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PROTECTION IN MAGNET DESIGN

CERN, WAMSDO workshop 15 th January 2012. PROTECTION IN MAGNET DESIGN. E. Todesco CERN, Geneva Switzerland With help from B. Auchmann , L. Bottura , H. Felice , J. Fleiter , T. Salmi , M. Sorbi. CONTENTS. Main physics given in previous talk [talk by L. Bottura ]

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PROTECTION IN MAGNET DESIGN

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  1. CERN, WAMSDO workshop 15th January 2012 PROTECTION IN MAGNET DESIGN E. Todesco CERN, Geneva Switzerland With help from B. Auchmann, L. Bottura, H. Felice, J. Fleiter, T. Salmi, M. Sorbi

  2. CONTENTS • Main physicsgiven in previous talk [talk by L. Bottura] • Hotspottemperature • Maximum temperature for Nb-Tiand Nb3Sn • Time margin • Case with a dump resistor:scalings • No dump resistor: intrinsiclimits, scalings, fielddependence • Budget for time margin: detection, heaterdelay, etc • Heaters • Delays vs operationalcurrent and vs field • How to quench the inner layer ? • Detection • Thresholds, scalings and the case of HTS • Otherterms: quenchback, … • Inductive voltages

  3. LIMITS TO HOTSPOT TEMPERATURE • Whatis the maximum acceptable hotspottemperature ? • Nb-Ti • Degradationof insulationat 500 K • Limitusually set at 300 K • Nb3Sn • Weak point: avoid local stress thatcould damage the Nb3Sn • Limitsaround 300 K, withsome more conservative down to 200 K and more daring up to 400 K • That’s a bigdifference … what to choose? Difficult to simulate, experimentsshould drive thischoice

  4. LIMITS TO HOTSPOT TEMPERATURE • Data from TQ series • Degradationfrom 8 to 9 MIITS • Estimate hot spot of 370-390 K • Data from HQ • High MIITs test, no degradation at 18 MIITS (300 K at 12 T) • Someuncertaintydue to ignorance of local field [G. Ambrosio et al., IEEE Trans. Appl. Supercond. 18 (2008) 268] 18.3 Miits 16.9 Miits 13.2 Miits [H. Bajas, et al., IEEE Trans. Appl. Supercond. 23 (2013) in press]

  5. CONTENTS • Hotspottemperature • Maximum temperature for Nb-Tiand Nb3Sn • Case with a dump resistor: scalings • Time margin • No dump resistor: intrinsiclimits, scalings, fielddependence • Budget for time margin: detection, heaterdelay, etc • Heaters • Delays vs operationalcurrent and vs field • How to quench the inner layer ? • Detection • Thresholds, scalings and the case of HTS • Otherterms: quenchback, … • Inductive voltages

  6. DUMPING ON RESISTOR • Weneglectmagnetresitance • Resistorislimited by the maximum voltage that the magnetcanwithstand • Protection condition: • Balance betweenquench capital and tax • So weconclude • External dump strategy not invariant on the magnetlength • If itworks for 1 m, itcanbe not viable for 10 m long magnets • External dump strategy: largercablesallow to gain time margin • Gscaleswith square of cable area • Gq scaleswith the cable area Quench capital Quenchtax

  7. DUMPING ON RESISTOR • Example of Q4 for the LHC upgrade [M. Segreti, J. M. Rifflet] • Twolayers of 8.8 mm cable or one layer of 15.1 mm cable ? • Similar gradient 120-128 T/m and currentdensity 700 A/mm2 • One layer design has a cable cross-section 3 times larger, 13 times lower inductance – no need of heaters • G=30 MIITs, Gq=18 MIITs for one layer • G=3.2 MIITs, Gq=6.2 MIITs for one layer

