Multipole Magnet Design Selection and
Permanent Magnet Material Selection
May 18, 2000
Stanford University
Manufacturing Modeling Lab
Shun Takai
$$
Agenda
1. Motivation
2. Cost-Specification Analysis– Flow Down of the Product Targets– Evaluation of the candidates– Selection of the best candidate
3. Conclusion
Motivation
• Needs for multiple requirements satisfaction
• NLC– Feature (physicists’ requirements)– Cost (Government’s requirements)
• Cost-Specification Analysis highlights design and/or material candidate that satisfies both target specification and target cost
Multipole Magnets• Quantity: 1500 quadrupole magnets in Main Linac system
6000 permanent magnet sets Permanent Magnet Set
Current Design (Electro-Magnets) Proposed Design (Hybrid Magnets)
Agenda
1. Motivation
2. Cost-Specification Analysis– Flow Down of the Product Targets– Evaluation of the candidates– Selection of the best candidate
3. Conclusion
Targets Flow Down• Flow down of the product targets to the focus structures
ProductTarget
Features (Specifications) Cost
- Identify structures that are focus of the analysis. - Identify specifications that are relevant only to the focus of the analysis.
- Calculate target cost from its worth relative to the worth of the product (NLC).
StructureTarget
Specifications Cost
Focus of the Analysis - Structure• Focus: (1) Main Linac multipole magnet system
(2) permanent magnet used in quads
Product Main Systems Sub-Systems Assemblies Parts
NLC Main LinacMultipole magnets
Quadrupole magnet
PM
PM for magnetic field adjustment
InjectionAccelerator structures
Magnetic field adjustment device
Steel poles
BPM Movers for quad Flux return
Beam Delivery
Vacuum systems
Quad support structure
Aluminum spacers
Movers End walls
RF system Base plate
Specification Flow Down - VOC and SpecsVOC NLC Main Linac Multipole Quadrupole Permanent
Magnet Magnet Magnet
Study the matter created
Energy Energy gradientMagnetic field gradient x effective length (Gdl)
Effective length Flux Density (Br)
when electrons 9and positrons collide
Length of the accelerator
Pole tip radius Coercivity (Hc)
Flexible latice Higher harmonics Pole tip fieldIntrinsic coercivity (Hci)
Luminosity Emittance Gdl rangeTemperature coefficients of Br
Pole tip field accuracy
Temperature coefficients of Hci
Beam position stability (Low jitter)
Gdl accuracy Strength toleranceRadiation Resistance
Background AberrationsMagnetic center accuracy (static)
Position tolerance (static)
Width (w)
Vacuum quality Thickness (t*)
Magnetic center latice dynamic
Position tolerance (dynamic)
Length (L)
Low background Tolerance of w
Availability Availability Availability Availability Tolerance of t*
Tolerance of L
9 : Most important
3 : Important
1 : Least important
Cost Flow Down
• Target cost of a structure
– Calculated relative to the worth of the NLC
Worth of a structure
Worth of NLCTarget cost of a structure
= X Target cost of NLC
How can I calculate the worth of a structure?
Worth Allocation: Main Systems• Worth of NLC is equal to the total worth of VOCProduct Main Systems Sub-Systems Assemblies Parts
NLC 9 Main Linac Multipole magnetsQuadrupole magnet
PM
PM for magnetic field adjustment
Injection Accelerator structuresMagnetic field adjustment device
Steel poles
BPM Movers for quad Flux return
Beam Delivery Vacuum systemsQuad support structure
Aluminum spacers
Movers End walls
RF system Base plate
9 : Most important
3 : Important
1 : Least important
Study the matter created when electrons 9and positrons collide
1. Calculate worth of NLC specification from worth of VOC
(Translate VOC to NLC specs)
2. Calculate worth of main systems from its contribution to achieve NLC specs
(Larger the contribution, larger the worth)
Worth Allocation: Main Systems1. Calculate worth of NLC specification from worth of VOC
(Translate VOC to NLC specs)
NLC Specification
VOCWorth of
