Text: Superconductivity Superconductivity is a phenomenon which occurs in certain materials and is characterized by the absence of electrical resistivity. Until recently, this phenomenon had been restricted to metals and alloys with transition temperatures of less than 23K. In 1986, superconductivity was discovered in a ceramic material. This precipitated an onrush of ceramic based superconductors with transition temperatures as high as 120K. The ceramic-based materials are commonly known as high temperature (HTc) superconductors while the metallic and alloy materials are called low temperature (LTc) superconductors. Currently, only low temperature superconductors are of interest to the magnet designer and manufacturer. Superconductors are divided into two types depending on their characteristic behavior in the presence of a magnetic field. Type I superconductors are comprised of pure metals, whereas Type II superconductors are comprised primarily of alloys or intermetallic compounds. Both, however, have one common feature: below a critical temperature, Tc, their resistance vanishes. The critical temperature at which the resistance vanishes in a superconductor is reduced when a magnetic field is applied. The maximum field that can be applied to a superconductor at a particular temperature and still maintain superconductivity is call the critical field, or Hc. This field varies enormously between Type I and Type II superconductors. The maximum critical field (Hc) in any Type I superconductor is about 2000 Gauss (0.2 Tesla), but in Type II materials superconductivity can persist to several hundred thousand Gauss (Hc2). At fields greater than Hc in a Type I superconductor and greater than Hc2 in a Type II superconductor, the conductor reverts to the normal state and regains its normal state resistance. A Type I superconductor excludes the applied magnetic field from the center of the sample by establishing circulating currents on its surface that counteract the applied field. Type II superconductors, however, permit the field to penetrate through the sample in quantized amounts of flux. These quanta are comprised of circulating vortices of current and the flux contained in the vortices. The total flux in a vortex is 2 x 10-7 Gauss-cm2. Great numbers of these vortices, or fluxoids as they are frequently called, can exist in a superconductor. For example, at a field intensity of 80 kilogauss (8 Tesla) there are 4 x 1011 fluxoids/cm2. These fluxoids and their interactions with defects in the superconductor give rise to the high current carrying capabilities of superconducting magnets. Flux Pinning and Flux Flow Properties of superconducting materials are altered locally by the presence of defects in the materials. A fluxoid encompassing or adjacent to such a defect in the material has its energy altered and its free motion through the superconductor is inhibited. This phenomenon, known as flux pinning, causes a field gradient in the superconductor and gives rise to a net current in the material. In the absence of defects in a Type II superconductor, no bulk current can be conducted without a transition into the normally conducting resistive state. Since the pinning force is small, fluxoids can be broken loose from their pinning centers, resulting in a net creep of the flux through a conductor as a function of time. This results in an effective voltage in a Type II superconductor. If the current density is low and the magnetic field is not intense, flux creep is insignificant and the induced voltage and effective resistance of the conductor will be essentially zero. At very high fields and high current densities, fluxoids will migrate rapidly, giving rise to a phenomenon called flux flow. Conductor Phenomena The maximum pinning force and the maximum current density sustainable by a conductor increases with reduced temperature. Similarly, as the magnetic induction, B, increases, the sustainable current density decreases. Consequently, the current density, magnetic field, and critical temperature are all interdependent. By increasing any of these parameters to a sufficiently high value, superconductivity can be destroyed and the conductor will revert to a normal, non-superconducting state. One of the most crucial factors in determining the performance of the final magnet is the design of the conductor. This design affects the ultimate field achieved by the magnet, the rate at which the magnet can be energized and the drift rate in the persistent mode of operation. Several phenomena observed in magnets are caused by the conductor itself. One of the earliest phenomena observed in superconducting magnets wound with single filament conductors was flux jumping. This phenomena arises from current induced in the conductor by the presence of the transverse field generated by the magnet. If a superconductor is placed transverse to the magnetic field, currents are induced in the conductor which shield the bulk of the conductor from the external magnetic field. These circulating currents extend for a finite length along the conductor, flowing in one direction on one side of the conductor and returning on the other side to complete the circuit. If the heat produced by the penetration of the magnet field into the superconductor cannot escape to the surface rapidly enough, then the temperature increase inside the superconductor triggers a runaway condition known as a flux jump. Consequently, the conductor is driven into the resistive state at fields and currents low in comparison with the critical values. Resistive heat is then dissipated in the small normal zone which increases in temperature causing the normal zone to expand and propagate both along the length of the conductor and transverse to it. This results in the magnet being discharged as the energy in the magnet is dissipated in the resistive portion of the conductor. To decrease the problem of transition to the normal state, it is common practice to shunt the conductor with