BNL FNAL LBNL SLAC Thermal study of Nb

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BNL - FNAL - LBNL - SLAC Thermal study of Nb 3 Sn magnets

BNL - FNAL - LBNL - SLAC Thermal study of Nb 3 Sn magnets Dariusz Bocian I would like to thank G. Ambrosio, G. Chlachlidze, S. Feher, V. V. Kashikhin, M. Whitson for their help during the course of this work LQ/LHQ meeting June 28, 2011

Motivation Energy deposits in the accelerator magnets increase for machine upgrade Heat load calculations

Motivation Energy deposits in the accelerator magnets increase for machine upgrade Heat load calculations for LHC IR magnets show (N. Mokhov): → Current LHC: 10 W/m → LHC upgrade: 50 W/m Thermal study of possible LHC upgrade IR magnet designs o LARP Nb 3 Sn quadrupole design → impregnated coil → no helium link between the bath and the cable o New CERN Nb. Ti quadrupole design → enhanced insulation scheme → open helium paths between the bath and the cable June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 1

First results TQC 02 model validation 12 MJR simulations (1. 9 K) - Network

First results TQC 02 model validation 12 MJR simulations (1. 9 K) - Network Model MJR measurements 10 - published MJR simulations (1. 9 K) - published Iquench [k. A] 8 6 What is wrong? - Network model? 4 - Material properties? 2 - Jc parametrization? - Measurement data? 0 0 June 28, 2011 5 10 15 20 25 30 35 40 Heat load [W/m] 45 Thermal analysis of LARP superconducting magnets 50 55 60 65 Dariusz Bocian 70 2

OUTLINE Network Model of LARP Nb 3 Sn quadrupole magnets Thermal model validation with

OUTLINE Network Model of LARP Nb 3 Sn quadrupole magnets Thermal model validation with TQC 02 b measurements Material properties at low temperatures Critical current parameterization Power dissipated to the magnet (heating stainless steel strip) HQ coil thermal study Conclusions June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 3

Nb 3 Sn Thermal model construction Detailed magnet geometry (Technical drawings) Temperature margin ΔT(B)

Nb 3 Sn Thermal model construction Detailed magnet geometry (Technical drawings) Temperature margin ΔT(B) / OTHER (non-beam induced heat sources) Jc parametrization TEMPERATURE MAP (MAGNET QUENCH LIMIT) HEAT FLOW MODEL Heat load profile Material properties at low temperature MEASUREMENTS Model validation June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 4

Magnet thermal model coil model June 28, 2011 Thermal analysis of LARP superconducting magnets

Magnet thermal model coil model June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 5

Network Model - Validation EXPERIMENT Heat source heat MAGNET - quench heaters - inner

Network Model - Validation EXPERIMENT Heat source heat MAGNET - quench heaters - inner heating apparatus measured quench current VALIDATION HEAT SOURCE MODEL heat MAGNET MODEL END predicted quench current More details for Nb. Ti magnets: 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; D. Bocian, B. Dehning, A. Siemko, Quench Limit Model and Measurements for Steady State Heat Deposits in LHC Magn accepted for publication in IEEE Transactions on Applied Superconductivity, 2009 June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 6

cable 8 1 POLE 2. Interlayer: S-2 glass + epoxy cable 5 b. Ground

cable 8 1 POLE 2. Interlayer: S-2 glass + epoxy cable 5 b. Ground insulation: Kapton 6 a. Midplane insulation: Kapton HELIUM 11. Yoke 10. Collar 9. Collaring shoe Stainless Steel 5 b. Ground insulation: Kapton 5 a. Ground insulation: Kapton 4 b. Outer layer: S-2 glass + epoxy 4 a. Quench heater: SS+Kapton 6 b. Midplane insulation: Kapton 7 a. Heater: Stainless Steel 7 b. Heater: Kapton shimm Model validation - TQ magnet 8 1 POLE 3 a. Quench heater: SS+Kapton 3 b. Inner layer: S-2 glass + epoxy HELIUM June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 7

Model validation procedure Model parameters → Measured coil insulation thickness → Material properties at

