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The major applications that are based on the properties of the superconducting phase are

(i) Lossless power transmission (ii) Superconducting magnets (iii) Magnetic levitation

(iv) Superconducting memories and switches (v) Superconducting quantum interference devices.

(i) Lossless power transmission: The transmission of electrical power on a large scale is limited due to the restrictions on the current carrying capacity of trans- mission lines and their maintenance. Loss of power due to power dissipation in transmission lines due to the finite resistance offered by the cables is quite consid- erable. Further, due to the passage of the current, the metallic cable gets heated up thereby increasing the electrical resistance of the cables. This increases the joule heating losses further. If the transmission lines are made of materials in their superconducting state, their current carrying capacity increases. Since these lines do not offer any resistance to the flow of electric current, there is no power

dissipation due to joule heating. Thus, power losses are minimised and current carrying capacity is improved. This is the principle used in lossless power trans- mission.

(ii) Superconducting magnets: The problem of joule heating again puts a limit on the magnetic field that can be obtained in an electromagnet. The magnetic field generated in a coil depends on the strength of the direct current flowing through it. Any attempt to increase the magnetic field by increasing the current through the coil results in increasing the joule heating . This puts an upper limit on the current carrying capacity of the wire used and hence on the magnetic field produced. Use of superconducting coils in the electromagnets can enhance the magnetic field generated as they can carry large currents with practically no dissipation. This is the principle used in the construction of superconducting magnets. However, the limitation now comes in the form of the effect of magnetic field on the su- perconducting state of the coils. When the magnetic field generated exceeds the critical value at the operating temperature, the metal wire used in the coils will return to their normal state and start offering large resistance to current flow and drastically reducing the magnetic field generated.

(iii) Magnetic levitation: The principle of the repulsion of magnetic flux from a superconductor can be used in magnetic levitation applications. When a magnet is brought near a superconductor, there will be a repulsion and the superconductor tries to move away from the magnet. One of the reasons for a limitation to the speed of a train, for example, is the friction between the wheels of the train and the tracks on which the train moves. Superconducting wheels experience reduced friction on magnetic tracks. Alternatively, magnetic levitation may be used to reduce friction between the wheels of a train and the track on which it moves. It is well known that like poles of magnets repel and the friction between the wheels and the tracks get reduced when they are made like poles of magnets. The large magnitude of repulsive force required may be realized with the help of superconducting magnets. The principle can also be used in making friction-less bearings.

Practically, Maglev is a vehicle that runs levitated from the guideway, which is similar to the tracks in railways. This is achieved by using electromagnetic forces between superconducting magnets on the vehicle and coils on the ground. Levita- tion coils shaped like figure 8 are installed on the sidewalls of guideway (Fig.4.6 a). When the superconducting magnet attached to the vehicle passes below the centre of these coils, electromagnetic force pushes the magnets upwards thereby

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Figure 4.6 Effect of magnetic field on Type II superconductor.

levitating the vehicle. A repulsive force and an attractive force induced between the magnets are used to propel the vehicle ( Fig.4.6 b). The propulsion coils are located on the sidewalls of the guideway energized by alternating current. The superconducting magnets are attracted and pushed by the changing field thereby propelling the vehicle.

(iv) Superconducting memories and switches: The disappearance of superconduc- tivity for magnetic fields higher than the critical field is the principle used in the construction of a cryotron.

Control, Nb(9.2K) Core.Ta(4.4K) Liq.He(4.2K)

Figure 4.7 Construction of cryotron.

It consists of a core wire A around which a control coil B is wound (Fig.4.7). The core A is made of tantalum (Tc = 4.4K) and control coil B is made of niobium (Tc = 9.2K) or lead (Tc = 7.2K). The whole assembly is maintained at liquid helium temperature (4.2 K). At this temperature, both the control coil and the core

wire are in the superconducting phase. Hence, the resistance of the core wire will be zero. A current can be passed through the control coil to produce a magnetic field sufficient to make the core wire ‘normal’. Thus, the core wire can be made to possess zero or finite resistance depending on the control current being ‘off’ or ‘on’ respectively. These two states of the core wire may be considered as the ON and OFF states. Thus, cryotrons can be used as switches.

Based on the same principle is the construction of superconducting memory. If a current is induced in a superconducting ring, the current persists and continues to flow until a magnetic field is applied to make the ring normal, thereby allowing the current to decay. The direction of current flow may be used to represent the state of memory, namely ‘0’ or ‘1’.

(v) Superconducting quantum interference devices: The phenomenon of quantum mechanical tunneling has been used in the construction of some superconducting devices. Consider two metal electrodes separated by an insulator as shown in Fig. 4.8. The insulator normally acts like a barrier and does not allow the flow of electrons from one metal to another.

M ET AL 1 M ET AL 2

IN SU LAT OR

Figure 4.8 Metal-insulator-metal structure to study tunneling.

However, if the barrier is made sufficiently thin, there will be a finite probability that an electron will pass through the insulator. This is called tunneling. When both the metals are normal conductors, the current-voltage relation will be ohmic at low voltage levels. If the metals are in superconducting state, then, we ob- serve some interesting effects. A dc current may flow across the junction even in the absence of any electric or magnetic field. This is known as dc Joseph- son e_{ffect. When a fixed dc voltage V is applied across the junction,the phase} will vary linearly with time and an alternating current with a frequency (2e/~)V is generated. This is known as ac Josephson e_{ffect. Hence, a Josephson junc-} tion can act as a voltage-to-frequency converter. Josephson effect may be used to detect magnetic fields. It may also be used in the generation and detection of

electromagnetic radiations. A dc magnetic field applied through a superconduct- ing circuit containing two junctions causes the maximum supercurrent to show interference effects as a function of the applied magnetic field intensity. This is used in the construction of Superconducting Quantum Interference Devices (SQUIDs). B JOU T JIN A J1 J2

Figure 4.9 Construction of a SQUID.

Figure 4.9 shows the construction of a SQUID. A and B are two Josephson junc- tions connected in parallel to form a ring. Any current that enters at JIN will be divided into two components J1 and J2 which will pass through the junctions A and B respectively and recombine to produce the output current JOUT. If δa and δbrepresent the phase difference between the input current and the output current while passing through the insulator junctions A and B respectively, then,

δa= δb =δ0

Application of a magnetic field results in the modification of the phases of the two current components. When a magnetic field of flux density φ is applied at the centre of the ring as shown in the figure, the phase term for the current out of the two junctions will be modified as

δa =δ0− (eφ/hc) δb =δ0+ (eφ/hc) Hence the total current out of the ring will be

JOUT = J0[sin(δ0+ eφ/hc) + sin(δ0− eφ/hc)] = 2J0sin δ0· cos(eφ/hc)

This expression indicates that the output current varies with the applied magnetic flux and shows oscillations(Fig.4.10).

Φ J

Figure 4.10 Output current oscillations as a function of Magnetic flux.

The maximum value of current is given by

JOUT,MAX = 2J0sin δ0 when (eφ/hc) = nπ

where n is an integer. The sensitivity of the output current to variations in the magnetic flux φ is the basis for the applications of SQUIDs. In addition to being a very sensitive tool to detect and measure minute magnetic fields, they also find application as storage devices for magnetic flux, in magnetometry for geological exploration for identifying magnetic ore deposits, oil exploration, under-water exploration, in medical field for magnetic resonance imaging(MRI),etc.