Q20-036
SI-06C4:MA-Q1	Q20-033
SI-07C1:MA-Q1	Q20-020
SI-07C4:MA-Q1	Q20-015
SI-08C1:MA-Q1	Q20-125
SI-08C4:MA-Q1	Q20-153
SI-09C1:MA-Q1	Q20-025
SI-09C4:MA-Q1	Q20-067
SI-10C1:MA-Q1	Q20-035
SI-10C4:MA-Q1	Q20-141
SI-11C1:MA-Q1	Q20-119
SI-11C4:MA-Q1	Q20-012
SI-12C1:MA-Q1	Q20-111
SI-12C4:MA-Q1	Q20-006
SI-13C1:MA-Q1	Q20-164
SI-13C4:MA-Q1	Q20-024
SI-14C1:MA-Q1	Q20-010
SI-14C4:MA-Q1	Q20-032
SI-15C1:MA-Q1	Q20-011
SI-15C4:MA-Q1	Q20-005
SI-16C1:MA-Q1	Q20-039
SI-16C4:MA-Q1	Q20-109
SI-17C1:MA-Q1	Q20-016
SI-17C4:MA-Q1	Q20-009
SI-18C1:MA-Q1	Q20-026
SI-18C4:MA-Q1	Q20-037
SI-19C1:MA-Q1	Q20-038
SI-19C4:MA-Q1	Q20-017
SI-20C1:MA-Q1	Q20-007
SI-20C4:MA-Q1	Q20-021
Q2
Magnet Name	Magnet Serial ID
SI-01C1:MA-Q2	Q20-096
SI-01C4:MA-Q2	Q20-034
SI-02C1:MA-Q2	Q20-092
SI-02C4:MA-Q2	Q20-122
SI-03C1:MA-Q2	Q20-136
SI-03C4:MA-Q2	Q20-174
SI-04C1:MA-Q2	Q20-056
SI-04C4:MA-Q2	Q20-059
SI-05C1:MA-Q2	Q20-128
SI-05C4:MA-Q2	Q20-115
SI-06C1:MA-Q2	Q20-126
SI-06C4:MA-Q2	Q20-158
SI-07C1:MA-Q2	Q20-073
SI-07C4:MA-Q2	Q20-087
SI-08C1:MA-Q2	Q20-137
SI-08C4:MA-Q2	Q20-082
SI-09C1:MA-Q2	Q20-050
SI-09C4:MA-Q2	Q20-117
SI-10C1:MA-Q2	Q20-105
SI-10C4:MA-Q2	Q20-124
SI-11C1:MA-Q2	Q20-120
SI-11C4:MA-Q2	Q20-118
SI-12C1:MA-Q2	Q20-134
SI-12C4:MA-Q2	Q20-135
SI-13C1:MA-Q2	Q20-068
SI-13C4:MA-Q2	Q20-098
SI-14C1:MA-Q2	Q20-072
SI-14C4:MA-Q2	Q20-175
SI-15C1:MA-Q2	Q20-178
SI-15C4:MA-Q2	Q20-104
SI-16C1:MA-Q2	Q20-046
SI-16C4:MA-Q2	Q20-154
SI-17C1:MA-Q2	Q20-167
SI-17C4:MA-Q2	Q20-094
SI-18C1:MA-Q2	Q20-062
SI-18C4:MA-Q2	Q20-102
SI-19C1:MA-Q2	Q20-131
SI-19C4:MA-Q2	Q20-138
SI-20C1:MA-Q2	Q20-065
SI-20C4:MA-Q2	Q20-152
Q3
Magnet Name	Magnet Serial ID
SI-01C2:MA-Q3	Q20-066
SI-01C3:MA-Q3	Q20-061
SI-02C2:MA-Q3	Q20-091
SI-02C3:MA-Q3	Q20-004
SI-03C2:MA-Q3	Q20-147
SI-03C3:MA-Q3	Q20-114
SI-04C2:MA-Q3	Q20-112
SI-04C3:MA-Q3	Q20-165
SI-05C2:MA-Q3	Q20-107
SI-05C3:MA-Q3	Q20-019
SI-06C2:MA-Q3	Q20-179
SI-06C3:MA-Q3	Q20-106
SI-07C2:MA-Q3	Q20-148
SI-07C3:MA-Q3	Q20-108
SI-08C2:MA-Q3	Q20-070
SI-08C3:MA-Q3	Q20-159
SI-09C2:MA-Q3	Q20-121
SI-09C3:MA-Q3	Q20-045
SI-10C2:MA-Q3	Q20-042
SI-10C3:MA-Q3	Q20-130
SI-11C2:MA-Q3	Q20-161
SI-11C3:MA-Q3	Q20-075
SI-12C2:MA-Q3	Q20-127
SI-12C3:MA-Q3	Q20-022
SI-13C2:MA-Q3	Q20-145
SI-13C3:MA-Q3	Q20-133
SI-14C2:MA-Q3	Q20-172
SI-14C3:MA-Q3	Q20-129
SI-15C2:MA-Q3	Q20-018
SI-15C3:MA-Q3	Q20-142
SI-16C2:MA-Q3	Q20-139
SI-16C3:MA-Q3	Q20-113
SI-17C2:MA-Q3	Q20-140
SI-17C3:MA-Q3	Q20-170
SI-18C2:MA-Q3	Q20-110
SI-18C3:MA-Q3	Q20-044
SI-19C2:MA-Q3	Q20-086
SI-19C3:MA-Q3	Q20-177
SI-20C2:MA-Q3	Q20-031
SI-20C3:MA-Q3	Q20-064
Q4
Magnet Name	Magnet Serial ID
SI-01C2:MA-Q4	Q20-081
SI-01C3:MA-Q4	Q20-097
SI-02C2:MA-Q4	Q20-051
SI-02C3:MA-Q4	Q20-168
SI-03C2:MA-Q4	Q20-166
SI-03C3:MA-Q4	Q20-043
SI-04C2:MA-Q4	Q20-080
SI-04C3:MA-Q4	Q20-047
SI-05C2:MA-Q4	Q20-163
SI-05C3:MA-Q4	Q20-048
SI-06C2:MA-Q4	Q20-103
SI-06C3:MA-Q4	Q20-116
SI-07C2:MA-Q4	Q20-089
SI-07C3:MA-Q4	Q20-077
SI-08C2:MA-Q4	Q20-093
SI-08C3:MA-Q4	Q20-063
SI-09C2:MA-Q4	Q20-100
SI-09C3:MA-Q4	Q20-054
SI-10C2:MA-Q4	Q20-156
SI-10C3:MA-Q4	Q20-169
SI-11C2:MA-Q4	Q20-057
SI-11C3:MA-Q4	Q20-058
SI-12C2:MA-Q4	Q20-090
SI-12C3:MA-Q4	Q20-150
SI-13C2:MA-Q4	Q20-144
SI-13C3:MA-Q4	Q20-085
SI-14C2:MA-Q4	Q20-052
SI-14C3:MA-Q4	Q20-069
SI-15C2:MA-Q4	Q20-123
SI-15C3:MA-Q4	Q20-084
SI-16C2:MA-Q4	Q20-143
SI-16C3:MA-Q4	Q20-171
SI-17C2:MA-Q4	Q20-053
SI-17C3:MA-Q4	Q20-157
SI-18C2:MA-Q4	Q20-078
SI-18C3:MA-Q4	Q20-146
SI-19C2:MA-Q4	Q20-060
SI-19C3:MA-Q4	Q20-160
SI-20C2:MA-Q4	Q20-173
SI-20C3:MA-Q4	Q20-083
Not Used
Magnet Name	Magnet Serial ID
---	Q20-041
---	Q20-088
---	Q20-040
---	Q20-055
---	Q20-099

Q30 Installation Order

Table 21: Storage Ring Quadrupoles Q30 Installation.
QFB
Magnet Name	Magnet Serial ID
SI-02M1:MA-QFB	Q30-016
SI-02M2:MA-QFB	Q30-032
SI-04M1:MA-QFB	Q30-010
SI-04M2:MA-QFB	Q30-019
SI-06M1:MA-QFB	Q30-008
SI-06M2:MA-QFB	Q30-036
SI-08M1:MA-QFB	Q30-011
SI-08M2:MA-QFB	Q30-035
SI-10M1:MA-QFB	Q30-009
SI-10M2:MA-QFB	Q30-020
SI-12M1:MA-QFB	Q30-029
SI-12M2:MA-QFB	Q30-014
SI-14M1:MA-QFB	Q30-013
SI-14M2:MA-QFB	Q30-024
SI-16M1:MA-QFB	Q30-005
SI-16M2:MA-QFB	Q30-021
SI-18M1:MA-QFB	Q30-025
SI-18M2:MA-QFB	Q30-030
SI-20M1:MA-QFB	Q30-023
SI-20M2:MA-QFB	Q30-022
QFP
Magnet Name	Magnet Serial ID
SI-03M1:MA-QFP	Q30-033
SI-03M2:MA-QFP	Q30-027
SI-07M1:MA-QFP	Q30-017
SI-07M2:MA-QFP	Q30-006
SI-11M1:MA-QFP	Q30-026
SI-11M2:MA-QFP	Q30-034
SI-15M1:MA-QFP	Q30-015
SI-15M2:MA-QFP	Q30-031
SI-19M1:MA-QFP	Q30-007
SI-19M2:MA-QFP	Q30-004
Not Used
Magnet Name	Magnet Serial ID
---	Q30-018
---	Q30-012
---	Q30-028

Storage Ring Sextupoles, Slow Orbit Correctors and Skew Quadrupoles

Sextupole magnets in Sirius are designed to be multifunctional: apart from providing sextupolar field for chromaticity correction and dynamical aperture optimization, they also provide horizontal and vertical slow dipolar correctors for steering the beam orbit, as well as skew quadrupolar field to correct linear coupling introduced by lattice errors. These functions are implemented as additional excitations coils in the magnets. A sextupole magnet with excitation coils for vertical and/or horizontal dipolar fields does not have coils for skew quadrupolar fields, and vice-versa.

SI Sextupole Magnet Specifications

Main Parameters

Table 22 lists main specifications for the strength of the sextupole magnets.

Table 22: Storage ring sextupole strength specifications.
Number of magnets	280
Magnetic length	0.15	m
Bore diameter	28	mm
Maximum sextupolar strength	240	m^-3
Maximum integrated sextupolar strength, ∫S.ds	36	m^-2
Maximum integrated sextupolar field gradient, ∫B"/2.ds	360.2	T·m^-1
Maximum sextupole field gradient	2402	T·m^-2
Maximum sextupolar field at pole tip	0.47	T

Table 23 lists main specifications for the orbit-corrector in the sextupole magnets.

Table 23: Storage ring orbit corrector specifications.
Coils	CH	CV
Number of correctors	120	160
Sextupole families with correctors	SDA0, SFB0, SFP0, SDx1, SFx2	SDA0, SFB0, SFP0, SDx1, SDx3, SFx2(C3)
Maximum kick angle	390	405	μrad
Maximum integrated dipolar field	0.00390	0.00405	T·m
Maximum dipolar field	0.0260	0.0270	T

Table 24 lists main specifications for the skew quadrupoles in the sextupole magnets.

Table 24: Storage ring skew quadrupole specifications.
Coil	QS
Number	80 (+ 10 QS in fast corrector)
Sextupole families with skew quadrupoles	SFA0, SDB0, SDP0, SDx2(C1), SDx3(C3)
Maximum skew quadrupolar strength ¹	0.0667	m^-2
Maximum integrated skew quadrupolar strength	0.0100	m^-1
Maximum integrated skew quadrupolar gradient	0.100	T

¹ Maximum value needed to correct linear coupling introduced by magnet alignment errors. Coupling introduced by IDs will be corrected using local skew quadrupoles.

Electric parameters

Table 25: Storage ring sextupole electric parameters
	S15	units
Main coil current	158.48	A
Main coil number of turns	11.25
Maximum CH coil current	10.00	A
CH coil number of turns	14 / 28
Maximum CV coil current	10.00	A
CV coil number of turns	28
QS coil current¹	4.30	A
QS coil number of turns	28
Stored magnetic energy	61.57	J
Magnet inductance	4.90	mH

¹ Value required to reach the specified skew quadrupolar strength.

Multipole Errors

Multipole errors from sextupolar excitation

Table 26: Storage ring sextupole multipole errors. Contribution of multipolar components relative to main sextupolar field at x = 12 mm. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
Multipole error	Systematic (normal)	Random
Multipole error	Systematic (normal)	Normal	Skew
B₃/B₂ (octupole)		7.0×10^-4	5.0×10^-4
B₄/B₂ (decapole)	-7.0×10^-5	5.0×10^-4	5.0×10^-4
B₅/B₂ (12-pole)		4.0×10^-4	5.0×10^-5
B₆/B₂ (14-pole)	-1.4×10^-4	2.0×10^-4	5.0×10^-5
B₈/B₂ (18-pole)	-2.4×10^-3
B₁₄/B₂ (30-pole)	+1.4×10^-3

¹ These spec values have been updated in 2018-04-23 after rotating coil measurements. They have been validated by beam dynamics calculations.

Multipole errors from slow horizontal corrector excitation

Table 27: Storage ring horizontal corrector magnet multipole errors. Contribution of multipolar components relative to main dipolar field at x = 12 mm. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
Multipole error	Systematic (normal)	Random
Multipole error	Systematic (normal)	Normal	Skew
B₄/B₀ (decapole)	+3.1×10^-1
B₆/B₀ (14-pole)	+3.3×10^-2
B₈/B₀ (18-pole)	-4.8×10^-2
B₁₀/B₀ (22-pole)	+1.4×10^-2

Multipole errors from slow vertical corrector excitation

Table 28: Storage ring vertical corrector magnet multipole errors. Contribution of multipolar components relative to main dipolar field at x = 12 mm. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
Multipole error	Systematic (skew)	Random
Multipole error	Systematic (skew)	Normal	Skew
B₄/B₀ (decapole)	-2.9×10^-1
B₆/B₀ (14-pole)	-3.5×10^-3
B₈/B₀ (18-pole)	+5.5×10^-2
B₁₀/B₀ (22-pole)	-1.1×10^-2

Multipole errors from skew quadrupole excitation

Table 29: Storage ring skew quadrupoles multipole errors. Contribution of multipolar components relative to main quadrupolar field at x = 12 mm. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
Multipole error	Systematic (skew)	Random
Multipole error	Systematic (skew)	Normal	Skew
B₃/B₁ (octupole)	-5.8×10^-1
B₇/B₁ (16-pole)	+2.7×10^-3
B₉/B₁ (20-pole)	+8.0×10^-3
B₁₃/B₁ (28-pole)	+2.4×10^-3

Alignment and Excitation Errors

Table 30: Maximum absolute value of random alignment and excitation errors for the Storage Ring Sextupoles. The errors are generated with a Gaussian distribution truncated at ±1σ.
	Sextupoles
Transverse position, $\text{[math]}$ , $\text{[math]}$	40	μm
Rotation around longitudinal axis	0.30	mrad
Strength error (static or low frequency)	0.05	%

SI Sextupole Magnet 3D Models

Figure 40: 3D drawing of the sextupole (with dipolar field coils) quadrupole model.