  8. NO DUMP: INTRINSIC LIMIT TO PROTECTION • No external dump • Idealisquenching all the magnet in zero time • An intrinsiclimit to protection is the trivial balance betweenenergydensity and heatcapacity • Nb-Ti • Typicalenthalpyat 300 K is 0.65 J/mm3 → withcopperis0.7 J/mm3→ with30% voids one has 0.5 J/mm3 (heliumneglected) • Nb3Sn • Typicalenthalpyat 300 K is0.45 J/mm3 → withcopperis0.6 J/mm3 → with30% insulation 0.5 J/mm3 • HTS: • YBCO: typicalenthalpyat 300 K is0.55 J/mm3 • A limitisgiven by the enthalpywhich looks rathersimilar for differentcoils – hard limitat~0.5 J/mm3

  9. NO DUMP: INTRINSIC LIMIT TO PROTECTION • Where are wewith respect to theselimits ? • Nb-Ti: 0.05 J/mm3, we are a factor 10 below (factor 3 in current ) • Nb3Sn: =0.10-0.12 J/mm3, we are a factor 4-5 below (factor 2 in current) Energydensity in the insulatedcable, and limitgiven by enthalpyat 300 K

  10. DEFINITION OF TIME MARGIN • There are several concepts of margin for superconductingmagnets • Currentdensitymargin • Loadlinemargin • Temperaturemargin • We propose a margin for protection: the time margin • Hypothesis: adiabaticapproximation (conservative) • j: currentdensityI: current • rcu: copperresistivitycpave: volumetricspecificheat • n: fraction of copperA: cable surface

  11. DEFINITION OF TIME MARGIN • Wedefine the MIITS of the cable (the capitalwecanspend) • Gq are the MIITS of a quench where all magnetquenchesat time 0 • How long canwestayat nominal currentI0 ? We call thisthe protection time marginTq

  12. NO DUMP: SCALINGS - 1 • No dump strategyisindependent of the length • BothR and Lscalewithlenghtso the problem in independent of magnetlength • No dump strategyisindependent of the size of the cable • To be more precise: replacing a double layer coilwith a single layer and double width, sameU and j (see case Q4), has no impact • w  w’=2w Io Io’=2Io U  U’=U • Same time constant: L  L’=L/4 R  R’=R/4 • 4 times MIITS and GqG G ’= 4G Gq Gq’= 4Gq • Same time marginTq’=Tq • Whatis relevant?

  13. NO DUMP: SCALINGS - 2 • We are goingfrom time margin of 100 ms (LHC NbTi) to 50 ms (Nb3Sn) and evenlower • Note thatstoredenergyis not relevant: TQ worsethan Fresca2 • Note the role of currentdensity (up to nowneglected I think, whilst the role of copper has been overestimated) Energydensity versus currentdensity in the insulatedcable

  14. NO DUMP: SCALINGS - 3 • So whatis relevant ? • One canderive an equationwith intensive properties Copper fraction cableenthalpyenergydensity Averageresistivitycurrentdensity wherehis a parameter 1 for energydensityapproachingcableenthalpy

  15. NO DUMP: SCALINGS - 4 • The role of currentdensityis not less important than Cu fraction ! Energydensity versus Cu no-Cu in the insulatedcable Time margin vs currentdensity in the insulatedcable

  16. NO DUMP: dependence on field • Depending on the initial quench location one has a large variation of the budget for MIITs →large variation time margin • Example HQ: from 25 (12 T) to 45 ms (2 T) • This additionalmargin for lowfieldwillbeneeded Time margin vs field in HQ (one marker per cable)

  17. TIME TO QUENCH ALL THE MAGNET • Detection time • Time to get over the threshold ( a few ms → 10, 20 ms?) • Larger for lowerfields ! • Validation time 10 ms, possiblylowered to 5 ms • Switch opening 2 ms • Quenchheaters • Delay to quench the first cable (5-10 ms) • Delay to quench the last cable (10-20 ms) • A time budget of 40 ms isat the limit Over the threshold Validation time Switch opening Delay of quenchheaters: first cablequenched Delay of quenchheaters: last cablequenched The budget for the time margin

  18. CONTENTS • Hotspottemperature • Maximum temperature for Nb-Tiand Nb3Sn • Time margin • Case with a dump resistor:scalings • No dump resistor: intrinsiclimits, scalings, fielddependence • Budget for time margin: detection, heaterdelay, etc • Heaters • Delays vs operationalcurrent and vs field • How to quench the inner layer ? • Detection • Thresholds, scalings and the case of HTS • Otherterms: quenchback, … • Inductive voltages

