An Experimental Device for Critical Surface Characterization of YBCO Tape Superconductors

PSFC/RR-13-1 An Experimental Device for Critical Surface Characterization of YBCO Tape Superconductors Franco Julio Mangiarotti January, 2013 Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge MA 02139 USA This work was supported by the U.S. Department of Energy, Grant No. DE-FC02-93ER54186. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

An Experimental Device for Critical Surface Characterization of YBCO Tape Superconductors by Franco Julio Mangiarotti Submitted to the Department of Nuclear Science and Engineering on January 18, 2013, in partial fulfillment of the requirements for the degree of Master of Science in Nuclear Science and Engineering Abstract The twisting stacked tape cabling (TSTC) method for YBCO superconductors is very attractive for high current density, high magnetic field applications, such as nuclear fusion reactors and high energy physics experiments. Industrial scale assembling methods have been proposed, and cable samples have been tested at 77 K and 4.2 K. A new experimental device has been designed and built to measure critical current of YBCO tapes and TSTC as a function of magnetic field and temperature. The probe allows controlling the temperature between 4.2 K and 80 K within ±1 K in liquid and gaseous helium ambient, and can be used in a 2 T magnet facility at MIT-PSFC and a 14 T magnet facility at NHMFL-FSU. Its current leads are designed to carry up to 5 ka. The device consists in a 0.9 m long, 25 38 mm rectangular vacuum-insulated canister. The superconducting sample and a superconducting current return lead fit inside the canister, in such a way that the Lorentz force and torque produced by the external magnetic field is cancelled. The sample temperature is controlled in a 200 mm long area inside the canister where critical current measurements are performed. Critical current measurements were performed on a single YBCO tape at self-field at temperatures between 20 K and 70 K. The results are similar to data provided by the superconductor s manufacturer. The temperature reached the set point in approximately 10 minutes, and was controlled within ±1 K. Results of heating power required and difference between set point temperature and measured temperature as functions of set point temperature are presented for two temperature control methods. Thesis Supervisor: Joseph V. Minervini Title: Senior Scientist, Division Head, Fusion Technology & Engineering Thesis Reader: Anne White Title: Assistant Professor of Nuclear Science and Engineering 3

Acknowledgments I would like to express my deep gratitude to my advisor, Dr. Joseph Minervini, for the great opportunity he gave me. Dr. Minervini has been very supportive and helpful, always giving great advice both academic and for real life. I am very grateful to Dr. Makoto Takayasu, who had infinite patience with me, showing me how to perform good experiments and how to get useful data, even when everything fails. His help was also invaluable during the several 30-minutes meetings we had practically every day, helping me solve every little problem I had. Thanks to Prof. Anne White for reading this thesis, and for her patience in making corrections until the very last moment. I would also like to thank Don Strahan, for his help designing and building the probe. He also taught me and helped me doing some basic machining on my own. Thanks to my fellow coworkers Dr. Andre Berger and Dr. Michael Cheadle, for being great friends and for the great talks during lunch. Their ability of thinking outside the box would always help me solve many issues in just a few minutes. Thanks to everyone in the group, especially Dr. Leslie Bromberg for help with Comsol, and Darlene Marble for her assistance. I am grateful for all the support and help I received from my family. I am very very thankful to Peter and Ruth, without their help I would not be here now. Thanks to them, and Andreas, Omar and Betty for receiving me in their house every now and then, for a much needed family break. Thanks to my parents, Celia and Daniel, and to my siblings, Dante, Irene and Sofía, for their support at six thousand miles away. And special thanks to Leticia, she is always there for me. Thanks to my friends in Boston. Mikhail, the best roommate ever; James, Emilio and Iain, tied in the second place (hahaha); Joaquín, who keeps following me from Argentina; Hans, Noemie, and the rest... And to my friends around the world: Fer, Julia, Pablo, Diego, Pablito, Ricar, Marie, Fede, Leo, Manna, Cris, Tito... This work was supported by the U.S. Department of Energy, Office of Fusion Energy Science under Grant DE-FC02-93ER54186. 5

Contents 1 Introduction 13 1.1 Background of Superconductivity.................... 13 1.2 Superconductivity Applications..................... 17 1.3 Status of Development of YBCO TSTC................. 20 1.4 Motivation and Scope of Thesis..................... 21 2 Design of the Experimental Device 23 2.1 Cross Section Design........................... 24 2.1.1 Size Constraints.......................... 24 2.1.2 Heat Loss Considerations..................... 25 2.1.3 Mechanical Considerations.................... 27 2.2 Operational Design............................ 30 2.3 Thermal Simulations........................... 34 2.3.1 Properties of Materials at Low Temperatures.......... 35 2.3.2 Model Description........................ 37 2.3.3 Simulation Results........................ 41 3 Device and Experiment Construction 47 3.1 Device Construction........................... 47 3.2 Sample Construction........................... 55 3.3 Instrumentation.............................. 57 3.4 Experimental Setup............................ 59 7

4 Experimental Results and Discussion 63 4.1 Temperature Control........................... 63 4.2 Critical Current Measurements..................... 68 4.3 Current Temperature Interaction.................... 71 5 Conclusions 77 5.1 Summary................................. 77 5.2 Future Work................................ 78 8

List of Figures 1-1 Resistance of a wire of mercury as function of temperature...... 14 1-2 Critical surface of a commercial alloy of NbTi............. 15 1-3 Critical surfaces of NbTi and BSCCO-2223............... 15 1-4 Critical current measurement of a commercial YBCO superconductor, at 77 K and self field........................... 16 1-5 Commercial SuperPower 2G HTS YBCO Wires............ 19 1-6 Cross section of SuperPower 2G HTS YBCO Wire, not to scale... 19 1-7 Illustration of four different YBCO cabling methods.......... 20 2-1 Schematic of the experimental device and how it is to be used.... 24 2-2 Cross section of the magnets and the maximum probe cross section. 25 2-3 Geometry used to calculate maximum heat loss due to conduction in the cross section.............................. 26 2-4 Canister configuration for a vacuum insulation............. 27 2-5 Forces in the sample and current lead, depending on the orientation of the magnetic field............................. 28 2-6 Schematic cross section of the 14 T split pair magnet at NHMFL.. 31 2-7 Schematic cross section of the 2 T dipole magnet at MIT-PSFC... 31 2-8 Schematic geometry of the probe, not to scale............. 32 2-9 Solid model of the probe, and detail of the vacuum canister...... 33 2-10 Cross section of the sample holder.................... 34 2-11 Longitudinal section of the sample holder................ 34 2-12 Cross section of SuperPower 2G HTS YBCO Wire, not to scale... 35 9

2-13 Specific heat of YBCO tape and its materials as function of temperature 36 2-14 Thermal conductivity of YBCO tape and its materials as function of temperature................................ 37 2-15 Reduced geometry for thermal simulations: exploded view...... 37 2-16 Reduced geometry for thermal simulation: bottom and top views.. 38 2-17 Cross section of the bottom copper joint, as modeled for the thermal simulations................................ 39 2-18 Cross section of the stainless steel structure, as modeled for the thermal simulations................................ 40 2-19 Solid model used for thermal simulations................ 41 2-20 Example of thermal simulation result.................. 42 2-21 Results of a simulation of temperature as function of time (top) and input heating power as function of time (bottom), with parameters f 1 =1.0, f 2 =0.1, f 3 =1.0........................... 42 2-22 Results of a simulation of temperature as function of time with parameters f 1 =1.0, f 2 =0.0, f 3 =1.0........................ 43 2-23 Results of a simulation of temperature as function of time with parameters f 1 =1.1, f 2 =0.0, f 3 =0.9........................ 44 2-24 Results of a simulation of temperature as function of time with parameters f 1 =1.13, f 2 =0.03, f 3 =0.87...................... 44 2-25 Simulated steady state axial temperature distribution in the sample at 16 W total heating power, for two sets of shape factors........ 45 3-1 Picture of the top of the vacuum canister................ 48 3-2 Picture of the bottom of the vacuum canister............. 48 3-3 Picture of the vacuum canister...................... 49 3-4 Picture of the probe without the vacuum canister........... 50 3-5 Picture of the top flange of the probe.................. 51 3-6 Detail of the joint between the current leads and the sample..... 52 10

