magnetization modeling and measurements n. amemiya (kyoto university) 1st workshop on accelerator...

Magnetization modeling and measurements

N. Amemiya(Kyoto University)

1st Workshop on Accelerator Magnets in HTSMay 21 – 23, 2014Hamburg, Germany

(May 22, 2014)

2N. Amemiya, WAMHTS-1, May 22, 2014

Background … When using a coated conductor with wide tape shape for an

accelerator magnet, its large magnetization is apparently a big concern.

Electromagnetic field analyses, which can clarify the electromagnetic phenomena inside coated conductors, must be powerful tools to study the magnetizations of coated conductors, cables, and coils.

Today’s presentation includes … Modeling cables and coils as well as coated conductors for

electromagnetic field analyses Comparing numerical analyses with experiments


Outline

Principle of modeling and formulation Magnetization modeling and comparison with

measurements in … Roebel cable: ac losses Striated coated conductor: ac losses Dipole magnet comprising race-track coils: field

quality (temporal evolution of magnetic field harmonics)

Recent challenge and future plan


Principle of modeling and formulation

M. Nii et al. SUST25(2013)095011


Key points when modeling and our approaches

Superconducting property Use of the extended Ohm’s law using equivalent

(nonlinear) conductivity or resistivity as the constitutive relation

Three-dimensional geometry and very thin superconductor layer of coated conductor

Use of the thin-strip approximation, where the thin strip of superconducting layer of a coated conductor follows a curved geometry of the coated conductor in a cable or in a coil

Governing equation and constitutive equation

Equivalent conductivity derived from E-J characteristic: Ex.


ncJJEE /0

dVrV

3

0

4

rJB

〔 Biot-Savart’s law〕

TJ

〔 Definition of current vector potential〕

0B

E

t

〔 Faraday’s law〕

0rT

T

S

dSrt

t3ss0

f

)(

4

1

0rT

T

V

dVrt 3s0

f

)(

4

1

Thin strip approximationHigh cross-sectional aspect ratio of coated-conductor allows its use.

Integrate along thickness of coated-conductor

Computational cost can be reduced drastically.

)(/ JJE

〔 Extended Ohm’s law〕


Consideration of three-dimensionally-curved coated conductors

0d

4

1ext

' 3s0

nB

nrnnn

SS'

r

Tt

tT

This term representing B in Faraday’s law is calculated by Biot-Savart’s law based on currents on arbitrary 3D-shaped conductors


Roebel cable

N. Amemiya et al. SUST27(2014)035007


Electromagnetic field analysesand magnetization loss measurements

Roebel cable as well as reference conductors

4 mm

4 mm

2 mm

0.53 mm

4 mm 0.53 mm

0.26 mm

2 mm

1 mm

3×2-stack of coated conductors

Roebel cable

3×1-stack of coated conductors

Single straight coated conductor

10

Transverse magnetic field only

N. Amemiya, WAMHTS-1, May 22, 2014

He / (Ic1 / pw) = 0.5 He / (Ic1 / pw) = 3.2 He / (Ic1 / pw) = 7


Transverse magnetic field only

He / (Ic1 / pw)= 3.2

• (Low field) Single CC > Roebel cable > 32-stack ~ 3-stack• (Mid field) Single CC > Roebel cable ~ 32-stack ~ 3-stack• (High field) Single CC ~ Roebel cable ~ 32-stack ~ 3-stack


Transport current + transverse magnetic field

It / Ic1 = 0.6, He / (Ic1 / pw) = 2


Striated coated conductor

N. Amemiya et al. SUST17(2004)1464N. Amemiya et al. IEEE-TAS15(2005)1637


Model of striated-and-twisted coated conductors

Length of sectionWidth ofconductor

r

External magnetic field

Self magnetic fieldcalculated usingBiot-Savart's law

Field point

Source point ofself magnetic field

Lp / 4

wc

Lp / 4

Groove (nc)

Filament (sc)

Lp / 2

Lp

Periodic boundary condition

Lp

Fixed boundary condition :T = 0

Lp / 2 Lp / 2

z x

y

wc0

x = -Lp / 4 x =L

Actual 2D analysis region untwisted on a flat plane


Specifications of conductors for analysis

Width of conductor 4.9 mm

Width of filament 900 mm

Width of groove between filaments 100 mm

Number of filaments 5

Twist pitch 200 mm

Thickness of YBCO layer 1 mm

Critical current density 2 1010 A/m2

n value 20

Transverse resistance between filaments for one meter Varied

Frequency of transport current and applied magnetic field is fixed at 50 Hz.