  19. HEATERS: FIRST OBSERVATIONS • Typicalquenchvelocities • Along a cable~10-20 m/s → 50-100 ms to make 1 m • Fromturn to turn~10 ms Fromouter to inner ~50 ms • The build up of resistance due to quench propagation isnegligible • Essential part of the modelingis the heattrasferfrom the quenchheaters to the coil • Interplay of heattransfer, temperaturemargin • Heaters power islimited by voltage • The heatergeometryis not indepedent of length ! • For long magnet one has to makeheating stations to preserve a large power (~50 W/cm2 for 25 mm thick – or bettersay 20 W/mm3?) • Distance of stations ~100 mm to have propagation in lessthan 5 ms • This alsomakes the problem more complex

  20. HEATERS: FIRST OBSERVATIONS • Simple model • Estimate the temperaturemarginTcs a • IntegratespecificheatfromTopto Tcsto get the energyneeded • Time proportional to energy (one free parameter) • The case 1.9 K vs 4.2 K • 1.9 K: Tcs=1.9 + 4.8 = 6.7 • 4.2 K: Tcs=4.2 + 3.3 = 7.5 • At the end «by chance» the twointegrals are similarwithin 10-20% - sosimilardelays as foundexperimentally • More refinedmodels • Thermal network [talk by T. Salmi]

  21. HEATERS DELAY • Case of HQ [see G. Ambrosio talk] • 25 mm Kaptonbaseline, 50 mm and 75 mm analysed • 20-80% I/Iss range lessthan 10 ms at 80% • Nominal power of 50 mW/cm2 • Very good modeling Heatersdelay vs powering[T. Salmi, H. Felice] Heatersdelay vs model [T. Salmi, H. Felice]

  22. HEATERS DELAY • Case of 11 T • 125 mm Kaptonbaseline, 250 mm alsoused • 20-60% I/Iss range • Nominal power of 25 mW/cm2 Heatersdelay for 11 T [see G. Chalchdize]

  23. HEATERS DELAY • Case of MQXC (Nb-Ti coil, permeable to HeII) • QH betweeninner and outer layer • 50 mm Kaptonbaseline • 10-80% I/Iss range • Nominal power of 15 mW/cm2 80% Heatersdelay for MQXC [see G. Kirby talk]

  24. DELAY VS LOCAL FIELD • Problem: the heateris on part of the coilwithdifferentfield → differenttemperaturemargin • Typically (LARP quads) wefind a factor 2-3 between the twodelays • So if first quenchisinducedafter 6 ms, last part of the outerquenchesat 15-20 ms Over the threshold Validation time Switch opening Delay of quenchheaters: first cablequenched Delay of quenchheaters: last cablequenched Delay estimatedthroughenergymargin versus fieldHQ

  25. HOW TO QUENCH THE INNER LAYER ? • 1st solution: quenchheaters on the inner layer innerside • Done in HQ, theywork but • Barrier to heatremoval • Indications of detatchement(thereis no support), i.e. efficiencycoulddegradewith time • 2ndsolution: quenchheatersbetweeninner and outer layer • Done in MQXC (Nb-Ti) • For Nb3Sn one has to findmaterial resistingcuringat 650 C (tried in HFD, abandoned) or make a splice • 3rd solution: use the outer layer as heater • Is itfastenough ? 50 ms measured in 11 T very relevant number for protection (to bemeasured and simulated)

  26. CONTENTS • Hotspottemperature • Maximum temperature for Nb-Tiand Nb3Sn • Time margin • Case with a dump resistor:scalings • No dump resistor: intrinsiclimits, scalings, fielddependence • Budget for time margin: detection, heaterdelay, etc • Heaters • Delays vs operationalcurrent and vs field • How to quench the inner layer ? • Detection • Thresholds, scalings and the case of HTS • Otherterms: quenchback, … • Inductive voltages

