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Current decay and temperatures during superconducting magnet coil quench
Current decay and temperatures during superconducting magnet coil quench V. Kadambi and B. Dorri Thermal Processes Program, Corporate Research and Development, General Electric Company, PO Box 8, Schenectady, NY 12301, USA
Received2 May 1985; revised 13 October 1985 A small superconducting magnet coil, 16.39 cm outer diameter and 7.62 cm inner diameter, has been quenched to determine the rate of decayof current in the coil and to measure the temperatures in the coil induced by the quench. The measured current decay and the temperatures have been compared with the theoretical predictions obtained by using a control volume-finite difference numerical scheme developed by us. Two sets of experiments have been performed: the first set results in a two-dimensional quench proPagation, while the second one results in three-dimensional quench propagation through the coil. The results of the experiment agree closely with those of the predictions indicating that the techniques used for the experimental observations and numerical modelling are sound and are applicable to the study of large magnet coils as well.
Keywords: superconducting magnets; current decay;, superconductivity
Superconducting magnet coils are used in medical diagnostics (n.m.r. imaging of body parts), superconducting coil a.c. generators, proton accelerator superconducting magnets and other similar applications. They operate at extremely high current densities (of the order of 30000 A cm -2) to achieve the high magnetic fields necessary in the above applications The coils consist of a large number of turns of superconducting wire maintained at liquid helium temperature, so that the electrical resistance of the wire is zero. In principle, a current established in the coil can last indefinitely, without the application of any voltage to sustain it There is no electrical energy dissipation in this condition. In practice, however, during continuous operation, it is found that at some point in the coil (usually where the magnetic field is very large), the material reverts from the superconducting state to the 'normal' state (i.e. it becomes an electrical resistor). Local electrical energy dissipation occurs and the coil temperature starts to rise around that point Thermal conduction occurs from the hot point resulting in a rise in temperature all around it The electrical resistivity at the neighbouring points now starts to rise so that the local resistance rises further, causing a larger dissipation and a further increase in temperature. An uncontrolled temperature rise is thus initiated increasing the electrical resistance and the temperature continuously and a very high speed normal front separating the superconducting zone from the resistive zone travels through the coil The current drops extremely rapidly until all the electrical energy is dissipated. The process in which a superconducting magnet reverts to the normal resistive state from an original superconducting state, resulting in a decay of current and a rapid rise in temperature, is referred to as 'quench '1. The local temperature at the point where the quench was originally
0011-2275/86/030157-08 $03.00 © ButterworthEt Co (Publishers) Ltd
initiated can become very high because of the large amounts of energy dissipation which may range up to several megajoules in very large magnets Because of the non-uniform and sudden rise in temperature, the coils are likely to be subjected to extreme thermal stresses and may even be damaged due to quench. The following experimental study was undertaken to determine the rate of current decay and the m a x i m u m temperatures during quench in a small superconducting magnet for comparison with the results of a numerical prediction. In addition, the experiment tested the feasibility of using ordinary thermocouples and resistance thermometers to measure cryogenic temperatures during fast transients, with the intention of using the same techniques for the measurement of quench temperatures in large superconducting magnets.
Experiment
Apparatus The magnet coil used in the experiment is of a hollow cylindrical form as shown in Figure 1, with a conductor which is a copper and niobium-titanium matrix. The inner and outer radii of the coil are 7.62 cm and 16.39 cm, respectively. The conductor is of external dimensions 0.254 cm × 0.127 cm, and contains 1531 filaments of the niobium-titanium superconductor, each 0.00321 cm average diameter, embedded in copper. The coil has 30 layers of conductor in the radial direction, with 24 turns in each layer. The turns and the layer are separated by epoxy resin (polyvinyl formal) impregnated cloth, 0.1-0.3 mm thick. The details of coil construction are also shown in Figure 1. The characteristics of the superconducting material are exhibited in Tablel and are the same as those given by Laskaris z.
Cryogenics 1986 Vol 26 March
157
Superconducting magnet coil quench: V. Kadambi and B. Dorri
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Details of test coil construction
Test coil with aluminium plates and suspending bolts
To maintain the coil in a superconducting state, it was necessary to place it in an environment at the temperature of boiling helium. For this purpose, the coil was held between two heavy aluminium plates each 17.5 mm thick and suspended in liquid helium by using six Table 1
Volt~le
locations
Characteristics of superconducting material Specification
Stabilizer matrix to superconductor ratio
1.6/1
Filament 360 ° twist pitch (cm)
1.5
Number of filaments
1531
Cross-section Material Resistivity ratio at zero field Resistivity v e r s u s flux density at 4.22 K
Copper 160
p = ( 0 . 9 +0.421 B) 10 ~e :(1 ~< a ~ < 7 )
Superconductor filament average diameter (cm)
0.0034
Wire insulation Material Thickness (cm)
Polyvinyl formal 0.00508
Critical current at 4.22 K v e r s u s flux density (T)
/o = 1.30952 B 2 - 3 0 2 . 2 6 2 B + 2 9 8 3 . 5 7
:(4 ~ B ~ 7) Critical flux density, B o (T) at zero current
versus
Cryogenics 1986 Vol 26 March
TC,
threaded brass screws, connected to the aluminium plates as shown in Figure 2. Heavy braided copper cables, 19.7 × 6.25 cm 2 each rated at 300 A at room temperature, were used to pass current into the superconducting coiL The cables were sufficiently long and passed through a dewar ~ 2 m in height The coil was so positioned that the leads were always surrounded by helium vapour nearly at the boiling temperature, so that the resistance of the cables was very low compared to that at room temperature and hence very little electrical power was dissipated in them. Efforts were also made to maintain the liquid helium level high enough so that part of the cables was dipped in the liquid during the operation of the coil. Temperature measurements were made at four locations on the inner perimeter of the coil indicated in Figure 3. Thirty six gauge copper-constantan thermocouples were bonded at two of these locations, while at the other two, platinum resistance thermometers (each with a nominal resistance of 50 ~ at room temperature) were bonded. To ensure good thermal contact between the temperature sensors and the copper surface, the epoxy impregnated cloth was scraped with a sharp pointed tool until the copper surface was exposed and then, the foilshaped sensing surfaces were bonded to the copper with an appropriate epoxy at each location. Care was taken to
Characteristic
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Dimensionsin cm
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temperature, T(K)
Bo= -0.103715 T2 -0.740336 T+ 15.3147 :(4.22 ~ T ~8)
