Patent Publication Number: US-2023146164-A1

Title: Passive quench protection techniques for non-insulated superconducting magnets

Description:
BACKGROUND 
     Superconductors are materials that have no electrical resistance to current (are “superconducting”) below some critical temperature. For many superconductors, the critical temperature is below 30 K, such that operation of these materials in a superconducting state requires significant cooling, such as with liquid helium or supercritical helium. 
     High-field magnets are often constructed from superconductors due to the capability of superconductors to carry a high current without resistance. Such magnets may, for instance, carry currents greater than 5 kA. 
     SUMMARY 
     According to some aspects, a magnet is provided comprising a coil comprising a plurality of windings of a non-insulated wire, the wire comprising a stack of high temperature superconductor (HTS) tapes, wherein each of the HTS tapes comprises an HTS material and is clad in a conductive material, a co-conductor layer, and a layer of solder arranged between and in contact with the stack of HTS tapes and the co-conductor layer. 
     According to some aspects, a magnet is provided comprising a coil comprising a plurality of windings of a non-insulated wire, the wire comprising a stack of high temperature superconductor (HTS) tapes, wherein each of the HTS tapes comprises a superconductor layer and is clad in a conductive material, wherein a ratio between a cross-sectional area of the conductive material and a cross-sectional area of the superconductor layer is at least 0.75. 
     According to some aspects, a magnet is provided comprising a coil comprising a plurality of windings of a non-insulated wire, the wire comprising a stack of high temperature superconductor (HTS) tapes, wherein each of the HTS tapes comprises an HTS material and is clad in a conductive material, and a stack of conductive non-superconductor tapes arranged in contact with the stack of HTS tapes. 
     According to some aspects, a magnet is provided comprising a coil comprising a plurality of windings of a non-insulated wire, the wire comprising a stack of high temperature superconductor (HTS) tapes, wherein each of the HTS tapes comprises an HTS material having a conductive material disposed over at least a portion thereof, a co-conductor layer arranged over the stack of HTS tapes, and solder disposed between and in electrical contact with the stack of HTS tapes and the co-conductor layer. 
     The foregoing apparatus and method embodiments may be implemented with any suitable combination of aspects, features, and acts described above or in further detail below. These and other aspects, embodiments, and features of the present teachings can be more fully understood from the following description in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       Various aspects and embodiments will be described with reference to the following figures. It should be appreciated that the figures are not necessarily drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. 
         FIG.  1    is a plan view of a non-insulated (NI) superconducting magnet; 
         FIGS.  2 A- 2 B  depict lumped-element circuit models of a NI superconducting coil, according to some embodiments; 
         FIGS.  3 A- 3 B  depict transformer graphics of a NI superconducting coil during steady state and during a quench, respectively, according to some embodiments; 
         FIG.  4    depicts a circuit model of a portion of a NI superconducting coil, according to some embodiments; 
         FIGS.  5 A- 5 G  are a series of cross-sectional views of different coil designs for a NI superconducting magnet, according to some embodiments; 
         FIGS.  6 A- 6 B  are a series of cross-sectional views of an illustrative stack of plates in a superconducting magnet, according to some embodiments; 
         FIGS.  7 A- 7 B  are perspective views of opposing surfaces of an illustrative individual plate of the type which may be included in a stack of plates in a superconducting magnet, according to some embodiments; 
         FIGS.  7 C- 7 D  are perspective views of opposing surfaces of an illustrative individual plate of the type which may be included in a stack of plates in a superconducting magnet, according to some embodiments; 
         FIG.  8    is a perspective view of an illustrative stack of plates of a superconducting magnet, according to some embodiments; 
         FIG.  9    is a perspective view of an illustrative stack of plates of a superconducting magnet with an exterior case, according to some embodiments; 
         FIG.  10    is a cross-sectional view of an illustrative plate in which the conducting channels comprise a stack of co-wound HTS tapes in addition to conductive co-wound tape, according to some embodiments; 
         FIG.  11    is a perspective view of a fusion power plant with a cutaway portion to reveal various illustrative components of the power plant, according to some embodiments; and 
         FIGS.  12 A,  12 B  are top views of illustrative coolant channels appropriate for use in a NI superconducting magnet, according to some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     A high-field superconducting magnet often comprises multiple electrically insulated cable turns grouped in a multi-layer arrangement. When a superconductor within the cable is cold enough to be below its critical temperature (the temperature below which the electrical resistivity of the material drops to zero), driving the magnet allows current to pass through the superconducting path without losses. However, for various reasons some or all of the superconductor may be heated to above its critical temperature and therefore lose its superconducting characteristics. If uncontrolled, such heating can lead to the superconductor losing its superconducting abilities, often referred to as a “quench.” Moreover, if the quench is not properly addressed by the system (e.g., by shutting down), components can be damaged by the heating. 
     Some superconducting magnet systems handle quench events via a system of active alarms and detection mechanisms. Other superconducting magnet systems handle quenches passively through design of the superconducting magnet itself. An example of one such design is a non-insulated (NI) magnet (also sometimes referred to as a no-insulation (NI) magnet), in which adjacent superconducting turns of the magnet are not insulated from one another but are instead separated by a conventional conductor (i.e., not a superconductor). When the magnet is operating below the superconductor&#39;s critical temperature, current flows through the superconductor and not across turns because the superconductor has zero resistance compared with the finite resistance of the conductor that lies between the turns. During a quench, however, current can flow between the turns and thereby be diverted from flowing through the superconductor which may have at least portions thereof in a “normal” (non-superconducting) state. Thus, NI magnets, and in particular NI-HTS magnets (NI magnets that comprise HTS superconductors), can in principle be passively protected against quench damage without the need to continuously monitor quench events and/or to actively engage external quench protection mechanisms. 
     As NI-HTS magnets grow in size, magnetic field strength and stored magnetic energy, however, the above-described self-protective feature may become increasingly stressed and potentially less reliable. For instance, the magnetic energy of a magnet scales with the volume enclosed by the magnet and scales with the magnetic field strength squared, whereas the heat capacity of the magnet scales with the volume of the winding pack and associated structures. This means that as the bore of the magnet and its field strength both increase in size, the magnet must be effective at dissipating stored magnetic energy uniformly. Otherwise, localized hot spots and/or thermal-gradient induced stresses, may damage the magnet. 