a low resistivity normal metal by embedding the superconductor in a copper matrix to form a composite conductor. The copper provides additional heat capacity as well as providing a path for the magnet current while the superconductor is driven normal during a flux jump. If the resistance of the copper is low enough, the temperature of the conductor can remain below the critical temperature at the ambient field, and superconductivity will resume after the currents in the superconductor have decayed. Embedding the superconductor in a low resistivity metal matrix is effective in reducing the chance of a flux jump which can cause a magnet quench. Magnets constructed with this type of material are dissipative and the heat generated during a flux jump must be conducted to the helium bath. Thus, the magnetic field must be changed slowly to allow time for the heat to be conducted to and dissipated in the liquid helium. Also, the diamagnetic currents in the superconductor contribute to the field generated by the magnet and can reduce its homogeneity. If, instead of one superconducting filament, many fine filaments of superconductor are used, the heat generated in individual filaments can easily be conducted a short distance to the filament surface thus avoiding flux jumps. Consequently, conductors are made in which many fine filaments of superconductor are coextruded and drawn in a matrix of either copper or aluminum stabilizers. Although this has the desired effect of avoiding flux jumping, circulating currents can again be formed if the conductors are parallel in the highly conductive normal matrix. In this case, the circulating current is between two or more filaments in parallel and the current crosses over through the normally conductive matrix. This gives rise to diamagnetism and unequal distribution of currents in the filaments that limits the rate at which the magnet can be charged. Problems arising from constructing the superconductor from filaments have been largely circumvented in modern conductors by twisting the filaments in the conductor. This causes the flux from the external magnetic field to be alternated through successive superconducting filaments, thereby reducing the unequal distribution of currents between the superconducting filaments and reducing the diamagnetism of the conductor. This reduction in diamagnetism or hysteresis has two desirable effects. First, it reduces the amount of energy dissipated in the magnet and permits it to be charged more rapidly. Secondly, the reduced diamagnetism causes the current in the magnet and the magnetic field generated by the magnet to be more linearly related. Such conductors are known as intrinsically stabilized conductors. Magnet Phenomena Many factors must be considered when designing a superconducting magnet to assure its proper performance. These factors include the mechanical structure of the magnet, the magnetic field design and the design of the conductor to be used. It is also important that the magnet be able to withstand the mechanical stresses caused by the magnetic and thermally induced forces encountered during normal operation, and the electrical voltages encountered during a quench. The following paragraphs provide a brief review of some of the more important topics which will assist you in selecting a magnet. Quenching An important phenomenon in superconducting magnets is quenching. Any superconducting magnet can be quenched by increasing the current and field indiscriminantly. A quench in a well encapsulated magnet typically occurs at the location of the highest field in the magnet. Resistance is restored to the conductor at this point and heating occurs in the magnet. This heat spreads to adjacent areas and drives more of the conductor normal, and the normal zone continues to spread until the magnet is completely discharged. If the resistance across the terminals of the magnet due to the power supply is low, the power supply may be ignored to a first approximation in analyzing a quench. Thus, the quench may be viewed as the discharge of an inductor into a time varying resistance. The resistive voltage, iR, is counteracted by an inductive voltage, Ldi/dt. Unlike the few volts used in charging the magnet, the voltages encountered during a quench discharge can be measured in kilovolts. Initially, the iR voltage is confined to the layers of windings near the point where the quench initiated and internal arcing can occur between layers if sufficient insulation has not been provided. During a quench a magnet can be damaged by high voltage, high temperature, and high forces. The magnet manufacturer takes all of these issues into consideration as part of the design. Although the magnet is designed to withstand an occassional accidental quench, quenches can shorten the useful life of the device. Training The heat capacities of the materials in a superconducting magnet at 4K are several orders of magnitude lower than the heat capacities of the same materials at room temperature. Thus, a small amount of heat dissipated inside the magnet can raise the temperature of the conductor above its critical temperature at the ambient field and current density. One source of heating is wire motion caused by the Lorentz force on the conductor in the magnet. Imperceptible motions of the wire can result in frictional heating sufficient to drive the conductor normal at fields well below the anticipated maximum field of the magnet. Upon reenergizing the magnet, it is frequently observed that it will "train" to successively higher fields before quenching, ultimately achieving the design field. In some cases, the wires will remain in their shifted positions and the magnet will perform well. In other cases, however, retraining is required after the magnet is warmed to room temperature. To avoid this training effect, it is necessary that the conductors be securely bonded in place to prevent them from moving. Bonding the conductor in the magnet entails a substantial risk