Calculated current lines

(a) Twisted monofilament conductor

It/Ic = 0

1.0 A/line

1.0 A/line

2.5 A/line

2.5 A/line

x = Lp/4x = 0

(d) Twisted multifilamentary conductor: Rg = 100

(c) Twisted multifilamentary conductor: Rg = 10

(b) Twisted multifilamentary conductor: Rg

Lp / 4 Lp / 4Lp / 2


Current distribution in monofilament conductor and multifilamentary conductors carrying no transport current

0

10

20

30

40

50

60

70

80

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-2 -1 0 1 2

J x (10

10 A

·m-2

)

Bz (m

T)

y (mm)

MonofilamentL

p = 200 mm

It / I

c = 0,

0H

m = 50 mT, f = 50 Hz

Bz

Jx

Monofilament

0

10

20

30

40

50

60

70

80

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-2 -1 0 1 2y (mm)

GrooveFilament

Rg = 10

Lp = 200 mm

It / I

c = 0, f = 50 Hz,

0H

m = 50 mTI

t / I

c = 0,

0H

m = 50 mT, f = 50 Hz

J x (10

10 A

·m-2

)

Bz (m

T)

Bz

Jx

MultifilamentRg = 10 mW

0

10

20

30

40

50

60

70

80

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-2 -1 0 1 2

J x (10

10 A

·m-2

)

Bz (m

T)

y (mm)

GrooveFilament

Rg = 0.1

Lp = 200 mm

It / I

c = 0,

0H

m = 50 mT, f = 50 Hz

Bz

Jx

MultifilamentRg = 0.1 mW


Specification of measured multifilamentary sample

Width of conductor 10 mm

Length of conductor ST40L: 100 mmST40M: 50 mmST40S: 25 mm

Width of filament 200 mm

Width of groove between filaments 50 mm

Number of filaments 40

Thickness of YBCO layer 1.4 mm

Thickness of silver protective layer 5.1 mm

Buffer layer Non-conducting (primarily YSZ)

Substrate Hastelloy

Critical current at 77 K, self-field 100 A

n value at 77 K, self-field 23

Non twisted but finite length


1D model and 2D model

Enabling us to calculate the current distribution in a cross section of an infinitely-long completely decoupled conductor

One-dimensional FEM model Two-dimensional FEM model

Enabling us to calculate the current distribution in a wide face of an finite-length conductor at partially decoupled state

AC loss reduced to the ideal levelin completely decoupled conductor

can be calculated. Coupling loss can be studied.


Measured losses in samples with various length

ST40L (100 mm) ST40M (50 mm) ST40S (25 mm)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

1 10 102

Qm at 11.3 Hz

Qm at 72.4 Hz

Qm at 171.0 HzM

ag

netiz

atio

n lo

ss (

Jm-1

cycl

e-1

)

Transverse magnetic field µ0H

m (mT)

Sample ST40L Qc,n

at 11.3 Hz,

72.4 Hz, 171.0 Hz

Qf,BI

Qf,n

at 11.3 Hz, 72.4 Hz, 171.0 Hz

Qc,BI

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

1 10 102

Qm at 11.3 Hz

Qm at 72.4 Hz

Qm at 171.0 HzM

ag

netiz

atio

n lo

ss (

Jm-1

cycl

e-1

)


m (mT)

Sample ST40M

Qc,BI

Qc,n

at 11.3 Hz,

72.4 Hz, 171.0 Hz

Qf,BI

Qf,n

at 11.3 Hz, 72.4 Hz, 171.0 Hz

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

1 10 102

Qm at 11.3 Hz

Qm at 72.4 Hz

Qm at 171.0 HzM

ag

netiz

atio

n lo

ss (

Jm-1

cycl

e-1

)


m (mT)

Sample ST40S

Qc,BI

Qc,n

at 11.3 Hz,

72.4 Hz, 171.0 Hz

Qf,BI

Qf,n

at 11.3 Hz, 72.4 Hz, 171.0 Hz

Frequency dependence in measured loss disappears with decreasing sample length.


Coupling loss and hystresis loss components

1.3Hz1m,2

m08

m, 3.111056.1 QfHQ f

1.3Hz1m,2

m09

m, 3.111001.3 QfHQ f

10-10

10-9

10-8

10-7

10-6

10-5

10-4

1 10 102

f = 25.1 Hzf = 72.4 Hzf = 111.9 Hzf = 171.0 Hz


m (mT)

1.56 10-8 (µ0H

m)2

ST40L

ST40M

3.01 10-9 (µ0H

m)2

(Qm

,f-Q

m,1

1.3

Hz)/

(f-1

1.3

) (J

m-1

s-1cy

cle

-1)

(Qm,f-Qm,11.3Hz)/(f-11.3) vs. m0Hm

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1 10 102

f = 11.3 Hzf = 25.1 Hzf = 72.4 Hzf = 111.9 Hzf = 171.0 Hz


m (mT)

ST40L

ST40M

(Qm

,f-Q

m,0)/

f/L

2 (Jm

-3s-1

cycl

e-1

)

1.4 10-6 (µ0H

m)2

(Qm,f-Qm,0)/(fL2)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

1 10 102

ST40L

ST40M

Qf,BI

Qf,n

at 72.4 Hz

Qm

,0 (

Jm-1

cycl

e-1

)


m (mT)

Loss of ST40 at 0 Hz (extrapolated)

Qm,0: extrapolated loss at 0 Hz

• Data for each samples collapse to one line.• Slope is 2: Proportional to (m0Hm)2

Hysteretic loss

• collapse to one line• slope is 2.

