7.1 Summary
157
distributed pinning potentials. In particular, it should be emphasized that the irreversibility can be directly derived from this theory using a statistical method for the
energetic interaction, i.e., independently of the breaking of time reversal symmetry.
As a result, the irreversibility in which pinning loss becomes thermal energy is also
obtained. On the other hand, this theory also explains reversible phenomena that
are experimentally confirmed, since the interaction is caused by the pinning energy.
Based on this aspect it was realized that the force-balance equation in the critical
state model could be derived by minimizing the free energy, taking account of the
work done by the Lorentz force in the pinning potential field, and by extending it to
the irreversible case. As a result, the critical state model, i.e., a phenomenological
model, could be improved as a general theory. In the irreversible state, including the
resistive state, in which energy is dissipated, the first principles of minimizing the
energy cannot be used. For example, this point is clear in the process from point A
to point P in Fig. 5.16. At each instance in this process, the state is, however, almost
close to the state derived from first principles, and the associated energy dissipation
is at a minimum. Even for non-isolated systems, the state with minimum free energy
is attained in the reversible region, such as those in the process from point P to point
Q (see Appendix A.8).
Looking over a series of phenomena in superconductors, the idea that the superconductivity is a peculiar phenomenon may be said to be biased. No resistivity seems
to be strange. The resistivity is, however, a phenomenological property that cannot be
theoretically proved. On the other hand, the phenomena in superconductors, including
the flux pinning can be explained by first principles to minimize the free energy.
That is, superconductors are pure materials in physics. In addition, superconducting
substances are not minor, since many elements or compounds show superconductivity, when conditions such as high pressure or thin film geometry are included.
Only the transition temperature to the superconducting state is low. If room temperature superconductors are found in the future, the concept that superconductors are
peculiar may fade away.
The high-temperature superconductors discovered in 1986 that showed a rapid
development in their quality are not discussed in this book. This is because the
critical current density caused by flux pinning can be defined, the electromagnetic
phenomena are explainable using the irreversible critical state model, and the pinning
loss has a hysteretic nature, as in metallic low temperature superconductors. That is,
the main properties are essentially the same as the description in this book, although
there are still some points that need to be considered. These are described in Appendix
A.17.
157
distributed pinning potentials. In particular, it should be emphasized that the irreversibility can be directly derived from this theory using a statistical method for the
energetic interaction, i.e., independently of the breaking of time reversal symmetry.
As a result, the irreversibility in which pinning loss becomes thermal energy is also
obtained. On the other hand, this theory also explains reversible phenomena that
are experimentally confirmed, since the interaction is caused by the pinning energy.
Based on this aspect it was realized that the force-balance equation in the critical
state model could be derived by minimizing the free energy, taking account of the
work done by the Lorentz force in the pinning potential field, and by extending it to
the irreversible case. As a result, the critical state model, i.e., a phenomenological
model, could be improved as a general theory. In the irreversible state, including the
resistive state, in which energy is dissipated, the first principles of minimizing the
energy cannot be used. For example, this point is clear in the process from point A
to point P in Fig. 5.16. At each instance in this process, the state is, however, almost
close to the state derived from first principles, and the associated energy dissipation
is at a minimum. Even for non-isolated systems, the state with minimum free energy
is attained in the reversible region, such as those in the process from point P to point
Q (see Appendix A.8).
Looking over a series of phenomena in superconductors, the idea that the superconductivity is a peculiar phenomenon may be said to be biased. No resistivity seems
to be strange. The resistivity is, however, a phenomenological property that cannot be
theoretically proved. On the other hand, the phenomena in superconductors, including
the flux pinning can be explained by first principles to minimize the free energy.
That is, superconductors are pure materials in physics. In addition, superconducting
substances are not minor, since many elements or compounds show superconductivity, when conditions such as high pressure or thin film geometry are included.
Only the transition temperature to the superconducting state is low. If room temperature superconductors are found in the future, the concept that superconductors are
peculiar may fade away.
The high-temperature superconductors discovered in 1986 that showed a rapid
development in their quality are not discussed in this book. This is because the
critical current density caused by flux pinning can be defined, the electromagnetic
phenomena are explainable using the irreversible critical state model, and the pinning
loss has a hysteretic nature, as in metallic low temperature superconductors. That is,
the main properties are essentially the same as the description in this book, although
there are still some points that need to be considered. These are described in Appendix
A.17.