Superconducting magnet coil quench: V. Kadambi and B. Dorri ensure that the copper surface was not damaged in any way during the scraping process and that the minimum of epoxy was used so that there was negligible thermal resistance between the copper and the sensors. The resistance thermometer elements were of the two-lead type and needed the connection of two extra leads to permit accurate temperature measurement. Thin copper wires (0.125 mm) were soldered to each of the two leads and the fine wires were held in place by embedding them in more epoxy, so that thermal losses through the wires were minimized(calculations showed that the maximum error in the measured temperature due to the leads was limited to ~ 0.5 K). These permitted the fourwire method of resistance measurement even though only two leads were available from the manufacturer. The resistance thermometers were powered using a small power supply which maintained a constant current of 10 p,A. To calibrate the sensors between liquid helium and liquid nitrogen temperatures, the whole coil was dipped first into liquid nitrogen along with the sensors and the readings of the sensors were noted in steady state. Thereafter, the whole coil was dipped in liquid helium and the readings were noted after steady state was obtained. In addition` the temperature of the liquid nitrogen as well as that of the liquid helium was measured with a pre-calibrated thermistor, whose characteristics at cryogenic temperatures were known. Thereafter, a double-walled vessel containing liquid nitrogen in the centre (with the coil immersed in it) and an outer chamber containing liquid helium, was constructed. Because of heat transfer, the nitrogen was solidified in a short while, after which the helium was removed and the nitrogen allowed to warm up to its boiling point As the solid nitrogen melted and rose in temperature, readings of its temperatures were obtained at various times both with the sensors (embedded in the magnet coil) and with the thermistor probe which had been placed in the nitrogen close to the coil. These readings permitted the calibration of all the sensors (the resistance thermometers and the thermocouples) at several temperatures between helium and nitrogen boiling points (4.2 - 76 K). Since the coil would have to be maintained in a bath of liquid helium during the experiment, it was felt that heat transfer between the helium and the sensors would lead to erroneous temperature readings after quench. To prevent liquid helium from coming in contact with the sensors, the central cylindrical opening in the coil was covered at the bottom with a circular piece of fiberglassimpregnated plastic which was glued to the surface using a bonding cement At the top, a shell-shaped piece of the same internal diameter as the central opening in the coil was glued with epoxy. This prevented the liquid helium from spilling into the central opening as long as the level of the liquid was below the top of the shell-shaped piece, as may be seen from Figure 5. Power was supplied to the magnet coil by operating two stabilized d.c. power supplies connected in parallel Each of the power supplies was capable of supplying a maximum electrical current of 500 A at any voltage up to 10 V. The current flowing through the coil was measured using a d.c. shunt of 100 /tl~, calibrated to provide an output of 100 mV at a rated current of 1000 A, Three dual-channel Nicolet storage type oscilloscopes were used to monitor the outputs of the thermocouples and the resistance thermometers, as well as to determine the current flowing through the circuit. Two voltage taps, which were located at the middle of the coil
(in contact with the copper conductor 360° apart from each other), were used to monitor the voltage across the middle turn and served to specifythe moment of initiation of quench in the coil. The voltage taps were also connected to one of the channels of a Nicolet so that a record was obtained during quench. A schematic diagram of the connections is indicated in Figure 4. The instrumented coil was suspended in the middle of a double-walled dewar vessel with appropriate seals at the top. Provision existed to measure the level of liquid helium in the inner vessel where the coil was suspended. to ensure that during the experiment, the coil was always immersed in the liquid. The outer jacket of the dewar contained liquid nitrogen to minimize heat transfer between the helium and the surroundings. Figure5 shows the details of the dewar and the coil with its suspension` immersed in liquid helium. To initiate the quench at a known poinL a small nichrome heater wire was wound around the current lead near the first turn (at the inner radius) within 0.25 cm of the coil. Whenever required, a current could be passed through the nichrome wire using a small 9 V battery which included a switch in its circuit It usually needed about I or 2 s after the switch was closed to initiate the quench by this heating process. A simple calculation showed that the total energy input to the system through this heating process was negligible in comparison with the stored electrical energy in the coil which amounted to ~16000 J at the rated current of 860 A (coil inductance = 0.043 H).
Experimental procedure The dewar in which the coil was to be tested was first cooled with liquid nitrogen in the outer chamber for about two days Then, the coil assembly was inserted along with the top cover plate, sealed appropriately and evacuated, after which liquid helium was gradually introduced into the central chamber containing the coil The level of liquid helium was always maintained such that it did not spill into the middle of the coil where the temperature sensing elements were located. Temperatures were monitored at reasonable intervals of time until the whole coil assembly reached 4.2 K. After ensuring that steady state temperature was obtained, as determined by the readings of the thermocouples and the resistance thermometers, the coil was energized using one d.c. power supply and raising the current slowly until it was close to 500 A. The second power supply was then turned on and the current raised further as desired. Quench could be initiated either by raising the current until it exceeded the critical value (nominally 860 A at4.2 K), or by maintaining the current at a set value below critical and heating the input lead with the nichrome wire until the critical temperature was locally exceeded. If the current is just raised above critical (without heating the wire), quench initiates itself at the coil inner radius all along the centre-line, since the magnetic field is a maximum here. Moreover, because of the two-dimensional nature of the field, the normal front propagation through the coil is likely to be very nearly two-dimensional as well. However, if the quench is initiated near the first turn of the coil by heating. (with the current below critical) the propagation will be completely three-dimensional in nature. For each type of quench initiation, data were obtained at different coil currents ranging from 500 to 900 A. No matter how the quench is initiated, the current through the coil decays rapidly in a few seconds. The sudden drop in current induces a large back-electromo-
Cryogenics 1986 Vo126 March
159
Superconducting magnet coil quench: V. Kadambi and B. Dorri
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160 Cryogenics1986 Vol 26 March
tive force due to the inductance of the coil. In our experiments, the back e.m.f, was used to trigger the Nicolets to start recording all the required data (current, voltage, thermocouple and resistance thermometer readings). However, this procedure could not be utilized when quench was initiated by heating since it would take a relatively long time for the normal front to propagate to the middle of the coil where the voltage taps were located. Hence, the Nicolets wre triggered by the closure of the switch required to pass the current through the nichrome heating wire. After the quench was initiated, tracings of the current decay, the voltage at the taps and of the temperature sensors (thermocouples at two locations and the resistance thermometers) were obtained by using the Nicolet oscilloscopes. Figure6 shows Nicolet tracings of resistance thermometer output (top curve, above the horizontal axis) and current decay (bottom curve, below the horizontal axis). Figure 7 shows the thermocouple output (top line) and the back e.m.f, measured at the voltage tap (bottom curve). (Each Figure caption gives the elapsed time from the start of the tracing to the location of the vertical axis. The magnitude of the quantity represented by the lower curve at the same instant is also indicated.) The digitial read-outs from the Nicolet were used later for comparison with the predictions of a numerical analysis program developed to analyse the quench problem.