     The inventors have recognized and appreciated techniques for designing NI-HTS magnets that mitigate problems that may arise during quench initiation and propagation. In particular, the inventors have recognized and appreciated that coupling the HTS material to a co-conductor along its length reduces the effective resistance of the conductive path along the HTS material when it is not superconducting, and that this leads to numerous advantages for quench mitigation. 
     As described further below, the inventors have recognized and appreciated that the effective resistance of the conductive path along the HTS material when it is not superconducting controls several aspects of a system during a quench, as follows. First, during a quench in a NI-HTS magnet, current continues to circulate within the turns for some time even though some or all of the HTS material has become normal (non-superconducting). This current decays with a characteristic time that is a function of the resistances of conductive paths within the magnet. Second, the highest possible magnetic energy dissipation power density that can occur during a quench is also a function of the resistances of the conductive paths within the magnet. Third, the maximum temperature gradient, the peak temperature, and the resulting temperature induced stresses that can occur during a quench are also a function of the resistances of the conductive paths within the magnet. Fourth, the stability of quenches in which normal zones arise within otherwise superconducting turns of the magnet may be predicted based on the resistances of the conductive paths within the magnet. The above-summarized relationships are described further below along with practical implementations of NI-HTS magnets that capitalize on said relationships, resulting in an improved NI-HTS magnet. 
     As used herein, a “high temperature superconductor” or “HTS” refers to a material that has a critical temperature above 30° K, wherein the critical temperature refers to the temperature below which the electrical resistivity of the material is zero. The critical temperature can in some cases depend on other factors such as the presence of an electromagnetic field. It will be appreciated that where the critical temperature of a material is referred to herein, this may refer to whatever the critical temperature happens to be for that material under the given conditions. 
       FIG.  1    illustrates a schematic of a non-insulated (NI) superconducting magnet, for purposes of explanation. In the example of  FIG.  1   , a two-turn coil  110  of a magnet  100  is shown. The coil  110 , which comprises a superconductor, is electrically coupled to a conductive material  120 . When the superconductor of the coil is sufficiently cold to be superconducting, current flows within the coil because it can do so with zero resistance, as opposed to flowing through the conductive material  120 , which has a finite resistance. During a quench in which some or all of the superconductor of the coil becomes normal (non-superconducting), the current that would otherwise flow through the coil will flow through the conductive material  120  as well as through the coil. In this manner, the design of the non-insulated superconducting magnet  110  in principle passively protects the superconductor in the coil  110  against quench damage that may be sustained by diverting at least some of the current that would flow through the superconductor. 
     The inventors have recognized and appreciated that a NI superconducting coil can be approximated by a lumped-element circuit model, as shown in  FIG.  2 A . In the example of  FIG.  2 A , circuit  210  represents a three-turn non-insulated coil as a number of inductors coupled to variable resistors along the turns, with additional resistors across the turns. The variable resistors represent the change in state of the superconducting turns, from their superconducting state in which there is a zero resistance path along the coil, to the normal state in which there is a finite resistance along the coil. For clarity, the variable resistors are shown only in the middle turn but could in general be considered to be present within each turn of the coil. A portion of the circuit  210 , identified by the dashed box and labeled  401  in  FIG.  2 A , is considered in relation to  FIG.  4    below. 
     The network circuit model of  FIG.  2 A  may be used to understand the physics that governs: (1) the rate and spatial distribution of stored magnetic energy dissipation during a full magnet quench; and (2) the magnitude of turn-to-turn current sharing arising from the prompt formation of a localized normal zone. These models indicate NI magnet design techniques that, when applied, can produce NI magnets that mitigate the impact of these events. 
     The network circuit model of  FIG.  2 A  may be simplified even further to the reduced lumped element circuit model shown in  FIG.  2 B . In the example of circuit  220  shown in  FIG.  2 B , the coils is represented by turns with respective turn-to-turn finite bypass resistances R S1 , R S2  and R S3  and a variable resistance within respective turns of R N1 , R N2  and R N3 . In cases in which the coils only contain a superconductor, the resistances of the coils R S1 , R S2  and R S3  represent the normal resistance of the superconductor. More generally, however, the coils may contain additional non-superconductor material (e.g., a conventional metal conductor), in which case the resistances of the coils R S1 , R S2  and R S3  represent the combined resistance of the superconductor in a non-superconducting (normal) state, plus that of the additional material. For this reason, hereinafter the coil is referred to as being formed from a “composite” material to refer to this more general combination of materials (superconductor plus additional material) from which the coil may be formed. 
     The circuit models of  FIGS.  2 A- 2 B  may be redrawn with a transformer graphic to explicitly indicate the mutual inductive coupling among turns of the coil, as shown in  FIGS.  3 A- 3 B . Steady state current flow through the coil is distributed according to bypass resistance R S1 , R S2  or R S3  and through-turn resistances of R N1 , R N2  and R N3 . 
     It may be noted that the magnitude of an operational current (I OP ) flowing in the composite material of the coil relative to a critical current rating of the superconductor within the composite material (I C ), determines the value of R N  (referring generally to the through-turn resistance of a given turn). When I OP  is much less than I C , the superconductor is superconducting and R N  is essentially zero. When I OP  is much greater than I C , the superconductor is normal and R N  becomes essentially the parallel resistance of the remaining (non-superconducting) material in the composite material of the coil. Because the turns enclose common magnetic flux areas they couple inductively. 
     As shown in  FIG.  3 A , when current flows through the coil in a superconducting mode, the through-turn resistances R N1 , R N2  and R N3  are zero, so the current all flows along the right-hand paths of each of the three illustrated blocks of the circuit. When the external current is interrupted, as shown in  FIG.  3 B , current in each turn continues to flow, closing via its bypass resistance. The characteristic “L/R” decay time of this current is set by the inductance of that turn (self-inductance) coupled with other turns (mutual inductances), and the sum of bypass and through-turn resistances for that turn (R S +R N ). 
     Generally, this “L/R” response is the mechanism by which the stored energy of the magnet is dissipated into the winding pack, which can occur both during planned events (e.g., open-circuit magnet interruption) and unplanned events (e.g., formation of a local normal zone leading to a full magnet quench). Initially the “L/R” decay times are long, as the HTS remains superconducting in some zones. But as the turns heat up and the HTS goes normal everywhere, the decay times asymptote to the shortest possible “L/R” values. 
     The inventors have recognized and appreciated that R S  and R N  (particularly the maximum attainable value of R N , i.e., its normal value) are determined entirely by the magnet design. This means that the shortest possible “L/R” quench decay time of the magnet is also determined by the magnet design. 