VOC En
erg
y
Lu
min
osi
ty
Bac
kgro
un
d
Ava
ilab
ility
Study the matter created when electrons and positrons collide
9 9 3 3 1
NLC Specification
VOCWorth of
VOC En
erg
y
Lu
min
osi
ty
Bac
kgro
un
d Ava
ilab
ility
Study the matter created when electrons and positrons collide
9 5.1 1.7 1.7 0.6
9Worth of NLC Specification 5.1 1.7 1.7 0.6 9.0
VOC NLC Specs
Study the matter created when electrons and positrons collide
9 Energy
Luminosity
Background
Availability
Large (9) contribution of NLC specMedium (3) contribution of NLC specSmall (1) contribution of NLC spec
Worth Allocation: Main Systems2. Calculate worth of main systems from its contribution to achieve NLC specs
(Larger the contribution, larger the worth) NLC Main Systems
NLC Specifications
Worth of NLC
Specs Mai
n l
inac
Inje
ctio
n
Bea
m d
eliv
ery
Energy 5.1 9 1
Luminosity 1.7 3 1 9Background 1.7 3 1 9Availability 0.6 9 9 9
NLC Main Systems
NLC Specifications
Worth of NLC
Specs Mai
n l
inac
Inje
ctio
n
Bea
m
del
iver
y
Energy 5.1 4.6 0.5Luminosity 1.7 0.4 0.1 1.2Background 1.7 0.4 0.1 1.2Availability 0.6 0.2 0.2 0.2
9Worth of Main Systems 5.5 1.0 2.5 9.0
NLC Specs Main Systems
Energy 5.1 Main linac
Luminosity 1.7Injection
Background 1.7
Availability 0.6 Beam delivery
Large (9) contributionMedium (3) contributionSmall (1) contribution
Worth Allocation: Main Linac Sub-systems• Calculate worth of Main Linac sub-systems
Product Main Systems Sub-Systems Assemblies Parts
NLC 9 Main Linac 5.5 Multipole magnetsQuadrupole magnet
PM
PM for magnetic field adjustment
Injection 1.0 Accelerator structuresMagnetic field adjustment device
Steel poles
BPM Movers for quad Flux return
Beam Delivery 2.5 Vacuum systemsQuad support structure
Aluminum spacers
Movers End walls
RF system Base plate
9 : Most important
3 : Important
1 : Least important
Study the matter created when electrons 9and positrons collide
Worth Allocation: Main Linac Sub-systems1. Calculate worth of Main Linac specs from worth of NLC specs
(Translate NLC specs to Main Linac specs)
Large contribution of lower level specificationMedium contribution of lower level specificationSmall contribution of lower level specification
Main Linac Specifications
NLC Specs
Worth of NLC Specs due to Main Linac E
ne
rgy
gra
die
nt
Le
ng
th o
f th
e
ac
ce
lera
tor
Fle
xib
le l
ati
ce
Em
itta
nc
e
Be
am
po
sit
ion
s
tab
ilit
y (
Lo
w
Ab
err
ati
on
s
Va
cu
um
qu
ali
ty
Lo
w b
ac
kg
rou
nd
Av
ail
ab
ilit
y
Energy 4.6 9 9 3 3Luminosity 0.4 3 3 3 1Background 0.4 9 9 1 1Availability 0.2 9
Main Linac Specifications
NLC Specs
Worth of NLC Specs due to Main Linac E
ne
rgy
gra
die
nt
Le
ng
th o
f th
e
ac
ce
lera
tor
Fle
xib
le l
ati
ce
Em
itta
nc
e
Be
am
po
sit
ion
s
tab
ilit
y (
Lo
w
Ab
err
ati
on
s
Va
cu
um
qu
ali
ty
Lo
w b
ac
kg
rou
nd
Av
ail
ab
ilit
y
Energy 4.6 1.7 1.7 0.6 0.6Luminosity 0.4 0.1 0.1 0.1 0.04Background 0.4 0.2 0.2 0.02 0.02Availability 0.2 0.2
5.5Worth of Main Linac Specs 1.7 1.7 0.6 0.3 0.1 0.3 0.6 0.02 0.2 5.5
Worth of NLC Specs Main Linac Specsdue to Main Linac
Energy 4.6 Energy gradient
Length of the accelerator
Flexible latice
Luminosity 0.4 Emittance
Beam position stability (Low jitter)
Background 0.4 Aberrations
Vacuum quality
Low background
Availability 0.2 Availability
Worth Allocation: Main Linac Sub-systems2. Calculate worth of Main Linac sub-systems from its contribution to achieve Main Linac specs
(Larger the contribution, larger the worth)
Large (9) contributionMedium (3) contributionSmall (1) contribution
Main Linac Sub-systems of Specs Main Linac
Energy gradient 1.7Multipole magnets
Length of the accelerator
1.7
Flexible lattice 0.6Accelerator structures
Emittance 0.3BPM
Beam position stability (Low jitter)
0.1
Aberrations 0.3Vacuum systems
Vacuum quality 0.6Movers
Low background 0.02
Availability 0.2 RF system
Main Linac Sub-systems
Main Linac Specs
Worth of Main Linac Specs M
ult
ipo
le m