Superconducting magnet coil quench: V. Kadambi and B. Dorri 2
the thermal resistance o f the glass-epoxy layers in the 0 direction (i.e. in the t~z plane) is very large c o m p a r e d with that o f the copper. Therefore, all the c o n d u c t i o n in that direction may be expected to occur only through the c o p p e r s u p e r c o n d u c t o r matrix, In the cross-sectional (r-0) plane, however, the thermal resistance of the c o n d u c t i n g wire is neglected c o m p a r e d with that o f the epoxy.
The m a t h e m a t i c a l e q u a t i o n s governing heat transfer and current flow through the coil are as follows.
Energy balance
Figure 6 Nicolet traces of the resistance thermometer (top curve) and current decay (lower curve) at 8 6 0 A. Elapsed time from start of tracing to location of vertical axis, 17.990s; magnitude of the quantity represented by the lower curve at the same instant, - 8.5 mV
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Circuit equations for current and voltage •
~,~
. ~ ,
Figure 7
Nicolet traces of thermocouple (top curve) and voltage (lower curve) at 8 6 0 A: Elapsed time from start of tracing to location of vertical axis, 18.260s; magnitude of the quantity represented by the lower curve at the same instant, 18.3 mV
Numerical analysis The following is a brief account o f the n u m e r i c a l model used in the calculations, the results of which were c o m p a r e d with those of the experiment. F o r a more detailed account of the n u m e r i c a l procedure, see Dorri and K a d a m b i 3. Because o f the c o m p l i c a t e d coil geometry, the density changes, orthotropic t h e r m a l conductivities as well as the extreme degree o f non-linearities involved in all the properties, it was found that the use o f spatially averaged properties and s i m p l e t w o - d i m e n s i o n a l calculations were not sufficiently accurate to predict quench propagation. Further, c o m m e r c i a l l y available codes could not be utilized because o f the large n u m b e r o f nodes a n d the i n o r d i n a t e l y long processing times that would be needed to execute such codes. Therefore, a simplified model and a n u m e r i c a l code were developed based on the following observations 1
the t h e r m a l resistance o f each c o n d u c t o r at any crosssection, (i.e. in the r-z plane), can be neglected in c o m p a r i s o n with its resistance in the 0 direction (i.e. a l o n g the coil circumference). Therefore, it is a s s u m e d that at any instant in time, each c o p p e r wire has a uniform t e m p e r a t u r e at a given cross-section:
-L
d/L art
- (R1 + R 2 ) I L
(2)
where: L = i n d u c t a n c e o f the coil: R~ = coil resistance which varies with time during quench: R 2= external resistance in the coil circuit due to contacts, leads, etc. = 0.0033 fI: I i . = current in the coil.
Critical current density in superconductor filaments (Laskaris 2) .I e (B,T) = Io [B + Bo (4.2) - Bo (T)]/,4 se
(3)
where: I o = 1.30952 B = - 302.262 B + 2983.57: B o = --0.103715 T 2 - 0.740336 T + 15.3147: B = magnetic field density: A s~-= cross-sectional area of superconductor. In E q u a t i o n (3) the flux density, B o, is c a l c u l a t e d at the t e m p e r a t u r e s i n d i c a t e d in parentheses. T h e i n d u c t a n c e s a n d the fields have been c o m p u t e d using the method described by Garrett 4. T h e thermal conductivities a n d electrical properties have been found using the data a n d p r o c e d u r e s in References 5-7. Figures8 and 9 are representative g r a p h s showing the variations of thermal conductivities o f c o p p e r and epoxy, respectively.
Cryogenics 1986 Vo126 March
161
Superconducting magnet coil quench: V. Kadambi and B. Dorri THERNALCONOUCTIVIWOF EPOXY
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Cryogenics 1 9 8 6 Vol 26 March
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For programming purposes, these property variations were used as input data using rational function curve- fits. The numerical model is based on a control volume finite-difference discretization of the energy balance equation. Each node represents an element with the cross-section of a copper wire, including half the thickness of the insulation surrounding it. Since the temperature of the copper at any section (i.e. at a given 0) is assumed to be uniform within the wire, the concept of a floating node has been used to write the energy balance equation at each control volume. The node floats freely over the wire crosssection, but the intermediate epoxy layer temperatures are computed assuming linear basis functions in the formulation. The Crank-Nicolson scheme has been implemented to ensure reasonable stability without sacrificing accuracy. Reduced computer storage requirements have been achieved using the Alternate Direction Implicit scheme (ADI), where the equations for all the radial twodimensional planes across the coil are solved first, followed by one-dimensional solutions for distributions along the tangential direction of the coiL By alternatively carrying out these two operations and using the Jacobi iterative scheme which can be vectorized for use on the CRAY computer, an efficient program which solves the problem in ,~ 10 min o f c p u time has been developed. The program varies both the number of nodes over which computation is carried out during a time step and the time
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step as required, to achieve the minimum processor time for the computation. Iteration for non-linearities is carried out along with that needed for ADI in the program. A surface heat transfer coefficient of 0.05 W m-2 °C-I has been used to account for heat transfer between the coil and the helium.