Figure 41: Field of the quadrupole (with dipolar field coils) half model.

Fieldmap Analysis

A 3D model of multifunctional sextupole magnet has been analyzed and approved. Fieldmap analysis for each function has been performed with maximum excitation currents, when residual multipoles are expected to be worse. For the analysis of horizontal and vertical orbit corrector fields, as well as for the skew quadrupole corrector field, the sextupolar function was also excited in order to guarantee fast convergence of the magnetic solution.

Sextupolar function

The latest analyzed fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at this folder.

Sextupolar+Horizontal functions

The latest analyzed fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at this folder.

Sextupolar+Vertical functions

The latest analyzed fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at this folder.

Sextupolar+Skew functions

The latest analyzed fieldmap can be accessed here. A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

Currently the hard-edge approximation is being used to model sextupoles for beam dynamics calculations purposes.

Figure 42: Strength profile of SI sextupole model

Table 31: SI sextupole half segmented model (maximum strength).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0750	0.000	-0.000e+00	+0.000e+00	+2.470e+02

^* K=B'/(Bρ), S=B"/(2Bρ)

SI Sextupole Magnet Measurements

A summary of magnet field measurements of SI S15 sextupoles.

Summary

       /-------------------------------------------------------------------------------------------\
       |      IntSext[(T/m)/A]     |     XCenter[um]   |    YCenter[um]    |    RollError[mrad]    |
       |    Avg ± Std     MaxMin   | Avg ± Std  MaxMin | Avg ± Std  MaxMin |   Avg ± Std    MaxMin |
/------|---------------------------|-------------------|-------------------|-----------------------|
| SDA0 | -2.2551 ± 0.00060 0.00166 | +11.2 ± 7.5  27.8 | +27.2 ± 6.3  21.0 | -0.022 ± 0.051  0.157 |
| SFA0 | -2.2555 ± 0.00038 0.00128 | +15.3 ± 5.0  16.6 | +22.6 ± 4.1  12.5 | +0.173 ± 0.076  0.266 |
| SDB0 | -2.2514 ± 0.00065 0.00226 | +14.5 ± 6.0  26.1 | +22.7 ± 4.6  18.3 | +0.165 ± 0.037  0.145 |
| SFB0 | -2.2488 ± 0.00079 0.00302 | +20.3 ± 7.8  27.7 | +27.8 ± 4.9  24.9 | +0.059 ± 0.058  0.239 |
| SDP0 | -2.2525 ± 0.00014 0.00046 | +12.1 ± 4.9  15.1 | +25.2 ± 4.6  13.7 | +0.074 ± 0.032  0.096 |
| SFP0 | -2.2543 ± 0.00033 0.00120 | +16.1 ± 6.9  24.1 | +23.6 ± 5.6  17.9 | +0.160 ± 0.050  0.193 |
| SDA1 | -2.2467 ± 0.00033 0.00111 | +10.2 ± 6.2  21.1 | +25.6 ± 4.8  14.9 | +0.175 ± 0.022  0.081 |
| SFA1 | -2.2332 ± 0.00035 0.00126 | +11.9 ± 2.9  10.6 | +23.0 ± 4.3  13.8 | +0.116 ± 0.023  0.069 |
| SDB1 | -2.2545 ± 0.00053 0.00181 | +11.3 ± 5.3  20.4 | +26.0 ± 4.3  14.4 | +0.021 ± 0.038  0.136 |
| SFB1 | -2.2003 ± 0.00105 0.00449 | +18.6 ± 5.2  17.9 | +25.5 ± 3.6  14.2 | +0.008 ± 0.080  0.325 |
| SDP1 | -2.2550 ± 0.00042 0.00125 | +13.7 ± 6.3  20.3 | +23.7 ± 5.5  17.0 | +0.276 ± 0.035  0.108 |
| SFP1 | -2.2030 ± 0.00029 0.00102 | +12.6 ± 3.8  12.7 | +25.9 ± 3.5  13.4 | +0.051 ± 0.044  0.124 |
| SDA2 | -2.2584 ± 0.00113 0.00301 | +11.6 ± 5.2  17.6 | +24.0 ± 3.9  12.2 | +0.091 ± 0.069  0.254 |
| SFA2 | -2.2481 ± 0.00044 0.00137 |  +9.7 ± 6.5  23.5 | +25.1 ± 3.5  11.8 | +0.068 ± 0.027  0.090 |
| SDB2 | -2.2532 ± 0.00100 0.00498 | +13.4 ± 5.4  25.0 | +24.4 ± 4.1  17.1 | +0.235 ± 0.110  0.544 |
| SFB2 | -2.2324 ± 0.00079 0.00306 | +15.5 ± 7.1  25.8 | +27.8 ± 3.9  14.4 | -0.081 ± 0.066  0.268 |
| SDP2 | -2.2523 ± 0.00032 0.00115 | +19.7 ± 6.1  16.8 | +28.2 ± 4.3  16.2 | +0.086 ± 0.042  0.132 |
| SFP2 | -2.2306 ± 0.00048 0.00169 | +14.0 ± 4.4  14.6 | +25.8 ± 2.8   7.8 | -0.011 ± 0.030  0.100 |
| SDA3 | -2.2494 ± 0.00064 0.00202 | +16.3 ± 2.9   9.1 | +25.2 ± 3.1  10.3 | +0.233 ± 0.059  0.217 |
| SDB3 | -2.2446 ± 0.00060 0.00199 | +14.6 ± 6.4  23.1 | +24.7 ± 4.1  15.0 | +0.220 ± 0.052  0.231 |
| SDP3 | -2.2484 ± 0.00038 0.00134 | +11.3 ± 5.2  18.0 | +22.0 ± 2.8  11.2 | +0.215 ± 0.034  0.094 |
\--------------------------------------------------------------------------------------------------/

Integrated Sextupole

Figure 43: Integrated sextupole strengths of S15 magnets.

Horizontal Magnetic Center

Figure 44: Horizontal magnet center of S15 magnets.

Vertical Magnetic Center

Figure 45: Vertical magnet center of S15 magnets.

Roll-Angle Error

Figure 46: Roll angle error of S15 magnets.

SI Sextupole Magnet Sorting

Table 32: Storage Ring Sextupoles Installation.
SDA0
Magnet Name	Magnet Serial ID
SI-01M2:MA-SDA0	S15-004
SI-05M1:MA-SDA0	S15-007
SI-05M2:MA-SDA0	S15-270
SI-09M1:MA-SDA0	S15-240
SI-09M2:MA-SDA0	S15-283
SI-13M1:MA-SDA0	S15-122
SI-13M2:MA-SDA0	S15-184
SI-17M1:MA-SDA0	S15-273
SI-17M2:MA-SDA0	S15-118
SI-01M1:MA-SDA0	S15-261
SFA0
Magnet Name	Magnet Serial ID
SI-01M2:MA-SFA0	S15-278
SI-05M1:MA-SFA0	S15-246
SI-05M2:MA-SFA0	S15-276
SI-09M1:MA-SFA0	S15-009
SI-09M2:MA-SFA0	S15-015
SI-13M1:MA-SFA0	S15-279
SI-13M2:MA-SFA0	S15-033
SI-17M1:MA-SFA0	S15-016
SI-17M2:MA-SFA0	S15-010
SI-01M1:MA-SFA0	S15-172
SDB0
Magnet Name	Magnet Serial ID
SI-02M1:MA-SDB0	S15-159
SI-02M2:MA-SDB0	S15-119
SI-04M1:MA-SDB0	S15-132
SI-04M2:MA-SDB0	S15-101
SI-06M1:MA-SDB0	S15-026
SI-06M2:MA-SDB0	S15-085
SI-08M1:MA-SDB0	S15-259
SI-08M2:MA-SDB0	S15-264
SI-10M1:MA-SDB0	S15-154
SI-10M2:MA-SDB0	S15-131
SI-12M1:MA-SDB0	S15-241
SI-12M2:MA-SDB0	S15-108
SI-14M1:MA-SDB0	S15-086
SI-14M2:MA-SDB0	S15-114
SI-16M1:MA-SDB0	S15-213
SI-16M2:MA-SDB0	S15-106
SI-18M1:MA-SDB0	S15-157
SI-18M2:MA-SDB0	S15-023
SI-20M1:MA-SDB0	S15-045
SI-20M2:MA-SDB0	S15-239
SFB0
Magnet Name	Magnet Serial ID
SI-02M1:MA-SFB0	S15-076
SI-02M2:MA-SFB0	S15-133
SI-04M1:MA-SFB0	S15-152
SI-04M2:MA-SFB0	S15-082
SI-06M1:MA-SFB0	S15-074
SI-06M2:MA-SFB0	S15-163
SI-08M1:MA-SFB0	S15-103
SI-08M2:MA-SFB0	S15-075
SI-10M1:MA-SFB0	S15-072
SI-10M2:MA-SFB0	S15-208
SI-12M1:MA-SFB0	S15-039
SI-12M2:MA-SFB0	S15-048
SI-14M1:MA-SFB0	S15-070
SI-14M2:MA-SFB0	S15-053
SI-16M1:MA-SFB0	S15-038
SI-16M2:MA-SFB0	S15-151
SI-18M1:MA-SFB0	S15-077
SI-18M2:MA-SFB0	S15-013
SI-20M1:MA-SFB0	S15-056
SI-20M2:MA-SFB0	S15-073
SDP0
Magnet Name	Magnet Serial ID
SI-03M1:MA-SDP0	S15-041
SI-03M2:MA-SDP0	S15-110
SI-07M1:MA-SDP0	S15-113
SI-07M2:MA-SDP0	S15-269
SI-11M1:MA-SDP0	S15-230
SI-11M2:MA-SDP0	S15-147
SI-15M1:MA-SDP0	S15-143
SI-15M2:MA-SDP0	S15-193
SI-19M1:MA-SDP0	S15-232
SI-19M2:MA-SDP0	S15-187
SFP0
Magnet Name	Magnet Serial ID
SI-03M1:MA-SFP0	S15-249
SI-03M2:MA-SFP0	S15-221
SI-07M1:MA-SFP0	S15-238
SI-07M2:MA-SFP0	S15-044
SI-11M1:MA-SFP0	S15-274
SI-11M2:MA-SFP0	S15-135
SI-15M1:MA-SFP0	S15-043
SI-15M2:MA-SFP0	S15-040
SI-19M1:MA-SFP0	S15-258
SI-19M2:MA-SFP0	S15-093
SDA1
Magnet Name	Magnet Serial ID
SI-01C1:MA-SDA1	S15-138
SI-04C4:MA-SDA1	S15-120
SI-05C1:MA-SDA1	S15-195
SI-08C4:MA-SDA1	S15-212
SI-09C1:MA-SDA1	S15-207
SI-12C4:MA-SDA1	S15-164
SI-13C1:MA-SDA1	S15-100
SI-16C4:MA-SDA1	S15-141
SI-17C1:MA-SDA1	S15-223
SI-20C4:MA-SDA1	S15-112
SFA1
Magnet Name	Magnet Serial ID
SI-01C1:MA-SFA1	S15-142
SI-04C4:MA-SFA1	S15-219
SI-05C1:MA-SFA1	S15-102
SI-08C4:MA-SFA1	S15-286
SI-09C1:MA-SFA1	S15-236
SI-12C4:MA-SFA1	S15-266
SI-13C1:MA-SFA1	S15-265
SI-16C4:MA-SFA1	S15-272
SI-17C1:MA-SFA1	S15-098
SI-20C4:MA-SFA1	S15-105
SDB1
Magnet Name	Magnet Serial ID
SI-01C4:MA-SDB1	S15-168
SI-02C1:MA-SDB1	S15-181
SI-03C4:MA-SDB1	S15-174
SI-04C1:MA-SDB1	S15-128
SI-05C4:MA-SDB1	S15-146
SI-06C1:MA-SDB1	S15-268
SI-07C4:MA-SDB1	S15-139
SI-08C1:MA-SDB1	S15-202
SI-09C4:MA-SDB1	S15-244
SI-10C1:MA-SDB1	S15-242
SI-11C4:MA-SDB1	S15-149
SI-12C1:MA-SDB1	S15-124
SI-13C4:MA-SDB1	S15-107
SI-14C1:MA-SDB1	S15-189
SI-15C4:MA-SDB1	S15-188
SI-16C1:MA-SDB1	S15-177
SI-17C4:MA-SDB1	S15-186
SI-18C1:MA-SDB1	S15-126
SI-19C4:MA-SDB1	S15-123
SI-20C1:MA-SDB1	S15-170
SFB1
Magnet Name	Magnet Serial ID
SI-01C4:MA-SFB1	S15-104
SI-02C1:MA-SFB1	S15-080
SI-03C4:MA-SFB1	S15-061
SI-04C1:MA-SFB1	S15-067
SI-05C4:MA-SFB1	S15-068
SI-06C1:MA-SFB1	S15-034
SI-07C4:MA-SFB1	S15-060
SI-08C1:MA-SFB1	S15-081
SI-09C4:MA-SFB1	S15-156
SI-10C1:MA-SFB1	S15-257
SI-11C4:MA-SFB1	S15-234
SI-12C1:MA-SFB1	S15-182
SI-13C4:MA-SFB1	S15-233
SI-14C1:MA-SFB1	S15-169
SI-15C4:MA-SFB1	S15-059
SI-16C1:MA-SFB1	S15-275
SI-17C4:MA-SFB1	S15-153
SI-18C1:MA-SFB1	S15-052
SI-19C4:MA-SFB1	S15-071
SI-20C1:MA-SFB1	S15-065
SDP1
Magnet Name	Magnet Serial ID
SI-02C4:MA-SDP1	S15-092
SI-03C1:MA-SDP1	S15-017
SI-06C4:MA-SDP1	S15-175
SI-07C1:MA-SDP1	S15-271
SI-10C4:MA-SDP1	S15-020
SI-11C1:MA-SDP1	S15-050
SI-14C4:MA-SDP1	S15-109
SI-15C1:MA-SDP1	S15-012
SI-18C4:MA-SDP1	S15-155
SI-19C1:MA-SDP1	S15-227
SFP1
Magnet Name	Magnet Serial ID
SI-02C4:MA-SFP1	S15-063
SI-03C1:MA-SFP1	S15-260
SI-06C4:MA-SFP1	S15-180
SI-07C1:MA-SFP1	S15-176
SI-10C4:MA-SFP1	S15-250
SI-11C1:MA-SFP1	S15-209
SI-14C4:MA-SFP1	S15-165
SI-15C1:MA-SFP1	S15-253
SI-18C4:MA-SFP1	S15-229
SI-19C1:MA-SFP1	S15-251
SDA2
Magnet Name	Magnet Serial ID
SI-01C1:MA-SDA2	S15-248
SI-04C4:MA-SDA2	S15-277
SI-05C1:MA-SDA2	S15-245
SI-08C4:MA-SDA2	S15-029
SI-09C1:MA-SDA2	S15-256
SI-12C4:MA-SDA2	S15-167
SI-13C1:MA-SDA2	S15-031
SI-16C4:MA-SDA2	S15-263
SI-17C1:MA-SDA2	S15-166
SI-20C4:MA-SDA2	S15-032
SFA2
Magnet Name	Magnet Serial ID
SI-01C2:MA-SFA2	S15-282
SI-04C3:MA-SFA2	S15-117
SI-05C2:MA-SFA2	S15-021
SI-08C3:MA-SFA2	S15-145
SI-09C2:MA-SFA2	S15-220
SI-12C3:MA-SFA2	S15-243
SI-13C2:MA-SFA2	S15-171
SI-16C3:MA-SFA2	S15-280
SI-17C2:MA-SFA2	S15-281
SI-20C3:MA-SFA2	S15-005
SDB2
Magnet Name	Magnet Serial ID
SI-01C4:MA-SDB2	S15-197
SI-02C1:MA-SDB2	S15-247
SI-03C4:MA-SDB2	S15-218
SI-04C1:MA-SDB2	S15-099
SI-05C4:MA-SDB2	S15-211
SI-06C1:MA-SDB2	S15-006
SI-07C4:MA-SDB2	S15-235
SI-08C1:MA-SDB2	S15-130
SI-09C4:MA-SDB2	S15-226
SI-10C1:MA-SDB2	S15-254
SI-11C4:MA-SDB2	S15-162
SI-12C1:MA-SDB2	S15-206
SI-13C4:MA-SDB2	S15-096
SI-14C1:MA-SDB2	S15-224
SI-15C4:MA-SDB2	S15-140
SI-16C1:MA-SDB2	S15-225
SI-17C4:MA-SDB2	S15-129
SI-18C1:MA-SDB2	S15-027
SI-19C4:MA-SDB2	S15-222
SI-20C1:MA-SDB2	S15-203
SFB2
Magnet Name	Magnet Serial ID
SI-01C3:MA-SFB2	S15-121
SI-02C2:MA-SFB2	S15-190
SI-03C3:MA-SFB2	S15-192
SI-04C2:MA-SFB2	S15-087
SI-05C3:MA-SFB2	S15-210
SI-06C2:MA-SFB2	S15-231
SI-07C3:MA-SFB2	S15-158
SI-08C2:MA-SFB2	S15-115
SI-09C3:MA-SFB2	S15-008
SI-10C2:MA-SFB2	S15-160
SI-11C3:MA-SFB2	S15-019
SI-12C2:MA-SFB2	S15-267
SI-13C3:MA-SFB2	S15-078
SI-14C2:MA-SFB2	S15-030
SI-15C3:MA-SFB2	S15-090
SI-16C2:MA-SFB2	S15-116
SI-17C3:MA-SFB2	S15-018
SI-18C2:MA-SFB2	S15-097
SI-19C3:MA-SFB2	S15-179
SI-20C2:MA-SFB2	S15-185
SDP2
Magnet Name	Magnet Serial ID
SI-02C4:MA-SDP2	S15-252
SI-03C1:MA-SDP2	S15-199
SI-06C4:MA-SDP2	S15-088
SI-07C1:MA-SDP2	S15-024
SI-10C4:MA-SDP2	S15-079
SI-11C1:MA-SDP2	S15-191
SI-14C4:MA-SDP2	S15-025
SI-15C1:MA-SDP2	S15-014
SI-18C4:MA-SDP2	S15-161
SI-19C1:MA-SDP2	S15-028
SFP2
Magnet Name	Magnet Serial ID
SI-02C3:MA-SFP2	S15-062
SI-03C2:MA-SFP2	S15-049
SI-06C3:MA-SFP2	S15-194
SI-07C2:MA-SFP2	S15-064
SI-10C3:MA-SFP2	S15-237
SI-11C2:MA-SFP2	S15-127
SI-14C3:MA-SFP2	S15-057
SI-15C2:MA-SFP2	S15-173
SI-18C3:MA-SFP2	S15-089
SI-19C2:MA-SFP2	S15-054
SDA3
Magnet Name	Magnet Serial ID
SI-01C2:MA-SDA3	S15-217
SI-04C3:MA-SDA3	S15-215
SI-05C2:MA-SDA3	S15-035
SI-08C3:MA-SDA3	S15-144
SI-09C2:MA-SDA3	S15-216
SI-12C3:MA-SDA3	S15-214
SI-13C2:MA-SDA3	S15-204
SI-16C3:MA-SDA3	S15-036
SI-17C2:MA-SDA3	S15-051
SI-20C3:MA-SDA3	S15-022
SDB3
Magnet Name	Magnet Serial ID
SI-01C3:MA-SDB3	S15-084
SI-02C2:MA-SDB3	S15-111
SI-03C3:MA-SDB3	S15-228
SI-04C2:MA-SDB3	S15-150
SI-05C3:MA-SDB3	S15-198
SI-06C2:MA-SDB3	S15-201
SI-07C3:MA-SDB3	S15-196
SI-08C2:MA-SDB3	S15-125
SI-09C3:MA-SDB3	S15-183
SI-10C2:MA-SDB3	S15-205
SI-11C3:MA-SDB3	S15-047
SI-12C2:MA-SDB3	S15-200
SI-13C3:MA-SDB3	S15-037
SI-14C2:MA-SDB3	S15-148
SI-15C3:MA-SDB3	S15-058
SI-16C2:MA-SDB3	S15-178
SI-17C3:MA-SDB3	S15-255
SI-18C2:MA-SDB3	S15-134
SI-19C3:MA-SDB3	S15-083
SI-20C2:MA-SDB3	S15-046
SDP3
Magnet Name	Magnet Serial ID
SI-02C3:MA-SDP3	S15-042
SI-03C2:MA-SDP3	S15-095
SI-06C3:MA-SDP3	S15-055
SI-07C2:MA-SDP3	S15-094
SI-10C3:MA-SDP3	S15-011
SI-11C2:MA-SDP3	S15-262
SI-14C3:MA-SDP3	S15-136
SI-15C2:MA-SDP3	S15-284
SI-18C3:MA-SDP3	S15-137
SI-19C2:MA-SDP3	S15-285
Not Used
Magnet Name	Magnet Serial ID
---	S15-091

