8
1 Introduction
In Chap. 2, the fundamental phenomena of elementary electromagnetism, which
are needed to understand electromagnetic phenomena in superconductors, are briefly
summarized. A special emphasis is placed on describing Maxwell’s equation for
electromagnetic induction, Poynting’s vector, which describes the flow of energy,
etc. These are used in other chapters. It may occur that knowledge on these matters
is required there. Please utilize effectively the knowledge in this chapter in such a
case.
In Chap. 3, the changes that occur in elementary electromagnetism are described,
when the magnetic phenomena in the Meissner state, i.e., perfect diamagnetism,
are introduced. The essential point is that the present E-B analogy becomes more
perfect, when the magnetic phenomena in superconductors satisfying B = 0 is
introduced, which corresponds to the electric phenomena in conductors satisfying
E = 0. The various advantages obtained by this introduction are introduced. It should
be mentioned that, in a substance in which B = 0, the electric resistivity must be
zero. Although this property might be peculiar from the experimental viewpoint, it
can be easily derived from Maxwell’s theory.
In Chap. 4, the Ginzburg-Landau theory, which describes electromagnetic
phenomena in type II superconductors used for various devices, is introduced. Based
on this theory, we study the structure of quantized magnetic flux (the flux line) with
a normal conducting region around the center, which is important in electromagnetic
phenomena in practical superconductors. Because of this structure, electrical resistance appears when flux lines are driven by the Lorentz force arising from current.
On the other hand, this structure contributes to the flux pinning that introduces a
non-dissipative current.
In Chap. 5, the flux pinning mechanism that determines the critical current density,
i.e., the most important parameter for application of superconductors, is introduced.
The pinning interaction between flux lines with spatial structure and defects is originally reversible with respect to the displacement of flux lines. In fact, reversible
electromagnetic phenomena can be observed within the range of small displacement
of flux lines, if we watch carefully, although practical phenomena are mostly irreversible. The irreversible phenomena can be described using the critical state model
that assumes the critical current density as a parameter. Magnetization and AC losses
are introduced, for example, as phenomena that can be explained by the critical state
model. On the other hand, a theory that estimates the critical current density caused
by pinning centers, which is called the summation theory, is reviewed from the
aspect of historical development. Summation theory that uses a statistical method is
also useful to explain a change from reversible to irreversible phenomena. Based on
this knowledge, the basic force-balance equation in the critical state model is derived
using first principles for the reversible case, and it is extended to the irreversible case.
As a result, the theory that describes the critical state can be obtained. In addition,
it is shown that the pinning loss power density calculated using a method equivalent to the statistical method in the summation theory agrees with the prediction of
the critical state model. Thus, two theories on the flux pinning, i.e., the summation
theory and the critical state theory, are unified. The argument is also discussed that
1 Introduction
In Chap. 2, the fundamental phenomena of elementary electromagnetism, which
are needed to understand electromagnetic phenomena in superconductors, are briefly
summarized. A special emphasis is placed on describing Maxwell’s equation for
electromagnetic induction, Poynting’s vector, which describes the flow of energy,
etc. These are used in other chapters. It may occur that knowledge on these matters
is required there. Please utilize effectively the knowledge in this chapter in such a
case.
In Chap. 3, the changes that occur in elementary electromagnetism are described,
when the magnetic phenomena in the Meissner state, i.e., perfect diamagnetism,
are introduced. The essential point is that the present E-B analogy becomes more
perfect, when the magnetic phenomena in superconductors satisfying B = 0 is
introduced, which corresponds to the electric phenomena in conductors satisfying
E = 0. The various advantages obtained by this introduction are introduced. It should
be mentioned that, in a substance in which B = 0, the electric resistivity must be
zero. Although this property might be peculiar from the experimental viewpoint, it
can be easily derived from Maxwell’s theory.
In Chap. 4, the Ginzburg-Landau theory, which describes electromagnetic
phenomena in type II superconductors used for various devices, is introduced. Based
on this theory, we study the structure of quantized magnetic flux (the flux line) with
a normal conducting region around the center, which is important in electromagnetic
phenomena in practical superconductors. Because of this structure, electrical resistance appears when flux lines are driven by the Lorentz force arising from current.
On the other hand, this structure contributes to the flux pinning that introduces a
non-dissipative current.
In Chap. 5, the flux pinning mechanism that determines the critical current density,
i.e., the most important parameter for application of superconductors, is introduced.
The pinning interaction between flux lines with spatial structure and defects is originally reversible with respect to the displacement of flux lines. In fact, reversible
electromagnetic phenomena can be observed within the range of small displacement
of flux lines, if we watch carefully, although practical phenomena are mostly irreversible. The irreversible phenomena can be described using the critical state model
that assumes the critical current density as a parameter. Magnetization and AC losses
are introduced, for example, as phenomena that can be explained by the critical state
model. On the other hand, a theory that estimates the critical current density caused
by pinning centers, which is called the summation theory, is reviewed from the
aspect of historical development. Summation theory that uses a statistical method is
also useful to explain a change from reversible to irreversible phenomena. Based on
this knowledge, the basic force-balance equation in the critical state model is derived
using first principles for the reversible case, and it is extended to the irreversible case.
As a result, the theory that describes the critical state can be obtained. In addition,
it is shown that the pinning loss power density calculated using a method equivalent to the statistical method in the summation theory agrees with the prediction of
the critical state model. Thus, two theories on the flux pinning, i.e., the summation
theory and the critical state theory, are unified. The argument is also discussed that