MATEFU Summer School on Superconductors for Fusion Quench and Protection MATEFU Summer School on Superconductors for Fusion June 17 th -22 nd, 2007, Rigi-Kaltbad, Switzerland

Luca Bottura ‘Quench and Protection’ slide no 2 MATEFU Summer School on Superconductors for Fusion What is a quench ? quench heat generation > heat removal noyes transition to normal state and Joule heat generation in current sharing temperature increase stable operating condition external energy input: flux jump conductor motions insulation cracks AC loss heat leaks nuclear … stable operating condition quench analysis and protection

Luca Bottura ‘Quench and Protection’ slide no 3 MATEFU Summer School on Superconductors for Fusion Why is it a problem ? the magnetic energy stored in the field: is converted to heat through Joule heating RI 2. If this process happened uniformly in the winding pack: Cu melting temperature 1356 K corresponding  E m = J/m 3 limit would be B max  115 T: NO PROBLEM ! BUT the process does not happen uniformly (as little as 1 % of mass can absorb total energy) L R Y. Iwasa, Case Studies in Superconducting Magnets, Plenum Press, 1994.

Luca Bottura ‘Quench and Protection’ slide no 4 MATEFU Summer School on Superconductors for Fusion This is why it is important ! Courtesy of A. Siemko, CERN

Luca Bottura ‘Quench and Protection’ slide no 5 MATEFU Summer School on Superconductors for Fusion Plan of the lecture local heating (hot-spot) normal zone propagation (heating induced flow) voltage development quench detectionsafety discharge yes heat generation > heat removal no transition to normal state and Joule heat generation in current sharing temperature increase stable operating condition external energy input: flux jump con ductor motions ins ulation cracks AC loss hea t leaks nuc lear … stable operating condition quench LTS magnets, adiabatic, indirect, stagnant or force-flow helium cooled

Luca Bottura ‘Quench and Protection’ slide no 6 MATEFU Summer School on Superconductors for Fusion Plan of the lecture Local heating (hot spot) Z function Effect of temperature gradients and heat transfer Normal zone propagation Adiabatic superconductors Bath-cooled superconductors Force-flow cooled superconductors (CICC’s) Resistance and Voltage development Quench detection and protection Detection Safety discharge Quench voltage limits Part IPart II

Luca Bottura ‘Quench and Protection’ slide no 7 MATEFU Summer School on Superconductors for Fusion Part I Local heating (hot spot) Z function Effect of temperature gradients and heat transfer Normal zone propagation Adiabatic superconductors Bath-cooled superconductors Force-flow cooled superconductors (CICC’s)

Luca Bottura ‘Quench and Protection’ slide no 8 MATEFU Summer School on Superconductors for Fusion Hot-spot the quench starts in a point and propagates with a quench propagation velocity the initial point will be the hot spot at temperature T max T max must be limited to: limit thermal stresses (see graph) avoid material damage (e.g. resins have typical T cure ≈ 100…200 °C) T max < 100 K for negligible effect T max < 300 K for highly supported coils (e.g. accelerator magnets)

Luca Bottura ‘Quench and Protection’ slide no 9 MATEFU Summer School on Superconductors for Fusion Heat balance during quench

Luca Bottura ‘Quench and Protection’ slide no 10 MATEFU Summer School on Superconductors for Fusion Material properties large variation over the range of interest ! copper resistivity as f(RRR)copper specific heat

Luca Bottura ‘Quench and Protection’ slide no 11 MATEFU Summer School on Superconductors for Fusion Adiabatic hot spot temperature adiabatic conditions at the hot spot : can be integrated: cable operating current density stabilizer fraction total volumetric heat capacity stabilizer resistivity Joule heating: B.J. Maddock, G.B. James, Proc. IEE, 115 (4), 543, 1968

Luca Bottura ‘Quench and Protection’ slide no 12 MATEFU Summer School on Superconductors for Fusion The Z(T max ) function the function Z(T max ) is a cable property: the volumetric heat capacity C is defined using the material fractions f i : Z(T max ) can be computed (universal function) for a given cable design (i.e. f i fixed) !