Storage Ring Vertical Corrector Magnets

Apart from slow horizontal and vertical slow orbit correctors implemented as additional coils in sextupole magnets, there will be 20 vertical corrector magnets located in C2 dispersion sections. These magnets will be identical to the ones used in the Booster.

Storage Ring Fast Orbit Correctors

Sirius storage ring is planned to have 80 horizontal and 80 vertical fast orbit correctors, as well as 10 skew quadrupole correctors. There will be two types of fast correctors: FC1 magnets with iron poles resembling skew quadrupoles, where horizontal, vertical and skew correctors are implemented as independent coils, and FC2 magnets, which are CF1 magnets rotated 45 degrees with no skew corrector coils. FC2 magnets are installed in odd-numbered C2 sectors to allow for synchrotron light of B2 dipoles to go to diagnostics beamlines. Fast correctors will sit on top of stainless steel vacuum chambers coated with a thin copper inner layer.

SI Fast Correctors Specifications

Main Parameters

Table 33: Storage Ring fast orbit correctors.
	Horizontal	Vertical	Skew
Number of fast correctors	80	80	10 ¹
Maximum fast corrector strength	30 μrad	30 μrad	0.1 T ²

¹ located at even C2 sectors.

² based on a 2.6%(2.3%) coupling value when one skew magnet is turned on in a straight high(low)-beta straight section.

Multipole Errors

The impact on the beam dynamics of residual multipole errors for the fast corrector magnets has been analyzed from fieldmaps of current models. The impact is very small and the current magnet models have been accepted. Magnetic measurements for prototypes are yet to be taken and analyzed.

SI Fast Correctors Magnet 3D Models

Figure 47: 3D drawing of the fast corrector model.

Figure 48: Field of the fast corrector model.

Fieldmap Analysis

A 3D model of multifunctional sextupole magnet has been analyzed and approved. Fieldmap analysis for each function has been performed with maximum excitation currents, when residual multipoles are expected to be worse. For the analysis of horizontal and vertical orbit corrector fields, as well as for the skew quadrupole corrector field, the sextupolar function was also excited in order to guarantee fast convergence of the magnetic solution.

FC1 Horizontal correction function

A summary of the analysis can be found in analysis.txt at this folder.

FC1 Vertical correction function

A summary of the analysis can be found in analysis.txt at this folder.

FC1 Skew quadrupole function

A summary of the analysis can be found in analysis.txt at this folder.

FC2 Horizontal correction function

A summary of the analysis can be found in analysis.txt at this folder.

FC2 Vertical correction function

A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

A hardedge model is being used for fast correctors.

SI Fast Correctors Magnet Measurements

Not available yet.

Storage Ring Magnet Families

The storage ring magnets are grouped into families. The tables below list the storage ring families with their individual magnets.

Storage Ring Dipole Families

Table 34: Storage Ring Dipole Families (including transverse gradient variation with QB1B2)
	SI-Fam:PS-B1B2-1	SI-Fam:PS-B1B2-2	SI-Fam:MA-QB1B2
1	SI-01C1:MA-B1	SI-01C1:MA-B1	SI-01C1:MA-B1
2	SI-01C2:MA-B2	SI-01C2:MA-B2	SI-01C2:MA-B2
3	SI-01C3:MA-B2	SI-01C3:MA-B2	SI-01C3:MA-B2
4	SI-01C4:MA-B1	SI-01C4:MA-B1	SI-01C4:MA-B1
5	SI-02C1:MA-B1	SI-02C1:MA-B1	SI-02C1:MA-B1
6	SI-02C2:MA-B2	SI-02C2:MA-B2	SI-02C2:MA-B2
7	SI-02C3:MA-B2	SI-02C3:MA-B2	SI-02C3:MA-B2
8	SI-02C4:MA-B1	SI-02C4:MA-B1	SI-02C4:MA-B1
9	SI-03C1:MA-B1	SI-03C1:MA-B1	SI-03C1:MA-B1
10	SI-03C2:MA-B2	SI-03C2:MA-B2	SI-03C2:MA-B2
11	SI-03C3:MA-B2	SI-03C3:MA-B2	SI-03C3:MA-B2
12	SI-03C4:MA-B1	SI-03C4:MA-B1	SI-03C4:MA-B1
13	SI-04C1:MA-B1	SI-04C1:MA-B1	SI-04C1:MA-B1
14	SI-04C2:MA-B2	SI-04C2:MA-B2	SI-04C2:MA-B2
15	SI-04C3:MA-B2	SI-04C3:MA-B2	SI-04C3:MA-B2
16	SI-04C4:MA-B1	SI-04C4:MA-B1	SI-04C4:MA-B1
17	SI-05C1:MA-B1	SI-05C1:MA-B1	SI-05C1:MA-B1
18	SI-05C2:MA-B2	SI-05C2:MA-B2	SI-05C2:MA-B2
19	SI-05C3:MA-B2	SI-05C3:MA-B2	SI-05C3:MA-B2
20	SI-05C4:MA-B1	SI-05C4:MA-B1	SI-05C4:MA-B1
21	SI-06C1:MA-B1	SI-06C1:MA-B1	SI-06C1:MA-B1
22	SI-06C2:MA-B2	SI-06C2:MA-B2	SI-06C2:MA-B2
23	SI-06C3:MA-B2	SI-06C3:MA-B2	SI-06C3:MA-B2
24	SI-06C4:MA-B1	SI-06C4:MA-B1	SI-06C4:MA-B1
25	SI-07C1:MA-B1	SI-07C1:MA-B1	SI-07C1:MA-B1
26	SI-07C2:MA-B2	SI-07C2:MA-B2	SI-07C2:MA-B2
27	SI-07C3:MA-B2	SI-07C3:MA-B2	SI-07C3:MA-B2
28	SI-07C4:MA-B1	SI-07C4:MA-B1	SI-07C4:MA-B1
29	SI-08C1:MA-B1	SI-08C1:MA-B1	SI-08C1:MA-B1
30	SI-08C2:MA-B2	SI-08C2:MA-B2	SI-08C2:MA-B2
31	SI-08C3:MA-B2	SI-08C3:MA-B2	SI-08C3:MA-B2
32	SI-08C4:MA-B1	SI-08C4:MA-B1	SI-08C4:MA-B1
33	SI-09C1:MA-B1	SI-09C1:MA-B1	SI-09C1:MA-B1
34	SI-09C2:MA-B2	SI-09C2:MA-B2	SI-09C2:MA-B2
35	SI-09C3:MA-B2	SI-09C3:MA-B2	SI-09C3:MA-B2
36	SI-09C4:MA-B1	SI-09C4:MA-B1	SI-09C4:MA-B1
37	SI-10C1:MA-B1	SI-10C1:MA-B1	SI-10C1:MA-B1
38	SI-10C2:MA-B2	SI-10C2:MA-B2	SI-10C2:MA-B2
39	SI-10C3:MA-B2	SI-10C3:MA-B2	SI-10C3:MA-B2
40	SI-10C4:MA-B1	SI-10C4:MA-B1	SI-10C4:MA-B1
41	SI-11C1:MA-B1	SI-11C1:MA-B1	SI-11C1:MA-B1
42	SI-11C2:MA-B2	SI-11C2:MA-B2	SI-11C2:MA-B2
43	SI-11C3:MA-B2	SI-11C3:MA-B2	SI-11C3:MA-B2
44	SI-11C4:MA-B1	SI-11C4:MA-B1	SI-11C4:MA-B1
45	SI-12C1:MA-B1	SI-12C1:MA-B1	SI-12C1:MA-B1
46	SI-12C2:MA-B2	SI-12C2:MA-B2	SI-12C2:MA-B2
47	SI-12C3:MA-B2	SI-12C3:MA-B2	SI-12C3:MA-B2
48	SI-12C4:MA-B1	SI-12C4:MA-B1	SI-12C4:MA-B1
49	SI-13C1:MA-B1	SI-13C1:MA-B1	SI-13C1:MA-B1
50	SI-13C2:MA-B2	SI-13C2:MA-B2	SI-13C2:MA-B2
51	SI-13C3:MA-B2	SI-13C3:MA-B2	SI-13C3:MA-B2
52	SI-13C4:MA-B1	SI-13C4:MA-B1	SI-13C4:MA-B1
53	SI-14C1:MA-B1	SI-14C1:MA-B1	SI-14C1:MA-B1
54	SI-14C2:MA-B2	SI-14C2:MA-B2	SI-14C2:MA-B2
55	SI-14C3:MA-B2	SI-14C3:MA-B2	SI-14C3:MA-B2
56	SI-14C4:MA-B1	SI-14C4:MA-B1	SI-14C4:MA-B1
57	SI-15C1:MA-B1	SI-15C1:MA-B1	SI-15C1:MA-B1
58	SI-15C2:MA-B2	SI-15C2:MA-B2	SI-15C2:MA-B2
59	SI-15C3:MA-B2	SI-15C3:MA-B2	SI-15C3:MA-B2
60	SI-15C4:MA-B1	SI-15C4:MA-B1	SI-15C4:MA-B1
61	SI-16C1:MA-B1	SI-16C1:MA-B1	SI-16C1:MA-B1
62	SI-16C2:MA-B2	SI-16C2:MA-B2	SI-16C2:MA-B2
63	SI-16C3:MA-B2	SI-16C3:MA-B2	SI-16C3:MA-B2
64	SI-16C4:MA-B1	SI-16C4:MA-B1	SI-16C4:MA-B1
65	SI-17C1:MA-B1	SI-17C1:MA-B1	SI-17C1:MA-B1
66	SI-17C2:MA-B2	SI-17C2:MA-B2	SI-17C2:MA-B2
67	SI-17C3:MA-B2	SI-17C3:MA-B2	SI-17C3:MA-B2
68	SI-17C4:MA-B1	SI-17C4:MA-B1	SI-17C4:MA-B1
69	SI-18C1:MA-B1	SI-18C1:MA-B1	SI-18C1:MA-B1
70	SI-18C2:MA-B2	SI-18C2:MA-B2	SI-18C2:MA-B2
71	SI-18C3:MA-B2	SI-18C3:MA-B2	SI-18C3:MA-B2
72	SI-18C4:MA-B1	SI-18C4:MA-B1	SI-18C4:MA-B1
73	SI-19C1:MA-B1	SI-19C1:MA-B1	SI-19C1:MA-B1
74	SI-19C2:MA-B2	SI-19C2:MA-B2	SI-19C2:MA-B2
75	SI-19C3:MA-B2	SI-19C3:MA-B2	SI-19C3:MA-B2
76	SI-19C4:MA-B1	SI-19C4:MA-B1	SI-19C4:MA-B1
77	SI-20C1:MA-B1	SI-20C1:MA-B1	SI-20C1:MA-B1
78	SI-20C2:MA-B2	SI-20C2:MA-B2	SI-20C2:MA-B2
79	SI-20C3:MA-B2	SI-20C3:MA-B2	SI-20C3:MA-B2
80	SI-20C4:MA-B1	SI-20C4:MA-B1	SI-20C4:MA-B1

