Superconducting magnets used for Magnetic Resonance Imaging (MRI) scanners need to keep temperature gradients minimized in order to retain thermal and operating current margin. We have used 3D finite element analysis (FEA) simulation in COMSOL Multiphysics software that includes both conductive heat transfer and radiative heating to calculate the temperature distribution both along the winding direction and across the cross-section of an MRI segment coil at its equilibrium operating temperature. We have also modelled the evolution of the thermal properties during cool-down from ambient temperature. The heat capacity and thermal conductivity of the magnet winding were computed for use within this simulation. The heat capacity as a function of temperature was calculated using a rule of mixtures. This procedure was also used for the thermal conductivity along the direction of the wire. However, the thermal conductivity within the composite cross section (x- and y-directions) was computed using a 2D FEA model. Based on this, a time-dependent, 3D coil model was built to calculate the coil temperature throughout the winding during cool-down in our test cryostat system. The model included a heat leak component to the coil current contacts via conduction through the current leads as well as a radiative component from the surfaces of the cryostat. A key result was that a maximum coil ΔTmax = 5.1 K (=maximum temperature within the winding -minimum temperature in the winding) was seen and a coil Ic margin of 12.75 A was predicted at steady state, with our first current lead design. A second set of more optimized current leads significantly lowered the ΔTmax within the coil at the steady state. The coil Ic margin has been analyzed for different current lead designs.

The active quench protection of a 1.5 T MgB2 conduction-cooled MRI magnet operating in persistent current mode is considered. An active quench protection system relies on the detection of the resistive voltage developed in the magnet, which is used to trigger the external energizing of quench heaters located on the surfaces of all ten coil bundles. A numerical integration of the heat equation is used to determine the development of the temperature profile and the maximum temperature in the coil at the origin, or 'hot spot', of the quench. Both n-value of the superconductor and magnetoresistance of the wire are included in the simulations. An MgB2 wire manufactured by Hyper Tech Research, Inc. was used as the basis to model the wire for the simulations. With the proposed active quench protection system, the maximum temperature was limited to 200 K or less, which is considered low enough to prevent damage to the magnet. By substituting Glidcop for the Monel in the wire sheath or by increasing the thermal conductivity of the insulation, the margin for safe operation was further increased, the maximum temperature decreasing by more than 40 K. The strain on the MgB2 filaments is calculated using ANSYS, verifying that the stress and strain limits in the MgB2 superconductor and epoxy insulation are not exceeded.

This paper describes a detailed design of a 6-T Nb 3 Sn superconducting racetrack coil designed for conduction cooling. We then describe a bench test pursued as a proof of concept for one winding of an actively shielded air-core electric machine with superconducting field windings. Electromagnetic design selection is drawn from previous optimization work. The coil former design is then discussed. Numerical simulations of thermal and structural features are pursued to determine temperature distribution and strain within the winding. A coil instrumentation and experimental setup of a quasi-conduction cooled system is described. Finally, test results are presented; a maximum critical current of 480 A was reached at a peak temperature of 7.9 K, surpassing the operational current goal of 435 A. Future work and planned improvements to the test setup are discussed.

The effect of magnetoresistance, magnetothermal conductivity (MTC), and RRR value on the active quench protection of a persistent-mode conduction-cooled 1.5 TMgB2 superconducting magnet is studied using numerical simulation. It is found that inclusion of magnetoresistance in the simulation can significantly decrease the calculated maximum temperature reached in this magnet during a quench, e.g., by 9K for RRR = 100. The inclusion of both magnetoresistance and MTC similarly decreases the peak temperature, but by a smaller amount, e.g., by 7 K for RRR = 100. Using copper with a lower RRR value can also significantly decrease the peak temperature reached in this magnet, e.g., by 16 K for RRR = 50 as compared to RRR = 200. However, decreasing the RRR value to much less than 50 results in a significantly higher voltage, e.g., decreasing the RRR value from 50 to 10 results in a 1000 V increase. A RRR value between 50 and 100 may provide a good balance.

The winding of composite superconducting wire around a mandrel is one of the first stages of manufacturing processes of a superconducting magnet. Depending on the method of mechanical support conditions during winding, the strain development at the final stage in a superconducting magnet may vary significantly. Therefore, proper selection of the winding process is important to increase the feasibility for a conduction cooled full body MRI magnet based on magnesium diboride (MgB2), a strain sensitive high-temperature superconductor. A multiscale multiphysics finite element analysis) model of an 18 filament MgB2 wire is developed for strain estimation. The computationally homogenized representative volume element of the composite wire is used in the coil bundle in place of the actual MgB2 wire. The simulation considers winding, thermal cool-down and electromagnetic charging to estimate total strain developed at the final step—electromagnetic charging. Four different types of support conditions are studied and strain development is reported. Results suggest that a combination of radial and axial support at the inner radial surface and outermost axial surfaces of the mandrel, respectively, is the most favorable winding condition with a minimum strain development of 0.021%, which is half in comparison to no mandrel support.