3-7 Detail of the joint between the current leads and the sample, with the sample mounted.............................. 52 3-8 Instrumentation wires connectors and top flange of the vacuum canister 53 3-9 Picture of the bottom joint........................ 53 3-10 Picture of the probe, assembled and prepared for an experiment... 54 3-11 Pictures of a sample and the current return lead, with sample holder 55 3-12 Schematic drawing of the three different samples............ 56 3-13 Picture of the sample with instrumentation, and schematic drawing of the sample................................. 57 3-14 Picture of the dewar and 2 T magnet.................. 60 3-15 Setup to leak-check the inside of the vacuum canister......... 61 3-16 Current supply response to a dump signal.............. 62 4-1 Evolution of the temperature measured by sensor C as a function of time for different set points....................... 64 4-2 Difference between the measured and set point temperature as a function of set point temperature for the temperature control method #1 65 4-3 Difference between the measured and set point temperature as a function of set point temperature for the temperature control method #2 65 4-4 Heating power required as function of temperature for the temperature control method #1............................ 66 4-5 Heating power required as function of temperature for the temperature control method #2............................ 66 4-6 Comparison of axial temperature distribution simulated and measured at 70 K.................................. 67 4-7 V I curves of a single 4 mm wide Super Power YBCO tape, measured at self-field and temperatures from 20 K to 70 K............ 69 4-8 V I curves of a single 4 mm wide Super Power YBCO tape, measured at self-field and temperatures from 20 K to 70 K in log-log scale.... 69 11

4-9 The critical current at 100 µv/m and n-value of a single 4 mm wide SuperPower YBCO tape as a function of temperature......... 70 4-10 Critical current at self-field normalized to the value at 77 K, self-field, as a function of temperature measurements for a single SuperPower YBCO tape. SuperPower data of normalized critical current at selffield as a function of temperature is shown for comparison...... 70 4-11 Temperature variation while performing critical current measurements in liquid nitrogen............................. 72 4-12 Temperature variation while performing critical current measurements in gaseous helium............................. 72 4-13 Temperature runaway and quench of sample #1............ 73 4-14 Temperature runaway and quench of sample #2............ 73 4-15 Picture of sample #1 after quench.................... 74 4-16 Picture of sample #2 after quench.................... 75 12

Chapter 1 Introduction Superconducting materials brought a breakthrough in the design and construction of large-scale electric and magnetic devices. The non-resistive characteristic of these materials allows achieving performances that would be either too demanding or economically impossible with conventional materials. In this chapter, the main characteristics of superconductors and its applications are discussed. A general background of superconductivity is given in the first section. The following section summarizes the most important applications for superconductors, and the engineering challenges in order to build them. In the third section the motivations for the work of this thesis are presented. 1.1 Background of Superconductivity Superconducting materials have virtually zero electrical resistivity under certain conditions. Most commonly, the superconductive state is reached by sufficiently lowering the temperature of the material. In Figure 1-1 the transition from normal to superconductor for a mercury wire is shown, as measured for the first time by H. K. Onnes in 1911. The other two major factors that influence in the superconducting property of these materials are the electrical current density through the superconductor, and the external magnetic field applied to it. These two factors and the temperature of 13

Figure 1-1: Resistance of a wire of mercury, in Ω, as a function of temperature, in K. At 4.2 K the mercury wire becomes superconductive. This is the first superconductive material discovered, in 1911 [11]. the material define what is known as the critical surface of the superconductor. As an example, the critical surface of a commercial alloy of NbTi is shown in Figure 1-2. For a superconductor to remain in the zero resistivity zone, its current density has to be lower than the critical current density: the current density of the point in the critical surface determined by the material s temperature and the magnetic field applied to it. From Figure 1-2 the parameter critical temperature of the superconductor can be defined. It is the temperature on the critical surface such that both the magnetic field and the current density are zero: at temperatures higher than the critical temperature the material is not superconductive. Often, commercially available superconductors are divided in two groups: low 14

Figure 1-2: Critical surface of a commercial alloy of NbTi [26]. Figure 1-3: Critical surfaces of NbTi and BSCCO-2223 [10]. 15

temperature superconductors (LTS) such as Nb 3 Sn and NbT i, and the high temperature superconductors (HTS) such as Y BCO 1 and BSCCO 2. In Figure 1-3 the critical surfaces of a LTS (NbTi) and a HTS (BSCCO-2223) are compared. There are several differences between LTS and HTS; the most important are the critical temperature (for LTS close to liquid helium, for HTS higher than liquid nitrogen), and the material characteristics (LTS are metallic alloys or compounds, while HTS are ceramics). Also, LTS were discovered decades earlier than HTS, and thus the development of fabrication and cabling methods for LTS conductors are much more advanced. Figure 1-4: Critical current measurement of a commercial YBCO superconductor, at 77 K and self field. In order to experimentally obtain the critical current density of a superconductor, measurements of voltage drop along its length are performed as a function of current through it. The voltage drop varies smoothly with current near the critical current, as is shown in Figure 1-4 for a commercial YBCO superconductor. In this work, the critical current will be obtained as the value of current, at a fixed magnetic field and temperature, when a voltage drop of 100 µv/m is developed through the superconductor. From Figure 1-4, the critical current is 108 A. The critical current density is 1 Yttrium Barium Copper Oxide (Y Ba 2 Cu 3 O 7 ). 2 Bismuth Strontium Calcium Copper Oxide. There are two main compounds: BSCCO-2212 (Bi 2 Sr 2 CaCu 2 O 8+x ) and BSCCO-2223 (Bi 2 Sr 2 Ca 2 Cu 3 O 10+x ). 16

obtained dividing the critical current by the cross section of the superconductor, in this case 0.4 mm, and the critical current density is 270 A/mm 2. This convention is usually referred to as critical current density at 100 µv/m. The steepness of the transition is an indicator of the quality of the superconductor. An ideal superconductor would have a step-like transition, while a degraded superconductor would present a flatter transition. The parameter that quantifies the steepness of the transition is the n-value, and is obtained from fitting a power law to the transition data: V J n (1.1) where V is the voltage drop in the superconductor, J the current density, and n the n-value. In the case shown in Figure 1-4, the n-value is 26. 1.2 Superconductivity Applications Superconductors are very attractive for high current density or high magnetic field applications, where the overall energy consumption would be prohibitive if a normal conductor (such as copper) was used. There are six major fields of application of superconductivity: Fusion Energy: magnetic confinement nuclear fusion reactors require high magnetic fields and high current densities to operate. The use of normal conductor coils would be prohibitive as they would consume 30% 50% of the electric power generated. Superconducting coils are ideal for this application, and the next milestone in fusion energy investigation and development, the International Thermonuclear Experimental Reactor (ITER) will be built using superconductors (NbTi and Nb 3 Sn) in all its magnet systems. High Energy Physics: in high energy physics experiments, superconducting magnets are used to accelerate, focus and analyze beams of energetic particles. 17

The largest particle accelerator in the world, the Large Hadron Collider (LHC), has more than 1600 NbTi magnets. Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI): superconducting magnets are widely used in NMR and MRI applications, since they produce a very stable and intense DC magnetic field over large volumes. The use of conventional magnets would consume much more power, and would not achieve the imaging quality of superconducting magnets. Power Transmission Cables: the zero resistance property of superconductors allows these materials to carry DC high currents with practically no power dissipation. In certain cases, the installation and operation cost of the superconductor cables (including the cryogenic systems to keep it below the critical temperature) are lower than the costs of normal conducting transmission cables. A superconducting power transmission cable has been built in the Long Island Power Grid, and it is operating since 2008. Superconducting Magnetic Energy Storage (SMES): a superconducting magnet does not experience DC power dissipation, and as such it can be used to store large amounts of magnetic energy with virtually no losses. Several SMES systems have been demonstrated since 1985, and are now commercially available. Magnetic Levitation (Maglev): several projects of magnetic levitation trains using superconductors are being developed, including the JR-Maglev in Japan which holds the world speed record for all trains. Magnetic levitation allows reducing maintenance of the trains, because they do not require the traditional moving parts (such as gears, wheels, axles... ). These applications require different superconducting cables technologies. For instance, the main challenge of power transmission cables is cooling the superconductors, and the external magnetic field in the superconductor is zero, thus high temperature superconductors operated with liquid nitrogen or gaseous helium are favored. For nuclear fusion reactors, the fusion power density increases dramatically with larger 18

magnetic fields, and subcooling the superconducting coils for increased performance is an economically attractive option. Figure 1-5: Commercial SuperPower 2G HTS YBCO Wires [9]. Figure 1-6: Cross section of SuperPower 2G HTS YBCO Wire, model SCS4050, not to scale [9]. The superconductor is 1 µm thick. Low temperature superconductors NbTi and Nb 3 Sn, and high temperature superconductor BSCCO-2212 are commercially available in fine round wires, and cabling methods for conventional conductors can be used to bundle them. YBCO and BSCCO-2223 conductors are tapes, usually 0.1 0.3 mm thick and 4 12 mm wide, and new cabling methods must be developed in order to use them for engineering applications. In Figure 1-5 a picture of SuperPower YBCO tapes is shown, and in Figure 1-6 a detail of the cross section of a standard commercial configuration. Depending on the manufacturer and model, different tape configurations are available; however, in all cases layers with high electrical resistivity are present (in the case of the figure, the substrate -hastelloy- and the buffer layers), allowing current into the YBCO layer only from one side of the tape. A few cabling methods for making high current YBCO cables have been proposed, 19

