OF HIGH-TEMPERATURE SUPERCONDUCTORS

This invention was made with Government support under Contract No. W-31-109-ENG-38 awarded by the Department of Energy. The Government has certain rights in this invention.

The present invention is concerned generally with a method and device for protecting and stabilizing a high temperature superconductor system. More particularly, the invention is concerned with a method and device for protecting high temperature superconductor systems from being damaged or from destabilizing by reason of momentary loss of superconductivity in part of the system. The inventive device operates to enable use of high current densities with very low ratio of stabilizer material to high temperature superconductor material. The device further functions to prevent catastrophic heat buildup in the high temperature superconductor system arising from sudden thermal anomalies in the system. Such thermal anomalies are also dissipated without damage to the superconducting system materials.

A major advantage of superconductors generally is their ability to carry very high current densities without electrical resistance. This advantage enables, for example, the production of high magnetic fields for electrical energy converters, such as motors and generators, with resulting high power density. As long as superconductivity is maintained, there is no heat generation in the device. However, if superconductivity is momentarily lost in any part of the device, local heating will develop. Such local heating can lead to melting of materials making up the superconducting system and even resulting in catastrophic failures. The ability to handle such a momentary loss of superconductivity, e _^ , to stabilize against such disturbances, is a major unresolved challenge in the design of superconducting equipment, particularly for high temperature superconductor systems.

There are two major approaches in stabilizing superconductors generally, and the preferred approzch is based on whether heat generation is larger or smaller than heat removal capacity. Both stabilizing approaches invariably involve fabricating the conductor in such a way that a normal metal conductor, or stabilizer, runs parallel to and has good electrical contact with the superconductor so that there is an alternate electrical path should the superconductor lose its superconductivity in any part of the circuit. Typically, the electrical resistivity of the superconductor when it is in the "normal" (nonsuperconducting) state is much higher than the resistivity of a normal metallic conductor, such as copper or silver. Another design feature for a stabilizing system generally is the presence of a cryogenic fluid to remove any heat that may be generated in the superconductor/stabilizer composite.

In the first stabilization method, one can effectively cryostabilize at all times. In this method, one ensures that the heat removal rate everywhere along the conduction path is larger than the maximum heat generation rate when all or part of the superconductor is in the normal state. In a conventional low-temperature (liquid helium typically) superconducting device, cryostability is usually characterized by a relatively low current density in the superconductor, and/or a relatively high ratio of stabilizer to superconductor. The net result is a low current density flow in the composite system of superconductor/stabilizer.

In the second stabilization method, the device is configured such that the occurrence of a normal zone in the superconductor is very unlikely to occur. However, if a transition to the normal state does occur, one allows the magnet to quench in such a way that the normal zone quickly propagates throughout the entire device. The energy that was stored in the magnetic field of the device is then dissipated uniformly through the device. The device warms up as it deenergizes, and usually the temperature rise is not large enough to damage the superconducting system. If the normal zone, however,

remains localized, then the entire energy in the magnet can be deposited in one spot. Because the heat generation rate is larger than the cooling rate, the temperature can increase substantially. If the superconducting system temperature increase becomes too large, the superconductor materials or the stabilizer portion could melt or the system otherwise be severely damaged. Typically, the composite current densities are relatively high in magnets or devices stabilized in this way, usually because a low ratio of stabilizer to superconductor is employed.

The stabilizer component is typically composed of copper, aluminum, or silver. Both stabilization methods have been used with low-temperature superconductors operating in liquid or superfluid helium. The heat flux in pool boiling of liquid helium is limited to about 2 W/cm^, and this in part gives rise to the limitation of the relatively low current density in cryostabilized conductors.

