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Unit 11 Protection Ezio Todesco European Organization for Nuclear Research (CERN) Based on the USPAS course of Helene Felice, LNBL, now at CEA, Saclay France E. Todesco, Milano Bicocca January-February 2016 CONTENTS 1. Heat capacity versus Joule heating 2. Energy extraction with dump resistor 3. Quench heaters 4. Scaling laws 5. Quench propagation and detection time E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 2 HEAT CAPACITY VS JOULE HEATING After quench, one has Joule heating power converter is switched off magnet has growing resistance depending on quench propagation dump maybe included in the circuit we have an RL circuit We assume that the heat stays where it is generated (adiabatic) Joule heating gives power heating the coil The resistance depends on the coil temperature, highly nonlinear problem Integrating we have The coil will reach the temperature Tmax But the unknown is j(t) E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 3 HEAT CAPACITY VS JOULE HEATING What is a safe Tmax that can be reached in the coil? Usually one does not want to go much beyond room temperature 30 C, at most 80 C (350 K) Main reasons For Nb-Ti damaging of insulation above 250 C (melts) For all cases this very rapid (in fraction of second) heating induces local thermal stresses that can damage the cable E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 4 HEAT CAPACITY VS JOULE HEATING Let us consider some orders of magnitude Below you see a typical plot of the right hand side integral for a typical Nb-Ti cable with half of copper in the cross-section The integral makes something of the order of 1017 J/W/m4 Let us assume the time decay is very rapid, how much time to react? So we can see that having 500 A/mm2, we can stay a time 0.5×1017/(5×108)2 = 0.2 s at that current I I0 t R = L/R tdet E. Todesco, Milano Bicocca January-February 2016 t Unit 9 - 5 HEAT CAPACITY VS JOULE HEATING The right part of the integral is a intensive property of the cable Let us go to extensive properties I: current in the cable rcu: copper resistivity n: fraction of copper cpave: volumetric specific heat A: cable surface Let us call the right hand side gamma This has a physical dimension of a square of current times time (A2 s) E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 6 HEAT CAPACITY VS JOULE HEATING The left hand term is much more difficult This is a L R circuit whose time constants is L/R One can put in series an external resistor If this resistor is much larger than the resistance of the magnet, the computation is easy We will see it in the next section Otherwise … E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 7 HEAT CAPACITY VS JOULE HEATING Otherwise one has to go for numerical methods Integration by steps in time and space, very careful since fine (adaptive) grid has to be used In the initial part, specific heat very small, time step should be of the order of 0.1 ms Simplified case, assuming that all magnet is resistive at the same temperature, we see explicitly how to solve In this case the coil will go at the same temperature … but only at first order since resistivity depends on magnetic field so parts of the coil at lower field will reach lower temperatures E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 8 HEAT CAPACITY VS JOULE HEATING In the community one usually defines the MIITS of the cable This is the capital we can spend Then we consider the a perfect protection system able to quench all magnet instantaneously at time 0 The current will decay, circuit L R where the resistance varies since the current is heating with the Joule effect Gq are the MIITS of such an hypotetical quench Gq I q (t ) dt 2 0 E. Todesco, Milano Bicocca January-February 2016 Protection in magnet design - 9 CONTENTS 1. Heat capacity versus Joule heating 2. Energy extraction with dump resistor 3. Quench heaters 4. Scaling laws 5. Quench propagation and detection time E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 10 ENERGY EXTRACTION To decrease the current as soon as possible, one can Switch off power converter Insert a resistor Re on the circuit One has a LR circuit with time constant L/R Neglecting the magnet resistance, the time constant is t=L/Re Integration gives E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 11 ENERGY EXTRACTION So increasing the dump resistor one can reduce the quench integral There is a severe limit is this strategy: the voltage induced on the magnet at the beginning of the discharge This voltage is usually limited to about 1 kV – due to the maximum voltage that can be withstand by insulation Since the inductance is proportional to the magnet length, for long magnets the inductance becomes too large and one cannot satisfy the above equation One has to go for another strategy, independent of the magnet length E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 12 CONTENTS 1. Heat capacity versus Joule heating 2. Energy extraction with dump resistor 3. Quench heaters 4. Scaling laws 4. Quench propagation and detection time E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 13 QUENCH HEATERS The idea of quench heaters is to quench rapidly all the magnet so that the resistance is growing rapidly The energy of the magnet is dumped on the coil itself, but not only on the small portion that is quenching Quench heaters are strips of stainless steel where an impulse of current is put as soon as the quench is detected Strips heat thanks to Joule heating, and since they are glused on the coil they turns all the coil resistive The reaction time that can be obtained is of the order of 10-50 ms E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 14 QUENCH HEATERS How much time needed to quench a magnet? Obviously, the larger the margin the longer the time So at lower current one needs more time to quench But at lower current the current density is lower … Limit to the heater delay is the thin strip of insulation that avoids electrical contact between the coil and the heaters Usually a good insulator is also a bad