152
6 Longitudinal Magnetic Field Effect
(f) People’s interest is completely different. When the theory of relativity appeared
at the beginning of the 20th century, people in various fields were very interested in physics. When the force-free torque was discovered at the end of the
20th century, each research field was subdivided and deeply developed, so that
interest from another research field was significantly reduced. Although the
explanation of the longitudinal magnetic field effect represented by the forcefree torque was a proposal of an essential problem in electromagnetism, there
was no research field of electromagnetism in the existing main journals, and
the submission of a paper was possible only in the field of superconductivity.
Thus, the opportunity to attract the attention of researchers in various fields is
quite small now. In addition, the discovery of high-temperature superconductivity in 1986 attracted great interest from people and this had a bad effect on
the research on the longitudinal magnetic field effects, which were mostly done
on metallic superconductors. Even in the field of superconductivity, most young
researchers do not know about the longitudinal magnetic field effect. Now, many
professional people in this field have passed away or retired from research.
The author is a member of the last generation who experienced research on the
longitudinal magnetic field effect. Hence, he believes that the arrangement of the
essential points of important features of the longitudinal magnetic field effect is
his task for researchers in the next generations. It is hoped that publication of this
book will be useful for the purpose. The longitudinal magnetic field effect may be
completely forgotten in the future, however, with the rapid development of science
and technology. It is necessary, therefore, to apply this effect in useful technologies to
prevent the effect from being forgotten. Such a duty may be required of the author. In
the next chapter, the electromagnetic phenomena in superconductors are summarized,
and the technologies that superconductivity supports are introduced, including an
example of an application of the longitudinal magnetic field effect.
Coffee break (6)
Continuity equation for flux lines
The continuity equation for flux lines (5.34) describes the variation in the magnetic
flux distribution with time in a superconductor, based on using the velocity v of flux
lines. Josephson’s formula (4.41) can be derived under a certain condition from this
equation and from (2.49) for induction. Equation (5.34) is used for calculation of
the AC loss energy, as shown in Sect. 5.2. In addition, this equation is also used for
estimation of the displacement of flux lines, analysis of the reversible flux motion in
Sect. 5.3, performance of the virtual displacement, and the derivation of the Lorentz
force in Sect. 5.7. Equation (5.34) also plays an important role in the derivation of
the rotational motion of flux lines in the longitudinal magnetic field treated in this
chapter.
Equation (5.34) was originally derived expecting the situation where flux lines
move translationally. It is worth noting, however, that this equation can describe
general flux motion, including the rotation. Such an evolution in a theoretical
approach can be found in other cases. For example, the derivation of the law of
6 Longitudinal Magnetic Field Effect
(f) People’s interest is completely different. When the theory of relativity appeared
at the beginning of the 20th century, people in various fields were very interested in physics. When the force-free torque was discovered at the end of the
20th century, each research field was subdivided and deeply developed, so that
interest from another research field was significantly reduced. Although the
explanation of the longitudinal magnetic field effect represented by the forcefree torque was a proposal of an essential problem in electromagnetism, there
was no research field of electromagnetism in the existing main journals, and
the submission of a paper was possible only in the field of superconductivity.
Thus, the opportunity to attract the attention of researchers in various fields is
quite small now. In addition, the discovery of high-temperature superconductivity in 1986 attracted great interest from people and this had a bad effect on
the research on the longitudinal magnetic field effects, which were mostly done
on metallic superconductors. Even in the field of superconductivity, most young
researchers do not know about the longitudinal magnetic field effect. Now, many
professional people in this field have passed away or retired from research.
The author is a member of the last generation who experienced research on the
longitudinal magnetic field effect. Hence, he believes that the arrangement of the
essential points of important features of the longitudinal magnetic field effect is
his task for researchers in the next generations. It is hoped that publication of this
book will be useful for the purpose. The longitudinal magnetic field effect may be
completely forgotten in the future, however, with the rapid development of science
and technology. It is necessary, therefore, to apply this effect in useful technologies to
prevent the effect from being forgotten. Such a duty may be required of the author. In
the next chapter, the electromagnetic phenomena in superconductors are summarized,
and the technologies that superconductivity supports are introduced, including an
example of an application of the longitudinal magnetic field effect.
Coffee break (6)
Continuity equation for flux lines
The continuity equation for flux lines (5.34) describes the variation in the magnetic
flux distribution with time in a superconductor, based on using the velocity v of flux
lines. Josephson’s formula (4.41) can be derived under a certain condition from this
equation and from (2.49) for induction. Equation (5.34) is used for calculation of
the AC loss energy, as shown in Sect. 5.2. In addition, this equation is also used for
estimation of the displacement of flux lines, analysis of the reversible flux motion in
Sect. 5.3, performance of the virtual displacement, and the derivation of the Lorentz
force in Sect. 5.7. Equation (5.34) also plays an important role in the derivation of
the rotational motion of flux lines in the longitudinal magnetic field treated in this
chapter.
Equation (5.34) was originally derived expecting the situation where flux lines
move translationally. It is worth noting, however, that this equation can describe
general flux motion, including the rotation. Such an evolution in a theoretical
approach can be found in other cases. For example, the derivation of the law of