     According to some embodiments, the composite material from which the coil in a NI magnet is formed may be configured to reduce the maximum resistance R N  of the composite material. In some cases, a co-conductor may be electrically coupled to the superconductor in the coil to provide a low-resistance path when the superconductor is normal. Particular examples of such a co-conductor are discussed further below, though generally speaking by increasing the cross-sectional area of the co-conductor in the windings, the maximum attainable value of R N  can be reduced. The resultant decrease in (R S +R N ) increases the lower limit for the shortest possible “L/R” quench decay time that the magnet can have. Decreasing R N  may be particularly effective given that the NI magnet may be configured such that the resistance R N  is much larger than the resistance R S , in which case R N  is the key controlling parameter determining the value of (R S +R N ). 
     Note that the thermal energy needed to raise the temperature of the entire winding pack from its operating temperature (e.g., 20K) to a temperature at which the HTS is fully normal (˜90K) can be just a small fraction (e.g., &lt;10%) of the total magnetic energy. Thus, what happens to the release of the remaining 90% is controlled entirely by magnet design—most importantly the cross-sectional area of the embedded copper windings (copper cap plus co-wind copper)—and its “L/R” decay time. 
     Similar to the above, the highest possible magnetic energy dissipation power density (watts per cubic meter) in the winding pack during a quench scales as the stored magnetic energy per unit winding pack volume divided by the shortest possible characteristic “L/R” time. Thus in controlling the shortest possible “L/R” time, the highest possible magnetic energy dissipation power density that can occur during a quench is also controlled. 
     With respect to temperature gradients induced during a quench, for magnets in which R N  is larger than R S , the volumetric joule heating which occurs in the composite material of the coil during a magnet quench is large compared with the amount of volumetric joule heating which occurs within the conductive material arranged between turns of the coil. Consequently, the composite material is expected to attain the highest temperature in the magnet during a quench event, and heat is therefore expected to flow from this composite material into the conductive material between the coils. The magnitude of this heat flow determines the magnitude of the temperature gradients in both the composite and conductive materials. 
     The inventors have recognized and appreciated that if the electrical conductivity of the composite material of the coil is much greater than the electrical conductivity of the conductive material arranged between the turns of the coil, the thermal conductivity of the composite material would also be greater (and in some instances, much greater) than the thermal conductivity of the conductive material (Wiedemann-Franz law). In such a magnet, the largest temperature gradients, and temperature gradient-induced stresses, would be expected to occur in the conductive material arranged between the turns of the coil. Thus, by controlling the highest possible magnetic energy dissipation power density (joule heating) in the manner noted above, the temperature gradient (e.g. the maximum temperature gradient) and temperature gradient induced stress during a quench is also controlled. 
     This distribution of heat may be reliant on good thermal contact between components of the composite material of the coil, and between the coil and the conductive material arranged between the turns of the coil. Such contact would reduce, and ideally minimize, temperature differences between components as heat is forced to flow through their interfaces during quench events. 
     The peak temperatures attained by the coil and the conductive material arranged between turns of the coil (together, the “winding pack”) during a quench, and the location of the temperature, are important parameters. The melting temperatures of various materials within the magnet may, for instance, set hard upper limits on the temperatures that may be experienced by the materials without permanent damage being caused to the magnet. As discussed above, temperature gradients (e.g. maximum temperature gradients) in the winding pack can be controlled by magnet design choices, in particular, choices for R N  and R S . These choices, in combination with fixing the overall thermal mass, are the means to control a temperature (e.g., a maximum temperature) that the winding pack could possibly experience during a quench. 
     Additionally, there may be a considerable advantage to choose R N  and/or R S  to vary with position (e.g., radial distance) in the magnet. For example, this can serve to preferentially decrease temperature gradients and peak temperatures in key areas, such as to limit the temperature rise at joint locations where particular materials may be used. An example of a magnet design in which R N  is varied with position is discussed further below. 
     In situations where the operating current of the magnet (I OP ) approaches locally the critical current rating (I C ) of the superconductor in the coil, the possibility of triggering a fast propagating quench, referred to herein as a “tsunami quench,” may be considered. Tsunami quenches can be triggered when, due to the formation of a local normal zone turn-to-turn current-sharing pushes current above I C  in one or more adjacent turns causing normal zones to appear in these turns as well. This can precipitate a cascade of normal zones in adjacent turns—propagating initially not via a temperature rise, but via spikes in the current in the turn-to-turn shared current. 
     Following a tsunami quench, the magnet proceeds to quench via the usual thermal processes, albeit with a modified distribution of currents in the turns compared with a quench in which the whole coil quenches at the same time. Currents in each turn decay and magnetic energy is correspondingly dissipated into the winding pack as discussed above. Since tsunami quench current sharing is an electrical response, the magnet can be designed so as to avoid triggering them. In other words, with suitable design, a NI magnet can be made to operate at high values of I OP /I C  and not be susceptible to tsunami quench propagation. 
     The lumped element circuit model shown in  FIG.  4    qualitatively reproduces the turn-to-turn current sharing physics involved in tsunami quench propagation. It represents a small section of the magnet—specifically, the dashed boxed region  401  shown in  FIG.  2 A ). In this model, a local normal zone is postulated to appear instantaneously at t=0, represented by a nonzero value of R′ N . R′ N  is the resistance of the composite material of the coil in the normal zone region. R′ S  is the corresponding turn-to-turn resistance in the vicinity of the normal zone. Both these values depend on the length of the normal zone, L N : R′ N  is proportional to L N  while R′ S  is proportional to 1/L N . 
     In order for R′ N  to be greater than zero, it may be assumed that some initial event causes I OP  to exceed I C  in this region (otherwise the superconductor would be superconducting and R′ N  would be zero). This could be caused by a local temperature perturbation in the magnet due to some off-normal event, such as a loss of coolant event. 
     Over short time scales, the total azimuthal current flowing in the coil is approximately conserved: I 1 +I 2 +I 3 =3I OP  (to conserve total magnetic flux). Therefore, if I 2  promptly decreases, I 1  and/or I 3  are expected to promptly increase to compensate. If either of these exceeds the local critical current level, a fast propagating “tsunami quench” could ensue. 