Conceptual designs of 1.5 and 3.0 T full-body magnetic resonance imaging (MRI) magnets using conduction cooled MgB2 superconductor are presented. The sizes, locations, and number of turns in the eight coil bundles are determined using optimization methods that minimize the amount of superconducting wire and produce magnetic fields with an inhomogeneity of less than 10 ppm over a 45 cm diameter spherical volume. MgB2 superconducting wire is assessed in terms of the transport, thermal, and mechanical properties for these magnet designs. Careful calculations of the normal zone propagation velocity and minimum quench energies provide support for the necessity of active quench protection instead of passive protection for medium temperature superconductors such as MgB2. A new 'active' protection scheme for medium Tc based MRI magnets is presented and simulations demonstrate that the magnet can be protected. Recent progress on persistent joints for multifilamentary MgB2 wire is presented. Finite difference calculations of the quench propagation and temperature rise during a quench conclude that active intervention is needed to reduce the temperature rise in the coil bundles and prevent damage to the superconductor. Comprehensive multiphysics and multiscale analytical and finite element analysis of the mechanical stress and strain in the MgB2 wire and epoxy for these designs are presented for the first time. From mechanical and thermal analysis of our designs we conclude there would be no damage to such a magnet during the manufacturing or operating stages, and that the magnet would survive various quench scenarios. This comprehensive set of magnet design considerations and analyses demonstrate the overall viability of 1.5 and 3.0 T MgB2 magnet designs.

Magnetic Resonance Imaging (MRI) background magnets are made from superconducting composite wires that are a metal matrix composite (MMC). Thermal and mechanical properties of the specific wire matrix must be known to optimize the wire configuration for MRI magnet designs. Computational analysis techniques based on numerical homogenization may provide an accurate characterization of a multifilament MMC wire and can reduce the expenses and time required for experimental tests. Recent developments in magnesium diboride (MgB2) superconducting wire has demonstrated their feasibility in a liquid helium (LHe) free conduction-cooled MRI magnet. Computational analysis of an entire superconducting magnet design requires the elastic and thermal properties of these wires. In this work, the temperature dependent elastic modulus, Poisson’s ratio, thermal expansion coefficients, thermal conductivity, and specific heat are estimated using Finite Element Analysis (FEA) and compared to analytical approaches. The orthotropic elastic and thermal properties of four different superconducting composite wire configurations are evaluated. The experimental thermal conductivity and specific heat at room temperature agree well with its corresponding computational results. FEA based computational homogenization has been demonstrated as an acceptable method to estimate the required material properties of the MMC superconducting wire for magnet analysis of MRI manufacturing and operation.

This paper describes a detailed design of a 6 Tesla Nb3Sn superconducting racetrack coil designed for conduction cooling. We then describe a bench test pursued as a proof of concept for one winding of an actively-shielded, air core electric machine with superconducting field windings. Design selection from a previously computed pareto-optimal front as well as electromagnetic performance of the test coil is discussed. The winding and support structure design is discussed. Analysis of the thermal performance is carried out to verify required temperatures given the cryostat and cryocooler setup. Finally, a strain analysis is performed in order to verify that the superconducting windings are within an acceptable strain level to avoid mechanical breakage as well as excessive degradation of the critical surface. Additionally, the structural integrity of the support components is verified. Test procedures and preliminary results are described.

High temperature superconductors such as MgB2 focus on conduction cooling of electromagnets that eliminates the use of liquid helium. With the recent advances in the strain sustainability of MgB2, a full body 1.5 T conduction cooled magnetic resonance imaging (MRI) magnet shows promise. In this article, a 36 filament MgB2 superconducting wire is considered for a 1.5 T full-body MRI system and is analyzed in terms of strain development. In order to facilitate analysis, this composite wire is homogenized and the orthotropic wire material properties are employed to solve for strain development using a 2D-axisymmetric finite element analysis (FEA) model of the entire set of MRI magnet. The entire multiscale multiphysics analysis is considered from the wire to the magnet bundles addressing winding, cooling and electromagnetic excitation. The FEA solution is verified with proven analytical equations and acceptable agreement is reported. The results show a maximum mechanical strain development of 0.06% that is within the failure criteria of -0.6% to 0.4% (-0.3% to 0.2% for design) for the 36 filament MgB2 wire. Therefore, the study indicates the safe operation of the conduction cooled MgB2 based MRI magnet as far as strain development is concerned.