Model validation procedure Model parameters → Measured coil insulation thickness → Material properties at low temperatures § G 10 (S-2 glas + epoxy) § Polyimide (Kapton, Apical) § Stainless steel heater resistance power dissipated → Critical current parametrizations fit to short sample data Measurement data → Measurements performed at Fermilab in 2008 with TQC 02 June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 8

cable Data from measurements TQC 02 a parameters layer 8 1 2. Interlayer: S-2

cable Data from measurements TQC 02 a parameters layer 8 1 2. Interlayer: S-2 glass + epoxy cable 5 b. Ground insulation: Kapton 6 a. Midplane insulation: Kapton HELIUM 11. Yoke 10. Collar 9. Collaring shoe Stainless Steel 5 b. Ground insulation: Kapton 5 a. Ground insulation: Kapton 4 b. Outer layer: S-2 glass + epoxy 4 a. Quench heater: SS+Kapton 6 b. Midplane insulation: Kapton 7 a. Heater: Stainless Steel 7 b. Heater: Kapton shimm Model validation - TQ magnet 8 1 3 a. Quench heater: SS+Kapton 3 b. Inner layer: S-2 glass + epoxy HELIUM June 28, 2011 POLE material MJR RRP [mil]/[mm] 1 S-2+epoxy 3. 9/ 0. 099 3. 75 / 0. 095 2 S-2+epoxy 12. 9/ 0. 327 6. 5/ 0. 165 3 a Kapton 1. 7/0. 043 0 3 b S-2+epoxy 11. 8 / 0. 299 8. 2 / 0. 208 4 a Kapton 1. 7/0. 043 4 b S-2 +epoxy 10. 77 / 0. 273 6. 5/ 0. 165 5 a Kapton 5 / 0. 127 5 b Kapton 5 / 0. 127 6 a Kapton 3 / 0. 0762 6 b Kapton 2 / 0. 0508 7 a Stainless steel 1/0. 0254 (9. 5 mm width) 7 b Kapton 1/0. 0254 8 S-2+epoxy 3 / 0. 0762 9 Stainless steel 31/0. 7874 Thermal analysis of LARP superconducting magnets Dariusz Bocian 9

Model parameters - Material properties at low temperatures experimental data available Material data implemented

Model parameters - Material properties at low temperatures experimental data available Material data implemented in Network Model 0. 20 0. 18 0. 16 0. 14 0. 12 0. 10 0. 08 0. 06 0. 04 0. 02 0. 00 G 10 -CRYOCOMP data POLYIMIDE-CRYOCOMP data Cryocomp 1 -300 K NIST 10 -300 K Saclay 1. 55 -2. 5 K 0 5 10 T [K] 15 20 Bibliography: 1. B. Baudouy, „Kapitza resistance and thermal conductivity of Kapton in superfluid helium”, Cryogenics 43(2003), 667 -672, 2. Lawrence et al. , „ The thermal conductivity of Kapton HN between 0. 5 and 5 K”, Cryogenics 40 (2000), 203 -207, 3. B. Baudouy, J. Polinski, „Thermal conductivity and Kapitza resistance of epoxy resin fiberglass tape at superfluid helium temperature”, Cryogenics 49(2009), 138 -143 June 28, 2011 10 T [K] 15 20 Cryocomp 1 -833 K 0. 07 0 5 Polyimide 0. 08 κ [W/m K] Polyimide & G 10 κ [W/m K] → Coil insulation (Polyimide, G 10) G 10 0. 20 0. 18 0. 16 0. 14 0. 12 0. 10 0. 08 0. 06 0. 04 0. 02 0. 00 NIST 4 -300 K 0. 06 Saclay 1. 4 -2 K 0. 05 Lawrence 0. 5 -5 K 0. 04 0. 03 0. 02 0. 01 0. 00 0 Thermal analysis of LARP superconducting magnets 5 10 T [K] Dariusz Bocian 10

