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AbstractCalculations of Harmonics of Quadrupole Magnets
Rybitskaya Tatyana, Budker Institute of Nuclear Physics, Russia
Design of pole profile and chamfers of NSLSII quadrupole magnets manufactured at BINP
are presented. Calculations of dependence skew-sextupole harmonic of current are shown. Way for correction the dependence is described. Calculations of harmonics correction by bronze bars, nose pieces and modified nose pieces are presented.
1
Calculations of harmonics of quadrupole magnets
Budker Institute of Nuclear PhysicsRybitskaya Tatyana
Plan of presentation
• Allowed harmonics
• Dependence of skew-sextupole harmonic of current
• Harmonics correction by bronze bars
• Harmonics correction by nose pieces
• Nose pieces with modified profile
Calculations of:
3
Software used for calculationsMERMAID Mermaid applies first order Finite
Elements Method on the mesh consisted of triangle prisms for field computation. Created at Budker Institute of Nuclear physics.
OPERAA finite element environment for the complete analysis and design of electromagnetic applications in 3 dimensions. Product of company COBHAM
4
Magnetic field expansion
1
1
0
)cossin(),,(0
0n
nn
nz
z
nBnArr
dzzrB
r
z
φ
1
1
0
)sincos(),,(0
0n
nn
nz
z
r nBnArr
dzzrB
4
2
10B
Aa n
n
4
2
10BB
b nn
On radius r0 = 2.5 cm
Skew harmonics
Normal harmonics
5
Profile features of magnets calculated
Flat parts of shims (necessary for stacking and gluing magnets with high precision).
Long (9804/9807) and middle (9810/9813) length magnets have nose pieces.
Chamfers are flat 45°.
45°
L
L
magnetic axis
chamfer
Pole/ nose piece
Flat part
6
chamfer
Allowed harmonics in magnet center were minimized
Yoke edges in 3D provide big b6
2D or magnetic field in magnet centre plane
MERMAID
Calculations of allowed harmonics
Chamfers decrease b6 but at the same time increase b10
3D without chamfer 120 A
3D with chamfer 120 A
7
Shimming of magnet
K.HalbachFirst order perturbation effect in iron-dominated two dimensional symmetric multipoles // NIM vol.74, 1969.
8
Relative changing of harmonic volume. Bumps along profile has the same area.
β
α
L
H
magnetic axis
chamfer
nose piece
Calculations of chamfers of long magnets
α - angle between magnetic axis and chamfer plane
Nose pieces size:• 15 mm along magnetic axis• 34.45 mm perpendicular magnetic axis
The sizes limit size of chamfer
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Calculations of chamfers of long magnets
Without chamfer
Current 125 A
MERMAID10
Sextupole harmonics of current
First measurements of sextupole harmonics of first long magnet
9807-0001 measurements
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a3 current dependence was quite big
Possible reasons of a3 current dependence • Different permeability of halves. Two samples were
cut from steel roll – one from beginning, another from middle of roll.
• Different packing factor of halves. Measurements shown maximum difference 0.25%
• Different halves lengths. Measurements shown maximum difference 0.2 mm.
12
Steel properties measured at DESY
Calculations of a3 current dependence for long magnets
MERMAID
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If the worst case variation of a3 can be 2.5 units.
Δ=1.1
Δ=1.5
Corrections of harmonic a3 dependence of current
• The most effective way for correction is special shuffling.• Additional way for correction :
OPERA
Face of nose piece
Shift need additional correction
Δ=1.94
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Harmonics correction by bronze bars
+ ∆l
- ∆l/2- ∆l/2 - ∆l
+ ∆l
+ ∆l
- ∆l
Calculations ∆l = 20 µm
OPERA15
Widths of two insertions can correct a3 and b4
One bar width is increased
Two bars widths are increased simultaneously
Harmonics correction by nose pieces
+ ∆l
+ ∆l
+ ∆l
+ ∆l
Calculations ∆l = 150 µm
OPERA16
Each nose pieces can be shifted independently.Advantage: In principal many harmonics can be corrected. Disadvantage: Nose pieces should be installed carefully not to reduce field quality.
Correction of allowed harmonics on ready magnet
17
Nose pieces with modified profile
Calculations of magnetic field of middle length magnets
(9810 and 9813)
Chamfer 12.8 mm Chamfer 9.6 mm
MERMAID18
Measurements of magnetic field of magnet 9813-0001
Chamfer 13mm Chamfer 10mm
modified profile
19
Summary• 2D profile was chosen with allowed
harmonics less then 0.7 units, as result chamfering increase b10 up to 2.5 units for short magnets.
• Material properties can increase a3 dependence of current up to 2.5 units.
• Bronze bars provide corrections of a3 and b4.
• Nose pieces provide correction of b3 and additional correction of a3 and b4.
• Using nose pieces with modified profile make integral fields and fields in the magnet center “good” at the same time.
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THE END
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Comparison measurements and calculations of long magnets without nose pieces and chamfers
22
Question
Why calculations and measurements has deviations?
• Different magnetic steel properties in program and in reality?
• Changes of permeability at the age of plates cause of stamping? • Something else?
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