Figure 1-7: Illustration of four different YBCO cabling methods. From left to right: helical winding on a round former [13], ROEBEL cable [7], CORC cable [24], TSTC cable [18]. such as helical windings on a round former [13], ROEBEL cabling of tapes cut in a zigzag pattern [7], conductors on round core (CORC) [24] and twisting stacked tape cables (TSTC) [20, 18]. These cabling methods are illustrated in Figure 1-7. TSTC provides high current density, efficient tape usage and allows constructing cables for high current density and high magnetic field applications, such as nuclear fusion reactors. 1.3 Status of Development of YBCO TSTC The excellent high current capabilities at high magnetic fields of HTS, especially YBCO, make them very attractive for magnet applications. In particular, the use of YBCO conductors instead of LTS for coils in nuclear fusion would greatly improve the performance, as has been proposed in several studies [8, 2, 1]. Though ITER is being built with LTS magnets, the next step in the development of magnetic confinement nuclear fusion energy, the DEMO reactor, could greatly benefit by using YBCO magnets. Of the four cabling methods mentioned in the previous section, TSTC is the only 20

one suitable for making long lengths of high current, high current density magnetgrade cables. The helical winding on a round former design has low current density, and is ideal for transmission cables. The ROEBEL and CORC designs, due to manufacturing difficulties, are hard to scale-up to the long lengths required for magnet construction, and the proposed electrical joint mechanisms between cables are very complex. TSTC, on the other hand, can meet the performance requirements on current and current density, and a simple industrial scale assembling method has been proposed [19]. As demonstrated in [21], a 2 m TSTC cable has been built and tested at self field and 77 K, and a 2.5 turn pentagon shaped coil of less than 165 mm diameter has been constructed and tested at a background field of 19.7 T at 4.2 K. A relatively simple method for building low-resistance electrical joints has been developed and tested [18]. For engineering applications of YBCO TSTC, a complete critical surface characterization is required. Some measurements have been performed at 77 K and 4.2 K, but intermediate temperatures (around 20 50 K) can be of practical interest due to lower cooling costs than 4.2 K, while keeping a much better performance than at 77 K. Single tape data is readily available, but some degree of degradation is expected due to increased self magnetic fields, and full cable experiments are required. 1.4 Motivation and Scope of Thesis Conventional experimental apparatus for testing superconducting samples can not be used for testing YBCO TSTC cables, due to their large characteristic length. An experimental device for testing TSTC, CORC and other YBCO cables has been developed by Barth et al. at the Karlsruhe Institute of Technology [3], but the temperature uncertainties of his measurements may be as high as ±5 10 K. In order to perform a complete and precise characterization of YBCO TSTC, a new experimental device for YBCO TSTC critical surface characterization has been 21

designed, built and tested. This probe 3 allows to characterize TSTC cables at temperatures between 4.2 K and 80 K within ±1 K, and in magnetic fields up to 2 T or 14 T. The cables will be subject of currents up to 5 ka. Characterization experiments can be performed in two different magnetic facilities, with magnets submerged in liquid helium, and the experimental device fits in both of them while providing adequate temperature control. In this thesis, the design and construction of this experimental probe are detailed, and results of temperature control and critical current measurements performed at self field in one of the magnet facilities for a single YBCO tape are presented. The critical current results are similar to data from the superconductor manufacturer, validating the design of the probe for TSTC characterization. The device consists of a helium gas filled canister, with a surrounding vacuum layer. The superconducting sample is in contact with liquid helium far away from the measuring area, and the temperature of the sample is controlled with three electric heaters. The design of the experimental probe is detailed in the second chapter of this thesis. The construction of the probe and the experimental setup is described in the third chapter. In the fourth chapter the results are presented and discussed. Finally, the fifth chapter concludes this thesis with a summary of the results, feedback to improve the experiment and planned future work. 3 Throughout this thesis the terms device and probe will be used indifferently, referring to the same experimental device. 22

Chapter 2 Design of the Experimental Device The experimental probe is designed to measure the critical current of YBCO TSTC samples as a function of magnetic field and temperature. The samples will be tested with currents up to 5 ka, and their temperature will vary between 4.2 and 80 K. The twist pitch of the superconducting cable is approximately 130 200 mm. To reduce end effects and current redistribution in the measurement area, the electrical joints will be placed at least a twist pitch away from it (making the total length of the sample at least 600 mm). The sample will be kept straight. In order to get a perpendicular magnetic field for such a long sample length, a dipole or split-pair magnet will be used. Available magnetic facilities are a 2 T superconducting dipole magnet, located in building NW22 at MIT-PSFC, and a 14 T superconducting split-pair magnet, located in the National High Magnetic Field Lab (NHMFL) at Florida State University, in Tallahassee, Florida. The selection of magnetic facilities, sample geometry and current and temperature ranges of operation give the conditions the probe must fulfill: 1. Operate at 4 80 K, with low temperature gradients in the measurement area. 2. Fit in both magnet facilities. 3. Operate with DC currents up to 5 ka, and be able to mechanically support the associated Lorentz forces. 23

4. Allow long YBCO TSTC samples to be mounted, tested and removed easily. 5. Consume as little power as possible and allow quick measurements, for liquid helium economy. 2.1 Cross Section Design 2.1.1 Size Constraints The 2 T dipole magnet has a 50 mm diameter circular bore, and a homogeneous field region approximately 220 mm long. The 14 T split-pair magnet has a 30 x 70 mm rectangular bore, and a homogeneous field region approximately 150 mm long. The magnetic field is perpendicular to the 70 mm side of the bore. Both magnets have to be immersed in liquid helium during operation. The probe, then, will have to operate in a liquid helium environment. A schematic of the device and how it is to be used is shown in Figure 2-1. Figure 2-1: Schematic of the experimental device and how it is to be used In order to fit in both magnets, the probe has to have a small enough cross section. In Figure 2-2 the maximum possible probe cross section is shown. 24

Figure 2-2: Cross section of the 2 T dipole magnet at MIT-PSFC, and the 14 T magnet at NHMFL. The maximum cross section of the probe is such that fits in both bores. Commercially available stainless steel components are preferred for the probe. The tube with the largest cross section that fits in both magnet bores is a rectangular 25.4 x 38.1 mm (1 x 1.5 ) tube, with wall thickness 1.65 mm (0.065 ). 2.1.2 Heat Loss Considerations Two thermal insulation methods were considered for the sample: a vacuum layer, or a thermal insulator. An estimate of the maximum heat loss due to conduction through a thermal insulator has been done, considering the geometry shown in Figure 2-3: the inside of the rectangular steel tube filled with Styrofoam, with a small rectangular section of 7 x 21 mm where the sample would be placed. The thermal conductivity of Styrofoam is approximately constant in the 4 80 K range, 0.01 W/mK [14]. Temperature gradients in the sample and steel tube have been neglected since the thermal conductivity of these materials is at least 100 times larger than that of Styrofoam. Heat loss per unit length can be approximated as: 25

Figure 2-3: Geometry used to calculate maximum heat loss due to conduction in the cross section. q = T1 T 2 [ k sty dt ] 1 [ dx k sty (T 1 T 2 ) P (x) ] 1 dx (2.1) P (x) where P (x) is the cross sectional perimeter at position x along the path of heat flow, T 1 is the inner temperature (80 K), T 2 is the outer temperature (4.2 K), and k sty is the thermal conductivity of Styrofoam (0.01 W/mK). As a conservative estimation of the heat path integral, P (x) was taken to be the outer perimeter of Styrofoam, 114 mm; with x the horizontal distance between the sample area and the border of the Styrofoam, 7 mm. In this situation, the heat loss per unit length is 12 W/m. An estimate of the heat loss due to radiation through a vacuum insulation has been done, considering the geometry shown in Figure 2-4: the system is composed of two circular steel tubes, with outer diameter 15.9 mm (5/8 ) and wall thickness 0.89 mm (0.035 ), inside the rectangular tube. Heat loss per unit length can be estimated as: q = σɛp T 4 (2.2) where σ is the Stefan-Boltzmann constant, ɛ is the emissivity of stainless steel, approximately 0.1 [5]; P the outer perimeter of the two tubes, and T the temperature of the tubes (80 K). In this situation, the heat loss per unit length is 0.023 W/m. 26

Figure 2-4: Canister configuration for a vacuum insulation The vacuum layer insulation method was chosen in order to minimize the heat loss on the cross section. 2.1.3 Mechanical Considerations The cross section shown in Figure 2-4 can balance the Lorentz forces in the conductors, if the magnetic field is aligned in such way that the forces in the sample and in the current return lead are inward against each other (Figure 2-5). In this situation, a small misalignment of the probe with respect of the magnetic field would not produce a net force, but a net torque. An estimate of the maximum torque expected is the maximum misalignment in the 14 T split pair magnet. In that case, the probe can be misaligned at a maximum angle such that the opposite corners of the cross section are in contact with the magnet bore walls. That angle θ can be estimated as: θ w a b (2.3) where w is the width of the magnet bore (30 mm), and a and b are the probe dimensions (25.4 mm and 38.1 mm respectively). The net torque T on the canister will be: 27