R e s u l t s and d i s c u s s i o n During the experiments for which the current was raised until quench initiated without heating, it was observed that the current and the voltage at quench initiation differed from test-to-test It was not clear what caused these variations in critical current. Among the possible reasons are the following: 1 the coil was initially stressed due to the fixtures and measuring instruments bonded to its surface and these stresses initiated the quench in an unpredictable way; 2
the current was raised too rapidly during the test, resulting in eddy current losses which could have initiated the quench at different levels;
3
the leads conducting current into the coil could have dissipated electrical energy due to the large currents flowing through them, especially if they were not dipped in liquid helium at the locations where they were connected to the coil. Even though the liquid
Superconducting magnet coil quench: V. Kadambi and B. Dorri level was sufficient to cover the coil in all the tests, it is quite likely that the leads were not cold enough near the coil In that case, the energy conducted along the leads could have initiated the quench even before the current reached the critical value for adiabatic normal front propagation.
Figure 6 shows a typical temperature rise curve obtained from the resistance thermometer located at the centre of the coil along with the current decay after quench. These curves were obtained when the current reached the critical value of 860 A and the quench initiated itself without heating. The corresponding voltage tap reading is seen in the bottom curve of Figure 7. The onset of quench is clearly indicated by the sudden rise in voltage at the tap and marks the start of current decay. As expected, the current decays exponentially while the temperature rises rapidly and reaches a nearly constant value. The temperatures indicated by the resistance thermometers at the start of the quench are likely to be inaccurate, since they are influenced by the changing magnetic field in the coil. However, after the current decays to low levels, the changes in magnetic fields are small and the errors in the resistance thermometer readings will be negligible. Hence, only the part of the resistance thermometer readings corresponding to the maximum observed temperature should be considered as sufficiently accurate and the earlier part used only for qualitative indications of the temperature rise rather than for comparison with the theory. Unfortunately, the Nicolet could not amplify the thermocouple outputs sufficiently to provide meaningful data, since the sensitivity of the thermocouple was small at cryogenic temperatures. The difficulty was compounded by the fact that the ice point was used as the reference junction for the thermocouple, so that the change in temperature due to quench was relatively small (< 50 K) as compared with the full-scale value of 268.8 K, (A more appropriate way would be to use liquid helium temperature as the reference for the thermocouple, with a full-scale reading of ~55 K, so that the rise in temperature during quench would be readily noticed.) The trace of the thermocouple response exhibited at the top in Figure 7, therefore, is not very useful for determining either the temperature rise during quench or the m a x i m u m temperature. All the comparisons with the theoretical predictions are therefore based on resistance thermometer outputs. OUENCH OF TEST COXL
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Plots of current decay obtained experimentally and by numerical calculation are exhibited in Figures 10. 12 andl4, for three quench tests. FigurelO is plotted from the data shown in Figure 6, when the critical current limit of 860 A was reached and resulted in quench. Figures 12 and 14 were obtained from data at currents of 800 and 600 A, respectively, when quench was induced using the nichrome heater wound around one input lead of the coil. Clearly, agreement for current decay provided by the theory and by the experiment is excellent in all cases. There seems to be very little difference in the predicted rate of current decay whether or not the effect of convection at the surface of the coil is taken into account. Figures 11, 13 and 15 show the measured and calculated temperature rise curves due to quench corresponding respectively, to the two current decay curves in FigureslO, 12 andl4. Here, too, the agreement between the measured and theoretical values is reasonably good when the effect of surface convection is taken into account. The lack of agreement at the start of quench is not of much consequence, since reliable information cannot be obtained from resistance thermometers at high magnetic fields. After the current and hence the magnetic field decay to low values, the measured temperatures may be considered as reliable and do show reasonably good agreement with the predictions.
Cryogenics
1986
Vol 26
March
163
Superconducting magnet coil quench: V. Kadambiand B. Dorri QUENCH OF TEST COIL
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In general, the good agreements between the measurements and the predictions indicate that the model and the code are sound and take account of all the variables reasonably well. We conclude that: 1
the method of temperature measurement was satisfactory. Platinum resistance thermometers can be used to obtain temperature data at cryogenic lemperatures during quench if only steady state lemperature data are to be obtained. If transient temperatures are to be measured with accuracy, the resistance thermometer readings have to be corrected for the effect of the magnetic field. Thermocouple readings (thot, gh not affected by the magnetic field) are small and have to be amplified by large factors to obtain satisfactory accuracy. The reference junction for the thermocouples should be the boiling point of liquid helium rather than the ice point:
164
,.s
Maximum temperature rise, I o = 6 0 0 A. Key as in
the best measurements are obtained if the measuring instruments are embedded in the test coil during
Cryogenics 1986 Vol 26 March
a superconducting switch must be included in the set-up to put the coil in a persistent current mode at any desired current below critical. Part of the difficulty in our experiment was that the lead resistance remained in the circuit even during quench. Hence, there was a voltage impressed across the coil at all times( by the power supply), even though it was quite small in comparison with the electromotive forces induced during quench. The effects of varying external load resistance and impressed voltage have not been modelled numerically due to the complexities involved.
In spite of the shortcomings listed above, the good agreement between the theory and the data indicates that the effects of quench are well modelled by the theory and that the procedures employed here can be used to obtain data on large superconducting magnets as welL with minor modifications.
References I 2 3
Wilson, M.N. Super,'onducting Magnets Monographs on Cryogenics. Clarendon Press. Oxlbrd. UK (1983) 68-69 Laskaris, T. Transient thermal analysis of epoxy-impregnated superconducting windings in linearly ramped fields J Heat Trans (1978) 100 (4) 702-707 Dorri, B. and Kadambi, V. Thermal analysis of quench propagation in superconducting coils submitted to Numerical
Heat Tran~fi'r 4
Garrett, M.W. Calculation of fields, lorces and mutual inductances of current systems by elliptic integralsJAppl Phys (1963) 34 2567-2573
5
Handbook o["Material Propertie.~.[or Superconducting Machineo'
6 7
2
Ls
SEC
epoxy impregnation. Since we had to scrape the coil and then bond the thermal sensors with epoxy cement, the bonding process could have induced local stresses and thus, premature coil quench:
OUENCH OF TEST COIL
A N P
I
Figure 12
800
C U R R E N T
1.s' 1.7,' TIRE
SEC
temperature
I
,
Battelle Columbus Laboratory and NBS, USA (1974) Harlwig, G. Low-temperature properties of resins and composites Adv Co,og Eng (1978) 24 17-36 Ho, J.C. Measurements of heat capacity lot epoxy and epoxyglass samples, personal communication. Physics Department, Wichita State University. Wichita. Kansas, USA (1983)
Received2 May 1985; revised 13 October 1985 A small superconducting magnet coil, 16.39 cm outer diameter and 7.62 cm inner diameter, has been quenched to determine the rate of decayof current in the coil and to measure the temperatures in the coil induced by the quench. The measured current decay and the temperatures have been compared with the theoretical predictions obtained by using a control volume-finite difference numerical scheme developed by us. Two sets of experiments have been performed: the first set results in a two-dimensional quench proPagation, while the second one results in three-dimensional quench propagation through the coil. The results of the experiment agree closely with those of the predictions indicating that the techniques used for the experimental observations and numerical modelling are sound and are applicable to the study of large magnet coils as well.