Luca Bottura ‘Quench and Protection’ slide no 13 MATEFU Summer School on Superconductors for Fusion Z(T max ) for pure materials assuming the cable as being made of stabilizer (good approximation): f st = 1, C =  st c st Z(T max ) is a material property that can be tabulated: Copper at B=0 T

Luca Bottura ‘Quench and Protection’ slide no 14 MATEFU Summer School on Superconductors for Fusion How to limit T max implicit relation between T max, f st, J op,  discharge to decrease T max reduce operating current density ( J op  ) discharge quickly (  discharge  ) add stabilizer ( f st  ) choose a material with large Z ( T max )  stabilizer material property electrical operation of the coil (energy, voltage) cable fractions design May reduce quench propagation speed and cause long detection times ! (see later)

Luca Bottura ‘Quench and Protection’ slide no 15 MATEFU Summer School on Superconductors for Fusion Z(T max ) for typical stabilizers T max  100 K

Luca Bottura ‘Quench and Protection’ slide no 16 MATEFU Summer School on Superconductors for Fusion Issues with the determination of T max other materials in the cable affect the value of T max structures (e.g. steel jacket in CICC’s) cable insulation in close proximity temperature gradients in the cable are difficult to estimate, and to take into account in Z(T max ) effect of heat transfer inter-turn heat transfer – small effect because of insulation heat transfer to helium – major effect for T <20 K, not so important afterwards additional heat capacity and heat transfer generally make the temperature lower the adiabatic calculation is conservative and a good method for design. HOWEVER, it may lead to excessive margins the characteristic time of the current discharge (  discharge ) is a function of quench propagation, quench detection, switching delays and dump time constant (thus in principle of T max )

Luca Bottura ‘Quench and Protection’ slide no 17 MATEFU Summer School on Superconductors for Fusion T max for composite conductors helium-jacket ( h ) strand-jacket ( H ) strand-helium ( h )

Luca Bottura ‘Quench and Protection’ slide no 18 MATEFU Summer School on Superconductors for Fusion Adiabatic T max Adiabatic calculation A cu = 38 mm 2 A sc = 38 mm 2 A jk = 68 mm 2 A he = 38 mm 2 Iop = A  delay = 250 ms  dump = 1.2 s h = 0 W/m 2 K H = 0 W/K T max ≈230 K specified

Luca Bottura ‘Quench and Protection’ slide no 19 MATEFU Summer School on Superconductors for Fusion T max with moderate heat transfer Modest heat transfer A cu = 38 mm 2 A sc = 38 mm 2 A jk = 68 mm 2 A he = 38 mm 2 Iop = A  delay = 250 ms  dump = 1.2 s h = 100 W/m 2 K H = 0.04 W/K T max ≈180 K specified

Luca Bottura ‘Quench and Protection’ slide no 20 MATEFU Summer School on Superconductors for Fusion T max with large heat transfer Large heat transfer A cu = 38 mm 2 A sc = 38 mm 2 A jk = 68 mm 2 A he = 38 mm 2 Iop = A  delay = 250 ms  dump = 1.2 s h = 1000 W/m 2 K H = 0.4 W/K T max ≈120 K specified

Luca Bottura ‘Quench and Protection’ slide no 21 MATEFU Summer School on Superconductors for Fusion A real life case The measured hot spot temperature is significantly lower than the adiabatic estimate based only on the copper in the conductor At 100 K (Q=1.1 kJ): Copper ( K): 0.5 kJ NbTi ( K): 0.1 kJ Helium ( K): 0.18 kJ The rest must be the SS conduit: 50 % of conduit cross section at 100 K, or The whole conduit cross section at 50 K J. Yoshida, K. Yoshida, T. Ando, ITER CDA Technical Report R4, JAERI-M 90, x 6 NbTi strands D strand = 0.98 mm ID conduit = 6.0 mm OD conduit = 8.2 mm L sample = 26 m 1.1 kJ

Luca Bottura ‘Quench and Protection’ slide no 22 MATEFU Summer School on Superconductors for Fusion On the importance of heat capacity at low temperature The ratio of heat absorption capacity to heat production rate c/  peaks at 20…40 K: c increases initially very fast with temperature, then flattens-out (above 100 K)  is initially flat, then increases rapidly (above 20 K) In the transient, any additional time below the knee decreases the total Joule heating produced and T max Take advantage of low temperature heat capacity to limit the hot-spot temperature

Luca Bottura ‘Quench and Protection’ slide no 23 MATEFU Summer School on Superconductors for Fusion Detection, switching and dump time precursor propagation detection detection threshold trigger (t=0) fire heaters switch dump  detection  delay  switch  dump  discharge ≈  detection +  delay +  switch +  dump By courtesy of M. Di Castro, CERN AT-MTM, 2007.