in that the conductor cannot be recovered and reused after it has been bonded in place. Since thermal conductivities are very low at these temperatures, the material used to bond the conductor also limits the thermal conductivity of the magnet. Consequently, the effects of wire motion are amplified in that the heat generated is less effectively dissipated to the liquid helium. The conductors in most laboratory sized magnets are bonded with epoxy. Most AMI magnets are wet wound using a filled high thermal conductivity epoxy that is too viscous for vacuum impregnation. Since each turn of the windings is visible as the magnet is being wound, voids in the epoxy can be avoided. Also, the relatively high thermal conductivity of this epoxy causes the heat generated during a quench to be better distributed throughout the coil, thereby reducing the thermal stresses caused by the quench. Premature quenching can also occur if the large forces between coil sections result in the motion of one coil with respect to another. This is most likely to occur in magnets having coils that are wound in opposition. Such coils are used in bucking coil magnets and magnets for nuclear demagnetization where a low field region is required close to a high field region. The alternative to bonded windings is to wind the magnet in such a manner that liquid helium permeates the windings. In this case, the liquid helium, which does have a high heat capacity at these temperatures, absorbs the heat generated when the windings move. The conductor used in this type of construction incorporates a much larger amount of normal conductor to limit the electrical resistance and consequently the temperature increase when the superconductor is driven normal. The operating current density in this type of cryostable magnet is much lower than in the intrinsically stabilized magnets described earlier. Persistent Mode After it has been energized, a superconducting magnet can be operated in the persistent mode by short circuiting the magnet with a superconductor. This is accomplished by connecting a section of superconducting wire across the terminals of the magnet. This section of superconductor can be heated to drive it into the resistive state so a voltage can be established across the terminals and the magnet can be charged or discharged. During the persistent mode of operation, the heater is turned off and the switch is permitted to cool into the superconducting state. In this condition, the power supply may be turned off and the magnet current will circulate through the magnet and the persistent switch. The decay of the magnet is given by: H = Hoe-T/t where T is the usual L/R time constant. The small residual resistance in the magnet occurs either from resistance in the joints or from the flux motion resistance discussed earlier. To achieve the best persistence, the magnet must be operated at less than the maximum field to reduce flux flow resistance in the conductor. High persistence magnets are bulkier, more costly, and require more liquid helium for cooldown than magnets having somewhat less persistence. Nevertheless, these magnets are quite desirable where great persistence is required, such as in nuclear magnetic resonance experiments. In addition, it is necessary that the resistance in joints between conductors be as low as possible. Characteristics of Superconducting Magnets The most outstanding feature of a superconducting magnet is its ability to support a very high current density with a vanishingly small resistance. This characteristic permits magnets to be constructed that generate intense magnetic fields with little or no electrical power input. This feature also permits steep magnetic field gradients to be generated at fields so intense that the use of ferromagnetic materials for field shaping is limited in effectiveness. Since the current densities are high, superconducting magnet systems are quite compact and occupy only a small amount of laboratory space. Another feature of superconducting magnets is the stability of the magnetic field in the persistent mode of operation. In the persistent mode of operation, the L/R time constant is extremely long and the magnet can be operated for days or even months at a nearly constant field, a feature of great significance where signal averaging must be performed over an extended period of time. Small superconducting magnets are frequently used to attain field intensities, stabilities or profiles that are not attainable with alternative magnets or because their cost is less than the cost of conventional magnets offering comparable to or inferior performance. In large magnets, the trade-off is frequently made in favor of superconducting magnets based on the relative costs of power for operating the magnets. The cost trade-off becomes more favorable for superconducting magnets as the period of operation increases. Magnetic field intensities of 1 Tesla or less, without demanding stability requirements, are frequently better generated with water cooled copper coils with or without iron. Materials and Performance Most superconducting magnets are wound using conductors which are comprised of many fine filaments of a niobium-titanium (NbTi) alloy embedded in a copper matrix. These conductors have largely replaced the single filament conductors since their magnetic field more readily penetrates the fine filaments, resulting in greater stability and less diamagnetism. Consequently, the linearity of the magnetic field and the magnet current is greatly improved. Another advantage of these conductors is the more rapid rate at which the magnet can be charged and discharged ½ typically a few minutes for most laboratory size magnets. Although most magnets are wound with multifilamentary niobium-titanium conductors, some are constructed with multifilamentary, niobium-tin (Nb3Sn) conductors and some with single filaments of niobium-titanium. Nb3Sn conductors are used when the field experienced by the conductor is in