High-temperature superconductors, comprised primarily of the three systems, Y-Ba-Cu-O, Bi-Sr-Ca-Cu-O, Tl-Ba-Ca-Cu-O, and their derivitives, offer the opportunity to operate superconducting devices at higher temperatures, for example at liquid nitrogen temperatures, and therefore reduce the refrigeration costs associated with such devices. Even though the heat flux from pool boiling in liquid nitrogen may be as high as 10 to 20 W/cm^, cryostability by pool boiling does not however result in much higher maximum current density at 77 K than is achievable at 4 K with low temperature superconductor systems.

Allowing the magnet to quench does not therefore appear to be a very useful stabilizing method at temperatures much above 20 K. Prior art analysis has shown that normal-zone progation velocities are sufficiently high at 20 K such that traditional magnet quench methods are adequate. However, at temperatures much higher than 20 K (such as at 77 K), these velocities are much too low and one cannot presume magnet protection can be achieved by propagation of the normal zone along the superconductor.

It is therefore an object of the invention to provide an improved method and device for stabilizing a high temperature superconducting system.

It is another object of the invention to provide a novel method and device for damping anomalous thermal events in a high temperature superconductor system.

It is a further object of the invention to provide an improved method and device for accommodating thermal spikes arising from high temperature superconductor quenching.

It is still another object of the invention to provide a novel thermal quench cooling system within a high temperature superconductor system.

It is an additional object of the invention to provide an improved method and device for allowing enhanced current carrying capacity in a high temperature superconductor system while avoiding catastrophic thermal anomalies or damage to the system during superconducting quench events.

It is yet a further object of the invention to provide a novel method and device for protecting a high temperature superconductor system against thermal quench anomalies while having minimum stabilizer material and enhanced current carrying ability.

It is still an additional object of the invention to provide an improved microchannel cooling system for control of thermal quenching of a high temperature superconductor system.

It is another object of the invention to provide a cryostable high temperature superconductor system constructed from a plurality of pancake coils operating with high current density and reduced stabilizer material.

The advantages and objects of the invention will become apparent by reference to the following Detailed Description, Claims and drawings described hereinbelow, wherein like reference numerals refer to like elements throughout the several drawings.

Brief Description of the Drawings

FIGURE 1A illustrates one embodiment of a partial section of a cryostabilizer system constructed in accordance with the invention and FIG. IB shows another embodiment of the invention;

FIGURE 2 illustrates a partial section of an integrated cryostabilizer system;

FIGURE 3 A shows a partial section of a cryostabilizer system with a separate truncated cooling fin element and FIG. 3B illustrates a partial section of a separate rounded cooling fin element;

FIGURE 4 illustrates a partial section of a pancake-coil geometry of a cryostabilizer system;

FIGURE 5 shows another form of series positioned pancake- coil section of a cryostabilizer system;

FIGURE 6 illustrates a further form of spiral wound pancake- coil geometry;

FIGURE 7A shows a cryostabilizer system having a preferred microchannel system and FIG. 7B illμstrates a cryostabilizer system with a macrochannel system;

FIGURE 8 illustrates the variation of a stability parameter ratio versus a coolant microchannel aspect ratio;

FIGURE 9 shows the variations of a pressure ratio as a function of thickness ratios and coolant channel aspect ratio; and

FIGURE 10 illustrates the variation of the thermal geometric variable ka/h versus coolant channel height and tip temperature. Detailed Description of Preferred Embodiments

A cryostabilizer system constructed in accordance with the invention is indicated generally at 10 in the drawings. A superconductor 12 is positioned in good electrical contact with a stabilizer 14. The stabilizer 14 has heat conducting fins 16 that act with cover plate 18 to make flow passages 20. A cryogenic fluid 22 flows in or out of the page through flow passages 20. The flow passages 20 (or "microchannels" 20), have a height "h" and the width "w" of these flow channels which are typically less than about

one mm and could be as small as several microns. The flow channels 20 and the fins 16 can take on a wide variety of aspect ratios (h/w). When the superconductor 12 is in the superconducting state, very little heat flows from the stabilizer 14 to the cryogenic fluid 22. If a disturbance causes the superconductor 12 to enter the "normal" high resistance electrical state, then most of the current in the vicinity of the disturbance will flow in the stabilizer 14. Joule heating in the stabilizer 14 will then cause it to warm, and significant amounts of heat will flow from the stabilizer 14 into the cryogenic fluid 22. Electrical current, j, can flow either left or right through the superconductor 12 or the stabilizer 14. In this case the microchannels 20 and flow of the cryogenic fluid 22 are transverse to the electrical current.