Luca Bottura ‘Quench and Protection’ slide no 24 MATEFU Summer School on Superconductors for Fusion MIITs sometimes (HEP accelerator and detector magnets) the energy balance is written as follows: the r.h.s is measured in: Mega I  I x Time (MIITs) however, now the l.h.s. is no longer a material property

Luca Bottura ‘Quench and Protection’ slide no 25 MATEFU Summer School on Superconductors for Fusion Quench propagation (adiabatic conductor) x v quench TJTJ T eq T op T x quench q’’’ J =q’’’ Jmax q’’’ J =0 T T cs T op TcTc TJTJ fixed reference frame moving reference frame

Luca Bottura ‘Quench and Protection’ slide no 26 MATEFU Summer School on Superconductors for Fusion for constant properties ( , k, C) Quench propagation (adiabatic conductor) Constant quench propagation speed Scales linearly with the current density (and current) Practical estimate. HOWEVER, it can give largely inaccurate (over-estimated) values

Luca Bottura ‘Quench and Protection’ slide no 27 MATEFU Summer School on Superconductors for Fusion Quench propagation (bath-cooled conductor) x v quench TJTJ T eq T op T x quench q’’’ J =q’’’ Jmax q’’’ J =0 fixed reference frame moving reference frame

Luca Bottura ‘Quench and Protection’ slide no 28 MATEFU Summer School on Superconductors for Fusion Quench propagation (bath-cooled conductor) recovery propagation Maddock equal area cryostable for constant properties ( , k, C) M. Wilson, Superconducting Magnets, Plenum Press, 1983.

Luca Bottura ‘Quench and Protection’ slide no 29 MATEFU Summer School on Superconductors for Fusion Quench propagation vs. data (bath-cooled conductor) J.R. Miller, J.W. Lue, L. Dresner, IEEE Trans. Mag., 13 (1), 24-27, Reproduced by courtesy of M. Wilson NbTi conductor A NbTi = 0.5 mm 2 A Cu = 5.1 mm 2 Adiabatic propagation velocities: 15 to 25 m/s

Luca Bottura ‘Quench and Protection’ slide no 30 MATEFU Summer School on Superconductors for Fusion Turn-to-turn propagation Heat conduction spreads the quench from turn to turn as it plods happily along a conductor at speed v longitudinal. The v transverse is approximated as: insulation conductivity (large) correction factors for geometry, heat capacity, non-linear material properties apply to the scaling ! conductor in normal state insulation M. Wilson, Superconducting Magnets, Plenum Press, 1983.

Luca Bottura ‘Quench and Protection’ slide no 31 MATEFU Summer School on Superconductors for Fusion Quench propagation (force-flow-cooled conductor) the helium is heated in the normal zone and expands (d  /dT < 0) pressure increase heating induced massflow of hot helium x v quench TJTJ T cable T op T x quench q’’’ Jmax q’’’ J =0 v helium T helium v quench > v helium v quench = v helium v quench < v helium ???

Luca Bottura ‘Quench and Protection’ slide no 32 MATEFU Summer School on Superconductors for Fusion x v quench TJTJ T cable T op T x quench q’’’ Jmax q’’’ J =0 v helium T helium Quench propagation (force-flow cooled conductor) helium conductor coupling

Luca Bottura ‘Quench and Protection’ slide no 33 MATEFU Summer School on Superconductors for Fusion Dresner’s helium bubble Dresner’s postulate: … the velocity of the normal zone propagation equals the local velocity of expansion of helium. consequence: … the normal zone engulfs no new helium, or in other words […] the heated helium comprises only the atoms originally present in the initial normal zone. We are thus led to the picture of a bubble of hot helium expanding against confinement by the cold helium on either side of it. OK if h is large and cable conduction is small L. Dresner, Proc. 11 th Symp. Fus. Eng.ng, 1218, 1985 L. Dresner, Proc. 10 th Symp. Fus. Eng.ng, 2040, 1983 v helium v quench v helium v quench

Luca Bottura ‘Quench and Protection’ slide no 34 MATEFU Summer School on Superconductors for Fusion quenched length quench intensity Shajii’s universe of quench A. Shajii, J. Freidberg, J. Appl. Phys., 76 (5), , normalization

Luca Bottura ‘Quench and Protection’ slide no 35 MATEFU Summer School on Superconductors for Fusion long coil high pressure rise long coil low pressure rise short coil high pressure rise short coil low pressure rise Propagation speed A. Shajii, J. Freidberg, J. Appl. Phys., 76 (5), , 1994.