Model parameters – Power dissipated to the magnet 60 7. 5 E-07 R(1. 9

Model parameters – Power dissipated to the magnet 60 7. 5 E-07 R(1. 9 K) 50 7. 0 E-07 R(4. 5 K) 40 6. 5 E-07 R(20 K) 30 ρ [Ω·m] P [W/m] AISI 304_Steel R(50 K) Heating strip l=1 m, w=9. 5 mm, t=25. 4 μm 20 10 5. 5 E-07 5. 0 E-07 0 0 2 4 6. 0 E-07 6 4. 5 E-07 0 50 100 150 200 250 300 350 I [A] AISI 304_Steel 3. 4 § Strip resistance confirmed at 300 K: rescalling resistance measured at CERN with 15 mm strip 3. 0 R [Ω] measurement of similar strip resistance at FNAL TQC 02 traveller 3. 2 TQC 02 traveller 2. 8 2. 6 Heating strip l=1 m, w=9. 5 mm, t=25. 4 μm 2. 4 2. 2 § There is no significant impact of strip resistance on 2. 0 calculated power dissipation in the range of 1. 9 – 50. 0 K resistance to 2. 10 Ω of LARP superconducting magnets June 28, 2011 vary between 2. 04 Thermal analysis 0 100 200 T [K] 300 Dariusz Bocian 400 11

Ic Calculated at 4. 2 K Model parameters - Critical current parametrization TQ 09

Ic Calculated at 4. 2 K Model parameters - Critical current parametrization TQ 09 -10 6000 5000 extr. 940 R SS V-I 4. 2 MJR coil Ic Calculated at 4. 2 K 4000 3000 2000 1000 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 B [T] TQ 16 -17 Ic Calculated at 4. 2 K 8000 7000 extr. 940 R SS V-I 4. 2 Ic Calculated at 4. 2 K RRP coil 6000 5000 4000 3000 Critical current parametrization: Bref=12 T, Tref=4. 2 K MJR: Jcref=1954 A/mm 2 Tc 0= 17. 6 K Bc 20= 26. 6 T C 0=31848 A/mm 2 T 1/2 RRP: Jcref=2404 A/mm 2 Tc 0=17. 2 K Bc 20=26. 3 T C 0=40558 A/mm 2 T 1/2 2000 1000 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 B [T] June 28, 2011 L. T. Summers, M. W. Guinan, J. R. Miller, P. A. Hahn, A model for the prediction of Nb 3 Sn critical current as a function of field, temperature, strain and radiation damage, IEEE Trans. Magn. , 27 (2): 2041 -2044, 1991. Thermal analysis of LARP superconducting magnets Dariusz Bocian 12

Simulation results TQC 02 model validation 12 MJR simulations (1. 9 K) - Network

Simulation results TQC 02 model validation 12 MJR simulations (1. 9 K) - Network Model MJR measurements - published MJR simulations (1. 9 K) - published 10 Iquench [k. A] 8 6 What is wrong? - Network model? 4 - Material properties? 2 - Jc parametrization? - Measurement data? 0 0 June 28, 2011 5 10 15 20 25 30 35 40 Heat load [W/m] 45 Thermal analysis of LARP superconducting magnets 50 55 60 65 Dariusz Bocian 70 13

PARAMETERS CHECK 10 10 9 9 8 8 7 7 6 6 5 MJR

PARAMETERS CHECK 10 10 9 9 8 8 7 7 6 6 5 MJR simulations (1. 9 K) - NM What is wrong? NO - Network model? cable (4. 5 K) - NM NO cable (4. 5 K) - COMSOL 0 20 40 60 P [W/m] - Material MJR simulations (1. 9 K) - NM 10 properties? NO 9 8 Iquench [k. A] T [K] NM & COMSOL comparison MJR simulations (1. 9 K) - NM 10 9 8 7 6 5 4 3 2 1 0 0 5 10 15 20 25 30 35 Heat load [W/m] 40 Material properties as in published results 7 Jc parameterization 6 5 (as in published data) 4 - Jc 3 Jc(4. 2, 12 T)=1960 A/mm 2, 2 1 parametrization? Bc 20=28 T, 0 0 5 10 15 June 28, 2011 20 25 30 35 Heat load [W/m] 40 45 50 Tc 0=18 K Thermal analysis of LARP superconducting magnets 45 Dariusz Bocian 14 50

SIMULATION RESULTS Power values calculated for Measurements data? MJR simulations (1. 9 K) -