The superconductor 12 is preferably a ceramic superconductor with a transition temperature above the boiling point of nitrogen; however superconducting materials with lower transition temperatures can also be used. The stabilizer 14 is preferably a metal with good electrical conductivity in the temperature range of operation. Silver is preferred because it does not chemically react with most of the ceramic superconductors. Other example stabilizer materials which can be used include, copper, aluminum, and beryllium. The cryogenic fluid 22 can be any fluid that remains a liquid in the temperature range of operation. A preferred type of the cryogenic fluid 22 is nitrogen, but other useful liquids can include hydrogen, neon, and oxygen. In addition, one can use mixtures of the above-mentioned cryogenic fluid 22 or with helium. The cover plate 18 can be either an electrical conductor or insulator. If the cover plate 18 is a conducting material, then an electrical insulator must also be used when more than one of the systems 10 are positioned parallel next to each other.

Preferably, the cryogenic fluid 22 is subcooled and remains liquid throughout, entering the system 10 and then leaving the system 10 at some higher temperature that is below the boiling point

of liquid nitrogen. We note here that this method would be impractical for superconductors cooled only by liquid helium because the temperature rise of the cryogenic fluid 22 is too small to remove much heat. It is thus a significant advantage that one can use high-temperature superconductors with the cryogenic fluid 22 having liquid-phase temperature ranges over many degrees while still maintaining the superconductor in the zero resistance state.

Alternatively, one can allow two-phase liquid flow (such as liquid oxygen and nitrogen) to occur in part or all of the microchannels 20 and to accomplish the desired effect.

In another embodiment of the invention, the electrical current flow is in and out of the page as depicted in FIG. 1. In this case the microchannels 20 and the flow of the cryogenic fluid 22 are parallel to the current flow direction. In another embodiment, shown in FIG. IB, the stabilizer 14 and the microchannels 20 are disposed on either side of the superconductor 12.

The superconductor 12 can be formed by any conventional technique, such as powder-in-tube, thick-film, or thin-film methods. For the embodiments shown in FIG. 1, the microchannels 20 are formed on the outside of the stabilizer 14. The microchannels 20 can be formed on the outside of the stabilizer 14. The cover plate 18 can be permanently attached to the stabilizer 14 by welding, soldering, or chemical bonding. Alternatively it could be mechanically clamped by compression, which would allow removal if needed.

A further embodiment is shown in FIG. 2. In this case the superconductor 12 and the stabilizer 14 are one connected or integrated unit. The microchannels 20 are formed within a separate channel container 24 in which the conducting fins 26 are contained. The advantage here is that the stabilizer 14 can be made out of silver which is expensive but does not chemically interact with the superconductor 12. It could be made relatively thin if desired. The channel containing piece 24 could be made out of a less expensive material such as copper or aluminum and joined to the

superconductor 12 and the stabilizer 14, after the superconductor 12 is fabricated. The joining can be performed chemically or by soldering, brazing, or welding, or via a mechanical compression. The pieces could also be joined by cleaning the respective surfaces in a vacuum and then bringing the pieces together. If the channel containing piece 24 is an electrical conductor, it can carry part of the current.

In another form of the invention shown in FIG. 2, the channel containing piece 24 is a non conductor, such as SiC, which has a high thermal conductivity at cryogenic temperatures. It is desirable that the fins 16 in FIG. 1 and the conducting fins 26 in FIG. 2, have a high thermal conductivity so that the height of the microchannels 20 can be made large and the width of the conducting fins 26, "b" in FIG. 2, can be made small. This results in an increase in the effective heat transfer area. As illustrated in FIG. 1, a further embodiment includes sandwiching the superconductor 12 between the stabilizer 14 and having the microchannels 20 on either side.