Keywords: superconducting magnets; current decay;, superconductivity
Superconducting magnet coils are used in medical diagnostics (n.m.r. imaging of body parts), superconducting coil a.c. generators, proton accelerator superconducting magnets and other similar applications. They operate at extremely high current densities (of the order of 30000 A cm -2) to achieve the high magnetic fields necessary in the above applications The coils consist of a large number of turns of superconducting wire maintained at liquid helium temperature, so that the electrical resistance of the wire is zero. In principle, a current established in the coil can last indefinitely, without the application of any voltage to sustain it There is no electrical energy dissipation in this condition. In practice, however, during continuous operation, it is found that at some point in the coil (usually where the magnetic field is very large), the material reverts from the superconducting state to the 'normal' state (i.e. it becomes an electrical resistor). Local electrical energy dissipation occurs and the coil temperature starts to rise around that point Thermal conduction occurs from the hot point resulting in a rise in temperature all around it The electrical resistivity at the neighbouring points now starts to rise so that the local resistance rises further, causing a larger dissipation and a further increase in temperature. An uncontrolled temperature rise is thus initiated increasing the electrical resistance and the temperature continuously and a very high speed normal front separating the superconducting zone from the resistive zone travels through the coil The current drops extremely rapidly until all the electrical energy is dissipated. The process in which a superconducting magnet reverts to the normal resistive state from an original superconducting state, resulting in a decay of current and a rapid rise in temperature, is referred to as 'quench '1. The local temperature at the point where the quench was originally
0011-2275/86/030157-08 $03.00 © ButterworthEt Co (Publishers) Ltd
initiated can become very high because of the large amounts of energy dissipation which may range up to several megajoules in very large magnets Because of the non-uniform and sudden rise in temperature, the coils are likely to be subjected to extreme thermal stresses and may even be damaged due to quench. The following experimental study was undertaken to determine the rate of current decay and the m a x i m u m temperatures during quench in a small superconducting magnet for comparison with the results of a numerical prediction. In addition, the experiment tested the feasibility of using ordinary thermocouples and resistance thermometers to measure cryogenic temperatures during fast transients, with the intention of using the same techniques for the measurement of quench temperatures in large superconducting magnets.
Experiment
Apparatus The magnet coil used in the experiment is of a hollow cylindrical form as shown in Figure 1, with a conductor which is a copper and niobium-titanium matrix. The inner and outer radii of the coil are 7.62 cm and 16.39 cm, respectively. The conductor is of external dimensions 0.254 cm × 0.127 cm, and contains 1531 filaments of the niobium-titanium superconductor, each 0.00321 cm average diameter, embedded in copper. The coil has 30 layers of conductor in the radial direction, with 24 turns in each layer. The turns and the layer are separated by epoxy resin (polyvinyl formal) impregnated cloth, 0.1-0.3 mm thick. The details of coil construction are also shown in Figure 1. The characteristics of the superconducting material are exhibited in Tablel and are the same as those given by Laskaris z.
Cryogenics 1986 Vol 26 March
157
Superconducting magnet coil quench: V. Kadambi and B. Dorri
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Test coil with aluminium plates and suspending bolts
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Volt~le
locations
Characteristics of superconducting material Specification
Stabilizer matrix to superconductor ratio
1.6/1
Filament 360 ° twist pitch (cm)
1.5
Number of filaments
1531
Cross-section Material Resistivity ratio at zero field Resistivity v e r s u s flux density at 4.22 K
Copper 160
p = ( 0 . 9 +0.421 B) 10 ~e :(1 ~< a ~ < 7 )
Superconductor filament average diameter (cm)
0.0034
Wire insulation Material Thickness (cm)
Polyvinyl formal 0.00508
Critical current at 4.22 K v e r s u s flux density (T)
/o = 1.30952 B 2 - 3 0 2 . 2 6 2 B + 2 9 8 3 . 5 7
:(4 ~ B ~ 7) Critical flux density, B o (T) at zero current
versus
Cryogenics 1986 Vol 26 March
TC,
threaded brass screws, connected to the aluminium plates as shown in Figure 2. Heavy braided copper cables, 19.7 × 6.25 cm 2 each rated at 300 A at room temperature, were used to pass current into the superconducting coiL The cables were sufficiently long and passed through a dewar ~ 2 m in height The coil was so positioned that the leads were always surrounded by helium vapour nearly at the boiling temperature, so that the resistance of the cables was very low compared to that at room temperature and hence very little electrical power was dissipated in them. Efforts were also made to maintain the liquid helium level high enough so that part of the cables was dipped in the liquid during the operation of the coil. Temperature measurements were made at four locations on the inner perimeter of the coil indicated in Figure 3. Thirty six gauge copper-constantan thermocouples were bonded at two of these locations, while at the other two, platinum resistance thermometers (each with a nominal resistance of 50 ~ at room temperature) were bonded. To ensure good thermal contact between the temperature sensors and the copper surface, the epoxy impregnated cloth was scraped with a sharp pointed tool until the copper surface was exposed and then, the foilshaped sensing surfaces were bonded to the copper with an appropriate epoxy at each location. Care was taken to
Characteristic
158
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Dimensionsin cm
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Superconducting magnet coil quench: V. Kadambi and B. Dorri ensure that the copper surface was not damaged in any way during the scraping process and that the minimum of epoxy was used so that there was negligible thermal resistance between the copper and the sensors. The resistance thermometer elements were of the two-lead type and needed the connection of two extra leads to permit accurate temperature measurement. Thin copper wires (0.125 mm) were soldered to each of the two leads and the fine wires were held in place by embedding them in more epoxy, so that thermal losses through the wires were minimized(calculations showed that the maximum error in the measured temperature due to the leads was limited to ~ 0.5 K). These permitted the fourwire method of resistance measurement even though only two leads were available from the manufacturer. The resistance thermometers were powered using a small power supply which maintained a constant current of 10 p,A. To calibrate the sensors between liquid helium and liquid nitrogen temperatures, the whole coil was dipped first into liquid nitrogen along with the sensors and the readings of the sensors were noted in steady state. Thereafter, the whole coil was dipped in liquid helium and the readings were noted after steady state was obtained. In addition` the temperature of the liquid nitrogen as well as that of the liquid helium was