SIMULATION RESULTS Power values calculated for Measurements data? MJR simulations (1. 9 K) - published measurement data: MJR measurement data (1. 9 K) - published heating strip resistance used in calculations not corrected properly (2 wires measurements) MJR simulations (1. 9 K) - Network Model MJR measurements data (1. 9 K) - corrected 12. 0 (3. 5 Ω instead ~2. 1Ω ) 10. 0 AISI 304_Steel dissipated power overestimated by ~1. 4*I 2 3. 4 Iquench [k. A] TQC 02 traveller 3. 2 R [Ω] 3. 0 2. 8 2. 6 8. 0 6. 0 4. 0 2. 4 2. 0 2. 2 2. 0 0 June 28, 2011 100 200 T [K] 300 400 0. 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Heat load [W/m] Thermal analysis of LARP superconducting magnets Dariusz Bocian 15

Thermal model of LARP TQ magnets Polyimide & G 10 TQC 02 model validation

Thermal model of LARP TQ magnets Polyimide & G 10 TQC 02 model validation 0. 25 Polyimide - Cryocomp G 10 - Cryocomp 12. 0 κ [W/m K] 0. 20 10. 0 0. 15 0. 10 Iquench [k. A] 0. 05 8. 0 0. 00 6. 0 Citical current parametrization: Bref=12 T Tref=4. 2 K 4. 0 RRP: Jcref=2404 A/mm 2 Tc 0=17. 2 Bc 20=26. 3 C 0=40558 0 RRP measurements (1. 9 K) 2. 0 MJR measurements (1. 9 K) MJR simulations (1. 9 K) Cryocomp RRP simulations (1. 9 K) Cryocomp 0. 0 0 June 28, 2011 5 10 15 20 25 30 Heat load [W/m] 35 40 45 Thermal analysis of LARP superconducting magnets 5 10 15 20 25 30 35 40 T [K] MJR: Jcref=1954 A/mm 2 Tc 0= 17. 6 Bc 20= 26. 6 C 0=31848 Dariusz Bocian 16

Thermal model of LARP TQ magnets Polyimide & G 10 TQC 02 model validation

Thermal model of LARP TQ magnets Polyimide & G 10 TQC 02 model validation 0. 25 12. 0 Polyimide - Cryocomp G 10 - Cryocomp κ [W/m K] 0. 20 10. 0 0. 15 0. 10 Iquench [k. A] 0. 05 8. 0 0. 00 6. 0 Citical current parametrization: Bref=12 T Tref=4. 2 K 4. 0 RRP: Jcref=2404 A/mm 2 Tc 0=17. 2 Bc 20=26. 3 C 0=40558 0 2. 0 MJR measurements (4. 2 K) MJR simulations (4. 5 K) Cryocomp 0. 0 0 June 28, 2011 5 10 15 20 25 30 Heat load [W/m] 35 40 45 Thermal analysis of LARP superconducting magnets 5 10 15 20 25 30 35 40 T [K] MJR: Jcref=1954 A/mm 2 Tc 0= 17. 6 Bc 20= 26. 6 C 0=31848 Dariusz Bocian 17

Thermal modeling – insulation thickness Nb 3 Sn coils parameters TQ (RRP 54/61) TQ

Thermal modeling – insulation thickness Nb 3 Sn coils parameters TQ (RRP 54/61) TQ (MJR) HQ (RRP 108/127) Network Model (TQ 19 measurements) NOMINAL Network Model (TQ 15 measurements) NOMINAL MEASURED (HQ 03) [mil]/[mm] [mil]/[mm] NOMINAL layer material 1 S-2+epoxy 5 / 0. 127 3. 75 / 0. 095 5 / 0. 127 3. 9/ 0. 099 5 / 0. 127 3. 5 / 0. 090 2 S-2+epoxy 10 / 0. 254 6. 5/ 0. 165 10 / 0. 254 12. 9/ 0. 327 10 / 0. 254 8 / 0. 203 3 a Kapton 0 0 3 / 0. 076 1. 7/0. 043 1. 7 / 0. 076 3/0. 076 3 b S-2+epoxy 5 / 0. 127 8. 2 / 0. 208 7 / 0. 178 11. 8 / 0. 299 5 / 0. 127 24 / 0. 610 4 a Kapton 3 / 0. 076 1. 7/0. 043 3 / 0. 0762 1. 7/0. 043 1. 7 / 0. 076 3 / 0. 076 4 b S-2 +epoxy 7 / 0. 178 6. 5/ 0. 165 7 / 0. 178 10. 77 / 0. 273 15 / 0. 381 5. 5 / 0. 140 5 a Kapton 5 / 0. 127 5 b Kapton 5 / 0. 127 6 a Kapton 5 / 0. 127 3 / 0. 076 5 / 0. 127 6 b Kapton x 2 / 0. 051 X 7 a Stainless steel x 1/0. 0254 (9. 5 mm width) x 7 b Kapton x 1/0. 0254 x 8 S-2+epoxy 5 / 0. 127 3 / 0. 076 5 / 0. 127 9 Stainless steel 31/0. 787 June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 18

