vi
Preface
The situation is similar in superconductors. When a constant direct current flows in
a superconductor and quantized magnetic flux lines do not move, there is no energy
dissipation, but when an alternating current flows or when an alternating magnetic
field is applied, quantized magnetic flux lines move, and energy is dissipated in the
superconductor. In particular, the loss energy in a unit cycle of applied AC magnetic
field is independent of the frequency, and the loss is iron type in nature. Since the loss
energy is proportional to the area of the closed magnetization curve, this is called
hysteresis loss. On the other hand, the loss energy in most metals is copper type and
proportional to the frequency. The irreversibility associated with the copper-type
loss comes from the breaking of time reversal symmetry of the equation of motion,
although the mechanism has not yet been proved theoretically.
The irreversibility in superconductors can be proved theoretically, as shown in
this book. Then, the force balance equation used in the phenomenological critical
state model that describes irreversible phenomena in superconductors can be derived
using first principles. Here it should be noted that the flux pinning that is responsible for hysteresis losses originates from the interaction between flux lines and
pinning potentials. Hence, this interaction is essentially reversible in nature. In fact,
if we watch carefully, reversible electromagnetic phenomena can be observed. It
is also proved that, if the displacement of flux lines exceeds a reversible regime,
the phenomena become irreversible. The essence of the irreversibility in the critical
state in superconductors can be summarized by the statement that the force of defects
works to prevent flux lines from being driven by the Lorentz force. This results from a
biased statistical distribution of flux lines inside innumerable potentials in the superconductor. A certain phenomenon, i.e., an instability of flux motion in a pinning
potential well, is inevitable for realization of the biased distribution, as shown in this
book. This is quite analogous to friction and hysteresis in ferromagnetic materials.
In this sense, it can be said that theoretical understanding on irreversibility is slightly
advanced in the field of superconductivity.
In addition, it can be emphasized that a certain electromagnetic phenomenon
in superconductors is not widely known. This is the longitudinal magnetic field
effect observed in a current-carrying superconductor in a parallel magnetic field.
The peculiarity is represented by a dramatic increase in the critical current density,
i.e., the maximum non-dissipative current density, and the appearance of negative
voltage. It is empirically known that the force-free state (J × B = 0) is achieved
in this field configuration. That is, the current density J and the magnetic flux
density B are parallel to each other. Research on this phenomenon started in 1963
and has been conducted on metallic low-temperature superconductors. The hightemperature superconductors were discovered in 1986; however, and attention of
most researchers was attracted to these new materials. In addition, an appreciable
longitudinal magnetic field effect was not observed in high-temperature superconductors fabricated at that time due to weak-link grain boundaries that disturb current
flow. For this reason, the longitudinal magnetic field effect has not been investigated
for a long period, and only small number of researchers know about this effect now.
Preface
The situation is similar in superconductors. When a constant direct current flows in
a superconductor and quantized magnetic flux lines do not move, there is no energy
dissipation, but when an alternating current flows or when an alternating magnetic
field is applied, quantized magnetic flux lines move, and energy is dissipated in the
superconductor. In particular, the loss energy in a unit cycle of applied AC magnetic
field is independent of the frequency, and the loss is iron type in nature. Since the loss
energy is proportional to the area of the closed magnetization curve, this is called
hysteresis loss. On the other hand, the loss energy in most metals is copper type and
proportional to the frequency. The irreversibility associated with the copper-type
loss comes from the breaking of time reversal symmetry of the equation of motion,
although the mechanism has not yet been proved theoretically.
The irreversibility in superconductors can be proved theoretically, as shown in
this book. Then, the force balance equation used in the phenomenological critical
state model that describes irreversible phenomena in superconductors can be derived
using first principles. Here it should be noted that the flux pinning that is responsible for hysteresis losses originates from the interaction between flux lines and
pinning potentials. Hence, this interaction is essentially reversible in nature. In fact,
if we watch carefully, reversible electromagnetic phenomena can be observed. It
is also proved that, if the displacement of flux lines exceeds a reversible regime,
the phenomena become irreversible. The essence of the irreversibility in the critical
state in superconductors can be summarized by the statement that the force of defects
works to prevent flux lines from being driven by the Lorentz force. This results from a
biased statistical distribution of flux lines inside innumerable potentials in the superconductor. A certain phenomenon, i.e., an instability of flux motion in a pinning
potential well, is inevitable for realization of the biased distribution, as shown in this
book. This is quite analogous to friction and hysteresis in ferromagnetic materials.
In this sense, it can be said that theoretical understanding on irreversibility is slightly
advanced in the field of superconductivity.
In addition, it can be emphasized that a certain electromagnetic phenomenon
in superconductors is not widely known. This is the longitudinal magnetic field
effect observed in a current-carrying superconductor in a parallel magnetic field.
The peculiarity is represented by a dramatic increase in the critical current density,
i.e., the maximum non-dissipative current density, and the appearance of negative
voltage. It is empirically known that the force-free state (J × B = 0) is achieved
in this field configuration. That is, the current density J and the magnetic flux
density B are parallel to each other. Research on this phenomenon started in 1963
and has been conducted on metallic low-temperature superconductors. The hightemperature superconductors were discovered in 1986; however, and attention of
most researchers was attracted to these new materials. In addition, an appreciable
longitudinal magnetic field effect was not observed in high-temperature superconductors fabricated at that time due to weak-link grain boundaries that disturb current
flow. For this reason, the longitudinal magnetic field effect has not been investigated
for a long period, and only small number of researchers know about this effect now.