Storage Ring Quadrupole Families

Table 35: Storage Ring Dispersive Quadrupole Families
	SI-Fam:MA-Q1	SI-Fam:MA-Q2	SI-Fam:MA-Q3	SI-Fam:MA-Q4
1	SI-01C1:MA-Q1	SI-01C1:MA-Q2	SI-01C2:MA-Q3	SI-01C2:MA-Q4
2	SI-01C4:MA-Q1	SI-01C4:MA-Q2	SI-01C3:MA-Q3	SI-01C3:MA-Q4
3	SI-02C1:MA-Q1	SI-02C1:MA-Q2	SI-02C2:MA-Q3	SI-02C2:MA-Q4
4	SI-02C4:MA-Q1	SI-02C4:MA-Q2	SI-02C3:MA-Q3	SI-02C3:MA-Q4
5	SI-03C1:MA-Q1	SI-03C1:MA-Q2	SI-03C2:MA-Q3	SI-03C2:MA-Q4
6	SI-03C4:MA-Q1	SI-03C4:MA-Q2	SI-03C3:MA-Q3	SI-03C3:MA-Q4
7	SI-04C1:MA-Q1	SI-04C1:MA-Q2	SI-04C2:MA-Q3	SI-04C2:MA-Q4
8	SI-04C4:MA-Q1	SI-04C4:MA-Q2	SI-04C3:MA-Q3	SI-04C3:MA-Q4
9	SI-05C1:MA-Q1	SI-05C1:MA-Q2	SI-05C2:MA-Q3	SI-05C2:MA-Q4
10	SI-05C4:MA-Q1	SI-05C4:MA-Q2	SI-05C3:MA-Q3	SI-05C3:MA-Q4
11	SI-06C1:MA-Q1	SI-06C1:MA-Q2	SI-06C2:MA-Q3	SI-06C2:MA-Q4
12	SI-06C4:MA-Q1	SI-06C4:MA-Q2	SI-06C3:MA-Q3	SI-06C3:MA-Q4
13	SI-07C1:MA-Q1	SI-07C1:MA-Q2	SI-07C2:MA-Q3	SI-07C2:MA-Q4
14	SI-07C4:MA-Q1	SI-07C4:MA-Q2	SI-07C3:MA-Q3	SI-07C3:MA-Q4
15	SI-08C1:MA-Q1	SI-08C1:MA-Q2	SI-08C2:MA-Q3	SI-08C2:MA-Q4
16	SI-08C4:MA-Q1	SI-08C4:MA-Q2	SI-08C3:MA-Q3	SI-08C3:MA-Q4
17	SI-09C1:MA-Q1	SI-09C1:MA-Q2	SI-09C2:MA-Q3	SI-09C2:MA-Q4
18	SI-09C4:MA-Q1	SI-09C4:MA-Q2	SI-09C3:MA-Q3	SI-09C3:MA-Q4
19	SI-10C1:MA-Q1	SI-10C1:MA-Q2	SI-10C2:MA-Q3	SI-10C2:MA-Q4
20	SI-10C4:MA-Q1	SI-10C4:MA-Q2	SI-10C3:MA-Q3	SI-10C3:MA-Q4
21	SI-11C1:MA-Q1	SI-11C1:MA-Q2	SI-11C2:MA-Q3	SI-11C2:MA-Q4
22	SI-11C4:MA-Q1	SI-11C4:MA-Q2	SI-11C3:MA-Q3	SI-11C3:MA-Q4
23	SI-12C1:MA-Q1	SI-12C1:MA-Q2	SI-12C2:MA-Q3	SI-12C2:MA-Q4
24	SI-12C4:MA-Q1	SI-12C4:MA-Q2	SI-12C3:MA-Q3	SI-12C3:MA-Q4
25	SI-13C1:MA-Q1	SI-13C1:MA-Q2	SI-13C2:MA-Q3	SI-13C2:MA-Q4
26	SI-13C4:MA-Q1	SI-13C4:MA-Q2	SI-13C3:MA-Q3	SI-13C3:MA-Q4
27	SI-14C1:MA-Q1	SI-14C1:MA-Q2	SI-14C2:MA-Q3	SI-14C2:MA-Q4
28	SI-14C4:MA-Q1	SI-14C4:MA-Q2	SI-14C3:MA-Q3	SI-14C3:MA-Q4
29	SI-15C1:MA-Q1	SI-15C1:MA-Q2	SI-15C2:MA-Q3	SI-15C2:MA-Q4
30	SI-15C4:MA-Q1	SI-15C4:MA-Q2	SI-15C3:MA-Q3	SI-15C3:MA-Q4
31	SI-16C1:MA-Q1	SI-16C1:MA-Q2	SI-16C2:MA-Q3	SI-16C2:MA-Q4
32	SI-16C4:MA-Q1	SI-16C4:MA-Q2	SI-16C3:MA-Q3	SI-16C3:MA-Q4
33	SI-17C1:MA-Q1	SI-17C1:MA-Q2	SI-17C2:MA-Q3	SI-17C2:MA-Q4
34	SI-17C4:MA-Q1	SI-17C4:MA-Q2	SI-17C3:MA-Q3	SI-17C3:MA-Q4
35	SI-18C1:MA-Q1	SI-18C1:MA-Q2	SI-18C2:MA-Q3	SI-18C2:MA-Q4
36	SI-18C4:MA-Q1	SI-18C4:MA-Q2	SI-18C3:MA-Q3	SI-18C3:MA-Q4
37	SI-19C1:MA-Q1	SI-19C1:MA-Q2	SI-19C2:MA-Q3	SI-19C2:MA-Q4
38	SI-19C4:MA-Q1	SI-19C4:MA-Q2	SI-19C3:MA-Q3	SI-19C3:MA-Q4
39	SI-20C1:MA-Q1	SI-20C1:MA-Q2	SI-20C2:MA-Q3	SI-20C2:MA-Q4
40	SI-20C4:MA-Q1	SI-20C4:MA-Q2	SI-20C3:MA-Q3	SI-20C3:MA-Q4

Table 36: Storage Ring Non Dispersive Quadrupole Families
	SI-Fam:MA-QFA	SI-Fam:MA-QDA	SI-Fam:MA-QFP	SI-Fam:MA-QDP1	SI-Fam:MA-QDP2	SI-Fam:MA-QFB	SI-Fam:MA-QDB1	SI-Fam:MA-QDB2
1	SI-01M1:MA-QFA	SI-01M1:MA-QDA	SI-03M1:MA-QFP	SI-03M1:MA-QDP1	SI-03M1:MA-QDP2	SI-02M1:MA-QFB	SI-02M1:MA-QDB1	SI-02M1:MA-QDB2
2	SI-01M2:MA-QFA	SI-01M2:MA-QDA	SI-03M2:MA-QFP	SI-03M2:MA-QDP1	SI-03M2:MA-QDP2	SI-02M2:MA-QFB	SI-02M2:MA-QDB1	SI-02M2:MA-QDB2
3	SI-05M1:MA-QFA	SI-05M1:MA-QDA	SI-07M1:MA-QFP	SI-07M1:MA-QDP1	SI-07M1:MA-QDP2	SI-04M1:MA-QFB	SI-04M1:MA-QDB1	SI-04M1:MA-QDB2
4	SI-05M2:MA-QFA	SI-05M2:MA-QDA	SI-07M2:MA-QFP	SI-07M2:MA-QDP1	SI-07M2:MA-QDP2	SI-04M2:MA-QFB	SI-04M2:MA-QDB1	SI-04M2:MA-QDB2
5	SI-09M1:MA-QFA	SI-09M1:MA-QDA	SI-11M1:MA-QFP	SI-11M1:MA-QDP1	SI-11M1:MA-QDP2	SI-06M1:MA-QFB	SI-06M1:MA-QDB1	SI-06M1:MA-QDB2
6	SI-09M2:MA-QFA	SI-09M2:MA-QDA	SI-11M2:MA-QFP	SI-11M2:MA-QDP1	SI-11M2:MA-QDP2	SI-06M2:MA-QFB	SI-06M2:MA-QDB1	SI-06M2:MA-QDB2
7	SI-13M1:MA-QFA	SI-13M1:MA-QDA	SI-15M1:MA-QFP	SI-15M1:MA-QDP1	SI-15M1:MA-QDP2	SI-08M1:MA-QFB	SI-08M1:MA-QDB1	SI-08M1:MA-QDB2
8	SI-13M2:MA-QFA	SI-13M2:MA-QDA	SI-15M2:MA-QFP	SI-15M2:MA-QDP1	SI-15M2:MA-QDP2	SI-08M2:MA-QFB	SI-08M2:MA-QDB1	SI-08M2:MA-QDB2
9	SI-17M1:MA-QFA	SI-17M1:MA-QDA	SI-19M1:MA-QFP	SI-19M1:MA-QDP1	SI-19M1:MA-QDP2	SI-10M1:MA-QFB	SI-10M1:MA-QDB1	SI-10M1:MA-QDB2
10	SI-17M2:MA-QFA	SI-17M2:MA-QDA	SI-19M2:MA-QFP	SI-19M2:MA-QDP1	SI-19M2:MA-QDP2	SI-10M2:MA-QFB	SI-10M2:MA-QDB1	SI-10M2:MA-QDB2
11						SI-12M1:MA-QFB	SI-12M1:MA-QDB1	SI-12M1:MA-QDB2
12						SI-12M2:MA-QFB	SI-12M2:MA-QDB1	SI-12M2:MA-QDB2
13						SI-14M1:MA-QFB	SI-14M1:MA-QDB1	SI-14M1:MA-QDB2
14						SI-14M2:MA-QFB	SI-14M2:MA-QDB1	SI-14M2:MA-QDB2
15						SI-16M1:MA-QFB	SI-16M1:MA-QDB1	SI-16M1:MA-QDB2
16						SI-16M2:MA-QFB	SI-16M2:MA-QDB1	SI-16M2:MA-QDB2
17						SI-18M1:MA-QFB	SI-18M1:MA-QDB1	SI-18M1:MA-QDB2
18						SI-18M2:MA-QFB	SI-18M2:MA-QDB1	SI-18M2:MA-QDB2
19						SI-20M1:MA-QFB	SI-20M1:MA-QDB1	SI-20M1:MA-QDB2
20						SI-20M2:MA-QFB	SI-20M2:MA-QDB1	SI-20M2:MA-QDB2