HQ modeling LARP Nb 3 Sn thermal modeling objectives: → HQ coil insulation study

HQ modeling LARP Nb 3 Sn thermal modeling objectives: → HQ coil insulation study feedback to coil design → size of the He channels in the HQ magnets § around cold bore § in the poles → Magnets quench limit calculation § MARS/FLUKA input needed Beam pipe also is a source of heat! MARS simulations for L=2. 5*10^34 (N. Mokhov) m. W/m Heat load simulations with MARS (3 mm segmented tungsten absorber Details: V. V. Kashikhin et al. , „Performance of Nb 3 Sn quadrupole magnet under localized thermal load”Fermilab-conf-09 -316 -TD) → Heat load interpolation algorithm implement (agree heat load map with conductor map) June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 19

HQ modeling - results LARP Nb 3 Sn thermal modeling : Temperature increase in

HQ modeling - results LARP Nb 3 Sn thermal modeling : Temperature increase in HQ coil Nominal: cable, Kapton 1. 7 mils, G 10 -5 mils → Heat load (HL) = 2*MARS simulations (L=5*10^34) → HQ inner coil insulation impact → size of the He channels in the HQ magnets cable + 5 mils G 10 § around cold bore set 1. 29 mm Only cable insulation § in the poles 1. 6 → set d=5 mm every 10 cm HL in the beam pipe = HL inner cable layer 1. 4 1. 2 m. W/m ΔT [K] 1. 0 0. 8 0. 6 0. 4 0. 2 0. 0 -30 -20 -10 0 # cable 10 20 30 MARS simulations for L=2. 5*10^34 (N. Mokhov) June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 20

HQ – Temperature margin H. Felice – HQ ROXIE simulations Temperature margin in HQ

HQ – Temperature margin H. Felice – HQ ROXIE simulations Temperature margin in HQ coil - inner layer Temperature margin in HQ coil - outer layer 10. 0 9. 0 HQ Temperature margin at 80% SSL at 1. 9 K 8. 0 ΔT [K] 8. 0 7. 0 6. 0 5. 0 HQ Temperature margin at 80% SSL at 1. 9 K 4. 0 -30 -20 June 28, 2011 -10 0 # cable 10 20 30 -20 Thermal analysis of LARP superconducting magnets -10 0 # cable 10 Dariusz Bocian 20 30 21

HQ modeling - results 2. 0 Temperature increase in HQ coil - inner layer

HQ modeling - results 2. 0 Temperature increase in HQ coil - inner layer Nominal: G 10 -5 mils, Kapton 1. 7 mils G 10 - 5 mils No ID HQ insulation 1. 8 1. 6 1. 4 1. 2 1. 0 0. 8 0. 6 0. 4 0. 2 Nominal: G 10 -5 mils, Kapton 1. 7 mils G 10 - 5 mils No ID HQ insulation 0. 0 -30 -20 -10 0 # cable 10 20 -30 30 ΔT - ΔTHL - inner layer HQ coil 8. 5 8. 0 7. 0 -20 -10 0 # cable 10 20 30 ΔT - ΔTHL - outer layer HQ coil 8. 5 Nominal: G 10 -5 mils, Kapton 1. 7 mils G 10 - 5 mils No ID HQ insulation 7. 5 80% SSL 1. 9 K 6. 5 ΔT [K] Temperature increase in HQ coil - outer layer 1. 8 ΔT [K] 2. 0 6. 0 5. 5 5. 0 Nominal: G 10 -5 mils, Kapton 1. 7 mils G 10 - 5 mils No ID HQ insulation 4. 5 4. 0 3. 5 -30 -20 June 28, 2011 -10 0 # cable 10 20 30 -30 Thermal analysis of LARP superconducting magnets -20 -10 0 # cable 10 Dariusz Bocian 20 22 30