To reduce the usage of liquid helium in MRI magnets, magnesium diboride (MgB2), a high temperature superconductor, has been considered for use in a design of conduction cooled MRI magnets. Compared to NbTi wires the normal zone propagation velocity (NZPV) in MgB2 is much slower leading to a higher temperature rise and the necessity of active quench protection. The temperature rise, resistive voltage, and NZPV during a quench in a 1.5 T main magnet design with MgB2 superconducting wire was calculated for a variety of wire compositions. The quench development was modeled using the Douglas–Gunn method to solve the 3D heat equation. It was determined that wires with higher bulk thermal conductivity and lower electrical resistivity reduced the hot-spot temperature rise near the beginning of a quench. These improvements can be accomplished by increasing the copper fraction inside the wire, using a sheath material (such as Glidcop) with a higher thermal conductivity and lower electrical resistivity, and by increasing the thermal conductivity of the wire’s insulation. The focus of this paper is on the initial stages of quench development, and does not consider the later stages of the quench or magnet protection.

To reduce the usage of liquid helium in MRI magnets, magnesium diboride (MgB2), a high temperature superconductor, has been considered for use in a design of conduction cooled MRI magnets. Compared to NbTi wires the normal zone propagation velocity (NZPV) in MgB2 is much slower leading to a higher temperature rise and the necessity of active quench protection. The temperature rise, resistive voltage, and NZPV during a quench in a 1.5 T main magnet design with MgB2 superconducting wire was calculated for a variety of wire compositions. The quench development was modeled using the Douglas-Gunn method to solve the 3D heat equation. It was determined that wires with higher bulk thermal conductivity and lower electrical resistivity reduced the hot-spot temperature rise near the beginning of a quench. These improvements can be accomplished by increasing the copper fraction inside the wire, using a sheath material (such as Glidcop) with a higher thermal conductivity and lower electrical resistivity, and by increasing the thermal conductivity of the wire's insulation. The focus of this paper is on the initial stages of quench development, and does not consider the later stages of the quench or magnet protection.

Main magnets for magnetic resonance imaging (MRI) are largely constructed with low temperature superconducting material. Most commonly used superconductors for these magnets are niobium-titanium (NbTi). Such magnets are operated at 4.2 K by being immersed in a liquid helium bath for long time operation. As the cost of liquid helium has increased threefold in the last decade and the market for MRI systems is on average increasing by more than 7% every year, there is a growing demand for an alternative to liquid helium. Superconductors such as magnesium-diboride (MgB2) and niobium-tin (Nb3Sn) demonstrate superior current carrying quality at higher critical temperatures than 4.2 K. In this article, electromagnetic designs for conduction cooled main magnets over the range of medium field strengths (1.5 T) to ultrahigh field strengths (7.0 T) are presented. These designs are achieved by an improved functional approach coming from a series of developments by the present research group and using properties of the state-of-the-art second generation MgB2 wires and Nb3Sn wires developed by Hyper Tech Research Inc. The MgB2 magnet designs operated at different field strengths demonstrate excellent homogeneity and shielding properties at an operating temperature of 10 K. At ultrahigh field, the high current density on Nb3Sn allowed by the larger magnetic field on wire helps to reduce the superconductor volume in comparison with high field NbTi magnet designs. This allows for a compact magnet design that can operate at a temperature of 8 K. Overall, the designs created show promise in the development of conduction cooled dry magnets that would reduce dependence on helium.

Main magnets for magnetic resonance imaging (MRI) are largely constructed with low temperature superconducting material. Most commonly used superconductors for these magnets are niobium-titanium (NbTi). Such magnets are operated at 4.2 K by being immersed in a liquid helium bath for long time operation. As the cost of liquid helium has increased threefold in the last decade and the market for MRI systems is on average increasing by more than 7% every year, there is a growing demand for an alternative to liquid helium. Superconductors such as magnesium-diboride (MgB2) and niobium-tin (Nb3Sn) demonstrate superior current carrying quality at higher critical temperatures than 4.2 K. In this article, electromagnetic designs for conduction cooled main magnets over the range of medium field strengths (1.5 T) to ultrahigh field strengths (7.0 T) are presented. These designs are achieved by an improved functional approach coming from a series of developments by the present research group and using properties of the state-of-the-art second generation MgB2 wires and Nb3Sn wires developed by Hyper Tech Research Inc. The MgB2 magnet designs operated at different field strengths demonstrate excellent homogeneity and shielding properties at an operating temperature of 10 K. At ultrahigh field, the high current density on Nb3Sn allowed by the larger magnetic field on wire helps to reduce the superconductor volume in comparison with high field NbTi magnet designs. This allows for a compact magnet design that can operate at a temperature of 8 K. Overall, the designs created show promise in the development of conduction cooled dry magnets that would reduce dependence on helium.