Storage Ring Sextupole Families

Table 37: Storage Ring Sextupole Families A
	SI-Fam:MA-SFA0	SI-Fam:MA-SFA1	SI-Fam:MA-SFA2	SI-Fam:MA-SDA0	SI-Fam:MA-SDA1	SI-Fam:MA-SDA2	SI-Fam:MA-SDA3
1	SI-01M1:MA-SFA0	SI-01C1:MA-SFA1	SI-01C2:MA-SFA2	SI-01M1:MA-SDA0	SI-01C1:MA-SDA1	SI-01C1:MA-SDA2	SI-01C2:MA-SDA3
2	SI-01M2:MA-SFA0	SI-04C4:MA-SFA1	SI-04C3:MA-SFA2	SI-01M2:MA-SDA0	SI-04C4:MA-SDA1	SI-04C4:MA-SDA2	SI-04C3:MA-SDA3
3	SI-05M1:MA-SFA0	SI-05C1:MA-SFA1	SI-05C2:MA-SFA2	SI-05M1:MA-SDA0	SI-05C1:MA-SDA1	SI-05C1:MA-SDA2	SI-05C2:MA-SDA3
4	SI-05M2:MA-SFA0	SI-08C4:MA-SFA1	SI-08C3:MA-SFA2	SI-05M2:MA-SDA0	SI-08C4:MA-SDA1	SI-08C4:MA-SDA2	SI-08C3:MA-SDA3
5	SI-09M1:MA-SFA0	SI-09C1:MA-SFA1	SI-09C2:MA-SFA2	SI-09M1:MA-SDA0	SI-09C1:MA-SDA1	SI-09C1:MA-SDA2	SI-09C2:MA-SDA3
6	SI-09M2:MA-SFA0	SI-12C4:MA-SFA1	SI-12C3:MA-SFA2	SI-09M2:MA-SDA0	SI-12C4:MA-SDA1	SI-12C4:MA-SDA2	SI-12C3:MA-SDA3
7	SI-13M1:MA-SFA0	SI-13C1:MA-SFA1	SI-13C2:MA-SFA2	SI-13M1:MA-SDA0	SI-13C1:MA-SDA1	SI-13C1:MA-SDA2	SI-13C2:MA-SDA3
8	SI-13M2:MA-SFA0	SI-16C4:MA-SFA1	SI-16C3:MA-SFA2	SI-13M2:MA-SDA0	SI-16C4:MA-SDA1	SI-16C4:MA-SDA2	SI-16C3:MA-SDA3
9	SI-17M1:MA-SFA0	SI-17C1:MA-SFA1	SI-17C2:MA-SFA2	SI-17M1:MA-SDA0	SI-17C1:MA-SDA1	SI-17C1:MA-SDA2	SI-17C2:MA-SDA3
10	SI-17M2:MA-SFA0	SI-20C4:MA-SFA1	SI-20C3:MA-SFA2	SI-17M2:MA-SDA0	SI-20C4:MA-SDA1	SI-20C4:MA-SDA2	SI-20C3:MA-SDA3

Table 38: Storage Ring Sextupole Families B
	SI-Fam:MA-SFB0	SI-Fam:MA-SFB1	SI-Fam:MA-SFB2	SI-Fam:MA-SDB0	SI-Fam:MA-SDB1	SI-Fam:MA-SDB2	SI-Fam:MA-SDB3
1	SI-02M1:MA-SFB0	SI-01C4:MA-SFB1	SI-01C3:MA-SFB2	SI-02M1:MA-SDB0	SI-01C4:MA-SDB1	SI-01C4:MA-SDB2	SI-01C3:MA-SDB3
2	SI-02M2:MA-SFB0	SI-02C1:MA-SFB1	SI-02C2:MA-SFB2	SI-02M2:MA-SDB0	SI-02C1:MA-SDB1	SI-02C1:MA-SDB2	SI-02C2:MA-SDB3
3	SI-04M1:MA-SFB0	SI-03C4:MA-SFB1	SI-03C3:MA-SFB2	SI-04M1:MA-SDB0	SI-03C4:MA-SDB1	SI-03C4:MA-SDB2	SI-03C3:MA-SDB3
4	SI-04M2:MA-SFB0	SI-04C1:MA-SFB1	SI-04C2:MA-SFB2	SI-04M2:MA-SDB0	SI-04C1:MA-SDB1	SI-04C1:MA-SDB2	SI-04C2:MA-SDB3
5	SI-06M1:MA-SFB0	SI-05C4:MA-SFB1	SI-05C3:MA-SFB2	SI-06M1:MA-SDB0	SI-05C4:MA-SDB1	SI-05C4:MA-SDB2	SI-05C3:MA-SDB3
6	SI-06M2:MA-SFB0	SI-06C1:MA-SFB1	SI-06C2:MA-SFB2	SI-06M2:MA-SDB0	SI-06C1:MA-SDB1	SI-06C1:MA-SDB2	SI-06C2:MA-SDB3
7	SI-08M1:MA-SFB0	SI-07C4:MA-SFB1	SI-07C3:MA-SFB2	SI-08M1:MA-SDB0	SI-07C4:MA-SDB1	SI-07C4:MA-SDB2	SI-07C3:MA-SDB3
8	SI-08M2:MA-SFB0	SI-08C1:MA-SFB1	SI-08C2:MA-SFB2	SI-08M2:MA-SDB0	SI-08C1:MA-SDB1	SI-08C1:MA-SDB2	SI-08C2:MA-SDB3
9	SI-10M1:MA-SFB0	SI-09C4:MA-SFB1	SI-09C3:MA-SFB2	SI-10M1:MA-SDB0	SI-09C4:MA-SDB1	SI-09C4:MA-SDB2	SI-09C3:MA-SDB3
10	SI-10M2:MA-SFB0	SI-10C1:MA-SFB1	SI-10C2:MA-SFB2	SI-10M2:MA-SDB0	SI-10C1:MA-SDB1	SI-10C1:MA-SDB2	SI-10C2:MA-SDB3
11	SI-12M1:MA-SFB0	SI-11C4:MA-SFB1	SI-11C3:MA-SFB2	SI-12M1:MA-SDB0	SI-11C4:MA-SDB1	SI-11C4:MA-SDB2	SI-11C3:MA-SDB3
12	SI-12M2:MA-SFB0	SI-12C1:MA-SFB1	SI-12C2:MA-SFB2	SI-12M2:MA-SDB0	SI-12C1:MA-SDB1	SI-12C1:MA-SDB2	SI-12C2:MA-SDB3
13	SI-14M1:MA-SFB0	SI-13C4:MA-SFB1	SI-13C3:MA-SFB2	SI-14M1:MA-SDB0	SI-13C4:MA-SDB1	SI-13C4:MA-SDB2	SI-13C3:MA-SDB3
14	SI-14M2:MA-SFB0	SI-14C1:MA-SFB1	SI-14C2:MA-SFB2	SI-14M2:MA-SDB0	SI-14C1:MA-SDB1	SI-14C1:MA-SDB2	SI-14C2:MA-SDB3
15	SI-16M1:MA-SFB0	SI-15C4:MA-SFB1	SI-15C3:MA-SFB2	SI-16M1:MA-SDB0	SI-15C4:MA-SDB1	SI-15C4:MA-SDB2	SI-15C3:MA-SDB3
16	SI-16M2:MA-SFB0	SI-16C1:MA-SFB1	SI-16C2:MA-SFB2	SI-16M2:MA-SDB0	SI-16C1:MA-SDB1	SI-16C1:MA-SDB2	SI-16C2:MA-SDB3
17	SI-18M1:MA-SFB0	SI-17C4:MA-SFB1	SI-17C3:MA-SFB2	SI-18M1:MA-SDB0	SI-17C4:MA-SDB1	SI-17C4:MA-SDB2	SI-17C3:MA-SDB3
18	SI-18M2:MA-SFB0	SI-18C1:MA-SFB1	SI-18C2:MA-SFB2	SI-18M2:MA-SDB0	SI-18C1:MA-SDB1	SI-18C1:MA-SDB2	SI-18C2:MA-SDB3
19	SI-20M1:MA-SFB0	SI-19C4:MA-SFB1	SI-19C3:MA-SFB2	SI-20M1:MA-SDB0	SI-19C4:MA-SDB1	SI-19C4:MA-SDB2	SI-19C3:MA-SDB3
20	SI-20M2:MA-SFB0	SI-20C1:MA-SFB1	SI-20C2:MA-SFB2	SI-20M2:MA-SDB0	SI-20C1:MA-SDB1	SI-20C1:MA-SDB2	SI-20C2:MA-SDB3

Table 39: Storage Ring Sextupole Families P
	SI-Fam:MA-SFP0	SI-Fam:MA-SFP1	SI-Fam:MA-SFP2	SI-Fam:MA-SDP0	SI-Fam:MA-SDP1	SI-Fam:MA-SDP2	SI-Fam:MA-SDP3
1	SI-03M1:MA-SFP0	SI-02C4:MA-SFP1	SI-02C3:MA-SFP2	SI-03M1:MA-SDP0	SI-02C4:MA-SDP1	SI-02C4:MA-SDP2	SI-02C3:MA-SDP3
2	SI-03M2:MA-SFP0	SI-03C1:MA-SFP1	SI-03C2:MA-SFP2	SI-03M2:MA-SDP0	SI-03C1:MA-SDP1	SI-03C1:MA-SDP2	SI-03C2:MA-SDP3
3	SI-07M1:MA-SFP0	SI-06C4:MA-SFP1	SI-06C3:MA-SFP2	SI-07M1:MA-SDP0	SI-06C4:MA-SDP1	SI-06C4:MA-SDP2	SI-06C3:MA-SDP3
4	SI-07M2:MA-SFP0	SI-07C1:MA-SFP1	SI-07C2:MA-SFP2	SI-07M2:MA-SDP0	SI-07C1:MA-SDP1	SI-07C1:MA-SDP2	SI-07C2:MA-SDP3
5	SI-11M1:MA-SFP0	SI-10C4:MA-SFP1	SI-10C3:MA-SFP2	SI-11M1:MA-SDP0	SI-10C4:MA-SDP1	SI-10C4:MA-SDP2	SI-10C3:MA-SDP3
6	SI-11M2:MA-SFP0	SI-11C1:MA-SFP1	SI-11C2:MA-SFP2	SI-11M2:MA-SDP0	SI-11C1:MA-SDP1	SI-11C1:MA-SDP2	SI-11C2:MA-SDP3
7	SI-15M1:MA-SFP0	SI-14C4:MA-SFP1	SI-14C3:MA-SFP2	SI-15M1:MA-SDP0	SI-14C4:MA-SDP1	SI-14C4:MA-SDP2	SI-14C3:MA-SDP3
8	SI-15M2:MA-SFP0	SI-15C1:MA-SFP1	SI-15C2:MA-SFP2	SI-15M2:MA-SDP0	SI-15C1:MA-SDP1	SI-15C1:MA-SDP2	SI-15C2:MA-SDP3
9	SI-19M1:MA-SFP0	SI-18C4:MA-SFP1	SI-18C3:MA-SFP2	SI-19M1:MA-SDP0	SI-18C4:MA-SDP1	SI-18C4:MA-SDP2	SI-18C3:MA-SDP3
10	SI-19M2:MA-SFP0	SI-19C1:MA-SFP1	SI-19C2:MA-SFP2	SI-19M2:MA-SDP0	SI-19C1:MA-SDP1	SI-19C1:MA-SDP2	SI-19C2:MA-SDP3

Booster Magnets

Booster Dipoles

There is only one type of dipole in the Booster. It is a multi-functional magnet with dipolar, defocusing quadrular and sextupolar functions.

BO Dipole Magnet Specifications

Main Parameters

Table 40: Booster dipole main parameters
	BD		units
Power supply type	monopolar¹
Number of magnets	50
Deflection angle	7.2		°
Magnetic length	1.221		m
Physical length	1.206		m
Integrated quadrupole strength²	-0.2477		m^-1
Integrated sextupole strength²	-2.5610		m^-2
Full central gap	28.0		mm
Hardedge bending radius	9.7164		m
Hardedge quadrupole strength	-0.2029		m^-2
Hardedge sextupole strength	-2.0975		m^-3
Hardedge sagitta²	18.836		mm
Good field region (GFR)	6		mm
Homogeneity in GFR	4/10000
Maximum integrated field³	-1.3204		T·m
	Injection	Extraction
Integrated field²	-0.0629	-1.2575	T·m
Integrated quadrupole gradient²	0.1239	2.4788	T
Integrated sextupole gradient²	1.2814	25.6277	T·m^-1
Hardedge field	-0.0515	-1.0299	T
Hardedge quadrupole gradient	0.1015	2.0302	T·m^-1
Hardedge sextupole gradient	1.0495	20.9891	T·m^-2

¹ Two monopolar power supplies will be used, each exciting alternate north and south pole coils of consecutive dipoles.

² On the Runge-Kutta trajectory.

³ The maximum integrated field is 5% higher than the integrated field at extraction energy. This is required by the adopted ramping curve.

Electric Parameters

Table 41: Booster dipole electric parameters
	BD	units
Main coil current	1034.00	A
Main coil number of turns	12
Stored magnetic energy	2450.92	J
Magnet inductance	4.58	mH

Multipole Errors

Field analysis of the 3D model of the dipole shows very small residual multipoles. The larger systematic multipole values in Table 42, which do not compromise beam quality, are kept as specifications for measurements of the magnets in the future. Random multipole errors were chosen so that the rms multipolar contribution at r₀ = 17.5 mm were 1/1000 of the nominal dipolar field. This contribution was then equally divided amoung the multipoles considered. On the other hand, normal sextupolar random 1σ value was set to 9 % of the maximum strength. All these values should be used as targets for the magnet modelling and measurements. Eventually the multipole values will be updated with measurement data and tested against beam dynamics simulations.

Table 42: Booster dipole multipole errors specification. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
	Multipole error	Systematic	Random
	Multipole error	Systematic	Normal	Skew
Dipoles @r = 17.5 mm	B₂/B₀ (sextupole)	--	5.5×10^-4 ^*	1.0×10^-4
	B₃/B₀ (octupole)	+4.0×10^-4	4.0×10^-4	1.0×10^-4
	B₄/B₀ (decapole)	-3.6×10^-4	4.0×10^-4	1.0×10^-4
	B₅/B₀ (12-pole)	+2.7×10^-4	4.0×10^-4	1.0×10^-4
	B₆/B₀ (14-pole)	-1.3×10^-4	4.0×10^-4	1.0×10^-4

^* This spec is replicated in the dipole alignment and rotation errors table
Actual designed dipole model shows numbers are that in accordance with these specs. (see fieldmap analysis)

Alignment and Excitation Errors

Table 43: Maximum absolute value of random alignment and excitation errors for the Booster Dipoles. The errors are generated with a Gaussian distribution truncated at ±1σ.
	Dipoles
Transverse position, $\text{[math]}$ , $\text{[math]}$	160	μm
Rotation around longitudinal axis	0.8	mrad
Excitation error (static or low frequency)	0.15	%
Dipole Gradient Error	2.4	%
Dipole Sextupolar Error	9	%

BO Dipole Magnet 3D Model

Figure 49: 3D drawing of the booster dipole model.