Luca Bottura ‘Quench and Protection’ slide no 36 MATEFU Summer School on Superconductors for Fusion Ando’s quench experiment The quench propagation speed has weak dependency on time v quench ≈ t m m ≈ 0.6 (m=0 from theory) strong dependency on the current v quench ≈ I op n n ≈ 2.8 (n=2 from theory) T. Ando, et al., Adv. Cryo. Eng., 35, , ? 3 x 6 NbTi strands D strand = 0.98 mm L sample = 26 m short coil - low p regime

Luca Bottura ‘Quench and Protection’ slide no 37 MATEFU Summer School on Superconductors for Fusion T. Ando, et al., Cryogenics, 34, , Some additional data from Ando… Fantastic acceleration of the quench front Pressure increase

Luca Bottura ‘Quench and Protection’ slide no 38 MATEFU Summer School on Superconductors for Fusion J.W. Lue, L. Dresner, Adv. Cryo. Eng., 39, , … as well as from Lue and Dresner ! 3 NbTi strands D strand = 1.27 mm L sample = 50 m shot Iop Bop TT sound speed

Luca Bottura ‘Quench and Protection’ slide no 39 MATEFU Summer School on Superconductors for Fusion Thermal-hydraulic quench-back The helium at the front: is compressed adiabatically (Dresner) performs work agains the frictional drag (Shajii and Freidberg) Both effects cause pre-heating of the helium and superconductor The normal front advances faster than the helium expulsion velocity v helium v quench v helium v quench x TJTJ T cable T op T x quench T helium The normal zone engulfes an increasing mass and the quench accelerates: a Thermal-Hydraulic Quench-Back !

Luca Bottura ‘Quench and Protection’ slide no 40 MATEFU Summer School on Superconductors for Fusion THQB in Shajii’s universe of quench A. Shajii, J. Freidberg, Int J. Heat Mass Transfer, 39(3), , THQB takes place when the quench has a sufficient intensity q, and length l The quench propagation speed in THQB is:

Luca Bottura ‘Quench and Protection’ slide no 41 MATEFU Summer School on Superconductors for Fusion Helium expulsion The helium in the normal zone is heated: The pressure increaseses: by how much ? (stresses in the conduit/pipe !) Helium is blown out of the normal zone: at which rate ? (venting and sizing of buffers !)

Luca Bottura ‘Quench and Protection’ slide no 42 MATEFU Summer School on Superconductors for Fusion Pressure rise Maximum pressure during quench for: full length normal constant heating rate Conduit thickness and diameter of venting lines must be sized accordingly ! Use codes to get proper estimates J.R. Miller, L. Dresner, J.W. Lue, S.S. Shen, H.T. Yeh, Proc. ICEC-8, 321, 1980.

Luca Bottura ‘Quench and Protection’ slide no 43 MATEFU Summer School on Superconductors for Fusion Part II Resistance and Voltage development Quench detection and protection Detection Safety discharge Quench voltage limits

Luca Bottura ‘Quench and Protection’ slide no 44 MATEFU Summer School on Superconductors for Fusion A propagating quench, what is next ? the quench propagates in the coil at speed v quench longitudinally (v longitudinal ) and transversely (v transverse )… …the total resistance of the normal zone R quench (t) grows in time following the temperature increase, and the normal zone evolution… …a resistive voltage V quench (t) appears along the normal zone… …that dissipates the magnetic energy stored in the field, thus leading to a discharge of the system in a time  discharge. the knowledge of R quench (t) is mandatory to verify the protection of the magnetic system !

Luca Bottura ‘Quench and Protection’ slide no 45 MATEFU Summer School on Superconductors for Fusion Quench resistance: 1-D take: short initial normal zone constant current I = I op so that maximum temperature as given by: 1-D quench propagation with v quench = constant then: x v quench T max T v quench M. Wilson, Superconducting Magnets, Plenum Press, 1983.

Luca Bottura ‘Quench and Protection’ slide no 46 MATEFU Summer School on Superconductors for Fusion Quench resistance: 3-D in reality the quench propagates in 3-D ! the resistance growth is computed solving a volume integral: 3-D vs.1-D v longitudinal v transverse M. Wilson, Superconducting Magnets, Plenum Press, 1983.