A further embodiment can include several of the channel containing pieces 24 stacked on top of each other to increase the total cryogen flow. This would be particularly desirable if the channel containing piece 24 were an electrical conductor.

In a further embodiment, if the channel containing piece 24 is an electrical conductor, the stabilizer 14 can be absent in FIG. 2 as long as good electrical contact can be made between the superconductor 12 and the channel containing piece 24.

A further embodiment is shown in FIG. 3 A wherein the superconductor 12 and the stabilizer 14 are as shown hereinbefore. Separate fin pieces 28 are positioned between the stabilizer 14 and the cover plate 18. The separate fin pieces 28 can be made by cutting small lengths of a long wire of the appropriate shape and placing them side by side along the stabilizer 14. The separate fin pieces 28 can be either chemically bonded to the stabilizer 14 or the cover plate 18 or can be held in compression mechanically between

the stabilizer 14 and the cover plate 18. The fin pieces 28 preferably have a high thermal conductivity, and can be either electrically conducting or nonconducting. The fin pieces 28 can also be a variety of shapes, for example, as shown in FIG. 3B.

In FIGS. 1-3, superconductor 12 takes the form of a tape conductor with the tape thickness in the vertical direction as viewing the figures. For example, in FIG. 1, if the current is from left to right, then the tape length is left to right and tape width is in and out of the page. If the current is in and out of the page, then the tape length is in and out of the page and the tape width is from left to right. It should be further understood that another embodiment of the cryostabilizer system 10 can have the superconductor/stabilizer part comprised of multifilaments of the superconductor 12 embedded in the stabilizer 14, and these filaments can be either parallel or twisted in such a way as to reduce eddy currents. The twisting and sizing of the filaments are well understood in the art of design and manufacturing of superconductors.

One of the primary applications of the cryostabilizer system 10 is to form magnets. This construction gives rise to manifolding structures for flow passages of the microchannels 20. One embodiment of the cryostabilizer system 10 for construction of a magnet is a pancake-coil geometry as shown in FIG. 4. In a pancake coil 30, a conductor 32, often a tape or ribbon shape, is wound in a spiral pancake 34, with the thickness of the ribbon conductor 32 being in the radial direction, and the width of the ribbon conductor 32 being in the vertical direction. Additional ones of the spiral pancake 34 can be disposed above and below the pancake 34 to form a long solenoid. The individual pancakes 34 are electrically connected together by joining strips 36 which can be either normal metal or superconductor. Other structures, such as toroids, can also be formed in a similar manner.

In this embodiment used to construct magnets, each of the conductors 32 is composed of the microchannel-cooled

cryostabilizer system 10 shown in FIGS. 1-3 and described hereinbefore. The flow for each of the microchannels 20 is derived from manifolds 38 which are fed from inlet ports 40 and feed outlet ports 42 (see FIG. 4). One or more of the inlet ports 40 and the outlet ports 42 can be present around the circumference of the solenoid at each level. One way to mechanically form the pancake coil 30 is to wrap each spiral on a forming structure 44. A tensioning strap 46 can be wrapped around each spiral to put the entire coil structure under compression. In FIG. 4 only three layers of the ribbon conductor 32 are shown for each of the spiral pancakes 34. It should be understood that many more of the ribbon conductor layers 32 can be used to form each of the spiral pancake 34.

It should be understood that the manifold structure can be subdivided so that one of the manifolds 38 need not feed the entire spiral pancake 34. For example, each individual one of the ribbon conductor layers 32 can have its own submanifold.