measured with a pre-calibrated thermistor, whose characteristics at cryogenic temperatures were known. Thereafter, a double-walled vessel containing liquid nitrogen in the centre (with the coil immersed in it) and an outer chamber containing liquid helium, was constructed. Because of heat transfer, the nitrogen was solidified in a short while, after which the helium was removed and the nitrogen allowed to warm up to its boiling point As the solid nitrogen melted and rose in temperature, readings of its temperatures were obtained at various times both with the sensors (embedded in the magnet coil) and with the thermistor probe which had been placed in the nitrogen close to the coil. These readings permitted the calibration of all the sensors (the resistance thermometers and the thermocouples) at several temperatures between helium and nitrogen boiling points (4.2 - 76 K). Since the coil would have to be maintained in a bath of liquid helium during the experiment, it was felt that heat transfer between the helium and the sensors would lead to erroneous temperature readings after quench. To prevent liquid helium from coming in contact with the sensors, the central cylindrical opening in the coil was covered at the bottom with a circular piece of fiberglassimpregnated plastic which was glued to the surface using a bonding cement At the top, a shell-shaped piece of the same internal diameter as the central opening in the coil was glued with epoxy. This prevented the liquid helium from spilling into the central opening as long as the level of the liquid was below the top of the shell-shaped piece, as may be seen from Figure 5. Power was supplied to the magnet coil by operating two stabilized d.c. power supplies connected in parallel Each of the power supplies was capable of supplying a maximum electrical current of 500 A at any voltage up to 10 V. The current flowing through the coil was measured using a d.c. shunt of 100 /tl~, calibrated to provide an output of 100 mV at a rated current of 1000 A, Three dual-channel Nicolet storage type oscilloscopes were used to monitor the outputs of the thermocouples and the resistance thermometers, as well as to determine the current flowing through the circuit. Two voltage taps, which were located at the middle of the coil
(in contact with the copper conductor 360° apart from each other), were used to monitor the voltage across the middle turn and served to specifythe moment of initiation of quench in the coil. The voltage taps were also connected to one of the channels of a Nicolet so that a record was obtained during quench. A schematic diagram of the connections is indicated in Figure 4. The instrumented coil was suspended in the middle of a double-walled dewar vessel with appropriate seals at the top. Provision existed to measure the level of liquid helium in the inner vessel where the coil was suspended. to ensure that during the experiment, the coil was always immersed in the liquid. The outer jacket of the dewar contained liquid nitrogen to minimize heat transfer between the helium and the surroundings. Figure5 shows the details of the dewar and the coil with its suspension` immersed in liquid helium. To initiate the quench at a known poinL a small nichrome heater wire was wound around the current lead near the first turn (at the inner radius) within 0.25 cm of the coil. Whenever required, a current could be passed through the nichrome wire using a small 9 V battery which included a switch in its circuit It usually needed about I or 2 s after the switch was closed to initiate the quench by this heating process. A simple calculation showed that the total energy input to the system through this heating process was negligible in comparison with the stored electrical energy in the coil which amounted to ~16000 J at the rated current of 860 A (coil inductance = 0.043 H).
Experimental procedure The dewar in which the coil was to be tested was first cooled with liquid nitrogen in the outer chamber for about two days Then, the coil assembly was inserted along with the top cover plate, sealed appropriately and evacuated, after which liquid helium was gradually introduced into the central chamber containing the coil The level of liquid helium was always maintained such that it did not spill into the middle of the coil where the temperature sensing elements were located. Temperatures were monitored at reasonable intervals of time until the whole coil assembly reached 4.2 K. After ensuring that steady state temperature was obtained, as determined by the readings of the thermocouples and the resistance thermometers, the coil was energized using one d.c. power supply and raising the current slowly until it was close to 500 A. The second power supply was then turned on and the current raised further as desired. Quench could be initiated either by raising the current until it exceeded the critical value (nominally 860 A at4.2 K), or by maintaining the current at a set value below critical and heating the input lead with the nichrome wire until the critical temperature was locally exceeded. If the current is just raised above critical (without heating the wire), quench initiates itself at the coil inner radius all along the centre-line, since the magnetic field is a maximum here. Moreover, because of the two-dimensional nature of the field, the normal front propagation through the coil is likely to be very nearly two-dimensional as well. However, if the quench is initiated near the first turn of the coil by heating. (with the current below critical) the propagation will be completely three-dimensional in nature. For each type of quench initiation, data were obtained at different coil currents ranging from 500 to 900 A. No matter how the quench is initiated, the current through the coil decays rapidly in a few seconds. The sudden drop in current induces a large back-electromo-
Cryogenics 1986 Vo126 March
159
Superconducting magnet coil quench: V. Kadambi and B. Dorri
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Test coil suspended in dewar
160 Cryogenics1986 Vol 26 March
tive force due to the inductance of the coil. In our experiments, the back e.m.f, was used to trigger the Nicolets to start recording all the required data (current, voltage, thermocouple and resistance thermometer readings). However, this procedure could not be utilized when quench was initiated by heating since it would take a relatively long time for the normal front to propagate to the middle of the coil where the voltage taps were located. Hence, the Nicolets wre triggered by the closure of the switch required to pass the current through the nichrome heating wire. After the quench was initiated, tracings of the current decay, the voltage at the taps and of the temperature sensors (thermocouples at two locations and the resistance thermometers) were obtained by using the Nicolet oscilloscopes. Figure6 shows Nicolet tracings of resistance thermometer output (top curve, above the horizontal axis) and current decay (bottom curve, below the horizontal axis). Figure 7 shows the thermocouple output (top line) and the back e.m.f, measured at the voltage tap (bottom curve). (Each Figure caption gives the elapsed time from the start of the tracing to the location of the vertical axis. The magnitude of the quantity represented by the lower curve at the same instant is also indicated.) The digitial read-outs from the Nicolet were used later for comparison with the predictions of a numerical analysis program developed to analyse the quench problem.