ag
ne
t s
ys
tem
sA
cc
ele
rato
r s
tru
ctu
res
Be
am
po
sit
ion
m
on
ito
rs (
BP
M)
Va
cu
um
sy
ste
ms
Mo
ve
rs
(Po
sit
ion
ers
)
RF
sy
ste
m
Energy gradient 1.7 9 3 3Length of the accelerator 1.7 9 3 3Flexible latice 0.6 9Emittance 0.3 9 9 3 3 1Beam position stability (Low jitter) 0.1 9 3 9Aberrations 0.3 9 9 3 3 1Vacuum quality 0.6 3 3Low background 0.02 3 3 1 1 1 1Availability 0.2 9 9 1 3 1 9
Main Linac Sub-systems
Main Linac Specs
Worth of Main Linac Specs M
ult
ipo
le m
ag
ne
t s
ys
tem
sA
cc
ele
rato
r s
tru
ctu
res
Be
am
po
sit
ion
m
on
ito
rs (
BP
M)
Va
cu
um
sy
ste
ms
Mo
ve
rs
(Po
sit
ion
ers
)
RF
sy
ste
m
Energy gradient 1.7 1.0 0.3 0.3Length of the accelerator 1.7 1.0 0.3 0.3Flexible latice 0.6 0.6Emittance 0.3 0.1 0.1 0.0 0.0 0.01Beam position stability (Low jitter) 0.1 0.1 0.0 0.1Aberrations 0.3 0.1 0.1 0.0 0.0 0.01Vacuum quality 0.6 0.3 0.3Low background 0.02 0.01 0.01 0.002 0.002 0.002 0.002Availability 0.2 0.1 0.1 0.01 0.0 0.01 0.1
5.5Worth of Main Linac sub-systems 0.9 2.6 0.1 1.0 0.1 0.8 5.5
Specification Flow Down - Result
Large contribution of lower level specificationMedium contribution of lower level specificationSmall contribution of lower level specification
VOC NLC Main Linac Multipole Quadrupole PermanentMagnet Magnet Magnet
Study the matter created
Energy 5.1 Energy gradient 1.7Magnetic field gradient x effective length (Gdl)
0.01 Effective length 0.003 Flux Density (Br) 0.005
when electrons 9and positrons collide
Length of the accelerator
1.7 Pole tip radius 0.03
Flexible latice 0.6 Higher harmonics 0.07 Pole tip field 0.03Intrinsic coercivity (Hci)
0.002
Luminosity 1.7 Emittance 0.3 Gdl range 0.6Temperature coefficients of Br
0.007
Pole tip field accuracy
0.02Temperature coefficients of Hci
0.001
Beam position stability (Low jitter)
0.1 Gdl accuracy 0.07 Strength tolerance 0.002Radiation Resistance
0.03
Background 1.7 Aberrations 0.3Magnetic center accuracy (static)
0.01Position tolerance (static)
0.001 Width (w) 0.005
Vacuum quality 0.6 Thickness (t*) 0.005
Magnetic center latice dynamic
0.1Position tolerance (dynamic)
0.02 Length (L) 0.005
Low background 0.02 Tolerance of w 0.0001
Availability 0.6 Availability 0.2 Availability 0.05 Availability 0.03 Tolerance of t* 0.0001
Tolerance of L 0.0001
Worth Allocation - Result
9 : Most important
3 : Important
1 : Least important
Product Main Systems Sub-Systems Assemblies Parts
NLC 9 Main Linac 5.5 Multipole magnets 0.9Quadrupole magnet
0.14 PM 0.06
PM for magnetic field adjustment
0.02
Injection 1.0 Accelerator structures 2.7Magnetic field adjustment device
0.64 Steel poles 0.04
BPM 0.1 Movers for quad 0.05 Flux return 0.004
Beam Delivery 2.5 Vacuum systems 1.0Quad support structure
0.05Aluminum spacers
0.01
Movers 0.1 End walls 0.002
RF system 0.8 Base plate 0.001
Study the matter created when electrons 9and positrons collide
Target Flow Down - Cost Calculation
0.9 / 1500 (Worth of a multipole magnet system)
9 (Worth of NLC)
Target cost of a multipole magnet system
= X Target cost of NLC
0.06 / 6000 (Worth of a permanent magnet set)
9 (Worth of NLC)
Target cost of a permanent magnet set
= X Target cost of NLC
Agenda
1. Motivation
2. Cost-Specification Analysis– Flow Down of the Product Targets– Evaluation of the candidates– Selection of the best candidate
3. Conclusion
Cost Evaluation
• Select structure candidates with
Actual Cost < Target cost
or
< 1Actual cost
Target cost
Relative Cost
Cost-Specification Analysis
0
1
2
3
0 1 2
Relative Performance (Spec = 1)
Re
lati
ve
Co
st
(Ta
rge
t C
os
t =
1)
Best
Worst
Hybrid
Electro
Performance Evaluation• Overall performance of each candidate is measured by weighted
average of individual spec satisfaction • Weighting is relative importance of each spec to the customer
Relative Performance = weighting a
material
property a
spec a
x + weighting b
material
property b
spec b
x + ...