     Approximating the circuit elements in all turns as being identical, the time-dependent currents in turns 1 and 2 can be computed as: 
     
       
         
           
             
               
                 
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     with the current sharing current distribution established in a characteristic time τ, which is a function of R′ S , R′ N  and inductances: 
     
       
         
           
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     For times longer than τ, the currents are expected to asymptote to: 
     
       
         
           
             
               
                 
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     As such, it is evident that the value of R′ N  compared with R′ S  is a significant parameter in the design of the magnet. In the example of  FIG.  4   , for instance, reducing R′ N  relative to R′ S  increases the level of current that is retained in turn 2, thereby reducing the magnitude of current spikes that appear in turns 1 and 3. As a result, decreasing R′ N  through suitable magnet design allows the magnet to be operated safely at higher values of I OP /I C , or equivalently, to be operated safety at the same value of I OP /I C  while accommodating the formation of a normal zone region of longer length. 
       FIGS.  5 A- 5 G  depict cross-sections of different coil designs for a NI superconducting magnet, according to some embodiments. To illustrate how the above-described principles may be applied to a NI superconducting magnet,  FIGS.  5 B- 5 G  depict various composite materials of a coil of an NI superconducting magnet, with  FIG.  5 A  depicting a bare superconductor for comparison. 
     In the example of  FIG.  5 A , coil  510  comprises only a superconductor layer  511 . The superconductor layer  511  may comprise a superconducting material in addition to one or more layers such as a substrate on which the superconducting material is deposited, and/or buffer layers (not shown in  FIG.  5 A ). The superconducting material of the superconductor layer  511  may for instance be an HTS such as a rare earth barium copper oxide (REBCO), e.g., yttrium barium copper oxide (YBCO). 
     As discussed above, a coil of a NI superconducting magnet consisting of or consisting essentially of only a superconductor (whether in the presence or absence of a substrate and/or buffer layers) may exhibit numerous problems during a quench. While the design of the NI superconducting magnet provides some protection to the superconductor by diverting current into the conducting material between the turns of the coil, the current in the coil may nonetheless decay too quickly (with an L/R characteristic time), sharp thermal gradients may be produced, etc. so as to damage the magnet. In the example of  FIG.  5 A , R N  is the resistance of the superconductor layer  511  when the superconducting material within the layer is normal. 
     For comparison,  FIG.  5 B  illustrates a coil  520  which comprises the superconductor layer  511  in addition to a cladding material  515 . As with  FIG.  5 A , the superconductor layer  511  may comprise a superconducting material and optionally may include one or more additional layers such as a substrate and/or buffer layers. A NI superconducting magnet may commonly include a thin layer of a conductive material (e.g. a cladding material, such as copper), surrounding the superconductor layer. In the case in which the superconductor layer  511  includes a substrate and/or buffer layers, the conductive material  515  may be deposited around these layers as well. For instance, a superconductor layer may have a conductive layer (e.g. a cladding layer) with a thickness of around 10% of the thickness of the superconductor layer deposited around the layer. As such, while coil  520  may have a lower resistance than coil  510  when the superconducting material in the superconductor layer  511  is normal, a means for a further reduction in R N  may be desirable as discussed above. 
     In the example of  FIG.  5 C , coil  530  comprises a conductive “cap”  516  that is electrically coupled to the superconductor layer  511  via a solder  514 . As shown, the cap  516  has a cross section that is larger than (and in some cases, much larger than) that of the superconductor layer  511 . As a result, assuming that the cap  516  is a sufficiently good conductor, the value of R N  is expected to be lower (and in some cases, substantially lower) than that of either coils  510  or  520 . In other words, when the superconducting material within superconductor layer  511  is normal, the current may flow through the cap  516  with comparatively low resistance (i.e. the resistance characteristic of the cap is low compared with the resistance characteristic of the coils). Solder  514  is provided to ensure electrical and thermal coupling between the superconductor layer  511  and the cap  516  and may comprise any suitable conductive material that may provide said coupling. 
     According to some embodiments, cap  516  may comprise, or may consist of, aluminum, copper or a copper alloy (e.g., AMZIRC). According to some embodiments, cap  516  may comprise, or may consist of, a high strength conductive alloy, such as a copper-based metal matrix composite alloy (e.g., Glidcop®). According to some embodiments, solder  514  may comprise a Pb and/or Sn solder. In some embodiments, solder  514  may comprise a metal having a melting point of less than 200° C., wherein at least 50 wt % of the metal is Pb and/or Sn, and at least 0.1 wt % of the metal is Cu. 
       FIG.  5 D  illustrates coil  540 , which comprises a stack  512  of superconductor “tapes.” Each of the superconductor tapes comprise a superconductor layer  511  which is clad in a conducting material, such as copper (as such, each tape is as the structure described in  FIG.  5 B ). In addition, the stack of tapes  512  is electrically coupled via solder  514  to a co-conductor cap  516  of thickness t. The superconducting material within the superconductor layer of each tape of stack  512  may be a long, thin strand of HTS material with cross-sectional dimensions in the range of about 0.001 mm to about 0.1 mm in thickness (or height) and a width (labeled w in  FIG.  5 D ) in the range of about 1 mm to about 12 mm (and with a length that extends along the length of the cable, e.g., into and out of the page in the example of  FIG.  5 D ). According to some embodiments, each strand of HTS tape may comprise an HTS material such as REBCO. In some embodiments, HTS tape may comprise a polycrystalline HTS and/or may have a high level of grain alignment. 
     In some embodiments, the cap  516  has a thickness t of greater than or equal to 1 mm, 2 mm, 4 mm, 6 mm, 8 mm, 10 mm, 12 mm, or 15 mm. In some embodiments, the cap  516  has a thickness t of less than or equal to 20 mm, 15 mm, 12 mm, 10 mm, 8 mm, 5 mm, 4 mm, or 2 mm. Any suitable combinations of the above-referenced ranges are also possible (e.g., a thickness t of greater or equal to 1 mm and less than or equal to 5 mm). 
     In some embodiments, the tapes of stack  512  have a width w of greater than or equal to 1 mm, 2 mm, 4 mm, 6 mm, 8 mm, 10 mm, 12 mm or 15 mm. In some embodiments, the tapes of stack  512  have a width w of less than or equal to 20 mm, 15 mm, 12 mm, 10 mm, 8 mm, 5 mm, 4 mm, or 2 mm. Any suitable combinations of the above-referenced ranges are also possible (e.g., a width w of greater or equal to 1 mm and less than or equal to 5 mm). 