Superconducting magnet coil quench: V. Kadambi and B. Dorri 2
the thermal resistance o f the glass-epoxy layers in the 0 direction (i.e. in the t~z plane) is very large c o m p a r e d with that o f the copper. Therefore, all the c o n d u c t i o n in that direction may be expected to occur only through the c o p p e r s u p e r c o n d u c t o r matrix, In the cross-sectional (r-0) plane, however, the thermal resistance of the c o n d u c t i n g wire is neglected c o m p a r e d with that o f the epoxy.
The m a t h e m a t i c a l e q u a t i o n s governing heat transfer and current flow through the coil are as follows.
Energy balance
Figure 6 Nicolet traces of the resistance thermometer (top curve) and current decay (lower curve) at 8 6 0 A. Elapsed time from start of tracing to location of vertical axis, 17.990s; magnitude of the quantity represented by the lower curve at the same instant, - 8.5 mV
aT =pCp
3"r
(1)
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Circuit equations for current and voltage •
~,~
. ~ ,
Figure 7
Nicolet traces of thermocouple (top curve) and voltage (lower curve) at 8 6 0 A: Elapsed time from start of tracing to location of vertical axis, 18.260s; magnitude of the quantity represented by the lower curve at the same instant, 18.3 mV
Numerical analysis The following is a brief account o f the n u m e r i c a l model used in the calculations, the results of which were c o m p a r e d with those of the experiment. F o r a more detailed account of the n u m e r i c a l procedure, see Dorri and K a d a m b i 3. Because o f the c o m p l i c a t e d coil geometry, the density changes, orthotropic t h e r m a l conductivities as well as the extreme degree o f non-linearities involved in all the properties, it was found that the use o f spatially averaged properties and s i m p l e t w o - d i m e n s i o n a l calculations were not sufficiently accurate to predict quench propagation. Further, c o m m e r c i a l l y available codes could not be utilized because o f the large n u m b e r o f nodes a n d the i n o r d i n a t e l y long processing times that would be needed to execute such codes. Therefore, a simplified model and a n u m e r i c a l code were developed based on the following observations 1
the t h e r m a l resistance o f each c o n d u c t o r at any crosssection, (i.e. in the r-z plane), can be neglected in c o m p a r i s o n with its resistance in the 0 direction (i.e. a l o n g the coil circumference). Therefore, it is a s s u m e d that at any instant in time, each c o p p e r wire has a uniform t e m p e r a t u r e at a given cross-section:
-L
d/L art
- (R1 + R 2 ) I L
(2)
where: L = i n d u c t a n c e o f the coil: R~ = coil resistance which varies with time during quench: R 2= external resistance in the coil circuit due to contacts, leads, etc. = 0.0033 fI: I i . = current in the coil.
Critical current density in superconductor filaments (Laskaris 2) .I e (B,T) = Io [B + Bo (4.2) - Bo (T)]/,4 se
(3)
where: I o = 1.30952 B = - 302.262 B + 2983.57: B o = --0.103715 T 2 - 0.740336 T + 15.3147: B = magnetic field density: A s~-= cross-sectional area of superconductor. In E q u a t i o n (3) the flux density, B o, is c a l c u l a t e d at the t e m p e r a t u r e s i n d i c a t e d in parentheses. T h e i n d u c t a n c e s a n d the fields have been c o m p u t e d using the method described by Garrett 4. T h e thermal conductivities a n d electrical properties have been found using the data a n d p r o c e d u r e s in References 5-7. Figures8 and 9 are representative g r a p h s showing the variations of thermal conductivities o f c o p p e r and epoxy, respectively.
Cryogenics 1986 Vo126 March
161
Superconducting magnet coil quench: V. Kadambi and B. Dorri THERNALCONOUCTIVIWOF EPOXY
THERNAL CONOUCTIVITYOF COPPERAT I TESI.A FIELD T H E
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Thermal properties of copper
Cryogenics 1 9 8 6 Vol 26 March
I
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lO 2-25
For programming purposes, these property variations were used as input data using rational function curve- fits. The numerical model is based on a control volume finite-difference discretization of the energy balance equation. Each node represents an element with the cross-section of a copper wire, including half the thickness of the insulation surrounding it. Since the temperature of the copper at any section (i.e. at a given 0) is assumed to be uniform within the wire, the concept of a floating node has been used to write the energy balance equation at each control volume. The node floats freely over the wire crosssection, but the intermediate epoxy layer temperatures are computed assuming linear basis functions in the formulation. The Crank-Nicolson scheme has been implemented to ensure reasonable stability without sacrificing accuracy. Reduced computer storage requirements have been achieved using the Alternate Direction Implicit scheme (ADI), where the equations for all the radial twodimensional planes across the coil are solved first, followed by one-dimensional solutions for distributions along the tangential direction of the coiL By alternatively carrying out these two operations and using the Jacobi iterative scheme which can be vectorized for use on the CRAY computer, an efficient program which solves the problem in ,~ 10 min o f c p u time has been developed. The program varies both the number of nodes over which computation is carried out during a time step and the time
162
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Thermal properties of epoxy
step as required, to achieve the minimum processor time for the computation. Iteration for non-linearities is carried out along with that needed for ADI in the program. A surface heat transfer coefficient of 0.05 W m-2 °C-I has been used to account for heat transfer between the coil and the helium.
R e s u l t s and d i s c u s s i o n During the experiments for which the current was raised until quench initiated without heating, it was observed that the current and the voltage at quench initiation differed from test-to-test It was not clear what caused these variations in critical current. Among the possible reasons are the following: 1 the coil was initially stressed due to the fixtures and measuring instruments bonded to its surface and these stresses initiated the quench in an unpredictable way; 2
the current was raised too rapidly during the test, resulting in eddy current losses which could have initiated the quench at different levels;
3
the leads conducting current into the coil could have dissipated electrical energy due to the large currents flowing through them, especially if they were not dipped in liquid helium at the locations where they were connected to the coil. Even though the liquid
Superconducting magnet coil quench: V. Kadambi and B. Dorri level was sufficient to cover the coil in all the tests, it is quite likely that the leads were not cold enough near the coil In that case, the energy conducted along the leads could have initiated the quench even before the current reached the critical value for adiabatic normal front propagation.
