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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 3
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 4
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 5
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).
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 6
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 7
Network Model
coil model
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 8
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 9
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 10
New inner triplet phase I simulation status
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)
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 11
New inner triplet phase I simulation status
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 12
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 13
New inner triplet phase I simulation status
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 14
New inner triplet phase II simulation status
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 15
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 16
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 18
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 19
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 20
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 21
BACKUP TRANSPARENCIES
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 22
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 23
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)
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 24
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.
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 25
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)
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 26
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
Dariusz Bocian Termodynamics Modeling of New LHC Quadrupole Magnet 27
New inner triplet phase II simulation status
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
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
Average power density (mW/g)
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