     In some embodiments, a ratio t/w (the ratio of the thickness t of the cap  516  to the width w of the tapes of stack  512 ) is greater than or equal to 0.5, 0.75, 0.9, 1.0, 1.1, 1.25, 1.5, 2.0, 5, 10, 15 or 20. In some embodiments, the ratio t/w is less than or equal to 20, 15, 10, 5, 2.0, 1.5, 1.25, 1.1, 1.0, 0.9, 0.75, or 0.5. Any suitable combinations of the above-referenced ranges are also possible (e.g., a ratio t/w of greater than or equal to 2 and less than or equal to 10). 
     In some embodiments, the resistance per unit length of the components of coil  540  that are non-superconducting at temperatures below the critical temperature of the HTS tapes in stack  512  (specifically, the components in question are the cap  516 , the solder  514  and the cladding around the tapes of stack  512 ) is greater than or equal to 2 micro ohms per meter (μΩ/m), 10 μΩ/m, 50 μΩ/m, 100 μΩ/m, 150 μΩ/m, or 200 μΩ/m. In some embodiments, the resistance per unit length of these components of coil  540  is less than or equal to 250 μΩ/m, 200 μΩ/m, 150 μΩ/m, 100 μΩ/m, 50 μΩ/m or 25 μΩ/m. Any suitable combinations of the above-referenced ranges are also possible (e.g., a resistance per unit length of these components greater than or equal to 150 μΩ/m and less than or equal to 200 μΩ/m). 
     In some embodiments, a ratio X of the resistance per unit length of the components of coil  540  that are non-superconducting at temperatures below the critical temperature of the HTS tapes in stack  512  (specifically, the components in question are the cap  516 , the solder  514  and the cladding around the tapes of stack  512 ) to the resistance per unit length of the coil  510  is greater than or equal to 100, 500, 1000, 10,000, 50,000, or 100,000. In some embodiments, X is less than or equal to 100,000, 50,000, 10,000, 1000, 500 or 100. Any suitable combinations of the above-referenced ranges are also possible (e.g., the ratio X is greater than or equal to 10,000 and less than or equal to 50,00). 
     In some embodiments, a ratio of the cross-sectional area of the co-conductor cap  516  to the cross-sectional area of the stack of tapes  512  is greater than or equal to 0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 2.5, 3.0, 3.5, or 4.0. In some embodiments, the ratio of the cross-sectional area of the co-conductor cap  516  to the cross-sectional area of the stack of tapes  512  is less than or equal to 4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.25, 1.0, 0.75, 0.5, 0.25, or 0.1. Any suitable combinations of the above-referenced ranges are also possible (e.g., a ratio of the cross-sectional area of the co-conductor cap  516  to the cross-sectional area of the stack of tapes  512  of greater than or equal to 1 and less than or equal to 4). 
       FIG.  5 E  illustrates coil  550 , which comprises a stack  512  of superconductor tapes that are each clad in a conducting material, such as copper, in addition to a co-conductor  556  that is electrically coupled to the stack of tapes via solder  514 . In contrast to the coil  540  shown in  FIG.  5 D , the coil  550  includes a co-conductor alongside the stack of tapes rather than over the stack of tapes as a cap. The superconducting material within the superconductor layer of each tape of stack  512  may be a long, thin strand of HTS material with cross-sectional dimensions in the range of about 0.001 mm to about 0.1 mm in thickness (or height) and a width (labeled w in  FIG.  5 E ) in the range of about 1 mm to about 12 mm (and with a length that extends along the length of the cable, e.g., into and out of the page in the example of  FIG.  5 E ). According to some embodiments, each strand of HTS tape may comprise an HTS material such as REBCO. In some embodiments, HTS tape may comprise a polycrystalline HTS and/or may have a high level of grain alignment. 
     In some embodiments, the tapes of stack  512  shown in  FIG.  5 E  have a width w of greater than or equal to 1 mm, 2 mm, 4 mm, 6 mm, 8 mm, 10 mm, 12 mm or 15 mm. In some embodiments, the tapes of stack  512  have a width w of less than or equal to 15 mm, 12 mm, 10 mm, 8 mm, 5 mm, 4 mm, or 2 mm. Any suitable combinations of the above-referenced ranges are also possible (e.g., a width w of greater or equal to 1 mm and less than or equal to 5 mm). 
     In some embodiments, the resistance per unit length of the components of coil  550  that are non-superconducting at temperatures below the critical temperature of the HTS tapes in stack  512  (specifically, the components in question are the cap  556 , the solder  514  and the cladding around the tapes of stack  512 ) is greater than or equal to 2 micro ohms per meter (μΩ/m), 10 μΩ/m, 50 μΩ/m, 100 μΩ/m, 150 μΩ/m, or 200 μΩ/m. In some embodiments, the resistance per unit length of these components of coil  550  is less than or equal to 250 μΩ/m, 200 μΩ/m, 150 μΩ/m, 100 μΩ/m, 50 μΩ/m or 25 μΩ/m. Any suitable combinations of the above-referenced ranges are also possible (e.g., a resistance per unit length of these components greater than or equal to 150 μΩ/m and less than or equal to 200 μΩ/m). 
     In some embodiments, a ratio of the cross-sectional area of the co-conductor  556  to the cross-sectional area of the stack of tapes  512  is greater than or equal to 0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 2.5, 3.0, 3.5, or 4.0. In some embodiments, the ratio of the cross-sectional area of the co-conductor  556  to the cross-sectional area of the stack of tapes  512  is less than or equal to 4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.25, 1.0, 0.75, 0.5, 0.25, or 0.1. Any suitable combinations of the above-referenced ranges are also possible (e.g., a ratio of the cross-sectional area of the co-conductor  556  to the cross-sectional area of the stack of tapes  512  of greater than or equal to 0.75 and less than or equal to 1.5). As referred to above, the cross-sectional area refers to the area of the element as shown in the example of  FIG.  5 E . 
       FIG.  5 F  illustrates coil  560 , which comprises a stack  512  of superconductor tapes that are each clad in a conducting material, such as copper, in addition to a co-conductor  562  in the form of a stack of non-superconducting conductive tapes. In the example of  FIG.  5 F , the co-conductor is provided in the form of tapes of a conductive material, rather than as a monolithic co-conductor as in the examples of  FIGS.  5 D and  5 E . 