Figure 50: Field of the booster dipole model.

Fieldmap Analysis

Each dipole in the booster deflects the beam in 7.2 ° nominally. A 3D magnetic model has been created and its fieldmap analyzed for a excitation current corresponding to 3.0 GeV. The model has been optimized in a way that the beam trajectory is roughly centered at the good-field region of the magnet, corresponding to the axis x = 0 mm. At the longitudinal center of the magnet the trajectory starts at x = 9.045 mm. The reference point, defined as the interception of the straight lines asymptotically tangent to the up and downstream trajectory branches, is located at x = 28.572 mm, at the longitudinal center of the magnet. Multipoles from fieldmap analysis are all very well within specifications. A summary of the analysis for extraction energy can be found in analysis.txt at this folder. As for low energy, the corresponding file can be found in here.

Segmented Model

In order to take into account the s-dependent field profile of the BO dipoles a symmetric model was created.

Figure 51: Booster dipole B_y field on the trajectory calculated by Runge-Kutta integration and the adopted segmented model used in simulation codes. Only half dipole is shown in longitudinal direction. The slight variation in the flat region is caused by the curved trajectory in a straight magnet with transverse field gradient.

Table with segmented dipole model

Table 44: Booster dipole segmented model.
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.1960	1.158	-1.032	-0.228	-1.990
02	0.1920	1.143	-1.040	-0.212	-1.930
03	0.1820	1.096	-1.052	-0.186	-1.920
04	0.0100	0.051	-0.889	-0.249	-2.030
05	0.0100	0.037	-0.641	-0.170	-1.470
06	0.0130	0.033	-0.440	-0.062	-1.820
07	0.0170	0.029	-0.299	-0.011	-1.970
08	0.0200	0.022	-0.195	+0.005	-1.600
09	0.0300	0.018	-0.107	+0.005	-0.930
10	0.0500	0.012	-0.043	+0.002	-0.361

^* K=B'/(Bρ), S=B"/(2Bρ)

Constructed from simulated fieldmap at extraction energy

BO Dipole Magnet Measurements

The magnetic measurement results for Booster dipoles at the extraction current, I= 991.63 A, are shown in Figure 52 , Figure 53 and Figure 54. The Hall probe measurement files can be found at this folder. The excitation curve measurement files can be found at this folder.

Figure 52: Integrated field on the Runge-Kutta trajectory, calculated for the Hall probe measurements of the Booster dipoles at the extraction current (991.63 A).

Figure 53: Integrated quadrupole gradient on the Runge-Kutta trajectory, calculated for the Hall probe measurements of the Booster dipoles at the extraction current (991.63 A).

Figure 54: Integrated sextupole gradient on the Runge-Kutta trajectory, calculated for the Hall probe measurements of the Booster dipoles at the extraction current (991.63 A).

Booster Quadrupoles

BO Quadrupole Magnets Specifications

Main Parameters

Table 45: Booster quadrupole main parameters
	QF	QD	QS	units
Power supply type	monopolar	bipolar	bipolar
Magnet model name	BQF	BQD	BQS
Number of magnets	50	25	1
Maximum integrated strength ¹	0.425	-0.052	0.017	m^-1
Magnetic length	0.228	0.100	0.100	m
Physical length	0.212	0.085	0.100	m
Maximum strength ¹	1.865	-0.525	0.168	m^-2
Bore diameter	40	40	40	mm
Maximum integrated field gradient ¹	-4.255	0.525	0.168	T
Maximum field gradient ¹	-18.664	5.254	1.600	T·m^-1
Maximum field at pole tip ¹	0.373	0.105	0.032	T

¹ The maximum field gradient is 5% higher than the field gradient at extraction energy. This is required by the adopted ramping curve.

Electric Parameters

Table 46: Booster quadrupole electric parameters
	QF	QD	QS	units
Main coil current	113.97	30.42	9.64	A
Main coil number of turns	26.25	27.50	28.00
Stored magnetic energy	59.34	2.42	0.22	J
Magnet inductance	9.14	5.22	4.68	mH

Multipole Errors

Quadrupole QF

Table 47: Booster QF quadrupole multipole errors. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
	Multipole error	Systematic¹	Random
	Multipole error	Systematic¹	Normal	Skew
quadrupoles @r = 17.5 mm	B₂/B₁ (sextupole)	--	7.0×10^-4	1.0×10^-3
	B₃/B₁ (octupole)	--	4.0×10^-4	5.0×10^-4
	B₄/B₁ (decapole)	--	4.0×10^-4	1.0×10^-4
	B₅/B₁ (12-pole)	-1.0×10^-3	4.0×10^-4	1.0×10^-4
	B₆/B₁ (14-pole)	--	4.0×10^-4	1.0×10^-4
	B₇/B₁ (16-pole)	--	4.0×10^-4	1.0×10^-4
	B₈/B₁ (18-pole)	--	4.0×10^-4	1.0×10^-4
	B₉/B₁ (20-pole)	+1.1×10^-3	--	--
	B₁₃/B₁ (28-pole)	+8.0×10^-5	--	--

¹ Multipoles of prototype magnets measured with radial rotating coils

Quadrupole QD

Table 48: Booster QD quadrupole multipole errors. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
	Multipole error	Systematic¹	Random
	Multipole error	Systematic¹	Normal	Skew
quadrupoles @r = 17.5 mm	B₂/B₁ (sextupole)	--	7.0×10^-4	1.0×10^-3
	B₃/B₁ (octupole)	--	4.0×10^-4	5.0×10^-4
	B₄/B₁ (decapole)	--	4.0×10^-4	1.0×10^-4
	B₅/B₁ (12-pole)	-4.7×10^-3	4.0×10^-4	1.0×10^-4
	B₆/B₁ (14-pole)	--	4.0×10^-4	1.0×10^-4
	B₇/B₁ (16-pole)	--	4.0×10^-4	1.0×10^-4
	B₈/B₁ (18-pole)	--	4.0×10^-4	1.0×10^-4
	B₉/B₁ (20-pole)	+1.2×10^-3	--	--
	B₁₃/B₁ (28-pole)	+5.4×10^-7	--	--

¹Relative multipoles calculated around the Runge-Kutta trajectory for the latest QD model-02 fieldmap at 3 GeV

Quadrupole QS

Table 49: Booster QS quadrupole multipole errors. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
	Multipole error	Systematic¹	Random
	Multipole error	Systematic¹	Normal	Skew
quadrupoles @r = 17.5 mm	A₃/A₁ (octupole)	-1.1×10^-3	--	--
	A₅/A₁ (12-pole)	+9.9×10^-3	--	--
	A₇/A₁ (16-pole)	-8.7×10^-3	--	--
	A₉/A₁ (20-pole)	+6.4×10^-3	--	--

¹Relative multipoles calculated around the Runge-Kutta trajectory for the latest QS model-01, fieldmap at 3 GeV

Alignment and Excitation Errors

Table 50: Maximum absolute value of random alignment and excitation errors for the Booster Quadrupoles. The errors are generated with a Gaussian distribution truncated at ±1σ.
	Quadrupoles
Transverse position, $\text{[math]}$ , $\text{[math]}$	160	μm
Rotation around longitudinal axis	0.8	mrad
Excitation error (static or low frequency)	0.3	%
Tracking error	100	ppm

BO Quadrupole 3D Models

Figure 55: 3D drawing of the QF booster quadrupole model.

Figure 56: Field of the booster QF quadrupole model.

Figure 57: 3D drawing of the QD booster quadrupole model.

Figure 58: Field of the booster QD quadrupole model.

Figure 59: 3D drawing of the QS booster quadrupole model.

Figure 60: Field of the booster QS quadrupole model.

Fieldmap Analysis

There will be two types of quadrupoles: QF and QD. QF quadrupoles are longer, 212-mm, whereas QD quadrupoles are shorter: 85-mm long. While QF magnets power supply is planed to be monopolar, the power supply for the QD family will be dipolar. 3D magnetic models for both QD and QF quadrupoles were analyzed. Nominal quadrupole field component in the booster dipoles provide most necessary defocusing for the optics and hence QD quadrupoles are installed in the lattice for optics correction purposes.

QF at Ejection Energy

A summary of the analysis can be found in analysis.txt at this folder.

QF at Injection Energy

A summary of the analysis can be found in analysis.txt at this folder.

QD at Ejection Energy

A summary of the analysis can be found in analysis.txt at this folder.

QD at Injection Energy

A summary of the analysis can be found in analysis.txt at this folder.

QS at Ejection Energy

A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

Currently booster quadrupoles are being modelled as a single segment within the hard-edge approximation.

Figure 61: Booster QF quadrupole strength on the trajectory calculated by Runge-Kutta integration and the adopted hard-edge model used in simulation codes. Only half quadrupole is shown in longitudinal direction.

Table 51: BO QF quadrupole segmented model (maximum current).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.1140	0.000	-0.000e+00	+1.870e+00	+0.000e+00

^* K=B'/(Bρ), S=B"/(2Bρ)

Figure 62: Booster QD quadrupole strength on the trajectory calculated by Runge-Kutta integration and the adopted hard-edge model used in simulation codes. Only half quadrupole is shown in longitudinal direction.

Table 52: BO QD quadrupole segmented model (maximum current).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0500	0.000	-0.000e+00	-5.000e-01	-0.000e+00

^* K=B'/(Bρ), S=B"/(2Bρ)

Figure 63: Booster QS quadrupole strength on the trajectory calculated by Runge-Kutta integration and the adopted hard-edge model used in simulation codes. Only half quadrupole is shown in longitudinal direction.

Table 53: BO QS quadrupole segmented model (maximum current).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0500	0.000	-0.000e+00	-1.680e-01	-0.000e+00

^* K=B'/(Bρ), S=B"/(2Bρ)

BO Quadrupole Magnet Measurements

The magnetic measurement results for Booster QF quadrupoles at high current, I=130 A, are shown in Figure 64 and Figure 65. The rotating coil measurement files can be found at this folder.

Figure 64: Rotating coil measurements of the Booster QF quadrupoles at high current (130 A).

Figure 65: Rotating coil measurements of the Booster QF quadrupoles at high current (130 A).

The magnetic measurement results for Booster QD quadrupoles at high current, I=32 A, are shown in Figure 66 and Figure 67. The rotating coil measurement files can be found at this folder.

Figure 66: Rotating coil measurements of the Booster QD quadrupoles at high current (32 A).

Figure 67: Rotating coil measurements of the Booster QD quadrupoles at high current (32 A).

Booster Sextupoles

BO Sextupole Magnet Specifications

Main Parameters

Table 54: Booster sextupole main parameters
	SF	SD	units
Power supply type	monopolar	bipolar
Number of magnets	25	10
Maximum integrated strength ¹	2.1	2.1	m^-2
Magnetic length	0.105	0.105	m
Physical length	0.100	0.100	m
Maximum strength ¹	20.0	20.0	m^-3
Bore diameter	40	40	mm
Maximum integrated field gradient ¹	21.015	21.015	T·m^-1
Maximum gradient ¹	200.1	200.1	T·m^-2
Maximum field at pole tip ¹	0.080	0.080	T

¹ The maximum field gradient is 5% higher than the field gradient at extraction energy. This is required by the adopted ramping curve.

Electric Parameters

Table 55: Booster sextupole electric parameters
	BS	units
Main coil current	142.00	A
Main coil number of turns	3.00
Stored magnetic energy	0.98	J
Magnet inductance	0.10	mH

Multipole Errors

Table 56: Booster sextupole multipole errors. Standard deviation for random multipole errors; simulations assume Gaussian distribution truncated at ±2σ.
	Multipole error	Systematic¹	Random
	Multipole error	Systematic¹	Normal	Skew
sextupoles @x = 17.5 mm	B₃/B₂ (octupole)	--	4.0×10^-4	1.0×10^-4
	B₄/B₂ (decapole)	--	4.0×10^-4	1.0×10^-4
	B₅/B₂ (12-pole)	--	4.0×10^-4	1.0×10^-4
	B₆/B₂ (14-pole)	--	4.0×10^-4	1.0×10^-4
	B₇/B₂ (16-pole)	--	4.0×10^-4	1.0×10^-4
	B₈/B₂ (18-pole)	-2.7×10^-2	4.0×10^-4	1.0×10^-4
	B₉/B₂ (20-pole)	--	4.0×10^-4	1.0×10^-4
	B₁₄/B₂ (30-pole)	-1.4×10^-2	--	--

¹Relative multipoles calculated around the Runge-Kutta trajectory for the latest sextupole model-03 fieldmap at 3 GeV

Alignment and Excitation Errors

Table 57: Maximum absolute value of random alignment and excitation errors for the Booster Sextupoles. The errors are generated with a Gaussian distribution truncated at ±1σ.
	Sextupoles
Transverse position, $\text{[math]}$ , $\text{[math]}$	160	μm
Rotation around longitudinal axis	0.8	mrad
Excitation error (static or low frequency)	0.3	%

BO Sextupole 3D Model

Figure 68: 3D drawing of the booster sextupole model.

Figure 69: Field of the booster sextupole model.

Fieldmap Analysis

There will be 25 focusing sextupoles (SF) and 10 defocusing sextupoles (SD) in the booster for chromaticity control. A 105-mm long 3D magnetic model for both SF and SD sextupoles was analyzed. SF family of magnets will be excited with a monopolar power supply whereas SD sextupoles family will be excited with a bipolar power supply. Analysis has been done for fieldmaps corresponding to injection and extraction energy currents. Since the magnetic field is very linear with the excitation current the two results are virtually identical with respect to field quality.

SD/SF at Ejection Energy

A summary of the analysis can be found in analysis.txt at this folder.

SD/SF at Injection Energy

A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

Currently booster sextupoles are being modelled as a single segment within the hard-edge approximation.

Figure 70: Booster sextupole strength on the trajectory calculated by Runge-Kutta integration and the adopted hard-edge model used in simulation codes. Only half sextupole is shown in longitudinal direction.