1.5= 0.51 lbs./in.3
1 lbs./in.3 x + 0.5
4 psi
2 psix
Density (Spec.) > 1 lbs./in.3
Density (Material) = 1 lbs./in.3
Strength (Spec.) > 2 psi.
Strength (Material) = 4 psi.
=Relative Performance
Performance Evaluation - Weighting Calculation• Weighting of each spec is calculated by relative weight of each
spec
Permanent Magnet
Specifications Worth WeightingFlux Density (Br) 0.005 9%Intrinsic coercivity (Hci) 0.002 4%Temperature coefficients of Br
0.007 13%
Temperature coefficients of Hci
0.001 1%
Radiation Resistance 0.03 46%Width (w) 0.005 9%Thickness (t*) 0.005 9%Length (L) 0.005 9%Tolerance of w 0.0001 0.2%Tolerance of t* 0.0001 0.2%Tolerance of L 0.0001 0.2%
Sum 0.06 100%
Multipole Magnet System
Specifications Worth WeightingMagnetic field gradient x effective length (Gdl)
0.01 1%
Higher order harmonics 0.07 8%Gdl range 0.6 64%Gdl accuracy 0.07 8%Magnetic center accuracy (static)
0.01 1%
Magnetic center lattice dynamic
0.1 13%
Availability 0.05 6%Sum 0.9 100%
Performance Evaluation• Select structure candidates with
Relative performance > 1Cost-Specification Analysis
0
1
2
3
0 1 2
Relative Performance (Spec = 1)
Rel
ativ
e C
ost
(Ta
rget
Co
st =
1)
Best
Worst
Hybrid
Electro
Design Selection of Multipole Magnet System• Design candidates: Electro-magnet vs hybrid magnet
(Strontium Ferrite)
Cost-Specification Analysis
0
1
2
3
0 1 2
Relative Performance (Spec = 1)
Rel
ativ
e C
ost
(Ta
rget
Co
st =
1)
Best
Worst
Hybrid
Electro
Material Selection of Permanent Magnet• Material candidates: Strontium Ferrite, Sm2Co17, Nd-Fe-B
Cost-Specification Analysis
0
1
2
0 1 2
Relative Performance (Spec = 1)
Rel
ativ
e C
ost
(Ta
rget
Co
st =
1)
Best
Worst
Strontium Ferrite
Nd-Fe-B
Sm2Co17
Trade-Off Analysis• Design can be optimized by trade-off analysis of each candidate
0
4000
8000
12000
16000
0.00 12.75 25.50 38.25 51.00
Cross Section of Permanenet Magnet, A (in.^2)
Co
st (
$)
0
20
40
60
80
100
120
140
160
Req
uir
ed F
lux
Den
sity
, Br
(kG
)
Cost of Parts Except Permanent Magnet
Include Assembly Cost
Cost of Permanent Magnet
Total Cost
Br(kG)
Strontium Ferrite, Br = 3.8 kG
Neodymium Iron Boron, Br = 12 kG
Cost of Parts Except Permanent Magnet
Cost Except Permanent Magnet
Br
Samarium Cobalt 2:17, Br = 10.5 kG
Total Cost
Cost of Permanent Magnet
Assumption
1) Br x A = Flux (Constant)
2) Size of a quadrupole magent changes propotaional to the cross section(A) of a permanent magent
Agenda
1. Motivation
2. Cost-Specification Analysis– Flow Down of the Product Targets– Evaluation of the candidates– Selection of the best candidate
3. Conclusion
Conclusion
• Cost-Specification Analysis enables an engineer to select the best candidate that satisfies both specification and cost targets
• By applying Cost-Specification Analysis to all components and by selecting the best candidate, the final product can satisfy both required feature and cost simultaneously
• Looking for second application in order to validate this approach
Questions?
