Current Lead Design - USPAS · exiting warm end of leads: ≈ 7 kW electrical power for pair of 1 kA conventional leads •Improve reliability by using a cryocooler to re-condense

University of Wisconsin - Madison

Current Lead Design

US Particle Accelerator SchoolJune 21-25, 2004


Current Lead Design• What is a current lead and what are the

design challenges?• Design goal - minimize cryogenic impact• Configurations• What do you expect?• Designing conventional leads

– Conduction cooled– Vapor cooled– Forced flow cooled

• Designing HTS (hybrid) leads– Cooling options– Additional factors to consider


Purpose, Design Challenge• Purpose: Communicate electric

power from room temperature tocryogenic coils, magnets,transmission lines, or devices.

• Design challenge:– Cryogenic heat load due to:

• Heat conduction

• Heat generation (I2R)

– Reducing conduction (reduce area,increase length, reduce k) increasesheat generation

– Reducing heat generation(increase area, decrease length,reduce ρ) increases conduction

– Optimization required

AMI 75 kAConventional, heliumvapor-cooled leads

75 kA leads atzero current


Goal: Minimize Impact on Cryogenic System

• Open systems: reduce cryogen boil-off• Benchmark: 1.1 W/kA-lead = 3 liter/hr-kA-pair

for conventional helium vapor cooled leads

• Closed cycle refrigerator: improve performance• Reduce the required electrical power to refrigerate vapor

exiting warm end of leads:

≈ 7 kW electrical power for pair of 1 kA conventional leads

• Improve reliability by using a cryocooler to re-condense vaporat 4.2 K

• Replacing conventional 5 kA leads with HTS versionsprovides Fermilab Tevatron excess refrigeration to reducemagnet temperature from 4.2 K to 3.5 K.


Configurations

• Conventional– Conduction cooled

– Vapor cooled

– Forced-flow cooled

• HTS - hybrid– Conduction cooled

– Vapor cooled

– Forced-flow cooled

Tc

Th

Th

Tc

Tint

cryocooler

1st stage

2nd stage

Cu

HTS

Lead

nitrogeninhelium

out


What Do You Expect?

• The functional dependence of Q on Imax:– For an optimized conduction cooled lead _______________

– For an optimized vapor cooled lead _______________

• The functional dependence of the aspect ratio L/A on Imax:– For an optimized conduction cooled lead ______________

– For an optimized vapor cooled lead _______________

• Compare the cold-end heat leak for a 1 kA vapor cooled lead:

Q (helium vapor cooled) ______ Q(nitrogen vapor cooled)

• Compare the aspect ratio for a 1 kA vapor cooled lead:

L/A (neon vapor cooled) __________ L/A (nitrogen vapor cooled)


Conduction Cooled Lead: Derivations• Energy balance on control volume:

Qin - Qout + Qgen = 0

note that if dT/dx > 0, Qin > 0

• Change variables: let

Th

Tc

x

Qin

Qoutdx

Qc

kA dTdx x+ d x

− kA dTdx x

+

I2ρA

dx = 0

s = k dTdx

ddx

k dTdx

+ ρJ

2

= 0

Tc

Th

dsdx

+ ρJ 2 = 0; ⇒dsdT

dTdx

+ ρJ 2 = 0

sk

dsdT

+ ρJ 2 = 0; ⇒ sds = −kρJ 2dT

s =QA

;⇒ ds =dQA

; QdQ =12

Q2

c

h

= −I 2 kρdTTc

Th∫c

h

∫


Conduction Cooled Lead: Derivation (cont.)

Qh2 − Qc

2 = −2I2 kρ dTTc

Th

∫ ⇒ Q c2 = Qh

2 + 2I2 kρ dTTc

Th

∫• Qc is minimized when Qh= 0.

kA dTdx

c

2

= 2I2 kρ dTTc

Th

∫ ⇒ dx =kA dT

2I kρ dTT

Th

∫( )1/ 2

As T is lowered, this equation defines the additional length required to produce Qmin at Tc

• Finally:LA

=1

I 2k dT *

kρ dTT*

Th

∫( )1/ 2Tc

Th

∫ OR JL = 12

k dT *

kρ dTT*

Th

∫( )1/ 2Tc

Th

∫

Qc, min = I 2 kρ dTTc

Th

∫

1/ 2

Tc

Th


Conduction Cooled Lead: Sample Results

0

1,000

2,000

3,000

4,000

5,000

6,000

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300

L/A

(m/m

^2)

Q (W

)

Temperature (K)