Figure 2-5: Forces in the sample and current lead, depending on the orientation of the magnetic field. + and - indicate current direction. T = θ d l I B (2.4) where d is the distance between the sample and current return lead (15.9 mm), l the length of the magnetic field zone (approximately 600 mm), I is the current intensity (maximum 5 ka), and B is the magnetic field intensity (maximum 14 T). The value of the torque is 81 Nm. To estimate the stress this torque generates in the tubes, one tube will be considered as a free tube, subject to half the torque. In this situation, the maximum shear 28

stress τ can be estimated as [22]: τ = T r 2J = T r 2 2πr 3 t (2.5) where r is the radius of the tube (7.9 mm), t its thickness (0.89 mm), and J the polar moment of inertia (equal to 2πr 3 t in the case of a thin cylindrical tube). The result is 115 MPa. Additional stresses will come from the pressure difference between the liquid helium at atmospheric pressure and the vacuum layer. The maximum stress of the system will be in the wider face of the rectangular tube. Since the length of the tube is much larger than the width, the stress on the tube depends on a parameter α [23], determined as the smaller positive root of: α(1 α) 2 = 3 t 2 ( 5 384 ) pa 4 2 (2.6) D where D is the flexural rigidity of the face of the tube, p the pressure difference (approximately 1 bar), t is the wall thickness of the tube (1.65 mm) and a the width (38.1 mm). D is calculated as: D = Et 3 12(1 ν 2 ) (2.7) where E is the material s Young modulus (approximately 250 GPa [16]), and ν its Poisson s ratio (0.3). The maximum tensile stress σ x and bending stress σ x calculated as: are σ x = απ2 D ta 2 (2.8) σ x = 3 [ ( pa 2 2 cosh π ) ] 2 α 1 4 t 2 ) 2 ( α cosh π ) (2.9) 2 α ( π 2 And the maximum stress is the sum of them. Using the values previously given, the maximum stress in the rectangular tube is 41 MPa. 29

The yield strength of stainless steel at cryogenic temperatures is about 400 MPa [5]. Since the maximum combined stress in both circular and rectangular tubes is much lower than their yield strength, the design is strong enough for this application. 2.2 Operational Design The 14 T split pair magnet is fixed inside a 1.9 m deep Dewar. In Figure 2-6 a schematic is shown of the 14 T magnet in its Dewar. The 2 T dipole magnet will be located in a 2.4 m deep Dewar. In Figure 2-7 a schematic is shown of the 2 T magnet in its Dewar. The final position of the magnet inside the Dewar can be adjusted, in such way that the same probe fits both magnets with the sample measurement area in the uniform magnetic field zone of each of them. The proposed geometry of the probe is shown in Figure 2-8, and a solid model of the probe is shown in Figure 2-9, with a detail of the vacuum canister. The bottom part ( A in Figure 2-8) houses the electrical joint between the sample and the current return lead. Most of the space in that area is occupied by a copper joint between the superconductors, in order to reduce joule heat generation. The middle part ( B ) is the vacuum canister, where the measurements will be performed. The top part ( C ) acts as mechanical support and features the current leads from room temperature to the cryogenic area. The longitudinal dimensions of the probe are determined by the 14 T magnet. The bottom of the probe is about 10 mm higher than the bottom of the magnet s Dewar. The top of the vacuum canister is about 100 mm higher than the top of the magnet. In order to keep a gaseous helium ambient inside the vacuum canister, it needs to be tightly sealed on the top. To reduce complexity of that joint, the sample and current return lead will be mounted from the bottom of the canister, with the instrumentation wires coming out of the measurement area also from the bottom. This way, the only openings required in the top of the canister are for the sample and current lead, and the structural components can be welded in place. 30

Figure 2-6: Schematic cross section of the 14 T split pair magnet at NHMFL Figure 2-7: Schematic cross section of the 2 T dipole magnet at MIT-PSFC 31

Figure 2-8: Schematic geometry of the probe, not to scale A steel tube section separates liquid and gaseous helium in zone A. For easy access to the electrical joint, the tube is not welded to the vacuum canister, and 32

Figure 2-9: Solid model of the probe, and detail of the vacuum canister. References: (1) outer rectangular tube; (2) inner circular tubes; (3) sample. instead just held mechanically. Hermetically sealing this area is desirable but not critical, since the heat generation in the joint would evaporate any small amount of liquid helium that comes into contact with it. Inside the vacuum canister, the sample and current lead must be supported against the Lorentz force, and electrically isolated from the metallic structure. The support design is shown in Figures 2-10 and 2-11, made from half a thin stainless steel tube with inner diameter 7 mm, supported by C -shaped G10 pieces. The G10 pieces fit tightly inside the circular tubes of the vacuum canister. The distance between the 33

Figure 2-10: Cross section of the sample holder. The white component is made of G10, the grey component is half a stainless steel tube. Dimensions in mm. Figure 2-11: Longitudinal section of the sample holder. The white components are made of G10, the grey component is half a stainless steel tube. Dimensions in mm. G10 pieces is such that the tube will support the maximum Lorentz load expected. At a magnetic field of 14 T with 5 ka of transport current, this force is 70 kn/m. 2.3 Thermal Simulations In the real experiment, the temperature of the sample has to be increased in steps of approximately 10 K, and the time between measurements needs to be short (10 to 15 minutes), to avoid consuming too much liquid helium. The temperature in the measurement area has to be very uniform, otherwise the hot spot will be a weak point in the sample and damage may occur. To check if appropriate temperature gradients can be theoretically achieved, and 34

in a short time period, a thermal simulation has been performed with the commercial software Comsol Multiphysics. A simplified geometry has been analyzed, with similar boundary conditions to those of the real experiment, as shown in Sections 2.3.2 and 2.3.3. 2.3.1 Properties of Materials at Low Temperatures As mentioned in the Introduction, commercial YBCO tapes are composed of several layers of different materials, depending on the manufacturer. The experimental probe was designed to measure SuperPower SCS4050 YBCO tapes. These tapes are 4 mm wide, and less than 0.1 mm thick; the cross section is illustrated in Figure 2-12. From a thermal perspective, the most important materials in the YBCO tapes are copper, silver and the substrate (Hastelloy), because they fill the largest area of the cross-section. Figure 2-12: Cross section of SuperPower 2G HTS YBCO Wire, model SCS4050, not to scale [9]. The superconductor is 1 µm thick. From a thermal point of view, the most significant layers are the substrate (Hastelloy, 50 µm thick), the silver overlayer (approximately 3.8 µm) and the copper stabilizer (40 µm). For modeling simplicity, this complicated cross section can be reduced to a homogeneous cross section, with an equivalent mass density ( ρ), specific heat ( c) and thermal conductivity ( k). The expression to obtain each equivalent property are: ρ = ti ρ i ti (2.10) 35

c = ti ρ i c i ti ρ i (2.11) k = ti k i ti (2.12) where t i is the thickness of the material i, ρ i its mass density, c i its specific heat and k i its thermal conductivity. The mass density of these materials varies much less than the other properties in the temperature range of interest (4 80 K), and will be assumed constant; these values, along with the equivalent mass density, are shown in Table 2.1. Material Thickness [µm] Mass density [kg/m 3 ] Silver 3.8 10490 Copper 40 8940 Hastelloy 50 8890 Equivalent 93.8 8979 Table 2.1: Thickness and mass density of the materials in a SuperPower 2G YBCO tape [4]. Figure 2-13: Specific heat of Copper [15], Silver [6] and Hastelloy [12, 25] as function of temperature, and equivalent specific heat for a homogeneous material with the same thermal characteristics. Matlab functions by Dr. A. Berger [4]. The specific heat and thermal conductivity of these materials as function of temperature, with the equivalent specific heat and thermal conductivity, are shown in Figures 2-13 and 2-14 respectively. 36

Figure 2-14: Thermal conductivity of Copper [15], Silver [17] and Hastelloy [12, 25] as function of temperature, and equivalent thermal conductivity for a homogeneous material with the same thermal characteristics. Matlab functions by Dr. A. Berger [4]. 2.3.2 Model Description It was inconvenient to perform a thermal simulation of the entire system, as shown in Figure 2-8, because the only part of interest is the sample, which represents a small fraction of the volume of the probe and is thermally isolated from those components. A reduced geometry was proposed, to obtain some insight of the thermal dynamics of the system. The reduced geometry is composed of six components: sample, current return lead, bottom electrical joint, sample holder, current return lead holder, and stainless steel structure. An exploded view of the reduced geometry is shown in Figure 2-15, and its bottom and top views are shown in Figure 2-16. Figure 2-15: Reduced geometry for thermal simulations: exploded view. References: (1) Sample; (2) Current lead; (3) joint between them; (4) Sample holder; (5) Current lead holder; (6) Stainless steel tubes. 37

