CHAPTER 3:

APPLICATIONS OF SUPERCONDUCTORS.

 A FEW WORDS ABOUT APPLICATIONS OF SUPERCONDUCTORS:

 BASIC JOSEPHSON JUNCTION CHARACTERISTIC:

    The gate may be biased in the "zero-voltage" state. The junction may be switched to the "non-zero" voltage state by one of two means:

  1. Increasing the gate current (Ig) above the critical (Icr) level.
  2. Decreasing the Icr level below the existing gate current level.
    The voltage rise-time on the junction is associated with parasitic junction capacitance and junction resistance.
    Generally, the superconductive state corresponds to a logic state of "0", the resistive state to a "1". The nonzero voltage level is essentially the threshold voltage Vg, which will range from about 1 to 3 mV for classical superconductors.
    Vg is related to the superconductor energy gap (D) by
 

    The symbol on the left is commonly used to represent the Josephson junction in circuit diagrams. On the right is the Stewart-McCumber equivalent circuit for a Josephson junction. The sinusoidal variation of current as a function of junction voltage V.

 LOGIC GATES:

    Gates may be placed into two general categories by the way they are driven:
 

 HIGH-ENERGY APPLICATIONS:

    High-Field Inuctors:
    Superconducting inductors that must transport relatively high current densities in high magnetic field have a variety of applicatrons:
  1. Coils for windings in motors and generators (Utility, automotive, marine propulsion applications).
  2. High-field magnets for research applications (Particle accelerators, material research).
  3. Magnetic Levitating (MAGLEV) coils for high-speed ground transportation.
  4. Superconducting Magnetic Energy Storage (SMES)(Electric utilities, Military applications).
  5. Magnetic containment fields for thermonuclear fusion research.
  6. MHD (Magnetohydrodynamic) EMT (electromagnetic thrust) systems for marine propulsion applications.
  7. MRI (Magnetic Resonance Imaging) which requires extremely uniform magnetic fields at the 10-20 kgauss level (formerly known as NMR, nuclear magnetic resonance).
 

 SUPERCONDUCTING MAGNETS:

    Twisting of superconducting Strands:
    An eddy current may be induced in adjacent strands of superconductor that are embeded in a normally-conducting substrate. This current, if substantial, can lead to quenching of the superconducting state. The eddy current is reduced by a practice familiar to electrical engineers who wish to reduce external magnetic fields around lines carrying alternating currents, that is, twisting of the individual pairs of superconductors. The shorter, the twist length L, of course, the more effective the technique. An approximate formula for the induced eddy current Jec is:

    Characteristic decay time t of the eddy currents after the source (B):

    In practice, strands are spaced rather closely together within the normal matrix material.
 

 MHD:

    The primary reason that superconducting generator configurations are being considered for utility applications is the reduction in size and weight, along with the capability of higher current densities.
    The torque tubes serve as torsional supports, but also retrain the field windings from the centrifugal forces and the enormous magnetic forces resulting from intense field currents. The armature winding (placed in stator-slots on the conventional rotor) is now an air-core winding coaxial to the torque tubes. The elimination of magnetic iron provides a number of advantages:
  1. The inherent inductive reactance of the armature is greatly reduced, resulting in improved dynamic machine perfomance and voltage regulation.
  2. Space for the armature winding is increased, which increases potential power density and generator efficiency.
  3. By elimination of the interleaved stator iron (at ground potential) insulation requirements on the armature are reduced and/or much higher voltage may be delivered at the armature terminals. Higher terminal voltage can eliminate the need for a step-up transformer.
    A pair of magnetic shields are used on the superconducting generator. The external shield serves the conventional purpose of shielding nearly metallic objects from eddy current induction as well as preventing forces from being exerted on magnetic objects. The rotor shield (which turns with the rotor) serves to prevent alternating voltage induction in the rotor structural components and in the superconducting field winding.
    It is important to note that superconducting generator, while benefiting enormously from the higher current densities that may be achieved with conventional superconductors, do not require the current densities that are commonly necessary for a variety of  high-field electromagnet applications.
 

