Thermodynamics Modeling of New LHC Quadrupole Magnetlarpdocs.fnal.gov/LARP/DocDB/0010/001036/001...Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 3 MOTIVATION Particles

BNL - FNAL - LBNL - SLAC

Thermodynamics Modeling

of New LHC Quadrupole Magnet

D. Bocian, G. Ambrosio, V. Khashikhin, M. Lamm, N. Mokhov, A. Zlobin / FNAL

F. Borgnolutti, F. Cerutti, P. Fessia, A. Mereghetti, E. Todesco / CERN

LARP CM13 Collaboration Meeting

Port Jefferson, NY, November 4-6, 2009

Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 2

Motivation

Heat sources in the accelerator magnets

Thermodynamics of magnet structureHeat evacuation path and heat flow barriers

Helium in the magnet

Modeling of heat flow in the magnetsNetwork model construction

Helium modeling

Model validation

New inner triplet phase I simulation status

New inner triplet phase II simulation status

Conclusions

Future plans

OUTLINE


MOTIVATION

Particles coming from proton-proton collision debris impacts the

inner triplet magnets

→ energy deposition in the coils.

Heat flow paths and heat flow barriers identification in the magnet

→ need to give a feedback to the magnet designers.

Phase I LHC upgrade → enhanced insulation scheme → open

helium paths between the bath and the cable

→ necessary studies of magnet thermodynamics

Thermal studies of LARP Nb3Sn LHC upgrade phase II magnets

→ implement method used in phase I magnet studies


Heat sources in the LHC magnets

Debris of the proton-proton interactions at accelerator interaction regions

Interaction of lost protons with collimators

Physics processes – BFPP (ion beam case)

Accidental beam losses

• Transient losses ~ns to ~ms• Enthalpy of the cable materials (~ns)

• Heat transfer to helium volume inside the cable (~ms)

• Enthalpy of the cable (~ms)

• Steady-state losses•Transfer of the heat from cable to the heat reservoir (~s)

•Magnet structure is vital

References:

D. Bocian, CERN AT-MTM note, EDMS 750204

P.P. Granieri, (D. Bocian), et al., CERN-LHC-PROJECT-Report-1089

D. Bocian et al., CERN-AB-2008-006


Heat evacuation paths & heat flow barriers

HEAT FLOW BARRIERS

cable insulation

interlayer insulation

ground insulation

helium channel around cold boreFor temperatures above 2.16 K: transition HeII HeI:helium channels are blocked = less effective heat flowdue to the changing of heat evacuation path

A sketch of the heat transfer in the magnet at nominal operations (a) and at quench limit (b).


NETWORK MODEL

HEAT FLOW

MODEL

ROXIE

magnet field

distribution,

temperature

margin

MAGNET

QUENCH

LEVELS

FLUKA

beam loss profiles

TECHNICAL

DRAWINGS

detailed magnet

coil geometry

Material properties

at low temperature

CRYODATA

OTHER

non beam induced

heat sources

Hysteresis losses

Eddy currents, etc.

A. Verweij

R. Wolf

Contribution to the quench level

is order of 1-2%

MEASUREMENTS

model validation


Network Model

coil model


Network Model

The volumes occupied by helium in the magnet are considered as:

-narrow channels,

-semi-closed volumes = inefficient inlet of fresh helium.

The steady heat load, heat up the helium in the semi- closed volumes:

- Helium temperature well above superfluid helium temperature at Tb=1.9K

- Critical helium temperature reached already below the calculated quench limit

Helium modeling


heat

heat

VALIDATION

predicted

quench

current

measured

quench

current

END

MAGNET

EXPERIMENT

Heat source

- quench heaters

- inner heating apparatus

HEAT SOURCE

MODEL

MAGNET

MODEL

Network Model Validation

More details:

D. Bocian, B. Dehning, A. Siemko, Modeling of Quench Limit for Steady State

Heat Deposits in LHC Magnets,IEEE Transactions on Applied

Superconductivity, vol. 18, Issue 2, June 2008 Page(s):112 – 115; CERN-AB-

2008-006, 2008;

D. Bocian, B. Dehning, A. Siemko, Quench Limit Model and Measurements for

Steady State Heat Deposits in LHC Magnets, IEEE Transactions on Applied

Superconductivity, vol. 19, Issue 3, June 2009 Page(s):2446 – 2449;

MQM magnets at 4.5 K

3700

3800

3900

4000

4100

4200

4300

4400

4500

4600

4700

25.00 30.00 35.00 40.00 45.00 50.00 55.00

P [mW/cm2]

