Multipole Magnet Design Selection and Permanent Magnet Material Selection

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


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


Injection Accelerator structuresMagnetic field adjustment device

Steel poles


Beam Delivery Vacuum systemsQuad support structure

Aluminum spacers

Movers End walls


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


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


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


NLC 9 Main Linac 5.5 Multipole magnetsQuadrupole magnet

PM


Injection 1.0 Accelerator structuresMagnetic field adjustment device

Steel poles


Beam Delivery 2.5 Vacuum systemsQuad support structure

Aluminum spacers

Movers End walls


9 : Most important

3 : Important

1 : Least important


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


Flexible latice

Luminosity 0.4 Emittance


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


1.7

Flexible lattice 0.6Accelerator structures

Emittance 0.3BPM


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


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


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


NLC 9 Main Linac 5.5 Multipole magnets 0.9Quadrupole magnet

0.14 PM 0.06


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


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


0.06 / 6000 (Worth of a permanent magnet set)

9 (Worth of NLC)

Target cost of a permanent magnet set


Agenda

1. Motivation


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


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)


0

1

2

3

0 1 2


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


0

1

2

0 1 2


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


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


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

Multipole Magnet Design Selection and Permanent Magnet Material Selection

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