I = 1000 ARRR = 100


Conduction Cooled Lead: Conclusions

• An ‘optimized’ lead is optimized for a single(maximum) current

• Qc, min ~ I

• Qc, min is a function of Th, Tc, I, and (weakly) onmaterial choice

• JL = constant dependent only on Th, Tc, and mtl.choice

• L/A ~ 1 / I

Tc

Th


Vapor Cooled Lead

• Energy balance at steady state is given by:

• Goal is to minimize

• Variety of solution methods: J.E.C. Williams (1963), Deines (1965),Lock (1969), Dresner (1995) - similarity solution: (special units)

• Qmin/I (ordinary units) =

• Examples:

Th

Tc

I2ρA

+ ddx

AkdTdx

− &mCp

dTdx

= 0

&m with &m=

1C

L

kAdTdx

x =0

ln Th

Tc

= ln sc

2

Tc2 −

sc2

Tc+ 1

1/ 2

+ sc 4 − sc2( ) −1/ 2

arctansc 4 − sc

2( )1/2

2Tc − sc2

scLo1/ 2 CL

Cp

Helium: Th= 300 K, Tc= 4 K, sc= 1.79, Q/I = 1.12 W/kA

Nitrogen: Th= 300 K, Tc= 77 K, sc= 0.855, Q/I = 25.4 W/kANeon: Th= 300 K, Tc= 27 K, sc= 1.23, Q/I = 16.1 W/kA


Vapor Cooled Lead (cont.)

• Optimum aspect ratio (similarity solution - special units)

using an integrated average value of k over the temperature range, and theLorentz constant Lo = 2.45 x 10-8 (WΩ/K2) gives (for a 1 kA lead)

• Helium VCL (300 K - 4.2 K)

• Neon VCL (300 K - 27 K)

• Nitrogen VCL (300 K - 77 K)

Th

Tc

Lk

= 2 4 − sc2( )−1/ 2

arctansc 4 − sc

2( )1/ 2

2Tc − sc2

; JL = Lk

special

units

∗k

Lo1/ 2

Lk

s.u.= 4.87 ⇒ LJ =

LIA

= 1.62x107 A / m ⇒LA

= 162 cm / cm2

Lk

s.u.= 1.985 ⇒ LJ =

LIA

= 6.28x106 A / m ⇒LA

= 62.8 cm / cm2

Lk

s.u.= 1.675 ⇒ LJ =

LIA

= 4.93x106 A / m ⇒LA

= 49.3 cm / cm2


Vapor Cooled Lead - Conclusions

• Minimum heat leak:– As with conduction cooled leads, Qmin ~ I

– Dependence of Qmin on coolant is dominated by (CL / Cp)

• Optimized aspect ratio:– L/Aopt ~ 1/I smaller current → larger aspect ratio

– L/Aopt dependence on coolant: colder range → larger aspect ratio


Forced Flow Cooled• Behavior governed by same energy balance equation as vapor cooled

• E. Barzi, (Fermi-lab, 1998): numerical solution, with variable massflow rate, for lead designed for a maximum current of 5 kA

0

50

100

150

200

250

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Nitrogen vapor cooledHe

at L

eak

(W)

mass flow rate (g/s)

L/A = 5.3 cm/cm2

I = 5000 A

2500 A

500 A

vapor cooled


HTS Current Leads

• Reduced cryogenic impact– Heat generation significantly

reduced (eliminated) in HTSsegment.

– Heat conduction reduced

– Cold end heat load reducedby factor of 3 - 10.

• Wide variety of coolingoptions

• Additional design issues toconsider

upper(conventional)stage

intercept

lower(HTS)stage

300 K

20 - 90 K

4 K


Cooling Options for HTS Leads

• Conduction cooled via cryocooler - Chang & Van Sciver

– Minimize combined 1st and 2nd stage cooling power

– Optimized joint temperature ~ 90 K for Bi2223

Wref

I=

1FOML

TH

TL− 1

1JLhts

khts ⋅ dTTL

TJ

∫ +1

FOMJ

TH

TJ− 1

2 ρkcu ⋅dT

TJ

TH

∫ −1

JLhtskhts ⋅ dT

TL

TJ

∫

Th

Tc

Tjoint

cryocooler

1st stage

2nd stage

Cu

HTS

Lead


Cooling Options for HTS Leads• Forced flow cooling - Fermilab, CERN, ITER

• Fermilab: 5 kA lead retrofit for Tevatron– helium vapor cooled HTS section– nitrogen gas cooled upper section– prototypes from ASC and IGC– heat loads: 101 W @ 80 K, 0.7 W @ 4 K