  27. DETECTION • Time to go above the threshold • Up to 40 K lowdependence of resistivity on temperature • Estimate for HQ, at 12 T • Vth=100 mV jo,Cu=1400 A/mm2 • vNPZ= 20 m/s r(12 T)=6 ×10-10W m • td=6 ms (reasonable)

  28. DETECTION • Time to go above the threshold • Strong influence of field • rk(12 T) /rk(0 T) ~2 or 1 • Tcs-Top~5 K at 12 T, Tcs-Top~15 K at 0 T • vNPZ(12 T)/ vNPZ(0 T) ~ 2.5 or 1.7 • vNPZr(12 T)/ vNPZ r(0 T) ~ 10 or 6 • So at 0 T NPZ canpropagate 10 times slower … • Detection time canbemuch longer for lowfield • Larger budget (20 ms) partiallycompensates • Carefulstudy of quenchvelocityneeded[SeeH. ten Kate talk] • For HTS the vNPZis a factor 100 lessso the detectionis the real bottleneck[See J. Schwartz talk]

  29. QUENCHBACK • For LARP quads we have evidence of strongquenchback • Method: open switch and dump current on resistor – estimateresistancefromdI/dt • This effectcanbe dominant! Wecangetwrong conclusions • The initial ramp rate ishuge! with I=15 kA, t=1, dI/dt= 15000 A/s … High MIITs test [H. Bajas, M. Bajko, H. Felice, G. L. Sabbi, T. Salmi, ASC 2012]

  30. CONTENTS • Hotspottemperature • Maximum temperature for Nb-Tiand Nb3Sn • Time margin • Case with a dump resistor:scalings • No dump resistor: intrinsiclimits, scalings, fielddependence • Budget for time margin: detection, heaterdelay, etc • Heaters • Delays vs operationalcurrent and vs field • How to quench the inner layer ? • Detection • Thresholds, scalings and the case of HTS • Otherterms: quenchback, … • Inductive voltages

  31. INDUCTIVE VOLTAGES • During the quench one has • a resistive voltage propto I (where the magnetisquenched) • an inductive voltage proptodI/dt (everywhere) • The twocompensateat the end of the magnet in case of no dump resistor • Worstestimate: • Outer layer quenched – inner layer not • Equal split of inductance • So the highest voltage vs time is • where the I(t) iscomputed for a fullyquenchedouter layer

  32. INDUCTIVE VOLTAGES - scaling • The inductive voltage isproportional to magnetlength • Currentinpendendent of length, derivative as well • Inductance proptolength • The inductive voltage isreduced for largercables • Usual case twomagnetssamefield and energy, one withtwolayers and widthw, one with one layer and width2w • I→I’=2I w→ w’=2w L→ L’=L/4 R→ R’=R/4 • t→ t’=t Vmax→ Vmax’=Vmax /2 • So smallcablescanbedangerous for long magnet

  33. INDUCTIVE VOLTAGES - scaling • Where are we ? • For all magnetswe are safe • alsoconsideringthatanywayafter 50 ms the inner has to quench (in this simulation innerneverquenches) • But we are not so far from the limit Estimate of maximum inductive voltage in some future magnets

  34. CONCLUSIONS • With Nb3Sn magnetswe are entering a new regime of protection • We are a factor 5 belowenergydensitylimit set by heatcapacity • It was a factor 10 with Nb-Ti • The time marginneeded to quench the magnetis of ~50 ms • It is a factor 2-4 larger for LHC MB and MQXC • Large currentdensities are challenging … • TQ wasprobably impossible to protect in long version • How heatersworkis a key point • Delays of 5-10 ms are acceptable • Optimize power, thickness of insulation, coverage • The question of the inner layer: what to do? • Measuring and modeling the delaybetweenouter and innerquench

  35. CONCLUSIONS • Detection time • Is the main bottlenck for HTS • It canbecomecritical for Nb3Sn atlowfields • Quenchbackcanbecome the dominant mechanism for LARP Nb3Sn magnetswithoutcoredcable • Measurementsneeded, withlow dump resistor • Inductive voltages are not a problem for the magnetsbeingplanned • Theyscalewithmagnetlength • The inner triplet for the HL-LHC isjustgoing close to thislimit

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