A further embodiment is shown in FIG. 5 wherein several of the spiral pancakes 34 have been placed in series flow to connect the inlet manifold 38 and outlet manifold 38*. Spacers 48 act to provide a small gap between the adjacent spiral pancakes 34 so that the microchannels 20 do not have to be aligned. The spacers 48 thus form a mini-manifold between the spiral pancakes 34, but form a manifold in which there is no feed port 42. The spacers 48 also act to electrically insulate the spiral pancakes 34 from each other, except for the connecting strips 36. The limit to the number of the spiral pancakes 34 that can be connected in series flow is typically determined by the maximum tolerable pressure drop through the microchannels 20, which in turn will depend on the size of the microchannels 20. It is expected that microchannel flow lengths can be up to at least about a meter.

A further embodiment is shown in FIG. 6. The cryostabilizer 10 is still wound to form the spiral pancake 34, but the conductor width is transverse to the magnet axis. The electrical current still

flows circumferentially around the magnet. In this particular embodiment, the superconductor 12 and the stabilizer 14 are in good thermal contact with the microchannels 20, forming a winding ring 52. The winding rings 52 can be stacked together and feed into or out of flow manifolds 54. One of the advantages is that the microchannels 20 can be fabricated separately from the overall cryostabilizer 10 and more than one of the cryostabilizer 10 can be used with each of the microchannels 20. Clearly the type of structure shown in FIG. 6 can be repeated radially and vertically to build a magnet.

In a preferred form of the cry stabilizer 10 one can choose to generate a range of performance output by performing a characterization analysis of the system shown schematically in FIG. 7. The stabilizer 14 (such as Ag) is bonded to the superconductor 12, and microchannels 20 are located on top of the stabilizer 14. A cover plate (not shown in the figure) confines the flow of the cryogenic fluid 22. For reasons discussed later, we assume that the coolant flow direction is peφendicular to the current direction as shown in FIG. 7. In the cryostabilizer 10, the microchannel 20 is subdivided by the conducting fins 16 that are in good thermal contact with the stabilizer 14. We begin the characterization analysis using the Stekly stability parameter α, which is defined as, -= G _c A /ΘH, (1) where G _c is the local critical heat generation rate per unit volume, A = b(tA + tHTS) i ^{s me} cross-sectional area of the "composite" conductor (the stabilizer 14 plus the superconductor 12) in the direction of the coolant flow, t is thickness, b is the length of the system in the direction of the current, θ is the cooled perimeter value, and H is the heat flux removed by the cryogenic fluid 22. A system is generally cryostable if α < 1. In Eq. (1), we have assumed that the current is completely transferred to the stabilizer 14 and the heat generation rate G _c is,

G _c = pλ ² J _c ² / (l - λ), (2) where p is the electrical resistivity of the stabilizer, λ = tHTS^HTS + Ag) is the fraction of the superconductor 12 in the composite, and J _c is the critical current density of the superconductor 12. The walls of the microchannels 20, with the exception of the cover plate 18, are assumed to be made of metals or alloys with high thermal conductivity. If the side wall thickness "a" is much smaller than the length of the conductor, "b", then the cooled perimeter is approximately (See FIG. 7A), θ = b[\ + 2t _t / {w + a)], (3) where w is the width of the microchannel 20, and tf is the height of the microchannel 20. The heat flux H at any axial location along the coolant flow direction is where h is the heat transfer coefficient, T _w is the temperature of the stabilizer 14, and T ₀ is the bulk coolant temperature. Substituting Eqs. (2), (3), and (4) into Eq. (1), α = pJ λt HTS (5)

(l - λ)A(7 - 7 )(l + 2η) where η is the coolant channel aspect ratio, r = t _f / (w + a) ≡ t _f / w. (6)

In Eq. (6), we have assumed that w » a. It is seen from Eq. (5) that the stability of the cryostabilizer 10 depends on (in addition to the usual parameters λ, p, h, etc.) the thickness of the superconductor 12, t _HTS , and the microchannel aspect ratio, η.