I m

agn

et [A

]MQM 627

MQM 677

MQMC 677

Ultimate current 4650 A

Nominal current 4310 A

MB magnet at 1.9K

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

100 150 200 250 300 350

P [mW/cm2]

I magn

et [

A]

measurements

simulation

Model validation



Courtesy D. Tommasini

The nominal LHC cable insulation:

two 11 mm tapes overlapping by 50%

one 9 mm tape with 2 mm spacing

Nominal parameters for current and phase I design of LHC inner triplet

Current design Phase I design

Operating temperature [K] 1.9 1.9

Nominal gradient [T/m] 205 120

Aperture diameter [mm] 70 120

Quadrupole length [m] 5.5 / 6.37 10

Nominal parameters for current and enhanced LHC cable insulation

Nominal Enhanced

Cable 1 Cable 2 Cable 1 Cable 2

Radial thickness 0.150 0.150 0.160 0.160

Azimuthal thickness 0.120 0.130 0.135 0.145

The enhanced insulation:

one 9 mm tape with 1 mm spacing

four 2.5 mm tapes with 1.5 mm spacing

one 9 mm tape with 1 mm spacingDetails: M. La China, et al., Phys. Rev. Spec. Top. Accel. Beams 11 (2008)



Peak Energy Deposit in coil

0

2

4

6

8

0 1000 2000 3000 4000

distance [cm]

E [

mW

/cc]

Q1 Q2A Q2B Q3

A combining particle tracking, FLUKA shower simulations in a single magnet coil

Peak Energy Deposit in cold bore

0

3

6

9

12

15

18

0 1000 2000 3000 4000

distance [cm]

E [

mW

/cc]

Q1 Q2A Q2B Q3

Energy deposits in selected bin of magnet cross

section with peak value. Magnet has been divided

longitudinally into 108 bins (~10 cm)

The inner triplet quadrupole FLUKA simulations

were ran with a thick Beam Screen (BS) in Q1

(10.15 mm extra stainless steel shield added to

the usual 2mm thick BS).L=2.5*1034 cm-2s-1


Temperature distribution in the magnet

Temperature distribution in the inner layer cables

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

-15 -10 -5 0 5 10 15

DT

[K

]

SF=1.0

SF=2.0

SF=3.0

SF=4.0

SF=5.0

SF=6.0

SF=7.0

SF=8.0

SF=9.0

SF=10.0

Temperature distribution in the helium channel

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

-15 -10 -5 0 5 10 15

DT

[K

]

SF=1.0

SF=2.0

SF=3.0

SF=4.0

SF=5.0

SF=6.0

SF=7.0

SF=8.0

SF=9.0

SF=10.0

lambda point

Temperature distribution in the cold bore

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

-15 -10 -5 0 5 10 15

# cable

DT

[K

]

SF=1.0

SF=2.0

SF=3.0

SF=4.0

SF=5.0

SF=6.0

SF=7.0

SF=8.0

SF=9.0

SF=10.0

Temperature distribution in the inner layer cables

0.0

0.5

1.0

1.5

2.0

2.5

-15 -10 -5 0 5 10 15# cable

DT

[K

]

SF=1.0

SF=1.1

SF=1.2

SF=1.3

SF=1.4

SF=1.5

SF=1.6

SF=1.7

SF=1.8

SF=1.9

Temperature distribution in the helium channel

0.0

0.5

1.0

1.5

2.0

2.5

-15 -10 -5 0 5 10 15

DT

[K

]

SF=1.0

SF=1.1

SF=1.2

SF=1.3

SF=1.4

SF=1.5

SF=1.6

SF=1.7

SF=1.8

SF=1.9

lambda point

Temperature distribution in the cold bore

0.0

0.5

1.0

1.5

2.0

2.5

-15 -10 -5 0 5 10 15

# cable

DT

[K

]

SF=1.0

SF=1.1

SF=1.2

SF=1.3

SF=1.4

SF=1.5

SF=1.6

SF=1.7

SF=1.8

SF=1.9

Temperature jump

due to normal fluid

helium heat

conduction decrease

Temperature jump

due to superfluid to

normal fluid

pahse transition

Temperature jump

due to normal fluid

helium zone

expansion in the

channel around

cold bore



0

5

10

15

20

0 2000 4000 6000 8000 10000 12000 14000

Imagnet [A]

Max

imum

hea

t loa

d [m

W/m

]