2m0

6 )(104.1 H

),()(104.1

),,(

m0m,02

m026

m0esm,

HQHfL

HfLQ


Measured and calculated coupling loss

Rt =4.8 mWfor 1 m

10-8

10-7

10-6

10-5

1 10 102 103

ST40L

Ma

gne

tizat

ion

loss

(Jm

-1cy

cle

-1)

0.5 mT

Frequency (Hz)

At 0.5 mT, 10-1k Hz, the measured loss and calculated loss is compared to determined the transverse resistance between filaments.

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1 10 102

f = 11.3 Hzf = 25.1 Hzf = 72.4 Hzf = 111.9 Hzf = 171.0 Hz


m (mT)

ST40L

ST40M

(Qm

,f-Q

m,0)/

f/L

2 (Jm

-3s-1

cycl

e-1

) Numerical values

1.Using this Rt, numerical calculations were made for f = 11.3 Hz, 72.4 Hz & 171.0 Hz, and L = 50 mm & 100 mm.

2.Calculated coupling losses reasonably agree with experimental values.


Dipole magnet

N. Amemiya et al. to be submitted to SUST?


Dipole magnet RTC4-F comprising race-track coils

Coated conductor Fujikura (FYSC-SC05)

Superconductor GdBCO

Width thickness 5 mm 0.2 mm

Stabilizer 0.1 mm – thick copper

Critical current 270 A – 298 A

48 mm

76.4 mm

58 mm250 mm

1 mm

5 mm

Shape of coils Single pancake race-track

Number of coils 4

Length of straight section 250 mm

Inner radius at coil end 48 mm

Outer radius at coil end 76.4 mm

Coil separation 58 mm

Number of turns 83 turn/coil

Length of conductor 74 m/coil 0

100

200

300

400

0 0.5 1

Ic-B

Cur

rent

(A

)

Coated conductorIc-B curve & load line

Load line (B||)

Load line (B)

Load line (|B|)

Magnetic flux density (T)

Ic ~ 110 A


Temporal evolutions of current distribution

5400Time (s)

50A

3600 72000 1800

(a) (b) (c)(d) (e) (f)

↓ ↓ ↓

↓↓↓

(a)

(b)

(c)

Excited

(d)

(e)

(f)

Shut down


Hysteresis loopComparison between experiment and calculation

Experiment Calculation

Designed value without magnetization substituted


Repeated (50 A, 1 h) – excitations

0

50

Cur

rent

(A

) 50.5 A

0 4 8 12 16Time (hour)

Comparison between experiment and calculation

2-pole

6-pole


Excited


Influence of 50 A – excitation between 30 A - excitations

0

50

Cur

rent

(A

) 50.5 A30.1 A

0 4 8 12 16Time (hour)

Comparison between experiment and calculation

2-pole

6-pole



Recent challenge and future plan


3D analyses of cosine-theta magnet

Dipole magnet for rotary gantry for carbon cancer therapy

Current 200 A

BL 2.64 Tm

Higher harmonics / dipole

< 10-4

Entire length 1084 mm

Number of turn 2844


Coil wound with Roebel cable

(1-1)Assuminguniform current

distribution

(1-2)

Assuminguniform current

distribution

Uniform

Analysis region


Summary

We have been developing models for numerical electromagnetic field analyses of cables and coils consisting of coated conductors.

They have been applied successfully to HTS Roebel cables Twisted striated coated conductors Dipole magnets (2D)

and compared with measurements. Applications to CORC cables as well as twisted stacked-tape

cables are possible in principle. Recent challenge and future plan

3D analyses of cosine-theta magnet Coil wound with Roebel cable


Overview of S-Innovation project

Name of project Challenge to functional, efficient, and compact accelerator system using high Tc superconductors

Objective •R&D of fundamental technologies for accelerator magnets using coated conductors

•Constructing and testing prototype magnet

Future applications

•Carbon caner therapy•Accelerator-driven subcritical reactor

Participating institutions

Kyoto University (PM: Amemiya), Toshiba, KEK, NIRS, JAEA

Period Stage I: 01/2010 – 03/2012Stage II: 04/2012 – 03/2016Stage III: 04/2016 – 03/2019

Funding program Strategic Promotion of Innovative Research and Development Program by JST

magnetization modeling and measurements n. amemiya (kyoto university) 1st workshop on accelerator...

Documents

stack slide

sust252013095011 slide

sust272014035007 slide

striated coated conductor

curved coated conductors

thickness of coated

electromagnetic field

extended ohms law slide