 ANTENNAS, WAVEGUIDES:

    The new high-temperature superconductors may have advantages in antenna applications. It is important in many applications to have antennas that are small compared to wavelength of the energy to be transmited or received. This is not a particularly efficient approach, with metals in the normal state, since the ohmic losses in the antenna may be large compared to the effective radiation resistance. Clearly, any means of reducing this inherent resistance would tend to improve radiation efficiency, and this observatin leads quite naturally to the consideration of superconducting antennas where such would be practical.
    Low-temperature superconductors have been used to construct fraction-al-wavelength antennas, leading to a significant improvement in radiation efficiency. Obviously, the use of liquid helium as a cryogen tends to limit the application of such antennas.
    Another potential application for superconductors is in the construction of electromagnetic waveguides. The advantage over conventional metal waveguides would be at the higher frequencies. In the case of mm-sized waveguides, attenuation becomes prohibitive except for applications where the guide length is very short, that is, usually less than a meter. At mm wavwlengths, conventional metal guides have attenuations on the orther of 10 dB/m due the high value of surface resistance (Rs) of the metal walls at ~200 GHz.
 

 MAGNETIC SHIELDING:

    Shielding from high-frequency electromagnetic fields and low-frequency electric fields is relatively straightforward with conventional materials. Alternating magnetic flux in the incident wave induces voltages in the conductor; the induced voltages create currents that generate magnetic fields to cancel the incident H fields. This is, of course, a statement of Lenz's law. As long as the thickness and radius of curvature of the conducting surface is large compared to skin depth shielding using ordinary conductors such as copper or aluminum is relatively straigthforward and inexpesive.
    In contrast, shielding of low-frequency (or especially dc) magnetic fields normally involves the use of relatively expensive (and sometimes very thick) magnetic materials. One may consider these materials to be "short-circuiting" the applied magnetic flux. The reduction of these low-frequency or dc fields to arbitrarily low values becomes essentially a problem of cost and, the mass of shielding that can be tolerated for a particular application.
    The concepts of zero (dc) resistivity and the Meissner effect which have already been intraoduced are, of course, of criticall importance in the use of superconductors for electromagnetic shielding. Limiting factors in the use of superconductors for shielding applications involve the critical field (Hc) above which the material "quenches" and behaves like a normal conductor and the fact that superconductor resistivity increases with frequency of the applied electromagnetic field. The subjects of flux pinning and flux creep are also critical to shielding for low-frequency or dc magnetic fields.
    Recall Ohm's law and Maxwell equation:
    E must be zero since dc conductivity (s) is infinite, but if E is zero then B cannot change with time in the superconductor. If external magnetic fields (at the superconductor surface) are changing in time, and B cannot change in the superconductor. Lenz's law requires that screening currents must develop superficial fields to cancel the external H-field effects inside the superconductor. Since the conductivity is infinite, the currents are persistent. The arguments so far only take infinite conductivity into account and this is quite sufficient for shielding at high frequencies. For dc magnetic shielding Meissner effect and flux quantization must also be considered.

    AC Shielding:
    In the normal state, surface resistance is a function of the skin depth (d) and conductivity (s) of the conductor, that is,

the surface resistivity (Rs) tends to increase with frequency, since skin depth is inversely proportional to the square root of frequency:
    If one is primarily concerned with the required thickness of the shield, superconductors are superior to normal metals until a frequency is reached where skin depth for a normal metal becomes comparable to London penetration depth for the superconductor (l).
    A comparison of skin depth and London penetration depth is not the dominating consideration. The superconductor will become normal at a cutoff frequency (fc) where the "photon" energy hfco is equal to the full energy gap (2D):
    There is interest in using the high-temperature ceramic superconductors is shield applications for the usual reasons: the availability and low cost of liquid nitrogen.

    DC and Low-Frequency Shielding:

    A fixed amount of flux is trapped by the deflated shield, but when the shield is expanded (below Tc), the internal flux density is reduced due to the greater affective area of the expanded shield. This method can (theoretically) be repeated, that is, expanding shields within expanding shields, to eventually provide a net shield where no trapped lines will exist in the innermost shielded volume. By this method, fields have been decreased on the order of 500 per folded enclosure. Such configurations are also referred to in the literature as "bladders" and "baloons".