Figure 2-16: Reduced geometry for thermal simulation: bottom and top views. References: (1) Sample; (2) Current lead; (3) joint between them; (4) Sample holder; (5) Current lead holder; (6) Stainless steel tubes. The sample and current return lead were simulated as cylinders of 7 mm and 8.4 mm in diameter respectively, and 1055 mm in length. The material has the equivalent properties calculated in the previous section. The bottom joint is a 70 mm long copper piece. Its cross section is shown in Figure 2-17. The two near-horizontal faces are tangent to the cylindrical faces, and these match perfectly the sample and current lead. The sample holder is as shown in Figures 2-10 and 2-11. The length is 985 mm. It is composed of two materials, G10 and stainless steel 316. The current return lead holder was modeled as a solid 985 mm long half-tube of G10, with inner diameter 8.4 mm and outer diameter 15.9 mm. The stainless steel structure represents the half of each of the circular steel tubes in the canister, with a steel filling between them, simulating a welded joint, to improve thermal contact. The length of the structure is 985 mm. The outer parts of the circular steel tubes have not been simulated because they have lower effect in thermal conduction, due to small cross section and not being in contact with other materials. A cross section of the simulated steel structure is shown in Figure 2-18. The cryogenic thermal properties of copper, stainless steel 316 and G10 were included in the simulation software. The system was modeled as completely isolated, except in the bottom where the bottom face of the sample, current lead and copper joint are forced to be 4.2 K (simulating those faces being in contact with liquid helium), and in the top where the top face of the sample and current lead are forced 38

Figure 2-17: Cross section of the bottom copper joint, as modeled for the thermal simulations. dimensions in mm. to be at 4.2 K. For this simulation, gaseous helium was completely neglected. This simplification removes a cooling mechanism from the simulation. Since the design of the probe does not provide a path for gaseous helium to circulate through the sample area, convective cooling of the sample would be minimal. The thermal conductivity of YBCO is very high, and conduction cooling axially through the sample will dominate the thermal dynamics. As a result, the heating power required to maintain a certain temperature will only be slightly underestimated. Simulating the control heaters, a distributed superficial heat source q (z, t) was placed around the sample, according to: q (z, t) = q 1(t) f(z) (2.13) with q 1(t) a factor related to the total heating power q(t), and f(z) a shape factor, 39

Figure 2-18: Cross section of the stainless steel structure, as modeled for the thermal simulations. dimensions in mm. function of the axial position. The shape factor was defined as follows: 0 z < 360 f 1 360 < z < 370 f(z) = f 2 370 < z < 500 f 3 500 < z < 510 0 z > 510 (2.14) with z in mm, and z = 0 at the bottom of the sample. The values of f 1, f 2 and f 3 are input parameters, kept constant during each simulation run. The relation between q 1(t) and q(t) is: q(t) = q (z, t)da = q 1(t) (2πr) f(z)dz (2.15) q(t) = q 1(t) (f 1 + 13f 2 + f 3 ) 2.2 10 4 m 2 (2.16) 40

To simulate the temperature PID control that will be used for the experiment, the heating power will be set with steps every 10 minutes; each step has an initial constant overshooting to improve the thermal dynamics, during the first 150 seconds, and then a lower constant power value during 450 seconds. The overshooting factor, the shape factors, and the power as function of time were changed between simulations, and a selection of results are presented in the next section. 2.3.3 Simulation Results In Figure 2-19 the solid model used for thermal simulations is shown. The area marked as measurement area corresponds to the area where the critical current measurement voltage taps are located, and is where the distributed heating source is located. Four point-temperature measurements were set up, three in the sample (T 1 T 3 ) and one in the current return lead (T 4 ). The axial position of the temperature measurements is: T 1 : 510 mm, T 2 : 420 mm, T 3 : 360 mm, T 4 : 420 mm. Figure 2-19: Solid model used for thermal simulations. The area marked as measurement area corresponds to the area where critical current measurement will be performed. The position of four point-temperature measurements is shown. The results of the simulation are the temporal evolution of the temperature of the system. A qualitative example is shown in Figure 2-20, for a maximum temperature 41

Figure 2-20: Example of thermal simulation result. The color code is not enough to measure the temperature gradients, and point temperature data is required. Figure 2-21: Results of a simulation of temperature as function of time (top) and input heating power as function of time (bottom), with parameters f 1 =1.0, f 2 =0.1, f 3 =1.0. 42

on the sample of 95 K. For quantitative analysis, the evolution of the four pointtemperatures mentioned before (T 1 T 4 ) and the input heating power as a function of time are better figures to analyze. The first simulation was intended to relate heating power with steady state temperature on the sample. A heating power overshooting of 20% was used, and the shape parameters were: f 1 =1.0, f 2 =0.1, f 3 =1.0. In Figure 2-21 the results of temperature as function of time are shown, along with the input heating power as function of time. Additional simulations were performed, changing the overshooting and the shape parameters. The goal of changing these parameters is to obtain a flat temperature profile in the measurement area, and reach a steady state temperature distribution in ten minutes. To better show the improvements, the results of temperatures T1, T2, T3 versus time for three sets of shape parameters and overshooting factors (obtained by trial and error) are shown in Figures 2-22, 2-23 and 2-24. For clarity only the last two temperature steps are shown. As can be seen in the figures, the progressive changes in the shape parameter helped obtain a flatter temperature distribution through the sample area. Figure 2-22: Results of a simulation of temperature as function of time with parameters f 1 =1.0, f 2 =0.0, f 3 =1.0. For the experiment, the heater can be set up to mimic the simulated heating power distribution (for example, different winding density in case of a wire heater); this 43

Figure 2-23: Results of a simulation of temperature as function of time with parameters f 1 =1.1, f 2 =0.0, f 3 =0.9. Figure 2-24: Results of a simulation of temperature as function of time with parameters f 1 =1.13, f 2 =0.03, f 3 =0.87. 44

Figure 2-25: Simulated steady state axial temperature distribution in the sample at 16 W total heating power, for two sets of shape factors. The shape factor is expressed as f = [f 1 f 2 f 3 ], and the corresponding areas are shown. The profile only changes in the measurement area, between the two temperature peaks: the distributed heat in the measurement area helps reduce the temperature gradients. The goal for the experiment is to have a flat temperature profile in the measurement area. solution however does not provide flexibility adjusting the shape factor if required. Dividing the heater in three separate heaters: one for the sample area, and one additional in either end of the sample area, and using separate power sources for these three heaters will help achieve a good temperature distribution while allowing to adjust the shape parameters during the experiment. The effect of the shape parameters can be seen in Figure 2-25. In that figure are shown the simulation results of steady state axial temperature distribution in the sample, at 16 W total heating power, for a simulation with shape factors f 1 =1.1, f 2 =0.0, f 3 =0.9 (corresponding to the simulation shown in Figure 2-23), and a simulation with shape factors f 1 =1.13, f 2 =0.03, f 3 =0.87 (corresponding to the simulation shown in Figure 2-24). Distributed heating along the measurement area helps to achieve a more uniform temperature profile in the area of interest. The temperature achieved in the measurement area is approximately 90 K. Several conclusions can be drawn from the simulations. First, that the temperature evolves quickly, and if given the correct overshooting value a steady state 45

temperature distribution can be reached in ten minutes. For a real experiment, the heating power can be feedback-controlled, for example with a PID controller. Effects not taken into account, such as cooling by helium gas, are not expected to influence greatly in the time evolution of the system. For the experiment, the settling time is expected to be close to ten minutes. The real power requirements are more difficult to estimate. To reach 80 K in the simulations, a total heating power of approximately 15 W is required. However, heaters such as the simulated may be difficult to construct. 46

Chapter 3 Device and Experiment Construction The probe was built according to the design described in the previous chapter, and shown in Figure 2-9. This chapter describes the construction of the probe and samples, and the experimental setup. In the first section critical points of the design and construction of the probe are shown and explained. The following section deals with sample design and construction. The third section summarizes the instrumentation and measuring devices used in the experiment. Finally, the last section describes the experiment setup, and the critical steps performed in order to obtain high quality measurements. 3.1 Device Construction The probe was built according to the design shown in Figure 2-9. In this section the critical points of the design are shown and explained. The top of the vacuum canister is shown in Figure 3-1. The rectangular tube and the circular tubes described in Figure 2-4 are welded to the top flange, and to a bottom cap (shown in Figure 3-2). A vacuum connection is provided through a 6.35 mm (1/4 ) stainless steel tube connected and welded to the side of the rectangular tube. The top of the canister flange is covered by a rectangular stainless steel plate. In its 47