Appendix
Relative Performance: Multipole Magnet Systems
Relative Performance(Qualitative)
Specification Weighting Hybrid ElectroMagnetic field gradient x effective length (Gdl)
1% 1 1
Higher order harmonics
8% 1 2
Gdl range 64% 1 2Gdl accuracy 8% 1 2Magnetic center accuracy (static)
1% 1 3
Magnetic center lattice dynamic
13% 3 1
Availability 6% 2 1
Sum 100% 1.32 1.81
Relative Performance: Permanent Magnet
PM Specs Weighting Material PropertyStrontium Ferrite Nd-Fe-B Sm2Co17
(Aster-8A) (NEOMAX35) (VACOMAX225HR)Flux Density (Br) > 3.9 kG 9% 3.9 12.1 11Intrinsic coercivity (Hci) > 3.25 Koe 4% 3.25 12 26Temperature coefficients of Br < - % / C 13% -0.2 -0.11 -0.03Temperature coefficients of Hci < - % / C 1% 0.5 -0.6 -0.25Radiation Resistance < -0.3 %Br / Grad 46% -0.3 -1.6 -0.25Width (w) - in 9%Thickness (t*) - in 9%Length (L) - in 9%Tolerance of w - in 0.2%Tolerance of t* - in 0.2%Tolerance of L - in 0.2%
100%
Relative PerformanceStrontium Ferrite Nd-Fe-B Sm2Co17
(Aster-8A) (NEOMAX35) (VACOMAX225HR)Flux Density (Br) > 3.9 kG 9% 1 3.10 2.82Intrinsic coercivity (Hci) > 3.25 Koe 4% 1 3.69 8Radiation Resistance < -0.3 %Br / Grad 46% 1 5.33 0.83
Flux Density (Br) > 3.9 kG 9% 1 1 2.82Intrinsic coercivity (Hci) > 3.25 Koe 4% 1 1 8Radiation Resistance < -0.3 %Br / Grad 46% 1 0.1875 1.2
1.00 0.63 1.52
Next Linear Collider (NLC)• NLC is a 20-mile long linear
collider that smashes electrons and positrons in order to create new particles
• The goal is to produce 10 times higher energies than the present linear collider (SLC)
• NLC is consists of three main systems– Injection (Beam injection) – Main Linac (Acceleration) – Beam Delivery (Collision and detection)
Quadrupole Magnets (Quads)• Quadrupole magnets are used in order to focus electron
and positron beams using magnetic field
• Without focusing beams, we can not collide beams accurately
Customer Needs Identification (Customer Value Chain Analysis & Priority Matrix)
USA Nation
US Gov.
SLAC
ARD-A
MML
NLC
C O AFeature O
Cost O
Time O
C O A
Feature O
Cost OTime O
$&!
$&!
$&!
$&!
$&!
!$&!
•US Gov. is the critical external customer and SLAC physicists are the critical internal customers
•The priorities of SLAC and the Gov. are different
•SLAC needs to satisfy both feature and cost
C O A
Feature O
Cost OTime O
ConstraintsOptimize
Accept
$: Flow of funds
! : Flow of information
Future Study
• Include lead time to Cost-Specification Analysis
– Consider availability of each material
• Trade-off analysis– High cost, high performance
vs
Low cost, low performance
Cost-Specification Analysis Diagram
0
0.5
1
1.5
2
2.5
3
0.0 0.5 1.0 1.5 2.0
Relative Performance (Spec = 1)
Rel
ativ
e C
ost
(Ta
rget
Co
st =
1)
Best
Worst
Samarium Cobalt
Strontium Ferrite
Neodymium Iron Boron
World Permanent Magnet MarketTable World Permanent Magnet Market (% of $4.4B)
Cast Sintered Bonded Other TotalAlnico 4 1 1 6Ferrite - 36 21 57Ne-Fe-B - 23 7 30Sm-Co - 5 - 5Other 2 2Total 4 65 29 2 100Source: MagneTrends 5/15/99
Percentage of $4.4 Billion Market: Material
Ferrite57%
Ne-Fe-B30%
Other2%
Alnico6%
Sm-Co5%
Percentage of $4.4 Billion Market: Process
Sintered65%
Bonded29%
Other2%
Cast4%
Chemical Component of Permanent Magnets
Type Chemical ComponentsAlnico Al-Ni-Co-FeFerrite SrO-Fe2O3
BaO-Fe2O3Rare Earth Nd-Fe-B
Sm-Co