     In some embodiments, a ratio of the cross-sectional area of the stack of conductive tapes  562  to the cross-sectional area of the stack of tapes  512  is greater than or equal to 0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 2.5, 3.0, 3.5, or 4.0. In some embodiments, the ratio of the cross-sectional area of the stack of conductive tapes  562  to the cross-sectional area of the stack of tapes  512  is less than or equal to 4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.25, 1.0, 0.75, 0.5, 0.25, or 0.1. Any suitable combinations of the above-referenced ranges are also possible (e.g., a ratio of the cross-sectional area of the stack of conductive tapes  562  to the cross-sectional area of the stack of tapes  512  of greater than or equal to 0.75 and less than or equal to 1.5). As referred to above, the cross-sectional area refers to the area of the element as shown in the example of  FIG.  5 F . 
       FIG.  5 G  illustrates coil  570 , which comprises a stack of tapes, each of which comprises a superconductor layer  511  in addition to a cladding material  515 . In contrast to the example of  FIG.  5 B , however, in  FIG.  5 G  the coil  570  includes a thick layer of cladding around each superconductor layer that is sufficient to act as a co-conductor that provides a sufficiently low value of R N  to provide the above-described benefits. For instance, instead of the superconductor layer  511  having a conductive layer with a thickness of around 10% of the thickness of the superconductor layer around it, the thickness of the conductive (cladding) layer may be much larger, such as 50% of the thickness of the superconductor layer or greater. As noted above, each superconductor layer  511  may comprise a superconducting material and optionally may include one or more additional layers such as a substrate and/or buffer layers. 
     In some embodiments, a ratio between a cross-sectional area of the conductive cladding material  515  and a cross-sectional area of the superconductor layer  511  in the coil  570  is greater than or equal to 0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 2.5, 3.0, 3.5, or 4.0. In some embodiments, the ratio is less than or equal to 4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.25, 1.0, 0.75, 0.5, 0.25, or 0.1. Any suitable combinations of the above-referenced ranges are also possible (e.g., the ratio is greater than or equal to 1.0 and less than or equal to 4.0). As noted above, the superconductor layer may comprise a superconducting material and optionally may include one or more additional layers such as a substrate and/or buffer layers. As such, the cross-sectional area of the superconductor layer  511  may represent a combined cross-sectional area of a superconducting material, a substrate, one or more buffer layers, etc. 
     To illustrate a particular implementation of the improved magnet design represented by the coil  540 ,  FIGS.  6 A- 6 B  show different cross-sections of an illustrative stack of plates in a NI superconducting magnet, according to some embodiments. Stack of plates  600  comprises two instances of plate  610  and two instances of plate  620 , in addition to terminal plates  630  and  640 . Layers of insulating material  650  are arranged at selected regions between neighboring plates. 
     The plates  610  and  620  include conductive channels in which the coil  540  is arranged, labeled in the example of  FIGS.  6 A- 6 B  as a stack of HTS tapes  612  or  622 , solder  614  or  624 , and cap  616  or  626  for plates  610  and  620 , respectively. The plates also include cooling channels  611 ,  621  and  631  which are arranged adjacent to the caps. The conductive material between turns of the coils is the baseplate material  610   a ,  620   a ,  630   a  and/or  640   a  in which the aforementioned channels are formed. 
     In the example of  FIGS.  6 A- 6 B , the conducting channel is arranged in a racetrack spiral (or simply “racetrack pattern”). In a racetrack spiral, the path follows a racetrack shape (e.g., a rectangle with rounded corners) without spiraling inward or outward for most of the circumference, but includes a number of “jogs” or “joggles” (i.e. portions of the path with curves and/or turns) in which the path jogs (or turns or curves) inward or outward. These jogs cause the racetrack spiral to wind inward or outward, depending on the direction of the jogs.  FIG.  6 A  represents a cross-section of the stack of plates through the racetrack portion of the channels of the plates, whereas  FIG.  6 B  represents a cross-section of the stack of plates in the region in which the conducting channels “jog” in or out to switch lanes of the racetrack spiral. 
     In the design of  FIGS.  6 A- 6 B , the open cooling channels in one plate may be arranged adjacent to the conducting channel of the neighboring plate. For example, as shown in  FIG.  6 A , which represents the racetrack portion of the channels, the cooling channels  611  in each instance of plate  610  are arranged adjacent to the cap  626  of the neighboring plate  620 . Similarly, the cooling channels  621  in plate  620  are arranged adjacent to the cap  616 , with cooling channels  631  arranged in the terminal cap  630  arranged adjacent to the uppermost instance of the plate  610 . 
     It may be noted that cooling channels  621  in the lowermost instance of plate  620  are not strictly needed since there are no conductors adjacent to these channels. However, due to the modular nature of the plates in the stack  600 , it may be more convenient to simply use an instance of plate  620  rather than fabricate a new type of plate that does not include the lowermost cooling channels  621 . 
     In the example of  FIGS.  6 A- 6 B , the plates  610 ,  620 ,  630  and  640  are held together, at least in part, by bolts  680 , which connect neighboring pairs of plates as shown in  FIG.  6 A . It may be presumed that such bolts are present at a number of locations around the plates  610 ,  620 ,  630  and  640 , although the cross-section shown in  FIG.  6 B  does not include any such bolts for clarity. 
     As shown in  FIG.  6 B , the plates may include conductive pads to connect the conductive paths in one plate to those of an adjacent plate. For example, the terminal plate  630  includes pad  639  which is adjacent to and electrically connected to the conductor  616  in the conducting channel of plate  610 . Thus, the terminal plate may be adjacent to and electrically connected to one end of the conductive channel of plate  610 , the other end of which is electrically connected to the pad  619 . Pad  619  is, in turn, adjacent to and electrically connected to, the conductor  626  in the conducting channel of plate  620 . The other end of the conductor  626  in the conducting channel of plate  620  is adjacent to and electrically connected to pad  629 , which is adjacent to and electrically connected to the next plate  610 , and so forth. In the example of  FIG.  6 B , the conductive pads  619 ,  629 ,  639  and  649  are shaded in the same manner as the caps of the plates, although it will be appreciated that in general the pads and caps need not comprise the same material(s). 
     According to some embodiments, insulating material  650  may comprise polyimide (e.g., Kapton®), epoxy resin, phenolic resin, glass epoxy laminate, a plastic, an elastomer, or combinations thereof. According to some embodiments, insulating material may have a breakdown voltage or dielectric strength of greater than 25 kV/mm, of greater than 50 kV/mm, of greater than 75 kV/mm, of greater than 1000 kV/mm. In some cases, the voltages in the superconducting magnet may be comparatively low, in which case a low voltage standoff insulating material such as anodized aluminum could be utilized as the insulating material  650 . 