HQ modeling - results ΔT - ΔTHL - inner layer HQ coil 6. 0

HQ modeling - results ΔT - ΔTHL - inner layer HQ coil 6. 0 5. 0 ΔT [K] 4. 0 3. 0 2. 0 Nominal: G 10 -5 mils, Kapton 1. 7 mils G 10 - 5 mils 1. 0 No ID HQ insulation 0. 0 -25 June 28, 2011 -20 -15 -10 -5 0 # cable 5 Thermal analysis of LARP superconducting magnets 10 15 20 Dariusz Bocian 25 23

Conclusions Reliable thermal models of Nb 3 Sn superconducting magnets have been developed Model

Conclusions Reliable thermal models of Nb 3 Sn superconducting magnets have been developed Model was validated with measurements performed at FNAL with TQ magnet Model was cross checked with COMSOL Model is used to study HQ design parameters impact on magnet thermal performance Insulation on ID has the largest impact Cooling channels dimensions in Nb 3 Sn magnets (in progress) require input from MARS/FLUKA teams Simulation error analysis (in progress) material properties at low temperatures for materials used in LARP magnets critical current dependence onoftemperature Thermal analysis LARP superconducting magnets June 28, 2011 Dariusz Bocian 24

EXTRAS June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 25

EXTRAS June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 25

PUBLISHED RESULTS DIFFERENCES MJR simulations (1. 9 K) - published q Measured insulation thickness

PUBLISHED RESULTS DIFFERENCES MJR simulations (1. 9 K) - published q Measured insulation thickness was larger than MJR measurement data (1. 9 K) - published implemented in COMSOL simulations MJR simulations (1. 9 K) - Network Model q Kapton trace in ID not included in COMSOL MJR measurements data (1. 9 K) - corrected 12. 0 simulations q G 10 heat conductivity data Iquench [k. A] 10. 0 κ [W/m K] Polyimide & G 10 0. 20 0. 18 0. 16 0. 14 0. 12 0. 10 0. 08 0. 06 0. 04 0. 02 0. 00 G 10 -COMSOL simul. G 10 -CRYOCOMP data POLYIMIDE-COMSOL simul POLYIMIDE-CRYOCOMP data 8. 0 6. 0 4. 0 2. 0 0 0 June 28, 2011 5 10 T [K] 15 20 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Heat load [W/m] Thermal analysis of LARP superconducting magnets Dariusz Bocian 26

Published results – insulation thickness Nb 3 Sn coils parameters TQ (RRP 54/61) TQ

Published results – insulation thickness Nb 3 Sn coils parameters TQ (RRP 54/61) TQ (MJR) Network Model (TQ 19 measurements) NOMINAL Network Model (TQ 15 measurements) [mil]/[mm] NOMINAL layer material 1 S-2+epoxy 5 / 0. 127 3. 75 / 0. 095 5 / 0. 127 3. 9/ 0. 099 2 S-2+epoxy 10 / 0. 254 6. 5/ 0. 165 10 / 0. 254 12. 9/ 0. 327 3 a Kapton 0 0 3 / 0. 076 1. 7/0. 043 3 b S-2+epoxy 5 / 0. 127 8. 2 / 0. 208 7 / 0. 178 11. 8 / 0. 299 4 a Kapton 3 / 0. 076 1. 7/0. 043 3 / 0. 0762 1. 7/0. 043 4 b S-2 +epoxy 7 / 0. 178 6. 5/ 0. 165 7 / 0. 178 10. 77 / 0. 273 5 a Kapton 5 / 0. 127 5 b Kapton 5 / 0. 127 6 a Kapton 5 / 0. 127 3 / 0. 076 6 b Kapton x 2 / 0. 051 X 2 / 0. 051 7 a Stainless steel x 1/0. 0254 (9. 5 mm width) 7 b Kapton x 1/0. 0254 8 S-2+epoxy 5 / 0. 127 3 / 0. 076 9 Stainless steel 31/0. 787 June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 27

NM and COMSOL comparison MODEL COMSOL NETWORK MODEL V. V. Kashikhin HELIUM Stainless Steel