Nominal Peak Heat Load

Nominal

magnet

current

Quench limit in the phase I quadrupole magnet

Nominal insulation

Enhanced insulation

Temperature increase in the coil at nominal heat load for nominal and enhanced LHC cable insulation

Cable insulation and helium channel around cold boreare the most criticalparameters limiting heatflow from the magnet coilat steady state heat load



0

20

40

60

80

100

120

140

160

180

200

220

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Luminosity (x1035

cm−2

s−1

)

Que

nch

grad

ient

(T/m

)

0 5 10 15 20 25 30 35 40 45 50 55 60

Average power density (mW/g)

T0=1.9K, SS collar

T0=4.5K, SS collar

T0=1.9K, Al collar

T0=4.5K, Al collar

Operating gradient

Work presented by V. Kashikhin on CECICMC09.

Arrow

indicates

phase II

nominal

luminosity

Nb3Sn

Courtesy N. Mokhov

The COMSOL simulation included:

• energy deposits in the coil

• cable material and insulation.

The simulation did not included:

• helium in the magnet

(channel around cold bore)

• energy deposits in the coldbore

L=2.5*1034 cm-2s-1


The analysis of thermal bahaviour of the phase I quadrupole magnet was presented.

The heat flow paths and heat flow barriers wereidentified with the thermal network simulation.

There is significant impact on magnet performance from energy deposits in cold bore.

The size of helium channel around cold bore and cable insulation are the most critical parameters.

Conclusions


Implementation of the thermal network to phase II Nb3Sn magnet is needed to calculate quench limits and compare with phase I simulation.

The analysis of impact of helium channel around cold bore is necessary to optimize the channel width.

An experiment devoted to study of helium channel around cold bore is welcome

Possible use of network model to study different Nb3Sn cable insulation properties, for instance radiation hardness.

Future Plans

BNL - FNAL - LBNL - SLAC

Modeling of Nb3Sn coil length change

during heat treatment

D. Bocian, G. Ambrosio, F. Nobrega, M. Whitson / FNAL

A. Bonasia, L. Bottura, L. Oberli / CERN

B. Walsh / NHMFL, M. Wake / KEK

To be presented at Low Temperature Superconductor Workshop

Monterey, CA, November 10-11, 2009


Introduction

Presented results are the part of general studies leading to

understanding coil elements behavior during heat treatments.

Work has been divided into several steps:

I. Collection of relevant data and material properties for simulations

II. Preparation and conduct of necessary measurements

III. FEM simulation of the strand/cable/coil behavior during reaction

IV. Feedback to the coil fabrication technology


Cable sample measurement

-1

-0,5

0

0,5

1

1,5

2

2,5

00:00:00 01:12:00 02:24:00 03:36:00 04:48:00 06:00:00 07:12:00 08:24:00 09:36:00 10:48:00

DIL

AT

AT

ION

[m

m]

TIME

DILATATION 5 kg

DILATATION 15 kg

Observed cable shrinkage was:

0.85 mm for 5 kg load

0.65 mm for 15 kg load.

Extrapolation to 0 kg load shows a 0.95 mm cable shrinkage.

Cable sample: LARP Nb3Sn

Strand: 54/61

Sample length: 104 cm

Target temperature: 210°CHeating time at 210°C: 360 min.

Temperature ramp time: 2h 19min

Cooling time: 1h


Strand sample measurement

Sample preparation:

Weld the ends of strand sample.

Resize the ends of strands to fit required diameter.

Chosen sample length ~ 48 mm Nb3Sn strand.

measured

sample

sample

holder

furnace

measurement tip

LVDT

reference

material

Results of nominal LQ heat treatment of strand smaple

Sample 1 Sample 2 Sample 3

Before HT [mm] 48.400 47.900 47.710

After HT [mm] 48.450 47.950 47.733

DL/L [%] 0.1 0.1 0.05

measurement of DL after HT - done

measurement during HT - in progress


BACKUP TRANSPARENCIES


Backup - Electrical equivalent

iRVqRT DD

t

VRCV

t

TCRT

22

The analogy of the equivalent thermal

circuit

Thermal circuit Electrical Circuit

T [K] Temperature V [V] Voltage

Q [J] Heat Q [C] Charge

q [W] Heat transfer rate i [A] Current

κ [W/Km] Thermal Conductivity σ [1/Ωm] Electrical Conductivity

RΘ [K/W] Thermal Resistance R [V/A] Resistance

CΘ [J/K] Thermal Capacitance C [C/V] Capacitance

The analogy between electrical and thermal circuit can be expressed as:

-steady-state condition Temperature rise Voltage difference

-transient condition Heat diffusion RC transmission line


Backup - Non beam loss heat loads

• Heat generated by electrical sources – For main dipole during ramp (R. Wolf) [J/m]

• Hysteresis loss 240

• Inter-strand coupling (Rc = 7.5 mW) 45

• Inter-filament coupling (t = 25ms) 6.6

• Other eddy currents (spacers, collars..) 4

• Resistive joints (splices) 30

– Total (per meter) ~325

A. Siemko, 14th “Chamonix Workshop”, January 2005

The first estimations shows contribution at the level of 0.5 mW/cm3

A detailed studies are ongoing (A. Verweij, R. Wolf)


Helium in the magnet

Normal fluid and gaseous helium

In case of channels inside of the cable and μ-channels which are of the order of 0.2 mm and

0.07 mm respectively, a typical nucleate boiling flux becomes much lower than that for

helium bath which is 10 000 W/m2 [1]. The gaseous phase in the narrow channels is

described by a constant heat transfer coefficient and is of the order of 70 W/m2/K as

extrapolated from [2]. The convective heat transfer in steady state mode is restricted to heat

fluxes not greater than a few mW/cm2 [3] as it is only relevant for large volumes. In case of

helium inside the cable and in the μ-channels this mode is negligible.

[1] S.W. Van Sciver, Helium Cryogenics.

[2] M. Nishi et all., Boiling helium heat transfer characteristics in narrow cooling channel, IEEE TRANSACTIONS

ON MAGNETICS, VOL. MAG-19, NO. 3, MAY 1983.

[3] C. Schmidt, Review of steady state and transient heat transfer in pool boiling helium I.

Superfluid helium

The heat flow in He II is calculated according formulae

[Claudet et al., CRYOGENIE et ses applications en

supraconductivite, IIF/IIR]

and X(T) is an experimental results fitting

2

29.0)()(

cm

W

l

TXTX

s

Q hc

eT

TX5.2

16.231520)(

The heat conductivity of superfluid

helium is very high at low heat currents,

but since it is non-linear it can be much

reduced at high heat currents.

(W. F. Vinen. Superfluidity. CERN CAS

School on Superconductivity, 1995.

At high heat currents the superfluid

helium in the channel can „quench”

resulting in transition to the normal fluid

helium means that heat evacuation from

the coil is reduced significantly resulting

in quenching of the magnet.


Cable parameters

Table 1: Cables parameters

unit Inner layer Outer layer

w mm 15.100 15.100

thick in mm 1.736 1.362

thick out mm 2.064 1.598

rad. insulation mm 0.160 0.160

az. insulation mm 0.135 0.145

n. strand 28 36

strand diameter mm 1.065 0.825

Cu/Sc ratio 1.65 1.95

Iss A 14800 (10T) 14650 (9T)

ΔIss/ΔB A/T 4680 (10T) 4050 (9T)


New inner triplet E deposits simulation

Peak Energy Deposit in coil

0

2

4

6

8

0 1000 2000 3000 4000

distance [cm]

E [

mW

/cc]

Q1 Q2A Q2B Q3

Peak Energy Deposit in cold bore

0

3

6

9

12

15

18

0 1000 2000 3000 4000

distance [cm]

E [

mW

/cc]

Q1 Q2A Q2B Q3

L=2.5*1034 cm-2s-1 FLUKAMARS



0

20

40

60

80

100

120

140

160

180

200

220

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Luminosity (x1035

cm−2

s−1

)

Que

nch

grad

ient

(T/m

)

0 5 10 15 20 25 30 35 40 45 50 55 60


T0=1.9K, SS collar

T0=4.5K, SS collar

T0=1.9K, Al collar

T0=4.5K, Al collar

Operating gradient

0

20

40

60

80

100

120

140

160

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

Luminosity (x1035

cm−2

s−1

)

Que

nch

grad

ient

(T/m

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5


T0=1.9K, SS collar

T0=1.9K, Al collar

T0=1.9K, transp. collar

Operating gradient

Work presented by V. Kashikhin on CECICMC09.

Arrow

indicates

nominal

luminosity

NbTi

Nb3Sn

Documents

Thermodynamics Modeling of New LHC Quadrupole Magnetlarpdocs.fnal.gov/LARP/DocDB/0010/001036/001...Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 3 MOTIVATION Particles