Figure 3-1: Picture of the top of the vacuum canister. Left: during its construction. Right: after finishing the canister construction. References: (1) vacuum port; (2) outer rectangular tube; (3) top flange; (4) inner circular tubes; (5) top flange cover; (6) canister vent; (7) sample and current return lead openings; (8) holes for structural attachment to the probe. Figure 3-2: Picture of the bottom of the vacuum canister. References: (1) bottom sample termination; (2) instrumentation wires; (3) bolt holes for holding bottom joint area cover; (4) inner circular tubes of canister; (5) bottom cap of canister; (6) current return lead in sample holder; (7) instrumentation wires connectors; (8) threaded rods for canister attachment to the probe. 48

final form, the top of the canister has only two openings for the sample and current return lead, and a 6.35 mm stainless steel tube for venting. The tube is connected to a valve that vents to the outside. The four circular holes in the top flange are for structural attachment to the rest of the probe. Figure 3-3: Picture of the vacuum canister. References: (1) outer rectangular tube; (2) vacuum port; (3) bottom cap; (4) sample termination and instrumentation wires; (5) bottom joint area cover; (6) current return lead and sample holder; (7) rest of the experimental device (see Figure 3-4). In Figures 3-2 and 3-3 other views of the vacuum canister are shown. A sample with instrumentation is mounted inside the canister, the instrumentation wires come out through the bottom. The current return lead is shown, lying next to the canister, 49

mounted in a sample holder. The rectangular steel tube for covering the joint area, shown in Figure 3-3, during operation is held in place with long bolts screwed into the tapped holes shown in Figure 3-2. The instrumentation wires that come out of the canister are terminated in pin connectors, which are plugged during the experiments to the socket connectors shown in Figure 3-2. Figure 3-4: Picture of the probe without the vacuum canister. References: (1) top flange; (2) vapor cooled current leads; (3) instrumentation wires; (4) cryogenic valve; (5) current leads and joint; (6) instrumentation socket connector; (7) canister vent connection; (8) canister vacuum port connection; (9) structural rods for canister attachment. The structure of the probe is made with 9.5 mm stainless steel threaded rods and 12.7 mm thick G10 plates. The probe without the vacuum canister is shown in Figure 3-4. The top flange is a 50

25 mm thick G10 plate; it has several penetrations to accommodate instrumentation wires, vacuum and vent tubes, valve operation and current leads. The structure of the probe, made with 9.5 mm stainless steel threaded rods and 12.7 mm thick G10 plates, is attached to the inside side of the flange. A detail of the top flange is shown in Figure 3-5. Figure 3-5: Picture of the top flange of the probe. References: (1) sample current connector; (2) vapor cooled current leads; (3) instrumentation connector; (4) canister vent; (5) cryogenic valve handle; (6) canister vacuum tube; (7) instrumentation wires port. The current leads are composed of two parts: a vapor cooled current lead on the top, which carries current from outside the cryogenic area to the inside, above the liquid helium level; and a flexible current lead made with copper rope style cables that connects the bottom of the vapor cooled current leads to the superconducting sample immersed in the liquid helium space. The current leads are rated for 5 ka. For the joint between the current lead and the superconducting sample a copper piece with a slot and hole is used; a detail of this piece, with the rope current leads, is shown in Figure 3-6. During operation, the joint mechanically clamps the superconducting sample as shown in Figure 3-7; the stainless steel bolts used for clamping are electrically insulated to avoid a short circuit between the copper pieces. 51

Figure 3-6: Detail of the joint between the current leads and the sample. The sample is terminated in a copper tube that fits in the circular hole, and it can be clamped to reduce the electrical resistance of the joint. In the background, copper rope style current leads. Figure 3-7: Detail of the joint between the current leads and the sample, with the sample mounted. References: (1) sample termination; (2) copper joint; (3) G10 plate for clamping; (4) electrically insulated stainless steel bolts for clamping. 52

Figure 3-8: Instrumentation wires connectors and top flange of the vacuum canister. The sample and current return lead are mounted in place, and the epoxy (in blue) has already cured. Figure 3-9: Picture of the bottom joint. References:(1) instrumentation wires; (2) copper terminator; (3) vacuum canister; (4) bolts for holding bottom joint area cover; (5) sample; (6) current return lead. 53

The canister vent and vacuum tubes shown in Figure 3-1 are connected with fittings to tubes, shown in Figure 3-4 as number 7 and 8 respectively. This design allows the vacuum canister to be entirely separated from the rest of the probe if necessary. The vent tube is connected as well to a cryogenic valve (number 4), that can be operated from outside of the cryogenic area (Figure 3-5, number 6). Figure 3-10: Picture of the probe, assembled and prepared for an experiment. The instrumentation wires are tied to the canister. In Figure 3-8 the final view of the top flange of the vacuum canister is shown. The clearance between the top flange holes and the copper tubes of the sample and current return lead is filled with a G10 ring, and sealed with an epoxy (Stycast). The bottom joint consists in two copper pieces with cylindrical grooves that clamp 54

the bottom termination of the sample and the current return lead together. A picture of the bottom joint, prepared for operation, is shown in Figure 3-9. The final view of the probe, once it is assembled and prepared for an experiment, is shown in Figure 3-10. 3.2 Sample Construction The samples tested are composed of a 1090 mm long, 4 mm wide SuperPower SCS4050AP YBCO tape, two 7.9 mm outer diameter copper tube terminations (330 mm long for the top termination, 114 mm long for the bottom termination), and a metallic structural support. The YBCO tape and the metallic support are mounted inside the copper tubes. The tubes are filled with copper strips and 60 40 SnPb solder. The soldered length is 114 mm in both ends. The current return lead is constructed in the same way, with two YBCO tapes to increase its current capacity, and with two 0.3 mm thick, 1090 mm long, 4 mm wide copper strips in each side of the tape as structural support. In Figure 3-11 pictures of a sample and the current return lead are shown. Figure 3-11: Pictures of a sample and the current return lead, with sample holder. Left: detail of the top terminations. The soldered area is marked. Right: entire sample and current lead. The bottom copper tube is completely filled with solder and copper strips. The wooden ruler is 305 mm (12 ) long. Three samples were built, with different structural support mechanism, as shown in Figure 3-12. Sample #1 has 0.3 mm thick, 4 mm wide copper strips on either side, 55

Figure 3-12: Schematic drawing of the three different samples. The first one was supported by two copper strips, with insulated copper in the sample area to avoid current sharing. The second one was supported by one stainless steel strip, attached to the hastelloy side of the sample. The third one was supported by two copper strips, not insulated to improve current sharing. cut and insulated in the middle section to avoid current sharing. Tape MIT ID# 12-01C. Sample #2 had a 0.3 mm thick, 1090 mm long, 4 mm wide stainless steel strip for protection on the back side of the tape (i.e. the hastelloy side of the tape). Current sharing between the superconductor and the stainless steel strip is nominally possible, but is negligible due to the low electrical conductivity of steel and the high electrical conductivity of the terminations. Tape MIT ID# 12-01F. Sample #3 had a 0.3 mm thick, 1090 mm long, 4 mm wide copper strip in each side of the tape, without any insulation to reinforce current sharing between the superconductor and the copper. This design improves the thermal stability of the superconductor. For critical current measurements, the current sharing is negligible. At the criteria of 100 µv/m, at 30 K, the copper strips are expected to transport approximately 2 A, while the superconductor would transport around 800 A. Tape MIT ID# 12-03F. 56