NM and COMSOL comparison MODEL COMSOL NETWORK MODEL V. V. Kashikhin HELIUM Stainless Steel Kapton G 10 Kapton T [K] Kapton shimm 10 10 9 9 8 8 7 7 6 6 5 < 1. 6% cable (4. 5 K) - NM cable (4. 5 K) - COMSOL 0 7 a. Heater: Stainless Steel Kapton cable G 10 NM & COMSOL comparison 10 20 30 40 50 P [W/m] G 10 HELIUM June 28, 2011 Thermal analysis of LARP superconducting magnets Dariusz Bocian 28

Previous study – „my headache” 16. 0 Nb 3 Sn coils parameters TQ (MJR)

Previous study – „my headache” 16. 0 Nb 3 Sn coils parameters TQ (MJR) 12. 0 NOMINAL Network Model (TQ 15) COMSOL (previous study) [mil]/[mm] 5 / 0. 127 3. 9/ 0. 099 5 / 0. 127 10 / 0. 254 12. 9/ 0. 327 10/ 0. 254 3 / 0. 076 1. 7/0. 043 0 7 / 0. 178 11. 8 / 0. 299 5 / 0. 127 3 / 0. 0762 1. 7/0. 043 5 / 0. 127 7 / 0. 178 10. 77 / 0. 273 5 / 0. 127 10. 0 5 / 0. 127 3 / 0. 076 8. 0 X 2 / 0. 051 x 1/0. 0254 (9. 5 mm width) x 1/0. 0254 5 / 0. 127 3 / 0. 076 5 / 0. 127 31/0. 787 COMSOL SIMULATIONS 10. 0 8. 0 6. 0 SSL: 4. 5 K 4. 0 SSL: 1. 9 K 2. 0 Calculation: 1. 9 K 0. 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Heater power (W/m) 16. 0 14. 0 NETWORK MODEL SIMULATIONS 12. 0 Iquench [k. A] Quench current (k. A) 14. 0 6. 0 Measurements 4. 0 10 / 0. 254 input as COMSOL 2. 0 Jc impact 0. 0 0 5 10 15 20 25 30 35 40 45 Heater power [W/m] June 28, 2011 50 55 60 65 70 Thermal analysis of LARP superconducting magnets Dariusz Bocian 29

Model parameters - Material properties at low temperatures experimental data available Material data implemented

Model parameters - Material properties at low temperatures experimental data available Material data implemented in Network Model 0. 20 0. 18 0. 16 0. 14 0. 12 0. 10 0. 08 0. 06 0. 04 0. 02 0. 00 G 10 -COMSOL simul. G 10 -CRYOCOMP data POLYIMIDE-COMSOL simul POLYIMIDE-CRYOCOMP data 0 5 10 T [K] 15 20 Bibliography: 1. B. Baudouy, „Kapitza resistance and thermal conductivity of Kapton in superfluid helium”, Cryogenics 43(2003), 667 -672, 2. Lawrence et al. , „ The thermal conductivity of Kapton HN between 0. 5 and 5 K”, Cryogenics 40 (2000), 203 -207, 3. B. Baudouy, J. Polinski, „Thermal conductivity and Kapitza resistance of epoxy resin fiberglass tape at superfluid helium temperature”, Cryogenics 49(2009), 138 -143 June 28, 2011 Cryocomp 1 -300 K NIST 10 -300 K Saclay 1. 55 -2. 5 K COMSOL simul 1 -300 K 0 κ [W/m K] Polyimide & G 10 κ [W/m K] → Coil insulation (Polyimide, G 10) G 10 0. 20 0. 18 0. 16 0. 14 0. 12 0. 10 0. 08 0. 06 0. 04 0. 02 0. 00 5 10 T [K] 15 20 Polyimide 0. 08 Cryocomp 1 -833 K 0. 07 NIST 4 -300 K 0. 06 Saclay 1. 4 -2 K COMSOL simul. 1 -300 K 0. 05 Lawrence 0. 5 -5 K 0. 04 0. 03 0. 02 0. 01 0. 00 0 Thermal analysis of LARP superconducting magnets 5 10 T [K] Dariusz Bocian 30

Outline - NIST data RRP - 8781 -6, doped with Ta 900 4. 02

Outline - NIST data RRP - 8781 -6, doped with Ta 900 4. 02 5 800 6 8 700 10 600 12 14 500 Ic [A] 15 400 300 200 100 0 0 June 28, 2011 2 4 6 8 H [T] 10 Thermal analysis of LARP superconducting magnets 12 14 16 Dariusz Bocian 18 31