Table 58: BO S sextupole segmented model (maximum current).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0525	0.000	-0.000e+00	+0.000e+00	+1.900e+01

^* K=B'/(Bρ), S=B"/(2Bρ)

BO Sextupole Magnet Measurements

The magnetic measurement results for Booster sextupoles at high current, I=150 A, are shown in Figure 71 and Figure 72. The rotating coil measurement files can be found at this folder.

Figure 71: Rotating coil measurements of the Booster sextupoles at high current (150 A).

Figure 72: Rotating coil measurements of the Booster sextupoles at high current (150 A).

Booster Correctors

BO Corrector Magnets Specifications

Main parameters

Table 59: Booster corrector main parameters
	CH	CV	units
Power supply type	bipolar	bipolar
Number of magnets	25	25
Maximum kick angle @ 3 GeV	310	310	μrad
Magnetic length	0.150	0.150	m
Physical length	0.112	0.112	m
Central Gap	43.0	43.0	mm
Minimum Gap	40.0	40.0	mm
Maximum integrated field	3.10×10^-3	3.10×10^-3	T·m
Maximum field	2.07×10^-2	2.07×10^-2	T

Electric parameters

Table 60: Booster corrector electric parameters
	CH/CV	units
Maximum main coil current	9.35	A
Main coil number of turns	38.50
Stored magnetic energy	0.15	J
Magnet inductance	3.37	mH

Multipole Errors

The impact of residual multipole errors of reasonable correctors on the booster beam parameters is expected to be negligible and therefore no specification had been defined. The designed 3D model of these correctors showed acceptable multipole erros.

BO Corrector 3D Model

Orbit correctors for the booster use a single model for both horizontal and vertical deflections.

Figure 73: 3D drawing of the booster orbit correctors model.

Figure 74: Field of the booster orbit correctors model.

Fieldmap Analysis

There will be 25 horizontal and 25 vertical orbit correctors in the booster for orbit control. There will be one magnet model for both corrector types. Vertical corrector magnets are the same as horizontal correctors rotated by 90 degrees. The following are the analysis summaries created with fma-analysis.py

CH at Ejection Energy

A summary of the analysis can be found in analysis.txt at this folder.

CV at Ejection Energy

A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

Currently the hard-edge approximation is being used to model all booster correctors.

Figure 75: Field profile of segmented booster correctors model

Table 61: BO correctors half segmented model (maximum strength).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0750	0.000	-2.121e-02	+3.400e-06	+1.940e-02

^* K=B'/(Bρ), S=B"/(2Bρ)

BO Corrector Magnet Measurements

The magnetic measurement results for Booster corrector at I=10 A are shown in Figure 76. The rotating coil measurement files can be found at this folder.

Figure 76: Rotating coil measurements of the Booster correctors at I=10 A.

Booster Magnets Ramping Curve

For beam energy ramping in the Booster from 0.15 GeV to 3.0 GeV, the booster main magnetic elements will follow cycling curves with main parameters defined in Table 62. The cycling waveform shape will be a rounded triangle with rise time longer than fall time, as shown in Figure 77, a scaled universal curve where the extraction current at 3.0 GeV is set to 1 A. The maximum current is 5% higher than the extraction current.

Table 62: Booster magnets ramping curve parameters.
Cycling frequency	2	Hz
Cycling period	500	ms
Number of points per cycle	2048
Uniform time interval between points	244	μs

Figure 77: Scaled ramping curve for Booster magnets with extraction current set to 1 A. The top graph shows the current vs time where the maximum current is 5% higher than the current at extraction energy. The curve is defined by the points (+) with either linear or cubic interpolations between them. The bottom graph shows the time derivative of the current.

Booster Magnets Installation

Table 63: Booster magnets installation.
Sector	Girder	Magnets	BS	BQF	BQS	BQD	BD	BC
B01	LS-CENTRAL-003-UNI-0029	CORR-QUAD	--	BQF-042	--	--	--	BC-022
B01	LS-DIPOLO-002-UNI-0011	DIP	--	--	--	--	BD-010	--
B02	LS-BSKEW-001-UNI-0001	SEXT-QUAD-QSKEW	BS-007	BQF-007	BQS-001	--	--	--
B02	LS-DIPOLO-002-UNI-0018	QUAD-DIP-SEXT	BS-035	--	--	BQD-002	BD-037	--
B03	LS-BCH-001-UNI-0003	CORR	--	--	--	--	--	BC-027
	LS-CENTRAL-003-UNI-0022	CORR-QUAD	--	BQF-045	--	--	--	BC-021
	LS-DIPOLO-003-UNI-0022	DIP	--	--	--	--	BD-050	--
B04	LS-CENTRAL-002-UNI-0016	SEXT-QUAD	BS-013	BQF-051	--	--	--	--
B04	LS-DIPOLO-003-UNI-0023	QUAD-DIP-CORR	--	--	--	BQD-007	BD-047	BC-062
B05	LS-CENTRAL-006-UNI-0051	CORR-QUAD	--	BQF-043	--	--	--	BC-020
B05	LS-DIPOLO-004-UNI-0040	DIP	--	--	--	--	BD-044	--
B06	LS-CENTRAL-002-UNI-0011	SEXT-QUAD	BS-014	BQF-024	--	--	--	--
B06	LS-DIPOLO-002-UNI-0012	QUAD-DIP-CORR	--	--	--	BQD-018	BD-008	BC-015
B07	LS-CENTRAL-003-UNI-0027	CORR-QUAD	--	BQF-015	--	--	--	BC-037
B07	LS-DIPOLO-001-UNI-0003	DIP-SEXT	BS-034	--	--	--	BD-024	--
B08	LS-CENTRAL-001-UNI-0001	SEXT-QUAD	BS-017	BQF-049	--	--	--	--
B08	LS-DIPOLO-003-UNI-0024	QUAD-DIP-CORR	--	--	--	BQD-017	BD-043	BC-060
B09	LS-CENTRAL-005-UNI-0050	CORR-QUAD	--	BQF-016	--	--	--	BC-036
B09	LS-DIPOLO-004-UNI-0038	DIP	--	--	--	--	BD-026	--
B10	LS-CENTRAL-002-UNI-0014	SEXT-QUAD	BS-016	BQF-034	--	--	--	--
B10	LS-DIPOLO-005-UNI-0041	QUAD-DIP-CORR	--	--	--	BQD-004	BD-027	BC-025
B11	LS-CENTRAL-001-UNI-0005	CORR-QUAD	--	BQF-023	--	--	--	BC-040
B11	LS-DIPOLO-002-UNI-0020	DIP	--	--	--	--	BD-004	--
B12	LS-CENTRAL-002-UNI-0015	SEXT-QUAD	BS-019	BQF-033	--	--	--	--
B12	LS-DIPOLO-001-UNI-0009	QUAD-DIP-SEXT	BS-039	--	--	BQD-006	BD-057	--
B13	LS-BCH-001-UNI-0005	CORR	--	--	--	--	--	BC-024
	LS-CENTRAL-003-UNI-0024	CORR-QUAD	--	BQF-035	--	--	--	BC-035
	LS-DIPOLO-005-UNI-0050	DIP	--	--	--	--	BD-017	--
B14	LS-CENTRAL-002-UNI-0017	SEXT-QUAD	BS-018	BQF-047	--	--	--	--
B14	LS-DIPOLO-001-UNI-0005	QUAD-DIP-CORR	--	--	--	BQD-024	BD-009	BC-047
B15	LS-CENTRAL-005-UNI-0041	CORR-QUAD	--	BQF-037	--	--	--	BC-034
B15	LS-DIPOLO-003-UNI-0026	DIP	--	--	--	--	BD-028	--
B16	LS-CENTRAL-002-UNI-0018	SEXT-QUAD	BS-020	BQF-053	--	--	--	--
B16	LS-DIPOLO-005-UNI-0043	QUAD-DIP-CORR	--	--	--	BQD-021	BD-041	BC-041
B17	LS-CENTRAL-006-UNI-0052	CORR-QUAD	--	BQF-041	--	--	--	BC-033
B17	LS-DIPOLO-003-UNI-0027	DIP-SEXT	BS-043	--	--	--	BD-025	--
B18	LS-CENTRAL-002-UNI-0013	SEXT-QUAD	BS-021	BQF-052	--	--	--	--
B18	LS-DIPOLO-003-UNI-0025	QUAD-DIP-CORR	--	--	--	BQD-016	BD-013	BC-044
B19	LS-CENTRAL-004-UNI-0035	CORR-QUAD	--	BQF-011	--	--	--	BC-039
B19	LS-DIPOLO-001-UNI-0004	DIP	--	--	--	--	BD-031	--
B20	LS-CENTRAL-001-UNI-0007	SEXT-QUAD	BS-022	BQF-032	--	--	--	--
B20	LS-DIPOLO-001-UNI-0008	QUAD-DIP-CORR	--	--	--	BQD-027	BD-054	BC-026
B21	LS-CENTRAL-004-UNI-0031	CORR-QUAD	--	BQF-048	--	--	--	BC-013
B21	LS-DIPOLO-006-UNI-0051	DIP	--	--	--	--	BD-021	--
B22	LS-CENTRAL-004-UNI-0034	SEXT-QUAD	BS-025	BQF-030	--	--	--	--
B22	LS-DIPOLO-002-UNI-0016	QUAD-DIP-SEXT	BS-037	--	--	BQD-014	BD-030	--
B23	LS-BCH-001-UNI-0001	CORR	--	--	--	--	--	BC-019
	LS-CENTRAL-005-UNI-0045	CORR-QUAD	--	BQF-009	--	--	--	BC-010
	LS-DIPOLO-005-UNI-0045	DIP	--	--	--	--	BD-035	--
B24	LS-CENTRAL-001-UNI-0003	SEXT-QUAD	BS-026	BQF-050	--	--	--	--
B24	LS-DIPOLO-004-UNI-0031	QUAD-DIP-CORR	--	--	--	BQD-012	BD-032	BC-059
B25	LS-CENTRAL-002-UNI-0020	CORR-QUAD	--	BQF-025	--	--	--	BC-016
B25	LS-DIPOLO-005-UNI-0042	DIP	--	--	--	--	BD-007	--
B26	LS-CENTRAL-001-UNI-0002	SEXT-QUAD	BS-029	BQF-040	--	--	--	--
B26	LS-DIPOLO-004-UNI-0035	QUAD-DIP-CORR	--	--	--	BQD-015	BD-018	BC-011
B27	LS-CENTRAL-004-UNI-0040	CORR-QUAD	--	BQF-036	--	--	--	BC-009
B27	LS-DIPOLO-002-UNI-0013	DIP-SEXT	BS-042	--	--	--	BD-029	--
B28	LS-CENTRAL-003-UNI-0028	SEXT-QUAD	BS-031	BQF-038	--	--	--	--
B28	LS-DIPOLO-003-UNI-0028	QUAD-DIP-CORR	--	--	--	BQD-026	BD-034	BC-029
B29	LS-CENTRAL-005-UNI-0047	CORR-QUAD	--	BQF-056	--	--	--	BC-012
B29	LS-DIPOLO-006-UNI-0052	DIP	--	--	--	--	BD-014	--
B30	LS-CENTRAL-001-UNI-0006	SEXT-QUAD	BS-023	BQF-031	--	--	--	--
B30	LS-DIPOLO-004-UNI-0032	QUAD-DIP-CORR	--	--	--	BQD-005	BD-052	BC-058
B31	LS-CENTRAL-005-UNI-0042	CORR-QUAD	--	BQF-055	--	--	--	BC-053
B31	LS-DIPOLO-002-UNI-0019	DIP	--	--	--	--	BD-053	--
B32	LS-CENTRAL-004-UNI-0038	SEXT-QUAD	BS-027	BQF-054	--	--	--	--
B32	LS-DIPOLO-001-UNI-0010	QUAD-DIP-SEXT	BS-036	--	--	BQD-009	BD-055	--
B33	LS-BCH-001-UNI-0002	CORR	--	--	--	--	--	BC-018
	LS-CENTRAL-003-UNI-0021	CORR-QUAD	--	BQF-029	--	--	--	BC-054
	LS-DIPOLO-005-UNI-0047	DIP	--	--	--	--	BD-036	--
B34	LS-CENTRAL-001-UNI-0009	SEXT-QUAD	BS-024	BQF-019	--	--	--	--
B34	LS-DIPOLO-003-UNI-0029	QUAD-DIP-CORR	--	--	--	BQD-011	BD-045	BC-014
B35	LS-CENTRAL-003-UNI-0026	CORR-QUAD	--	BQF-028	--	--	--	BC-055
B35	LS-DIPOLO-001-UNI-0002	DIP	--	--	--	--	BD-046	--
B36	LS-CENTRAL-002-UNI-0012	SEXT-QUAD	BS-015	BQF-020	--	--	--	--
B36	LS-DIPOLO-001-UNI-0006	QUAD-DIP-CORR	--	--	--	BQD-019	BD-022	BC-038
B37	LS-CENTRAL-003-UNI-0023	CORR-QUAD	--	BQF-027	--	--	--	BC-049
B37	LS-DIPOLO-005-UNI-0048	DIP-SEXT	BS-040	--	--	--	BD-038	--
B38	LS-CENTRAL-001-UNI-0010	SEXT-QUAD	BS-033	BQF-012	--	--	--	--
B38	LS-DIPOLO-005-UNI-0049	QUAD-DIP-CORR	--	--	--	BQD-022	BD-039	BC-048
B39	LS-CENTRAL-004-UNI-0037	CORR-QUAD	--	BQF-046	--	--	--	BC-050
B39	LS-DIPOLO-004-UNI-0034	DIP	--	--	--	--	BD-042	--
B40	LS-CENTRAL-005-UNI-0049	SEXT-QUAD	BS-030	BQF-022	--	--	--	--
B40	LS-DIPOLO-002-UNI-0015	QUAD-DIP-CORR	--	--	--	BQD-001	BD-016	BC-043
B41	LS-CENTRAL-003-UNI-0030	CORR-QUAD	--	BQF-057	--	--	--	BC-051
B41	LS-DIPOLO-004-UNI-0036	DIP	--	--	--	--	BD-040	--
B42	LS-CENTRAL-005-UNI-0044	SEXT-QUAD	BS-028	BQF-058	--	--	--	--
B42	LS-DIPOLO-002-UNI-0017	QUAD-DIP-SEXT	BS-041	--	--	BQD-023	BD-049	--
B43	LS-BCH-001-UNI-0004	CORR	--	--	--	--	--	BC-028
	LS-CENTRAL-005-UNI-0043	CORR-QUAD	--	BQF-044	--	--	--	BC-056
	LS-DIPOLO-003-UNI-0030	DIP	--	--	--	--	BD-005	--
B44	LS-CENTRAL-004-UNI-0033	SEXT-QUAD	BS-008	BQF-039	--	--	--	--
B44	LS-DIPOLO-004-UNI-0037	QUAD-DIP-CORR	--	--	--	BQD-010	BD-048	BC-057
B45	LS-CENTRAL-005-UNI-0046	CORR-QUAD	--	BQF-018	--	--	--	BC-052
B45	LS-DIPOLO-001-UNI-0007	DIP	--	--	--	--	BD-023	--
B46	LS-CENTRAL-003-UNI-0025	SEXT-QUAD	BS-010	BQF-014	--	--	--	--
B46	LS-DIPOLO-004-UNI-0039	QUAD-DIP-CORR	--	--	--	BQD-013	BD-051	BC-046
B47	LS-CENTRAL-001-UNI-0008	CORR-QUAD	--	BQF-021	--	--	--	BC-017
B47	LS-DIPOLO-003-UNI-0021	DIP-SEXT	BS-038	--	--	--	BD-033	--
B48	LS-CENTRAL-004-UNI-0032	SEXT-QUAD	BS-012	BQF-017	--	--	--	--
B48	LS-DIPOLO-005-UNI-0044	QUAD-DIP-CORR	--	--	--	BQD-003	BD-019	BC-045
B49	LS-CENTRAL-002-UNI-0019	CORR-QUAD	--	BQF-026	--	--	--	BC-023
B49	LS-DIPOLO-005-UNI-0046	DIP	--	--	--	--	BD-011	--
B50	LS-CENTRAL-004-UNI-0039	SEXT-QUAD	BS-032	BQF-013	--	--	--	--
B50	LS-DIPOLO-002-UNI-0014	QUAD-DIP-CORR	--	--	--	BQD-008	BD-020	BC-061

TB Transfer Line Magnets

TB Dipoles and septum

The TB dipoles and septum main parameters are shown in Table 64.