Luca Bottura ‘Quench and Protection’ slide no 47 MATEFU Summer School on Superconductors for Fusion Quench propagation in reality matters are (even) more complex: a magnet has boundaries (e.g. the inner outer radius of a solenoid) the quench can byte its tail as it travels along the conductor the real R quench (t) falls then between the 1-D and the 3-D limits, depending on the details of the conductor and winding considered art-work by M. Wilson M. Wilson, Superconducting Magnets, Plenum Press, 1983.

Luca Bottura ‘Quench and Protection’ slide no 48 MATEFU Summer School on Superconductors for Fusion Quench protection What if ½ L I 2 > R I 2 ? Balance the initial magnetic energy vs. dissipated resistive power during the discharge: initial magnetic energy total dissipated resistive power during  decay yesno self-protected: detect, switch-off power and let it go… most likely OK WARNING: the reasoning here is qualitative, conclusions require in any case detailed checking requires protection: detect, switch-off power and do something !

Luca Bottura ‘Quench and Protection’ slide no 49 MATEFU Summer School on Superconductors for Fusion Quench detection: voltage a direct quench voltage measurement is subject to inductive pick-up (ripple, ramps) immunity to inductive voltages (and noise rejection) is achieved by compensation L R quench L1L1 L2L2 R1R1 R2R2

Luca Bottura ‘Quench and Protection’ slide no 50 MATEFU Summer School on Superconductors for Fusion The LCT quench detection scheme A symmetric bridge does not see a symmetric quench ! BEWARE of all possible conditions G. Noether, et al., Cryogenics, 29, ,1989.

Luca Bottura ‘Quench and Protection’ slide no 51 MATEFU Summer School on Superconductors for Fusion Co-wound voltage taps co-wound (non-inductive) voltage taps are an alternative to achieve compensation sometimes the voltage tap can be directly inserted in the conductor, thus providing the best possible voltage compensation and noise rejection L coil R quench L V-tap jacket equipotential with conductor

Luca Bottura ‘Quench and Protection’ slide no 52 MATEFU Summer School on Superconductors for Fusion Quench detection: indirect quench antenna’s: variation of magnetization and current distribution in cables generates a voltage pick-up from a magnetic dipole change localised at the quenching cable optical fibers in cables/coils: variation of fiber refraction index with temperature is detected as a change of the interference pattern of a laser beam traveling along the fiber pressure gauges and flow- meters: heating induced flow in internally cooled cables is detected at the coil inlet/outlet co-wound superconducting wires: variation of resistance with temperature can be measured voltage measurement is still best the QUELL experiment: a quench detection nightmare

Luca Bottura ‘Quench and Protection’ slide no 53 MATEFU Summer School on Superconductors for Fusion Strategy 1: energy dump the magnetic energy is extracted from the magnet and dissipated in an external resistor: the integral of the current: can be made small by: fast detection fast dump (large R dump ) B.J. Maddock, G.B. James, Proc. Inst. Electr. Eng., 115, 543, 1968 L R quench R dump S normal operation quench

Luca Bottura ‘Quench and Protection’ slide no 54 MATEFU Summer School on Superconductors for Fusion Dump time constant magnetic energy: maximum terminal voltage: dump time constant: operating current maximum terminal voltage interesting alternative: non-linear R dump or voltage source increase V max and I op to achieve fast dump time

Luca Bottura ‘Quench and Protection’ slide no 55 MATEFU Summer School on Superconductors for Fusion Switches switching kA’s currents under kV’s of voltage is not easy: mechanical interrupters thyristor’s Gate Turn-Off thyristor’s Insulated Gate Bipolar Transistor’s fuses (explosive, water cooled) superconducting cost and reliability are most important ! By courtesy of J.H. Schlutz, MIT-PSFC, 2002.