For the purposes of comparison, a similar expression can be derived for a macrochannel system 70 shown in FIG. 7B, α* = p ^j _c λ t _HTS

(7)

(l - λ *)Λ * (r, _P - r _β )(l + 2η) * where the superscript denotes the parameters of the macrochannel system 70. Assuming that t _HTS = t * _HTS and (T _w - T ₀ ) = (T _w - T ₀ )*, dividing Eq. (5) by Eq. (7) gives,

If we further assume that t Ag ⁼ tf + tA σ, then Eq. (8) becomes,

5-* * (i+Q ₍₉₎

Λ(l + 2η) where ζ is the coolant to stabilizer ratio, = i t _Ag (10)

Equation (8) or (9) determines the improvement in cryostability when switching from the macrochannel 70 to the microchannel system 20. One would usually like to have an o ratio as small as possible in order to maximize the gain in stability. However, there are other design constraints which also depend on the parameters that appear in Eq. (9), and these features are considered hereinafter.

The pressure drop increases as the size of the system generally decreases. It is know in general that there is some difference in pressure drop between a microtube and a larger system which satisfies the conventional correlations. However, the difference is not very large, and for the puφose of comparison here we can ignore this difference and employ the conventional formula for both the microchannels 20 and the macrochannel system 70. We consider the flow to be laminar (the analysis for turbulent flow can be carried out in a similar manner), and the pressure drop for the microchannels 20 is, δ P = f(>? / d)(γ v ² / 2) = (64 / Re)(^ / d)(γ v ² / 2) = 32μ>? v / d ² , (11) where f = 64/Re is the friction coefficient, £ is the axial length in the flow direction, Re is the Reynolds number, d is the hydraulic diameter, γ is coolant density, μ is coolant viscosity, and v is coolant average velocity. The hydraulic diameter of the microchannel 20 is, d = 2wt _f / (w + t _{ ). (12)

The pressure drop and the hydraulic diameter for the macrochannel 70 are, δP = 32μi * v * /{d *f , (13)

d* = 2bt * _ϊ l(b + t * _i ). (14)

Since b is usually much larger than t _f and i = t , Eqs. (11) to (14) can be combined and simplified to give

The heat transfer coefficient of laminar flow in the microchannels 20 can be evaluated by the following correlation, h = 0.00972 k (γ / μ)' ¹⁷ (Pr) ⁰³³³ d ^ul v ¹¹⁷ (16) where k is the thermal conductivity of the coolant, and Pr is the Prandtl number of the coolant. Equation (16) is also applicable to the macrochannels 70, and we can obtain the following equation for

Substituting Eq. (17) into Eq. (9)

A second constraint is the overall coolant temperature rise through the microchannels 20. To prevent boiling in the microchannels 20, the coolant temperature rise should be kept within a certain limit. The coolant temperature rise, δT, can be calculated by applying an energy balance for the system, δT = (G _c / yC _p ) τ (l + α / w) / ζ, (19) where Cp is the specific heat of the cryogenic fluid 22, τ is the coolant residence time, τ = r? / v, (20) and ζ is the coolant to conductor ratio, ζ = '- / (' 'rr ( ²¹ )

A third constraint is related to the cooling efficiency of the side walls of the microchannels 20. These side walls are the fins 16 which serve to increase the heat transfer area between the conductor stabilizer and the cryogenic fluid 22. Using a one-dimensional approximation, the temperature at the tip of the fin 16 (T _t jp) can be calculated by,

where k _w is the thermal conductivity of the side walls of the microchannel 20 and T* is the dimensionless tip temperature,

T* = (τ _tιp - T ₀ ) / {T _W - T ₀ ) (23)

In order for the entire side wall to be most effective, T^p should not deviate too much from T _w .

The characterization analysis has been performed in accordance with the above conditions and shown here in two parts. First, we present a comparison between the microchannels 20 and the macrochannel system 70. An example is provided to demonstrate how various design constraints affect a specific microchannel based system.