     According to some embodiments, the baseplates  610   a ,  620   a ,  630   a  and  640   a  may each comprise, or may consist of, a high mechanical strength material such as but not limited to steel, Inconel®, Nitronic® 40, Nitronic® 50, Incoloy®, or combinations thereof. In some embodiments, the baseplates  610   a ,  620   a ,  630   a  and  640   a  may be plated with a metal such as nickel to facilitate adhesion of other components of the plate, including solder. 
     In the example of  FIGS.  6 A , bolts  690  are arranged within through holes of the plates  610 ,  620 ,  630  and  640  and affix neighboring pairs of plates to one another. 
     To further illustrate the structure of a stack of plates such as those shown in  FIGS.  6 A- 6 B ,  FIGS.  7 A- 7 D  depict upper and lower views of individual plates  610  and  620 . 
       FIGS.  7 A and  7 B  depict upper and lower views, respectively, of plate  610 , wherein the cross-section of  FIG.  6 A  is through the section marked A-A′ and the cross-section of  FIG.  6 B  is through the section marked B-B′. In the example of  FIGS.  7 A- 7 B , the location of cooling channels  621 , which are part of plate  620  arranged above the plate  610 , are shown for purposes of explanation, although it will be appreciated that these cooling channels are not in fact part of the plate  610 . As may be noted, the conducting channel of plate  610  in this example has an inward spiral when following the channel in a clockwise direction viewed from above. 
     As may be seen in  FIG.  7 A , for the bulk of the racetrack sections of the conducting channel of the plate  610 —of which the cap  616  is visible—the cooling channels  621  of the neighboring plate  620  are aligned with the conducting channel. As such, cryogen passing through the cooling channels may directly contact the cap  616  and deliver cooling to the HTS material arranged beneath the cap as discussed above. 
     The region of the plate  610  between the coolant inlet and outlet (the two regions where the coolant channels meet the edge of the plate) includes, in the example of  FIG.  7 A , a “meandering” region of the cooling channel  621  that meanders back and forth over the conducting channels  616 . Various other arrangements may be envisioned, including a cooling channel that is aligned with a single conducting channel, but runs back and forth over successive cooling channels in the region between the inlet and outlet. 
     In some embodiments, the inlet and outlet regions of the plate may be further apart than is shown in the example of  FIG.  7 A , such as at opposite ends of the plate from one another. In such cases, the cooling channels may be arranged so that some cooling channels (e.g., half) pass along one side of the plate with the other cooling channels passing along the other side of the plate. An example of such a cooling channel configuration is depicted in  FIG.  12 A , which shows a single layer of cooling channels  1211  in an aerial view.  FIG.  12 B  depicts the cooling channels  621  of the layer of the plate shown in  FIG.  7 A  with the same aerial view for comparison. It may be noted that alternative cooling channel arrangements such as that shown in  FIG.  12 A  may be arranged on a plate without altering the structure of the other elements of the plate except for the portion(s) of the baseplate that connect the cooling channels to the edge of the plate. For instance, as shown in  FIG.  3 A  the cooling channels may be arranged as shown in  FIG.  12 A  without altering the conductive channels of the plate. 
       FIG.  7 B  illustrates the underside of plate  610 , and includes portions to which insulating material  650  is attached, and portions for which the baseplate  610   a  is exposed. 
       FIGS.  7 C and  7 D  depict upper and lower views, respectively, of plate  620 , wherein the cross-section of  FIG.  6 A  is through the section marked A-A′ and the cross-section of  FIG.  6 B  is through the section marked B-B′. In the example of  FIGS.  7 C- 7 D , the location of cooling channels  611 , which are part of plate  610  arranged above the plate  620 , are shown for purposes of explanation, although it will be appreciated that these cooling channels are not in fact part of the plate  620 . As may be noted, the conducting channel of plate  620  in this example has an outward spiral when following the channel in a clockwise direction viewed from above. 
     As may be seen in  FIG.  7 C , for the bulk of the racetrack sections of the conducting channel of the plate  620 —of which the cap  626  is visible—the cooling channels  611  of the neighboring plate  610  are aligned with the conducting channel. As such, cryogen passing through the cooling channels may directly contact the cap  626  and deliver cooling to the HTS material arranged beneath the cap as discussed above. 
     The region of the plate  620  between the coolant inlet and outlet (the two regions where the coolant channels meet the edge of the plate) includes, in the example of  FIG.  7 C , a “meandering” region of the cooling channel  611  that meanders back and forth over the conducting channels  626 . Various other arrangements may be envisioned, including a cooling channel that is aligned with a single conducting channel, but runs back and forth over successive cooling channels in the region between the inlet and outlet. 
     In some embodiments, the inlet and outlet regions of the plate may be further apart than is shown in the example of  FIG.  7 C , such as at opposite ends of the plate from one another. In such cases, the cooling channels may be arranged so that some cooling channels (e.g., half) pass along one side of the plate with the other cooling channels passing along the other side of the plate. 
       FIG.  7 D  illustrates the underside of plate  620 , and includes portions to which insulating material  650  is attached, and portions for which the baseplate  620   a  is exposed. 
       FIG.  8    is a perspective view of an illustrative stack of plates of a superconducting magnet, according to some embodiments. Stack of plates  800  represents an exterior perspective view of the stack of plates shown in cross-section in  FIGS.  6 A- 6 B . As in  FIGS.  7 A- 7 D , the cross-section of  FIG.  6 A  is through the section marked A-A′ and the cross-section of  FIG.  6 B  is through the section marked B-B′. 
     As shown in the example of  FIG.  8   , the terminal plates at the top and the bottom of the stack each comprise a conductive portion  838  and  848 , respectively, that extends outward from the stack and that are electrically connected to one another through the spiral conducting paths within the stack. Each cooling channel of the plates of the stack terminates at a common set of ports  870  at one end of the channel and at a common set of ports  880  at the other end of the channel. Since the ends of the cooling channels are arranged together, with all the inlets together and all the outlets together, a single large inlet or outlet port may be formed around the set of channels at each end, as shown in  FIG.  9   . This may allow coolant to pass through all the cooling channels of the stack of plates using just a single inlet pipe and a single outlet pipe. 