3.3 Instrumentation During the experiment, the temperature of the sample must be measured and controlled, the level of liquid helium must be monitored and kept over a minimum height above the canister, and the voltage, current and magnetic field on the sample must be measured. Temperature sensors, heaters and voltage taps are mounted in the sample, as shown in Figure 3-13; a helium level sensor and a magnetic field sensor are mounted in other areas of the probe, as described below. Figure 3-13: (Top) Picture of the sample with instrumentation mounted. (Bottom) Schematic drawing of the sample, showing voltage taps (in black: V1, V2), heaters (red: H1, H2, H3) and temperature sensors (grey squares: A, B, C, D, E). For temperature measurement, five LakeShore Cernox temperature sensors were mounted along the sample for measurements of its temperature distribution. These temperature sensors are well suited for cryogenic temperature measurements at high magnetic fields (2 14 T). Sensors A, B, C, D (model number CX-1050-SD) are calibrated between 4 K and 100 K; sensor E (model number CX-1070-SD-HT) is calibrated between 4 K and 325 K. Sensors A, C and E were operated with a LakeShore 336 Temperature Controller (LS336-TC); sensors B and D were monitored with a LakeShore 218 Temperature Monitor (LS218-TM). The temperature of the sample was controlled with three 25 Ω heaters. Heater H1 and H3 are 150 mm long, heater H2 is 200 mm long. Heaters H1, H2 and H3 correspond loosely to the areas f 1, f 2 and f 3 in the thermal simulation; however, the length of the simulated heaters could not be reproduced due to mechanical limitations 57

of the materials. Temperature sensor A is used to control the power in heater H1; sensor C is used for heater H2, and sensor E is used for heater H3. The power sources are the LS336-TC (it has a 100 W output, and a 50 W output; each can be controlled with a PID loop using any of the temperature measurements as input) and a Keithley 2440 5A SourceMeter (K2440-SM, manually operated and limited to 1 A and 50 V). Two control mechanisms were considered: using the LS336-TC for heaters H1 and H3 and the K2440-SM for heater H2, and using the LS336-TC for heaters H2 and H3 and the K2440-SM for heater H1. Liquid helium level measurement in the canister was performed with a 914 mm long NbTi liquid helium level sensor, and a LakeShore silicon diode temperature sensor (model number DT-470-SD-12A). The NbTi level sensor is mounted along the current return lead, and measures the level of liquid inside the vacuum canister. The diode sensor is located just below the bottom electrical joint, and measures whether that area is in contact with liquid helium (if the temperature is 4.2 K) or not (if the temperature is higher). Additionally, liquid helium level measurements are implemented in the magnetic facilities, and during operation the helium level must be kept such that it completely covers the part of the sample that is outside the vacuum canister. For magnetic field measurements, a F. W. Bell bulk Indium transverse Hall sensor (model number BHT-021) was prepared. It was mounted outside the vacuum canister, on the wide rectangular face, 355 mm from the bottom of the vacuum canister. However, the magnet was not used in the experiments reported in this thesis, and there was no need for a magnetic field measurement. Voltage taps were soldered to the sample and current lead. The distance between the sample voltage taps (V 1 ) is 203 mm within ±3 mm; the distance between the sample control voltage taps (V 2 ) and between the current return lead control voltage taps (V 3 ) is in both cases 560 mm within ±5 mm. The voltage taps wires are twisted to avoid electromagnetic interference. Voltage was measured with Keithley 2182A Nanovoltmeters. The current in the sample was measured with a calibrated shunt, at room temperature, with a Keithley 2010 Multimeter. 58

Due to the low voltages that develop along the sample during critical current testing (tens to hundreds of µv), the voltage taps must be mounted in such a way that thermal voltages are avoided as much as possible. For that reason, there is only one connection for the voltage taps wires, inside the cryogenic area, and always covered in liquid helium to serve as a static reference temperature (see Figure 3-4, number 6); from that connection, the wires come out of the cryogenic area (through the port shown as number 3 in Figure 3-5) and are connected to the nanovoltmeters. The rest of the instrumentation handles much higher voltages: tens of mv to several V. Thermal voltages are not a problem in this case, and for convenience the wires of the rest of the instrumentation have two connectors: one in the cryogenic area just like the voltage taps, and another on the top flange (number 4 in Figure 3-5). 3.4 Experimental Setup The experiments were performed in the 2 T MIT-PSFC magnetic facility. However, due to a failure in the power supply of the magnet, the tests were performed without an external magnetic field. The facility has a 2 T magnet inside a double-layer dewar. In operation, the inner volume is filled with liquid helium, and the outer jacket is filled with liquid nitrogen to reduce radiation heat loss. The experiments are performed in the inner volume. In Figure 3-14 are shown the 2 T magnet and the dewar. Before mounting the probe inside the magnet dewar, the inside of the canister (that in operation must be filled with gaseous helium) was checked for leaks. To do this, the instrumentation wires were disconnected and placed in a plastic bag, which was in turn tightly taped to the bottom of the canister (Figure 3-15). The canister vent was used to input gaseous nitrogen inside the canister, and all the joints were checked for leaking nitrogen gas with Snoop Liquid. The instrumentation was connected and the probe mounted in the magnet dewar. The day before the experiment, liquid nitrogen was poured in both volumes of the dewar, and left overnight to cool all components down to 77 K. The day of the experiment, the liquid nitrogen left inside the inner layer of the dewar was pushed to 59

Figure 3-14: Picture of the dewar and 2 T magnet. References: (1) magnet; (2) liquid helium feed line; (3) dewar; (4) inner volume of the dewar; (5) outer volume of the dewar. the outer jacket by pressuring with nitrogen gas; after all liquid nitrogen was removed from the inner volume, liquid helium was transferred into the dewar. Two separate computers were used during the experiment. One collected data from the temperature monitors, and the other was used for critical current measurements. A 1 ka current supply was used to provide electrical current to the sample. The current supply was controlled with a remote controller that allows varying the current smoothly. During the first use, an unexpected interaction between the remote controller and the current supply provoked damage to samples #1 and #2. This interaction occurred when the remote controller sent a dump signal. Instead of immediately reducing the current to zero, the current supply responded with a sharp increase in current before going to almost zero amps. When operating at 640 A and dumping, the maximum current reached with this off-normal event is 760 A. This issue was resolved by adding an electronic adapter between the remote controller and the current supply. The adapter consists in a switch that either connects the remote 60

Figure 3-15: Setup to leak-check the inside of the vacuum canister controller to the current supply input, or connects the two current supply input terminals together, effectively dumping the supply s current to zero without an increase of current. In Figure 3-16 a detail of the current supply response to a dump signal is shown, before and after solving the issue. For each critical current measurement, a new temperature set point was chosen. Once the temperature was stable, and the difference between the temperatures measured by sensors B, C and D was as small as possible, typically ±1 K, the critical current measurement was performed. The current was increased slowly, at a rate of approximately 10 A/s, and voltage was measured. The current was dumped once any 61

Figure 3-16: Current supply response to a dump signal. The original problem was a current spike when a dump signal is sent. In this case, dumping at 640 A elevated the current to a maximum of 760 A (black curve). The overshoot lasts 0.4 s. After solving the problem, the dump signal does not provoke a current peak. one of the three voltages that were being monitored (sample voltage V 1, sample control voltage V 2, or current return lead control voltage V 3 ) reached a value equivalent to 1000 µv/m, or when the temperature started to increase due to joule heating in the sample. 62

Chapter 4 Experimental Results and Discussion Three liquid helium experiments were performed, one per sample. Samples #1 and #2 were damaged early in their experiments, as was mentioned in the previous chapter. Sample #3 was tested successfully, and the results for temperature control and critical current of this sample are presented below. In the first section details of the temperature control operation are given, with measurements of the time evolution of temperature, temperature difference between different points in the sample, and required heating power. The second section presents the results of critical current measurements at self-field results for sample #3. Finally, in the last section the interaction between temperature control and critical current measurement are shown, including the case of quenching samples #1 and #2. 4.1 Temperature Control As mentioned in section 3.3, two heater control methods were considered: Method #1: heater H1 and H3 controlled with a PI loop, using as input temperature sensors A and E respectively; and heater H2 controlled manually. 63

Method #2: heater H2 and H3 controlled with a PI loop, with sensors C and E as inputs (respectively); and heater H1 controlled manually. Using the control method #1, and starting with the vacuum canister filled with liquid helium, the temperature was first raised to 75 K and then gradually stepped down. The temperature evolved quickly when changing the set point, typically reaching the set point temperature within ±1 K in 10 15 minutes. In Figure 4-1 the temporal evolution of the temperature measured by sensor C is shown, for different set points. The quality of the temperature control is indicated by the difference between the set point and the measured temperature in the sample area (sensors B, C, and D) at the start of the critical current measurement, and is shown in Figure 4-2. The heating power required at each set point is shown in Figure 4-4. At 75 K, the total heating power required was 65 W, and 30 W at 20 K. Figure 4-1: Evolution of the temperature measured by sensor C as a function of time for different set points. The system reaches the set point temperature, within ±1 K, in 10 15 minutes. For each evolution the temperature set point is selected at time=0. The experiments with control method #2 were performed increasing the temperature from 4.2 K. The temporal evolution of the temperature after changing the set point was similar to the previous results, reaching the set point temperature in approximately 10 minutes. Since the sensor C was used as input for a PI loop, the temperature it measured at the start of the critical current measurement was almost 64

Figure 4-2: Difference between the measured and set point temperature as a function of set point temperature for the temperature control method #1. The curves are marked B, C, D for the three temperature sensors located on the sample as shown in Figure 3-13. Figure 4-3: Difference between the measured and set point temperature as a function of set point temperature for the temperature control method #2. The curves are marked B, C, D for the three temperature sensors located on the sample as shown in Figure 3-13. 65