thermal bridge 70 Cover 3 cm 3rd turn l fie d PH delay (ms) 60 50 40 Cover 6 cm 7th turn l fie d 30 20 10 HQ01e - CERN 4.4 K 0 0 E. Todesco, Milano Bicocca January-February 2016 20 40 60 I/Iss (%) 80 100 Heaters delay vs model [T. Salmi, H. Felice] Unit 9 - 15 TIME MARGIN Let us assume that after a time Tq, all the magnet is quenched, at the critical temperature And let us assume that Iq(t) is the current decay in a magnet quenching « on itself » This can be estimated through numerical codes, and the quench integral can be computed It is a property of the magnet design How long we can survive at maximal current ? E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 16 TIME MARGIN Tq is the time margin for protection This gives the time required to react to the quench and to spread all the quench through the quench heaters before the magnet reaches Tmax Order of magnitude: For Nb-Ti high field magnets the magnet design aims at having around 100 ms For Nb3Sn high field magnets we try to go towards 50 ms Less becomes impossible .. I will show why E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 17 CONTENTS 1. Heat capacity versus Joule heating 2. Energy extraction with dump resistor 3. Quench heaters 4. Scaling laws 4. Quench propagation and detection time E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 18 SCALING LAWS 1. A very old discussion between magnet designers: Large cable and large current but small inductance or viceversa ? The same magnet, with same field and same energy, can be built with a large or a small cable w w’=2w A A’=2A Io Io’=2Io L L’=L/4 U U’=U Re Re’=Re/2 G G’= 4G LI2o/2Re 2 L’I’2o/2R’e So if we extract on a dump resistor, increasing the current and the cable size we manage to protect better E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 19 SCALING LAWS 2. The energy extraction on a dump does not work for long magnets: A longer and longer magnet will not be protected by a dump resistor Consider a magnet with the same cable but with double length w w’=w A A’=A Io Io’=Io L L’=2L U U’=2U Re Re’=Re G G’= G LI2o/2Re 2 L’I’2o/2R’e So at a certain length the energy extraction becomes not effective E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 20 SCALING LAWS 3. The quench heater strategy works for any length Consider a magnet with the same cable but with double length w w’=w A A’=A Io Io’=Io L L’=2L U U’=2U Rm Rm’=2Rm G G’= G LI2o/2Rm L’I’2o/2R’m This happens because we now dump on the magnet, and a longer magnet has also a larger resistance E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 21 SCALING LAWS 4. The quench heater strategy does not depend on small or large inductance Consider a magnet with the double cable width w w’=2w A A’=2A Io Io’=2Io L L’=L/4 U U’=U Rm Rm’=4Rm G G’= 4G LI2o/2Re 4 L’I’2o/2R’e The small or large inductance becomes important for other aspects (inductive voltages) not treated here E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 22 SCALING LAWS Consider a magnet with the double cable width w w’=2w A A’=2A Io Io’=2Io L L’=L/4 U U’=U Rm Rm’=4Rm G G’= 4G LI2o/2Re 4 L’I’2o/2R’e The small or large inductance becomes important for other aspects (inductive voltages) not treated here E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 23 ANALYTICAL ESTIMATE OF TIME MARGIN One can work out an analytical estimate of the time margin Copper fraction strand current density strand enthalpy stored energy/strand volume Main message is Since the coil takes the heat, the energy density on the coil should not be larger than the enthalpy from operational temperature to Tmax (300 K), that is about 0.5 J/mm3 As usual, there is a dependence on j 2: larger current densities reduce the margin with a square Once more we see a barrier for high current densities E. Todesco, Milano Bicocca January-February 2016 Protection in magnet design - 24 ANALYTICAL ESTIMATE OF TIME MARGIN Strand energy density (J/mm3) Ud Case of some magnets 0.20 FrescaII MQXF (200 ms) 0.15 (33 ms) HD2 (80 ms) HQ (23 ms) 11 T (33 ms) LHC MB (220/110 ms) 0.10 0.05 TQ (17 ms) MQXC (160/60 ms) 0.00 0 400 800 Strand current density (A/mm2) jo 1200 Energy density Nb-Ti 0.07 J/mm3 (1/10 of Cpave) Energy density Nb3Sn 0.10-0.15 J/mm3 (up to 1/4 of Cpave) E. Todesco, Milano Bicocca January-February 2016 Protection in magnet design - 25 CONTENTS 1. Heat capacity versus Joule heating 2. Energy extraction with dump resistor 3. Quench heaters 4. Scaling laws 5. Quench propagation and detection time E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 26 QUENCH PROPAGATION AND TIME MARGIN Why do we need a time margin of at least 50 ms ? 10-20 ms to quench the coil through heaters But there are other contributions To detect a quench one measures the voltage generated by the resistance Voltage threshold are typically 100 mV, and it takes about 5-10 ms for the quench propagation to generate this voltage There is also the time necessary to open the switch, that can be of the order of a few ms Studies are ongoing to reduce this limit towards 25 ms Innovative method: CLIQ, patent at CERN (G. Kirby, E. Ravaioli) One discharges a capacitor in the coil, the dB/dt induces heating tha quenches the coil E. Todesco, Milano Bicocca January-February 2016 Protection in magnet design - 27 SUMMARY Quench protection consisits in getting rid of the current as soon as the quench is detected This should be done within 0.3 – 0.5 ms for typicl accelerator magnets Since the inductance is given one has to work on the increase resistance External dump resistor is valid only for small magnets Dumping the energy on the coil itself is limited by the coil enthalpy The quench velocity is small, and to the quench propagation has to be helped by heaters to quench all the coil as soon as possible to increase the resistance This can be done in 10-20 ms Protection sets phyisical limits on current density That is the coil enthaply must be much larger than the energ density on the coil If the coil is too compact, it cannot take the energy of the magnet E. Todesco, Milano Bicocca January-February 2016 Unit 9 - 28