       FIG.  9    is a perspective view of an illustrative stack of plates of a superconducting magnet with an exterior case, according to some embodiments. Subsequent to assembly of the stack of plates, some or all of the exterior of the stack may be wrapped in an insulating material. In the example of  FIG.  9   , the entire stack of plates except for the cooling inlet and outlet  970  and  980 , and the ends of the terminal plates that include conductive portions  928  and  948 , are wrapped in an insulating material  950  such as polyimide (e.g., Kapton®), epoxy resin, phenolic resin, glass epoxy laminate, a plastic, an elastomer, or combinations thereof. According to some embodiments, the insulating material  950  may have a breakdown voltage or dielectric strength of greater than 25 kV/mm, of greater than 50 kV/mm, of greater than 75 kV/mm, of greater than 1000 kV/mm. In some cases, the voltages in the superconducting magnet may be comparatively low, in which case a low voltage standoff insulating material such as anodized aluminum could be utilized as the insulating material  950 . 
     Subsequent to application of the insulating material  950 , the stack of plates are enclosed within a case  990 , which provides further structural stability to the stack of plates and may comprise fiberglass, for instance. 
     As noted above, in some situations in which the HTS material is provided as an HTS tape, it may be desirable to vary the number of HTS conductors in a stack of co-wound HTS tapes according to their location within the magnet, thereby reducing the total amount of HTS tape needed to construct the magnet and controlling the value of R N  to be different for different turns of the coil. 
       FIG.  10    illustrates an example of one of the plates of the magnet design of  FIGS.  6 A- 6 B  in which the conducting channels  1014  comprise a stack of co-wound HTS tapes  1022  in addition to conductive co-wound tape  1023  (e.g., copper tape). As may be noted from  FIG.  10   , the number of HTS tapes is decreased in each turn going from right to left in  FIG.  10   , while the number of conductive co-wound tapes is increased right-to left. The width of the cap  1026  is varied in conjunction with number of conductive co-wound tapes such that their combined cross-sectional area is roughly constant in every turn. In this way, the resistance per unit length of the co-conductor is maintained constant throughout the winding pack. 
     Tuning the amount of HTS tape  1022 , co-wound conductive tape  1023 , and the size of the cap  1026  may provide a way to control the rate of magnetic energy dissipation during a quench, and in some cases may dissipate the magnetic energy uniformly throughout the winding pack during a full magnet quench event. In addition, tuning the amount of HTS tape  1022 , co-wound conductive tape  1023 , and the size of the cap  1026  may alter an amount of magnetic energy deposition in adjacent areas. This may allow, for instance, reduction of the magnetic energy deposition in critical areas such as in regions with joints. 
       FIG.  11    is a three-dimensional graphic of a fusion power plant with a cutaway portion illustrating various components of the power plant, according to some embodiments. A magnet within a fusion power plant may be formed from a superconductor arrangement as described above.  FIG.  11    shows a cross-section through a power plant and includes a magnet coil  1114 , which is fabricated from, or otherwise includes, a superconducting magnet comprising a stack of plates as discussed and described above, a neutron shield  1112 , and a core region  1111 . According to some embodiments, the magnet coil  1114  may be, or may form part of, a toroidal field coil. Magnet coil  1113  may be fabricated from, or otherwise includes, a superconducting magnet comprising a stack of plates as discussed and described above. According to some embodiments, the magnet coil  1113  may be, or may form part of a central solenoid and/or other poloidal field solenoidal coils. 
     Persons having ordinary skill in the art may appreciate other embodiments of the concepts, results, and techniques disclosed herein. It is appreciated that superconducting cables configured according to the concepts and techniques described herein may be useful for a wide variety of applications, including applications in which the superconducting cable is wound into a coil to form a magnet. For instance, one such application is conducting nuclear magnetic resonance (NMR) research into, for example, solid state physics, physiology, or proteins, for which such cables may be wound into a magnet. Another application is performing clinical magnetic resonance imaging (MRI) for medical scanning of an organism or a portion thereof, for which compact, high-field magnets are needed. Yet another application is high-field MM, for which large bore solenoids are required. Still another application is for performing magnetic research in physics, chemistry, and materials science. Further applications is in magnets for particle accelerators for materials processing or interrogation; electrical power generators; medical accelerators for proton therapy, radiation therapy, and radiation generation generally; superconducting energy storage; magnetohydrodynamic (MHD) electrical generators; and material separation, such as mining, semiconductor fabrication, and recycling. It is appreciated that the above list of applications is not exhaustive, and there are further applications to which the concepts, processes, and techniques disclosed herein may be put without deviating from their scope. 
     As used herein, a “high temperature superconductor” or “HTS” refers to a material that has a critical temperature above 30 K, wherein the critical temperature refers to the temperature below which the electrical resistivity of the material drops to zero. 
     Illustrative examples of conducting channels and cooling channels are described herein and illustrated in the drawings. It will be appreciated that the particular size and shape of these channels are provided merely as examples and that no particular cross-sectional shape or size is implied as being necessary or desirable unless otherwise noted. 
     Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled in the art. 
     Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Further, though advantages of the present invention are indicated, it should be appreciated that not every embodiment of the technology described herein will include every described advantage. Some embodiments may not implement any features described as advantageous herein and in some instances one or more of the described features may be implemented to achieve further embodiments. Accordingly, the foregoing description and drawings are by way of example only. 
     Various aspects of the present invention may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments. 
     Also, the invention may be embodied as a method, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments. 
     Further, some actions are described as taken by a “user.” It should be appreciated that a “user” need not be a single individual, and that in some embodiments, actions attributable to a “user” may be performed by a team of individuals and/or an individual in combination with computer-assisted tools or other mechanisms. 
     Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. 
     The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. The term “substantially equal” may be used to refer to values that are within ±20% of one another in some embodiments, within ±10% of one another in some embodiments, within ±5% of one another in some embodiments, and yet within ±2% of one another in some embodiments. 
     The term “substantially” may be used to refer to values that are within ±20% of a comparative measure in some embodiments, within ±10% in some embodiments, within ±5% in some embodiments, and yet within ±2% in some embodiments. For example, a first direction that is “substantially” perpendicular to a second direction may refer to a first direction that is within ±20% of making a 90° angle with the second direction in some embodiments, within ±10% of making a 90° angle with the second direction in some embodiments, within ±5% of making a 90° angle with the second direction in some embodiments, and yet within ±2% of making a 90° angle with the second direction in some embodiments. 
     Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” “containing,” “involving,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.