Figure 4-4: Heating power required as function of temperature for the temperature control method #1. The curves are marked H1, H2, H3 for the three heaters mounted on the sample as shown in Figure 3-13. Figure 4-5: Heating power required as function of temperature for the temperature control method #2. The curves are marked H1, H2, H3 for the three heaters mounted on the sample as shown in Figure 3-13. 66

exactly the set point temperature after 10 minutes, as shown in Figure 4-3; at the same time, the temperature measured by sensors B and D was within ±1 K of the set point. The required heating power as function of set point temperature is presented in Figure 4-5. The total heating power required at 70 K was 60 W, and 25 W at 20 K. Control method #2 provides a very accurate temperature measurement (sensor C), while control method #1 does not. The maximum difference between temperatures in the sample measurement area is lower for control method #2 at lower temperatures; however, at 70 K the difference between temperatures B and D with control method #2 is almost 2 K, while with control method #1 the maximum temperature difference at 75 K as approximately 1.2 K. Figure 4-6: Comparison of axial temperature distribution simulated and measured. The simulated data was obtained for shape factors f 1 =1.13, f 2 =0.03, f 3 =0.87 and total power 13 W. The experimental data was obtained with the temperature control method #2, and set point 70 K. The white squares in the experimental data series represent the boundaries of the vacuum canister. Those points were not measured but are assumed to be at liquid helium temperature. The heating power required during the experiment was much higher than that was calculated in section 2.3. This is due to the difference in the heater distribution assumed for the thermal simulation, and the real heater distribution as constructed. The total length of the constructed heaters is 500 mm, while the simulated heaters 67

span 150 mm. This gives rise to a different temperature profile, with increased heat losses, as shown in Figure 4-6. In that example, the required total heating power to achieve 70 K in the sample area was 13 W, while during the experiment the heating power required was 60 W. In order to obtain a smaller power requirement, the heaters must be modified to reduce their total length. This can be achieved by using a different wire, with higher resistance per unit length. To obtain a better temperature control quality, one additional PI power controller is necessary, as well as also changing the control inputs for heaters H1 and H3 to sensors B and D, respectively. 4.2 Critical Current Measurements For each set point temperature, the critical current measurements of sample #3 were performed once the temperature was stable (about 10 15 minutes after the set point change, as mentioned in the previous section). For the measurements between 20 K and 60 K temperature control method #1 was used, and method #2 was used for the measurement at 70 K. The current ramping up rate was kept between 2 A/s and 4 A/s. Voltage current results for sample #3 at self-field and temperatures between 20 K and 70 K are shown in Figure 4-7 in linear scale, and in Figure 4-8 in logarithmic scale. In those figures, the 20 K curve showed a slight change of slope at 40 µv/m due to a temperature control problem. Critical current at 100 µv/m and n-value are shown as function of temperature in Figure 4-9. The uncertainties of the critical current measurement are negligible. The uncertainties of the temperature measurement are due to the temperature distribution along the sample area, as shown in Figures 4-2 and 4-3, and to the variation of temperature during the critical current measurement, as described in section 4.3. In all cases, the temperature uncertainty is approximately ±1 K. The n-value does not have an uncertainty associated, and was calculated with two methods: Two point method: from the value of critical current at 100 µv/m (I 100 ) and 68

Figure 4-7: V I curves of a single 4 mm wide Super Power YBCO tape, measured at self-field and temperatures from 20 K to 70 K. Figure 4-8: V I curves of a single 4 mm wide Super Power YBCO tape, measured at self-field and temperatures from 20 K to 70 K in log-log scale. 69

Figure 4-9: The critical current at 100 µv/m and n-value of a single 4 mm wide SuperPower YBCO tape as a function of temperature. Uncertainties in critical current are negligible. Uncertainties in temperature are represented by the size of the plot markers. Figure 4-10: Critical current at self-field normalized to the value at 77 K, self-field, as a function of temperature measurements for a single SuperPower YBCO tape. SuperPower data of normalized critical current at self-field as a function of temperature is shown for comparison. Uncertainties in the critical current measurement are negligible. Uncertainties in the measured temperature are represented by the size of the plot markers. 70

at 10 µv/m (I 10 ) the n-value was calculated as: n = [ log ( I100 I 10 )] 1 (4.1) Curve fitting method: a power law was fitted to the data using a Matlab routine, and the n-value is the exponent of the current in the regression. In Figure 4-9 the dependence of the n-value with temperature showed a minimum at 40 K. Further investigation is required to understand this phenomenon better. The critical current can be compared to the superconductor s manufacturer s data. In Figure 4-10 normalized critical current as a function of temperature at self-field for sample #3 is compared to the manufacturer s data of a similar tape. The critical current was normalized to the value in liquid nitrogen, self-field. The critical current for sample #3 at 77 K was not measured, but extrapolated from the data in Figure 4-9. The value obtained is 102 A, which is consistent with manufacturer s data for the YBCO spool used. As shown in that figure, the normalized critical current of sample #3 is very similar to the manufacturer s data. 4.3 Current Temperature Interaction The temperature of the sample slightly varies when approaching the critical current. For sample #1, at self-field in liquid nitrogen, reaching critical current increases the sample temperature about 3 mk, as shown in Figure 4-11. The temperature measurement resolution was 0.8 mk. The peak current achieved was 113 A at approximately 260 µv/m, and this gives rise to a joule heating in the sample of 30 mw/m. In gaseous helium, for a set point of 40 K and using temperature control method #1, the temperature of sample #3 increases approximately 1 K, as shown in Figure 4-12. The peak current achieved was 611 A at 1360 µv/m, and this gives rise to a joule heating in the sample of 800 mw/m. The temperature sensors B, C and D show that the sample temperature gradually decreases as the sample current is increased, and then the temperature increases at the critical current similarly to that shown in 71

Figure 4-11: Temperature and voltage measurements as a function of time, while performing critical current measurements for a single SuperPower YBCO tape, in liquid nitrogen (77 K) and self-field. The temperature measurement resolution is 0.8 mk. Figure 4-12: Temperature and voltage measurements as a function of time, while performing critical current measurements for a single SuperPower YBCO tape, in gaseous helium at 40 K and self-field. 72

Figure 4-13: Temperature runaway and quench of sample #1. The temperature rises very quickly, in a few seconds, and surpasses 100 K. The calibration limit of sensor D was 100 K. Figure 4-14: Temperature runaway and quench of sample #2. The temperature rises very quickly, in less than a second, and it reaches about 240 K. Sensor C was not as precisely calibrated above 100 K as it was between 4 K and 100 K; the calibration error for temperatures higher than 100 K might be a few degrees kelvin. 73

Figure 4-11. The initial reduction of temperature shown in Figure 4-12 (at 2 4 min) is due to joule heating of the bottom joint proportional to the square of the sample current (I). This forces a reduction of the bottom heater power by the bottom heater controller. As current increases, a voltage is developed along the superconducting sample (at 4 5 min), and a distributed heating power (proportional to I n+1 ) gives rise to an increase of temperature along the sample. The joule heating in the gaseous helium case was about 25 times higher than in the liquid nitrogen case, but the temperature difference was 300 times higher due to the worse cooling properties of gaseous helium, compared to liquid nitrogen. Figure 4-15: Picture of sample #1 after quench. A kink is observed at 260 mm (10.25 ) from the bottom of the sample, close to the location of temperature sensor D. The temperature increase for samples #1 and #2 while testing in gaseous helium was uncontrolled, due to the current supply interaction with the remote controller, as mentioned in section 3.4. In Figures 4-13 and 4-14 the temperature runaway for samples #1 and #2 (respectively) is shown. The temperature rose very quickly, in 2 5 seconds; however, the cool down of the sample back to the initial temperature took much longer, from 25 seconds to about a minute, due to the poor cooling characteristics of gaseous helium. 74

Figure 4-16: Picture of sample #2 after quench. Two damaged zones are observed: one at 400 mm (16 ) from the bottom of the sample, between temperature sensors B and C, and the other at 265 mm (10.5 ), close to the location of sensor D. During the temperature runaway the voltage measurement devices were off-line, probably because the measurement range was not as larger as the large voltage developed in the sample. After the thermal runaway incidents, samples #1 and #2 were found to be completely resistive upon ramping up the current from zero. An inspection of the samples after the quench showed physical damage to them, as shown in Figures 4-15 and 4-16 for samples #1 and #2 respectively. Sample #1 had a kink, close to the location of sensor D, and the insulating teflon tape that covered the structural copper strip in that area was blackened. Sample #2 had two completely burned zones, one at the position of sensor D and another between sensors C and B; in this case, the temperature reached during the quench was enough to melt the cross section of the superconductor. While performing critical current measurements in a controlled temperature environment, the additional heating from the sample itself must be taken into account, and current must be controlled very precisely. The additional heating may increase the temperature only a few milikelvin, as shown in Figure 4-11, or several hundreds of kelvin, as in Figure 4-14. In order to prevent this in future test, the sample should be stabilized by adding extra copper in thermal and electrical contact with the sample. 75