*

FIG. 8 shows the variations of the ratio α/α with η and ζ, calculated by Eq. (18) with v/v = 1 and tf t*f = 0.2. It is clear that stability can be enhanced by using the microchannels 20 in the system as compared to the macrochannel system 70. It is seen that

^* 4 ^* the ratio α/α decreases shaφly with η until η reaches approximately ten, then the variation becomes more gradual.

FIG. 9 shows the variations of the pressure ratio δP/δP* with η and the ratio tf tf , calculated by Eq. (15) with v/v* = 1. The pressure ratio increases shaφly with η and decreases with the ratio tf tf* (note that the vertical scale in FIG. 9 is logarithmic). Thus, cryostability can be enhanced by using the microchannels 20. but there is an increased pressure drop when compared to the

macrochannel system 70. The larger the gain in stability, the higher the pressure drop.

As an example, we carry out the following calculations to determine the stability margin of a liquid nitrogen-cooled form of the microchannels 20 and to demonstrate how the various design constraints affect a given system. We base the example on use of the stabilizer 14 being made of silver. Assuming that the following parameters are provided as input:

J _c = 10 ⁹ A / m ² , T _w - T ₀ = 20 K,t _ms -= l50μm, t _Ag = 150μ , t _f = 200 μ , w = 40 μm, a = 10 μm, and v = 5 m / s.

The electrical resistance of pure annealed silver at T=80K is p = 2.90 x 10 ^~ 9 Ωm. From these values, we obtain the following, η = t _f / w = 5 λ = t _HTS / (t _HTS + t^ ) = 0.50 d = 66.1 μm, Re = 1703, and h = 1.624 x lO ⁴ W/ m ² - K. The flow is laminar because the Reynolds number is less than 2300. Substituting these values into Eq. (5), α=0.122<l . Thus the system is not only stable but also has a large margin which can be used, for example, to reduce pressure drop and increase the fraction of the superconductor 12 in the composite. The pressure drop can be calculated by Eq. (11) and the results are, δP=0.284MPa; if >?=0.05m, and δP=0.568MPa, if ).10m. The pressure drop increases linearly with the flow length I. At i =0.10m, the pressure drop is already close to 5.7 atms. In order to keep the pressure drop at acceptable levels, the flow length of the microchannels 20 should preferably be minimized. Thus, in the most preferred form of the invention one can make the flow of the cryogenic fluid 22 in a direction peφendicular to the direction of the

current shown in FIG. 7. In this configuration one has the flexibility of varying the flow length. This has major impact on the design of superconducting magnets and manifolding systems.

From the values given previously in the example, we can calculate the heat generation rate per unit volume of the composite conductor and some other relevant parameters,

G _c = 1.45 x l0 ⁹ Wl m ζ = 0.666, and a / w = 0.25 The density and specific heat of liquid nitrogen at T=80K are γ = 807.3 kg I m and C _p = 2.05 \kJ I kg - K; respectively. If we choose a flow length of _* ?=0.05m, then τ =0.0 Is. Substituting these values into Eq. (19) resulted in δT=16.5K. This temperature rise is not unreasonable for liquid nitrogen or nitrogen/neon mixture.

Finally, we check the tip temperature which preferably does not deviate substantially from the stabilizer temperature. FIG. 10 shows the variation of the parameter k a/h with the coolant channel height and the dimensionless tip temperature, as calculated by Eq. (22). The thermal conductivity of silver (k _w ) at T=80K is 471 W/m- K. From the values given in the example, we have t _τ = 200 mm, and k _w a / h = 2.90 x 20 ^~7 . From either FIG. 10 or Eq. (22), we obtain

T* = (τ _tip - T _o ) - (T _w - T _o ) = 0.Sll, md

T _ύp - T ₀ = \1.54K Therefore, instead of 20K, the temperature difference available for heat removal at the tip is 17.54K.

While preferred forms of the invention have been shown and described, it shall be understood by those of ordinary skill in the art that the full scope of the invention is described by the claims and their equivalents.