Luca Bottura ‘Quench and Protection’ slide no 56 MATEFU Summer School on Superconductors for Fusion Strategy 2: coupled secondary the magnet is coupled inductively to a secondary that absorbs and dissipates a part of the magnetic energy advantages: magnetic energy partially dissipated in R s (lower T max ) lower effective magnet inductance (lower voltage) heating of R s can be used to speed-up quench propagation (quench-back) disadvantages: induced currents (and dissipation) during ramps L R quench R dump S LsLs RsRs normal operation M quench

Luca Bottura ‘Quench and Protection’ slide no 57 MATEFU Summer School on Superconductors for Fusion the magnet is divided in sections, with each section shunted by an alternative path (resistance) for the current in case of quench Strategy 3: subdivision advantages: passive only a fraction of the magnetic energy is dissipated in a module (lower T max ) transient current and dissipation can be used to speed-up quench propagation (quench-back) disadvantages: induced currents (and dissipation) during ramps P.F. Smith, Rev. Sci. Instrum., 34 (4), 368, L1L1 R1R1 L2L2 R2R2 L3L3 R3R3 heater normal operation quench charge

Luca Bottura ‘Quench and Protection’ slide no 58 MATEFU Summer School on Superconductors for Fusion T max in subdivided system in a subdivided system the energy dumped in each section is reduced because of the resistive bypass inductive coupling, reducing the effective inductance of each section : the hot spot temperature scales as: ratio of T max N in a system subdivided in N sections relative to the T max 1 in the same system with no subdivision construction becomes complicated ! P.F. Smith, Rev. Sci. Instrum., 34 (4), 368, 1963.

Luca Bottura ‘Quench and Protection’ slide no 59 MATEFU Summer School on Superconductors for Fusion Magnet strings magnet strings (e.g. accelerator magnets, fusion magnetic systems) have exceedingly large stored energy (10’s of GJ): energy dump takes very long time (10…100 s) the magnet string is subdivided and each magnet is by- passed by a diode (or thyristor) the diode acts as a shunt during the discharge M1M1 M2M2 M3M3 MNMN

Luca Bottura ‘Quench and Protection’ slide no 60 MATEFU Summer School on Superconductors for Fusion Strategy 4: heaters the quench is spread actively by firing heaters embedded in the winding pack, in close vicinity to the conductor heaters are mandatory in: high performance, aggressive, cost-effective and highly optimized magnet designs… …when you are really desperate advantages: homogeneous spread of the magnetic energy within the winding pack disadvantages: active high voltages at the heater winding heater

Luca Bottura ‘Quench and Protection’ slide no 61 MATEFU Summer School on Superconductors for Fusion Quench voltage electrical stress can cause serious damage (arcing) to be avoided by proper design: insulation material insulation thickness electric field concentration REMEMBER: in a quenching coil the maximum voltage is not necessarily at the terminals the situation in subdivided and inductively coupled systems is complex, may require extensive simulation V ext R quench V ext V quench

Luca Bottura ‘Quench and Protection’ slide no 62 MATEFU Summer School on Superconductors for Fusion Helium breakdown during a quench helium undergoes drastic changes in its state (p,T,  ) that affect its dielectric strength:  = helium density (Kg/m 3 ) d = gap (mm) K = 1279  =  = WATCH-OUT for pool boiling magnets and/or helium leaks gap that sustains a voltage of 1 kV liquid vapour leak V breakdown in kV

Luca Bottura ‘Quench and Protection’ slide no 63 MATEFU Summer School on Superconductors for Fusion When everything goes wrong… Normal voltage signals Quench 1 Anomalous signals Extensive ringing Quench 2 Anomalous signals Very high voltages Quench voltage recorded during training of LHC dipoles B=8.33 T E=10 MJ Courtesy of A. Siemko, CERN

Luca Bottura ‘Quench and Protection’ slide no 64 MATEFU Summer School on Superconductors for Fusion …Oooops ! Courtesy of A. Siemko, CERN

Luca Bottura ‘Quench and Protection’ slide no 65 MATEFU Summer School on Superconductors for Fusion Summary… Quenches can and will always happen: protection must be reliable and fail-safe Protection is an integral part of the magnet design, and cannot be (easily) added afterwards : Consider the design criteria for hot-spot, detection, and protection from the outset (in the conductor optimization loop) Balance of cost/complexity (e.g. structure, electrical insulation) vs. design margins (e.g. stabilizer fraction)

Luca Bottura ‘Quench and Protection’ slide no 66 MATEFU Summer School on Superconductors for Fusion …and where to find out more M.N. Wilson, Superconducting Magnets, Plenum Press, P.J. Lee ed., Engineering Superconductivity, J. Wiley & Sons, B. Seeber ed., Handbook of Applied Superconductivity, IoP, Y. Iwasa, Case Studies in Superconducting Magnets, Plenum Press, 1994.