Table 64: Main parameters for LTB transfer line dipoles.
	Spectrometer	Dipole	Septum
Number	1	3	1
Magnetic length	0.450	0.304	0.500	m
Physical length	--	0.2945	--	m
Deflection angle	15.0	15.0	21.75	°
Hardedge bending radius	1.719	1.161	1.317	m
Hardedge magnetic field	0.291	0.431	0.380	T
Quadrupole gradient	0	0	0	T/m
Hardedge sagitta	14.7	9.293	23.7	mm

Table 65: TB dipole electric parameters
	TB Dipole	units
Main coil current	254	A
Main coil number of turns	23
Stored magnetic energy	116.6	J
Magnet inductance	3.7	mH

TB Dipole Magnet 3D Model

Figure 78: 3D drawing of the TB dipole model.

Figure 79: Field of the TB dipole model.

Fieldmap Analysis

A 3D magnetic model has been created and its fieldmap analyzed. A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

In order to take into account the s-dependent field profile of the TB dipoles a symmetric model was created.

Figure 80: TB dipole B_y field on the trajectory calculated by Runge-Kutta integration and the adopted segmented model used in simulation codes. Only half dipole is shown in longitudinal direction.

Table with segmented dipole model

Table 66: TB dipole segmented model.
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0800	3.966	-0.433	-0.001	-0.074
02	0.0200	0.990	-0.432	-0.021	-0.268
03	0.0200	0.940	-0.410	-0.644	-4.760
04	0.0200	0.645	-0.282	-1.630	-6.590
05	0.0200	0.382	-0.167	-0.775	-13.400
06	0.0200	0.244	-0.107	-0.374	-14.100
07	0.0300	0.205	-0.060	-0.213	-9.210
08	0.0300	0.129	-0.037	-0.138	-6.080

^* K=B'/(Bρ), S=B"/(2Bρ)

Constructed from simulated fieldmap at nominal energy

TB Dipole Magnet Measurements

A summary of magnet field measurements will eventually be documented here.

TB Quadrupoles

The quadrupoles in the TB transfer line (TB-QD) use the same yoke as the Booster 8.5 cm long quadrupoles BQD (effective length of 10 cm). A new set of coils is used to allow higher gradient with a 10 A power supply. In the first TB sector (just after the last Linac accelerating structure), there are 4 quadrupoles (a quadrupole triplet and a focus quadrupole) that will be purchased as part of the Linac. The TB quadrupoles main parameters are shown in Table 67 and their detailed configuration in Table 69.

Table 67: Main parameters for LTB transfer line quadrupoles.
	Part of Linac	TB
Model name	Linac	BQD
Number	4	10
Physical length	0.050 / 0.100	0.085	m
Magnetic length	--	0.100	m
Maximum field gradient	10.0	8.000	T·m^-1
Bore diameter	40.0	40.0	mm
Maximum field at pole tip	0.2	0.16	T

Table 68: TB quadrupole electric parameters
	TB Quadrupole	units
Main coil current	10.00	A
Main coil number of turns	140
Stored magnetic energy	5.62	J
Magnet inductance	112.4	mH

Table 69: Quadrupole configuration for TB transfer line modes.
Quadrupole	Eff. Length [m]	dB/dx [T/m] @ E=150 MeV
Quadrupole	Eff. Length [m]	M1	M2	M3	M4	M5	M6
QD1	0.100	-8.42	--	--	--	--	--
QF1	0.100	13.15	--	--	--	--	--
QD2A	0.100	-5.00	--	--	--	--	--
QF2A	0.100	6.78	--	--	--	--	--
QF2B	0.100	2.90	--	--	--	--	--
QD2B	0.100	-2.98	--	--	--	--	--
QF3	0.100	7.96	--	--	--	--	--
QD3	0.100	-2.01	--	--	--	--	--
QF4	0.100	11.53	--	--	--	--	--
QD4	0.100	-7.08	--	--	--	--	--

TB Quadrupole Magnet 3D Model

Figure 81: 3D drawing of the TB quadrupole model.

Figure 82: Field of the TB quadrupole model.

Fieldmap Analysis

A 3D magnetic model has been created and its fieldmap analyzed. A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

In order to take into account the s-dependent field profile of the TB quadrupoles a symmetric model was created.

Figure 83: TB quadrupole B_y field on the trajectory calculated by Runge-Kutta integration and the adopted segmented model used in simulation codes. Only half quadrupole is shown in longitudinal direction.

Table with segmented quadrupole model

Table 70: TB quadrupole segmented model.
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0500	0.000	-0.000e+00	+1.600e+01	+0.000e+00

^* K=B'/(Bρ), S=B"/(2Bρ)

Constructed from simulated fieldmap at maximum excitation current.

TB Quadrupole Magnet Measurements

A summary of magnet field measurements will eventually be documented here.

TB Correctors

The main TB corrector parameters are shown in Table 71.

TB Corrector Magnet Specifications

Main Parameters

Table 71: Main parameters for LTB transfer line correctors.
Type of corrector	Number	Max. θ (mrad)	∫B.ds [T.m] @ E=150 MeV
Septum	1	± 6.8	± 3.4E-03
CH	5	± 2.5	± 1.25E-03
CV	6	± 2.5	± 1.25E-03

TB Corrector Magnet 3D Model

Figure 84: 3D drawing of the TB corrector model.

Figure 85: Field of the TB corrector model with its CH coils excited.

Fieldmap Analysis

CH

A summary of the analysis can be found in analysis.txt at this folder.

CV

A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

Currently the hard-edge approximation is being used to model TB correctors.

Figure 86: TB corrector B_y field on the trajectory calculated by Runge-Kutta integration and the adopted segmented model used in simulation codes. Only half of corrector is shown in longitudinal direction.

Table 72: TB corrector half segmented model (maximum strength).
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.0405	0.000	-1.916e-02	-4.400e-06	-4.840e+01

^* K=B'/(Bρ), S=B"/(2Bρ)

TB Corrector Magnet Measurements

TS Transfer Line Magnets

TS Dipoles and septa

The TS dipoles and septum main parameters are shown in Table 73.

The TS dipoles are mechanically the same as the Booster dipoles but the deflection angle has been reduced from +7.2 ° (Booster) to +5.012 ° (TS). This is necessary to avoid overheating of the coils since BTS dipoles will operate in DC regime while Booster dipoles operate in CW mode.

Table 73: Main parameters for BTS septa and dipoles.
	Dipoles	Thin ext. septum	Thick ext. septum	Thick inj. septum	Thin inj. septum
Number	3	1	1	2	1
Magnetic length	1.216	0.577	0.577	0.577	0.500	m
Physical length	1.206	--	--	--	--	m
Deflection angle	+5.012	-3.600	-3.600	+3.600	+3.118	°
Hardedge bending radius	13.902	-9.188	-9.188	9.188	9.188	m
Integrated magnetic field	0.875	-0.629	-0.629	0.629	0.545	T·m
Integrated quadrupole strength	-0.169	-	-	-	-	m^-1
Hardedge sagitta	13.40	4.53	4.53	4.53	3.40	mm

Table 74: TS dipole electric parameters
	TS Dipole	units
Main coil current	680.10	A
Main coil number of turns	12
Stored magnetic energy	1075.88	J
Magnet inductance	4.65	mH

TS Dipole Magnet 3D Model

Same model as for BO dipoles.

Figure 87: 3D drawing of the booster dipole model.

Figure 88: Field of the booster dipole model.

Fieldmap Analysis

A 3D magnetic model has been created and its fieldmap analyzed. A summary of the analysis can be found in analysis.txt at this folder.

Segmented Model

In order to take into account the s-dependent field profile of the TS dipoles a symmetric model was created.

Figure 89: TS dipole B_y field on the trajectory calculated by Runge-Kutta integration and the adopted segmented model used in simulation codes. Only half dipole is shown in longitudinal direction.

Table with segmented dipole model

Table 75: TS dipole segmented model.
Segment#	Length [m]	Deflection [deg.]	Field [T]	K [m^-2] ^*	S [m^-3] ^*
01	0.1960	0.808	-0.720	-0.151	-1.350
02	0.1920	0.796	-0.724	-0.144	-1.330
03	0.1820	0.761	-0.730	-0.132	-1.320
04	0.0100	0.035	-0.618	-0.158	-1.140
05	0.0100	0.025	-0.445	-0.100	-0.858
06	0.0130	0.023	-0.306	-0.036	-1.100
07	0.0170	0.020	-0.208	-0.007	-1.240
08	0.0200	0.016	-0.136	+0.002	-1.040
09	0.0300	0.013	-0.074	+0.002	-0.616
10	0.0500	0.009	-0.030	+0.001	-0.243

^* K=B'/(Bρ), S=B"/(2Bρ)

Constructed from simulated fieldmap at nominal energy

TS Quadrupoles

Table 76 lists main specifications for TS quadrupoles (same as the storage ring quadrupoles) and Table 77 their detailed configuration.

Table 76: Main parameters for TS transfer line quadrupoles.
Magnet model name	Q14	Q20
Number	5	3
Quadrupoles	QF1A,QF1B,QD2,QD4A,QD4B	QF2,QF3,QF4
Maximum gradient	37.23	45.43	T·m^-1
Bore diameter	28	28	mm
Maximum field at pole tip	0.52	0.64	T

Table 77: BTS transfer line quadrupole configuration for modes M1 and M2.
Quadrupole	Length [m]	dB/dx [T/m] @ E=3 GeV
Quadrupole	Length [m]	M1	M2
QF1A	0.14	16.4	17.6
QF1B	0.14	12.6	15
QD2	0.14	-34	-34.1
QF2	0.2	26.9	27.1
QF3	0.2	32.7	31.5
QD4A	0.14	-33.4	-32.1
QF4	0.2	40.8	40.5
QD4B	0.14	-17	-17.7

TS Correctors

Table 78 lists main specifications for TS correctors

Table 78: Main parameters for BTS transfer line correctors.
Length	0.1	m
Number of horizontal correctors	4
Number of septa used as horizontal correctors	2
Number of vertical correctors	6
Maximum strength	±0.35	mrad
Maximum field (E=3 GeV)	± 3.50E-03	T.m

Magnet Colors

Table 79: Magnet colors
dipoles	RAL 5012
quadrupoles	RAL 2008
sextupoles	RAL 6021
correctors	N6,5 Munsell
coils
girders	RAL 9010
pulsed magnets	RAL 3000

Machine:Magnets

Contents

Storage Ring Magnets

SI Dipole Magnet Specifications

Main Parameters

SI Dipole Magnet 3D Models

BC

B1

B2

BC

Summary

Deflection Angle

Integrated Quadrupole

Integrated Sextupole

B1

Summary

Deflection Angle

Integrated Quadrupole

Integrated Sextupole

B2

Summary

Deflection Angle

Integrated Quadrupole

Integrated Sextupole

B1 Installation Order

B2 Installation Order

SI Quadrupole Magnet Specifications

Main Parameters

SI Quadrupole Magnet 3D Models

Fieldmap Analysis

Q14

Summary

Integrated Quadrupole

Horizontal Magnetic Center

Vertical Magnetic Center

Roll-Angle Error

Q20

Summary

Integrated Quadrupole

Horizontal Magnetic Center

Vertical Magnetic Center

Roll-Angle Error

Q30

Summary

Integrated Quadrupole

Horizontal Magnetic Center

Vertical Magnetic Center

Roll-Angle Error

Q14 Installation Order

Q20 Installation Order

Q30 Installation Order

SI Sextupole Magnet Specifications

Main Parameters

Multipole Errors

SI Sextupole Magnet 3D Models

Sextupolar function

Sextupolar+Horizontal functions

Sextupolar+Vertical functions

Sextupolar+Skew functions

Summary

Integrated Sextupole

Horizontal Magnetic Center

Vertical Magnetic Center

Roll-Angle Error

SI Fast Correctors Specifications

SI Fast Correctors Magnet 3D Models

FC1 Horizontal correction function

FC1 Vertical correction function

FC1 Skew quadrupole function

FC2 Horizontal correction function

FC2 Vertical correction function

Storage Ring Magnet Families

Storage Ring Dipole Families

Storage Ring Quadrupole Families

Storage Ring Sextupole Families

Booster Magnets

BO Dipole Magnet Specifications

Multipole Errors

BO Dipole Magnet 3D Model

BO Quadrupole Magnets Specifications