excess of about 9 Tesla (90 kilogauss). Typical magnets of this type are wound with a combination of NbTi windings in the low field region and Nb3Sn windings in the high field region. Since multifilamentary Nb3Sn is expensive, brittle, and difficult to wind, these magnets cost more than NbTi magnets. Single filament NbTi magnets are preferred where the stability of the magnetic field over a long period of time is essential ½ usually in nuclear magnetic resonance measurements. Better persistent mode operation can be obtained with this material, and since the field is held constant for long periods of time, the extra time required to charge the magnet is inconsequential. During a quench, the magnet generates high internal voltages and locally elevated temperatures. These cause electrical and mechanical stresses in the windings. The consequences of a quench depend on the design of the magnet and its auxiliary equipment. Permanent damage to the magnet can occur. Normal operation of the magnet at the specified temperature and at magnetic fields equal to or less than the rated field are not expected to cause damage to the magnet, and a warranty covering this type of operation accompanies each magnet. Niobium-titanium magnets are sometimes operated at temperatures below the normal boiling temperature of liquid helium (4.2K) to achieve even higher fields. Typically, an 8 Tesla solenoid will achieve 9.5-10 Tesla when operated at 2K. AMI magnets are rated in terms of their performance at 4.2K. Fields achievable at lower temperatures are only guaranteed if the magnet is designed for lower temperature operation. Some improvement in performance can also be achieved by reducing the temperature of Nb3Sn magnets, but the increase in field is not as significant as it is in NbTi magnets. When operated at reduced temperatures and higher fields, the energy in the magnet can be increased by 50% or more. Consequently, the magnet might be irreparably damaged if a quench occurs and the magnet is not sufficiently protected. This type of operation should not be attempted without checking with the manufacturer of the magnet ½ you may invalidate your warranty. Magnetic Field Intensity Underspecifying the intensity and homogeneity of the magnetic field used in your experiments may seriously impact your experimental results. However, overspecifying these parameters can greatly increase the costs. An economic compromise occurs in magnets in which the field experienced by the windings exceeds about 9 Tesla, which is the highest field at which NbTi superconducting alloys can conveniently be used at 4.2K. Higher fields can be attained at this temperature using Nb3Sn conductors, but the increase in cost deserves careful attention. A 10 Tesla magnet operating at 4.2K is substantially more expensive than a 9 Tesla magnet of the same size. Homogeneity Specifications Different manufacturers of homogeneous magnets have adopted different standards for specifying the homogeneity of their magnets. Most manufacturers specify the homogeneity in terms of the width of the resonant signal at half the signal height. AMI uses a more conservative approach that measures the magnetic field at various points in the specified homogeneous volume using a small volume NMR sample. Consequently, small deviations at any point in the volume will be detected. Using an NMR sample equal to the homogeneous volume does not necessarily reveal such small deviations. If a region of the sample occupying 10% of the specified volume resided in a field having a maximum inhomogeneity five times greater than specified, it is likely that this inhomogeneity would not be noticed. The reason is that the area under this part of the curve is only 10% of the total area and that the resonant line width is five times as broad. Consequently, this inhomogeneous region results in a long shallow tail on the base of the resonant signal. The cost of homogeneity may be misleading. Homogeneities of ±0.1% in a one-centimeter diameter spherical volume (DSV) are routine. Homogeneities of ±0.001% in the same volume require larger magnets and considerably more effort in their construction. Still more homogeneous magnets require that separately energized superconducting or room temperature trim coils be employed. These coils can escalate the cost quite rapidly. The inside diameter of the magnet scales approximately with the diameter of the homogeneous region specified. Persistent Switches Persistent switches are provided on many magnets to increase their stability over long periods of time or to reduce the rate of helium boil-off associated with continually supplying current to the magnet. A persistent switch is comprised of a short section of superconducting wire connected across the input terminals of a magnet and an integral heater used to drive the wire into the resistive, normal state. When the heater is turned on and the wire is resistive, a voltage can be established across the terminals of the magnet and the magnet can be energized. Once energized, the heater is turned off, the wire becomes superconducting and further changes in the magnet current cannot be made. In this persistent mode of operation, the external power supply can be turned off to reduce the heat input to the helium bath and the current will continue to circulate through the magnet and the persistent switch. Persistent mode current switches are installed on and become an integral part of the magnet. This is necessary since special care must be taken in making the joints between the switch and the magnet leads. For a typical switch, the electrical heater in the persistent switch has a nominal resistance of 60 Ohms and requires 35 mA of current to drive the superconductor into the resistive state. The superconductive wire typically has 15 to 20 Ohms of resistance in the normal state. AMI's standard persistent switch is 1.25 inches high and has a maximum outside diameter of 1.0 inches.

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