Appendix
195
A.12 On the Flux Cutting
Various contradictions that arise under the assumption that flux lines must move
translationally have been evaded by assuming that flux cutting exists. Almost all of
them can be reasonably explained, however, by the rotational motion of flux lines
driven by the force-free torque, although it is not easy to directly identify which
mechanism is at work from the experimental results that have been explained by the
flux cutting model. This is the reason why the flux cutting model is used even now.
Hence, it is necessary to examine it theoretically from various aspects. In this section
the problems related to flux cutting are comprehensively argued. An argument will
be presented following each viewpoint.
(1) No inevitability of flux cutting
All of the electromagnetic phenomena that were believed to be explained only by
the flux cutting, such as the deviation of the induced electric field from Josephson’s
formula or the steady magnetization in the resistive state, as shown in Fig. 6.3, can
be explained without the flux cutting. It is possible to raise other examples. This
is because the flux cutting and flux rotation are equivalent to each other from the
viewpoint of macroscopic electromagnetic phenomena.
This theoretical point was already presented in Sect. 6.1. That is, the flux cutting
is a concept used to explain the phenomena by assuming Josephson’s relationship
for translational movement of each component of flux lines, although Josephson’s
formula does not hold.
As shown in Sects. 5.7 and 6.3, and Appendix A.7, when a current is induced in
a superconductor by changing the external magnetic field, the energy that invades
the superconductor exceeds the increase in the magnetic energy, and the excess
energy, i.e., the work done by the driving force or torque to release the strain of
flux lines in the regime of reversible flux motion, is stored as an increase in the
pinning energy. If the rotational shear distortion of flux lines cannot be stabilized
by the pinning interaction in the longitudinal magnetic field, such an energy balance
cannot be explained, resulting in a theoretical contradiction. If it is assumed that flux
cutting occurs in this situation, the excess energy is the magnetic energy itself of the
interacting flux lines, as discussed in Sect. 6.1, and cannot be absorbed. Thus, there
is no inevitability of flux cutting. Since this is in the regime of reversible flux motion,
it is impossible to explain how the excess energy is dissipated due to flux cutting.
In addition, the flux cutting cannot be the mechanism that determines fundamental
phenomena such as the critical current density.
(2) No possibility for flux cutting
Some processes of flux cutting have been proposed, such as the inter-cutting process
in which flux lines with different angles cut directly across each other, as shown
in Fig. 6.7, and the intra-cutting process in which such flux lines recombine [6],
although any real process of flux cutting has not been confirmed. In addition, the
195
A.12 On the Flux Cutting
Various contradictions that arise under the assumption that flux lines must move
translationally have been evaded by assuming that flux cutting exists. Almost all of
them can be reasonably explained, however, by the rotational motion of flux lines
driven by the force-free torque, although it is not easy to directly identify which
mechanism is at work from the experimental results that have been explained by the
flux cutting model. This is the reason why the flux cutting model is used even now.
Hence, it is necessary to examine it theoretically from various aspects. In this section
the problems related to flux cutting are comprehensively argued. An argument will
be presented following each viewpoint.
(1) No inevitability of flux cutting
All of the electromagnetic phenomena that were believed to be explained only by
the flux cutting, such as the deviation of the induced electric field from Josephson’s
formula or the steady magnetization in the resistive state, as shown in Fig. 6.3, can
be explained without the flux cutting. It is possible to raise other examples. This
is because the flux cutting and flux rotation are equivalent to each other from the
viewpoint of macroscopic electromagnetic phenomena.
This theoretical point was already presented in Sect. 6.1. That is, the flux cutting
is a concept used to explain the phenomena by assuming Josephson’s relationship
for translational movement of each component of flux lines, although Josephson’s
formula does not hold.
As shown in Sects. 5.7 and 6.3, and Appendix A.7, when a current is induced in
a superconductor by changing the external magnetic field, the energy that invades
the superconductor exceeds the increase in the magnetic energy, and the excess
energy, i.e., the work done by the driving force or torque to release the strain of
flux lines in the regime of reversible flux motion, is stored as an increase in the
pinning energy. If the rotational shear distortion of flux lines cannot be stabilized
by the pinning interaction in the longitudinal magnetic field, such an energy balance
cannot be explained, resulting in a theoretical contradiction. If it is assumed that flux
cutting occurs in this situation, the excess energy is the magnetic energy itself of the
interacting flux lines, as discussed in Sect. 6.1, and cannot be absorbed. Thus, there
is no inevitability of flux cutting. Since this is in the regime of reversible flux motion,
it is impossible to explain how the excess energy is dissipated due to flux cutting.
In addition, the flux cutting cannot be the mechanism that determines fundamental
phenomena such as the critical current density.
(2) No possibility for flux cutting
Some processes of flux cutting have been proposed, such as the inter-cutting process
in which flux lines with different angles cut directly across each other, as shown
in Fig. 6.7, and the intra-cutting process in which such flux lines recombine [6],
although any real process of flux cutting has not been confirmed. In addition, the