Introduction: With a threefold increase in helium price over the last 10 years, and nearly a 7% annual increase in the MRI market, a drive towards helium free MRI magnet design is at the forefront of the hardware research. A superior critical current density characteristic of magnesium diboride (MgB2) at 10-15K temperature has made it a good candidate for conduction cooled magnet design. Different designs are proposed and developed for conduction-cooled magnet using MgB2 tape [1] and wire [2,3]. Most of these designs deal with low-field (generally 0.5T or less) magnets due to limitations of MgB2 wire technology. Designing a magnet of higher strength would require a current density on wire that would not exceed the critical field on wire at operating temperature range. A small bore test coil bundle for 3T magnet has been designed and tested recently [3]; however, a complete 3T full body MgB2 shielded magnet is yet to be built or even designed. An optimized design for 3T main magnet for whole body MRI using the second generation of MgB2 wire developed by Hyper Tech research, Inc. is presented in this paper. Theory and Method: An improved functional approach that achieves optimized design by nulling external moments along with a certain series of internal moments of the magnetic fields [4] is used to design an actively shielded magnet. A continuous current distribution is obtained for the magnet design using the aforementioned functional method. A first approximation for the position of discretized coil bundles carrying constant current through 1mm is achieved from this continuous solution. These discrete bundle positions are then optimized again using the same functional to achieve desired magnet properties. The particular challenge in discretizing MgB2 is to ensure that the current is limited such that the maximum field on wire of any bundle does not exceed the critical value yet sufficient field homogeneity inside the DSV and a small enough 5-Gauss footprint are maintained. Results: Figure 1 shows the three-dimensional layout of the newly designed 3T MgB2 magnet. It has 4 pairs of primary coils and 1 pair of secondary coil. The magnet has an inner and outer diameter of 1.1m and 2.15m and length of 1.8m. These dimensions are similar to typical 3T NbTi magnet [5]. A 45cm DSV is considered. Figure 2 shows the peak-to-peak field homogeneity inside the DSV. The maximum inhomogeneity for the design is 11 ppm. The MgB2 wire cross-section is considered to be 1mm 2 and carries 101 Amps current. The highest field on wire is found to be 5.15 Tesla, which is sufficiently below the critical field of more than 6T at 10K. Figure 3 shows the 5-Gauss contour that extends 3.5m radially and 4.4m in axial direction. The highest hoop stress on the wire is approximately 336MPa and the highest for a bundle is 80MPa. Maximum axial force on the bundle is about 7131kN. The total volume of the coil is calculated to be 0.438m. Discussion: An actively shielded 3T MgB2 main magnet design is presented that could operate at 10-15K temperature as conduction cooled dry magnet. The 45cm DSV shows a few ppm higher inhomogeneity than a conventional 3T magnet. The 5-Gauss footprint area is about 15% larger than the typical design due to bigger outer diameter of the shield coil of magnet design. The latest manufacturing guidelines available to us indicate that these hoop stresses and axial forces represent technological challenges but not insurmountable ones. The total volume of the wire for the magnet is large due to the lower current level resulting from the critical field-on-wire restriction. This translates into higher inductance and higher energy for the design. Further improvements in wire design are expected in the future that will increase the critical B field by optimizing the copper-MgB2 ratio. These will reduce the wire volume and energy of the design. Acknowledgement: The authors are grateful for the support of the Ohio Third Frontier and an NIH grant 5R44CA144415-03, References : [1] Alessandrini, M., et al, IEEE Trans. Appl. Supercond., 17, 2, pp 2252-57, 2007, [2] Park, K., et al, IEEE Trans. Appl. Supercond., 22, 3, p 4400305, 2012, [3] Li, X., et al, IEEE Trans. Appl. Supercond., 21, 3, pp1616-19, 2011, [4] Mine, S., IEEE Trans. Appl. Supercond., 22, 2, p 4400604, 2012, [5] Cheng N., MAGMA, 16, pp 57-67, 2003, [6] Wang, Z., Physics C: Superconductivity, 482, pp 80-6, 2012.