HTS sectionCu section

IGC prototype

ASC prototype - HTS section

• CERN: 13 kA, 6 kA, 0.6 kA for LHC• ITER Toroidal Field Coils: 10kA, 20kA

– conduction cooled HTS– helium gas cooled 50 K - 300 K– multiple vendors– < 1 g/s helium flow @ 20 K inlet

13kA prototype for CERNEurus/NHMFL

10 kA prototype for ITER-FEAT FZK, CRPP-TF, Aventis/Nexans


Cooling Options for HTS Leads

• Vapor cooling - AMI / MIT– Hybrid lead designed so that HTS section operates above Ic

• 6 kA

• Stacked tapes (240 vs 480) of Bi-2223/Ag-4%Au

• Short (~ 0.4 cm / 28 cm) portion of HTS produces jouleheating

• Additional joule heat removed by effluent helium vapor

– Improved characteristics as compared to fullysuperconducting version

• Optimized versions: Qc = 0.36 W vs. 0.71 W

• Quantity of Ag & Au reduced by a factor of ~2.

addl.

helium in


Additional Considerations for HTS Leads

• Field dependence of Jc

• Fabrication process / materials

Stacked tapes of Bi2223 / Ag+4%AuAmerican Superconductor Corporation

Melt Textured YBCOATZ GmbH

MCP Bi2212ACCEL/ART GmbH


Additional Considerations for HTS Leads• Joint resistance ~ 0.1 µΩ

• Protection– Localized hot spots, cracking

– Fault mode behavior: loss of cooling, overcurrent

0

50

100

150

200

250

300

350

400

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Position

0 seconds

500 seconds

1000 seconds

1250 seconds

1500 seconds

1600 seconds

1700 seconds

1725 seconds

1750 seconds

Uppersection

HTSsection

1.5 kA cryocooled interceptand helium vapor cooled lead.Response following loss ofintercept cooling,(Pfotenhauer & Lawrence, 1998)


References• S. Deiness, “The Production and Optimization of

High Current Leads,” Cryogenics, vol. 5, pp. 269-271, October 1965

• J.E.C. Williams, “Counterflow Current Leads forCryogenic Applications,” Cryogenics, vol. 3, pp.234-238, December 1963.

• Yu.L. Buyanov, “Current Leads for use inCryogenic Devices. Principle of Design andFormulae for Design Calculations,” Cryogenics,vol. 25, pp. 94-110, February 1985.

• J.R. Hull, “High Temperature SuperconductingCurrent Leads,” IEEE Trans. on AppliedSuperconductivity, vol. 3 (1), pp. 869 - 875, 1992.

• L. Dresner, Stability of Superconductors, Plenum,1995, pp. 190-197.

• R. Wesche and A.M. Fuchs, “Design ofSuperconducting Current Leads,” Cryogenics, vol.34, pp. 145-154, February 1994.

• E. Barzi, “Gas/Vapour-Cooled Binary CurrentLeads: Copper Part,” Fermilab internal reportnumber TD-98-026, March 1998.

• H.M. Chang and S.W. Van Sciver,“Thermodynamic Optimization of ConductionCooled HTS Current Leads,” Cryogenics, vol. 38(7), pp. 729-736, July 1998.

• T.M. Taylor, “HTS Current Leads for the LHC,”IEEE Trans. on Applied Superconductivity, vol. 9(2), pp. 412 - 415, June 1999.

• J.M. Pfotenhauer and J.W. Lawrence,“Characterizing Thermal Runaway in HTS CurrentLeads,” IEEE Trans. on Applied Superconductivity,vol. 9 (2), pp. 424 - 427, June 1999.

• A. Hobl et.al., “HTc Current Leads in CommercialMagnet Systems Applying Bi 2212 MCP BSCCOMaterial,” IEEE Trans. on Appl. Superconductivity,vol. 9 (2), pp. 495-498, June 1999.

• R. Heller et.al., “Status of the DevelopmentProgram of a 60 kA HTSC Current Lead for theITER Toroidal Field Coils,” IEEE Trans. onApplied Superconductivity, vol. 9 (2), pp. 507 -510, June 1999.

• G. Citver, S. Feher, T.J. Peterson, C.D. Sylvester,“Thermal Tests of 6 kA HTS Current Leads for theTevatron,” Advances in Cryogenic Engineering,vol. 45, pp. 1549 - 1564 2000.

• Y. Iwasa and H. Lee, “High TemperatureSuperconducting Current Lead IncorporatingOperation in the Current-sharing Mode,”Cryogenics vol. 40 pp. 209-219, 2000.

Documents

Current Lead Design - USPAS · exiting warm end of leads: ≈ 7 kW electrical power for pair of 1 kA conventional leads •Improve reliability by using a cryocooler to re-condense