Figure 6 shows a typical temperature rise curve obtained from the resistance thermometer located at the centre of the coil along with the current decay after quench. These curves were obtained when the current reached the critical value of 860 A and the quench initiated itself without heating. The corresponding voltage tap reading is seen in the bottom curve of Figure 7. The onset of quench is clearly indicated by the sudden rise in voltage at the tap and marks the start of current decay. As expected, the current decays exponentially while the temperature rises rapidly and reaches a nearly constant value. The temperatures indicated by the resistance thermometers at the start of the quench are likely to be inaccurate, since they are influenced by the changing magnetic field in the coil. However, after the current decays to low levels, the changes in magnetic fields are small and the errors in the resistance thermometer readings will be negligible. Hence, only the part of the resistance thermometer readings corresponding to the maximum observed temperature should be considered as sufficiently accurate and the earlier part used only for qualitative indications of the temperature rise rather than for comparison with the theory. Unfortunately, the Nicolet could not amplify the thermocouple outputs sufficiently to provide meaningful data, since the sensitivity of the thermocouple was small at cryogenic temperatures. The difficulty was compounded by the fact that the ice point was used as the reference junction for the thermocouple, so that the change in temperature due to quench was relatively small (< 50 K) as compared with the full-scale value of 268.8 K, (A more appropriate way would be to use liquid helium temperature as the reference for the thermocouple, with a full-scale reading of ~55 K, so that the rise in temperature during quench would be readily noticed.) The trace of the thermocouple response exhibited at the top in Figure 7, therefore, is not very useful for determining either the temperature rise during quench or the m a x i m u m temperature. All the comparisons with the theoretical predictions are therefore based on resistance thermometer outputs. OUENCH OF TEST COXL
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Plots of current decay obtained experimentally and by numerical calculation are exhibited in Figures 10. 12 andl4, for three quench tests. FigurelO is plotted from the data shown in Figure 6, when the critical current limit of 860 A was reached and resulted in quench. Figures 12 and 14 were obtained from data at currents of 800 and 600 A, respectively, when quench was induced using the nichrome heater wound around one input lead of the coil. Clearly, agreement for current decay provided by the theory and by the experiment is excellent in all cases. There seems to be very little difference in the predicted rate of current decay whether or not the effect of convection at the surface of the coil is taken into account. Figures 11, 13 and 15 show the measured and calculated temperature rise curves due to quench corresponding respectively, to the two current decay curves in FigureslO, 12 andl4. Here, too, the agreement between the measured and theoretical values is reasonably good when the effect of surface convection is taken into account. The lack of agreement at the start of quench is not of much consequence, since reliable information cannot be obtained from resistance thermometers at high magnetic fields. After the current and hence the magnetic field decay to low values, the measured temperatures may be considered as reliable and do show reasonably good agreement with the predictions.
Cryogenics
1986
Vol 26
March
163
Superconducting magnet coil quench: V. Kadambiand B. Dorri QUENCH OF TEST COIL
OUENCH OF TEST COIL 70
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(3 D normal front). Key as in Figure 12
Figure 15
700
3
6O0 500
400
300
200
100
0 0.25
0.5
0.75
1
t.25 TINE
Figure 1 4
1.5
1.75
2
2.;~5
2.5
SEC
Current decay, /o = 6 0 0 A (3D normal front).
Key as in Figure 12
In general, the good agreements between the measurements and the predictions indicate that the model and the code are sound and take account of all the variables reasonably well. We conclude that: 1
the method of temperature measurement was satisfactory. Platinum resistance thermometers can be used to obtain temperature data at cryogenic lemperatures during quench if only steady state lemperature data are to be obtained. If transient temperatures are to be measured with accuracy, the resistance thermometer readings have to be corrected for the effect of the magnetic field. Thermocouple readings (thot, gh not affected by the magnetic field) are small and have to be amplified by large factors to obtain satisfactory accuracy. The reference junction for the thermocouples should be the boiling point of liquid helium rather than the ice point:
164
,.s
Maximum temperature rise, I o = 6 0 0 A. Key as in
the best measurements are obtained if the measuring instruments are embedded in the test coil during
Cryogenics 1986 Vol 26 March
a superconducting switch must be included in the set-up to put the coil in a persistent current mode at any desired current below critical. Part of the difficulty in our experiment was that the lead resistance remained in the circuit even during quench. Hence, there was a voltage impressed across the coil at all times( by the power supply), even though it was quite small in comparison with the electromotive forces induced during quench. The effects of varying external load resistance and impressed voltage have not been modelled numerically due to the complexities involved.
In spite of the shortcomings listed above, the good agreement between the theory and the data indicates that the effects of quench are well modelled by the theory and that the procedures employed here can be used to obtain data on large superconducting magnets as welL with minor modifications.
References I 2 3
Wilson, M.N. Super,'onducting Magnets Monographs on Cryogenics. Clarendon Press. Oxlbrd. UK (1983) 68-69 Laskaris, T. Transient thermal analysis of epoxy-impregnated superconducting windings in linearly ramped fields J Heat Trans (1978) 100 (4) 702-707 Dorri, B. and Kadambi, V. Thermal analysis of quench propagation in superconducting coils submitted to Numerical
Heat Tran~fi'r 4
Garrett, M.W. Calculation of fields, lorces and mutual inductances of current systems by elliptic integralsJAppl Phys (1963) 34 2567-2573
5
Handbook o["Material Propertie.~.[or Superconducting Machineo'
6 7
2
Ls
SEC
epoxy impregnation. Since we had to scrape the coil and then bond the thermal sensors with epoxy cement, the bonding process could have induced local stresses and thus, premature coil quench:
OUENCH OF TEST COIL
A N P
I
Figure 12
800
C U R R E N T
1.s' 1.7,' TIRE
SEC
temperature
I
,
Battelle Columbus Laboratory and NBS, USA (1974) Harlwig, G. Low-temperature properties of resins and composites Adv Co,og Eng (1978) 24 17-36 Ho, J.C. Measurements of heat capacity lot epoxy and epoxyglass samples, personal communication. Physics Department, Wichita State University. Wichita. Kansas, USA (1983)