Chapter 6
Longitudinal Magnetic Field Effect
Abstract Under the usual electromagnetic conditions, magnetic flux lines and
current are perpendicular to each other, and electromagnetic phenomena are determined by the balance between the Lorentz force and the pinning force. On the
other hand, various peculiar phenomena are observed when a current is applied to
a superconductor in a parallel magnetic field. These phenomena are introduced in
this chapter. These phenomena are also determined by a general driving force on
flux lines and the pinning force to maintain the distorted structure of the flux lines.
The Lorentz force is zero, however, because the current and magnetic flux lines are
parallel to each other. Hence, another force is driving the flux lines. Following the
general idea that the driving force is a restoring force to release the distortion, it is
easy to suppose that it is a torque to rotate the flux lines. In fact, this torque can
be derived similarly from the principle of virtual displacement as was done in the
derivation of the Lorentz force in Chap. 5. Various peculiar phenomena associated
with the longitudinal magnetic field effect are generally explained by the rotational
flux motion caused by the torque. These phenomena can occur only in superconductors with the pinning effect, and new phenomena that have not been considered in
electromagnetism can be seen.
6.1 Experimental Results
The magnetic field produced by a current is usually normal to the current, and electromagnetic phenomena in superconductors are determined by the balance between
the Lorentz force on flux lines and the pinning force, as described by the critical state
model. Such a magnetic field is called a transverse magnetic field.
When a magnetic field is applied along the length of a superconducting wire or
slab, and then, a current is applied, as shown in Fig. 6.1, electromagnetic phenomena
completely different from those in transverse magnetic fields are observed. Since
such a magnetic field is called a longitudinal magnetic field, these phenomena are
classed together as the longitudinal magnetic field effect. The main phenomena are
introduced here.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
T. Matsushita, Superconductivity and Electromagnetism, Springer Series
in Solid-State Sciences 195, https://doi.org/10.1007/978-3-030-67568-4_6
115
Longitudinal Magnetic Field Effect
Abstract Under the usual electromagnetic conditions, magnetic flux lines and
current are perpendicular to each other, and electromagnetic phenomena are determined by the balance between the Lorentz force and the pinning force. On the
other hand, various peculiar phenomena are observed when a current is applied to
a superconductor in a parallel magnetic field. These phenomena are introduced in
this chapter. These phenomena are also determined by a general driving force on
flux lines and the pinning force to maintain the distorted structure of the flux lines.
The Lorentz force is zero, however, because the current and magnetic flux lines are
parallel to each other. Hence, another force is driving the flux lines. Following the
general idea that the driving force is a restoring force to release the distortion, it is
easy to suppose that it is a torque to rotate the flux lines. In fact, this torque can
be derived similarly from the principle of virtual displacement as was done in the
derivation of the Lorentz force in Chap. 5. Various peculiar phenomena associated
with the longitudinal magnetic field effect are generally explained by the rotational
flux motion caused by the torque. These phenomena can occur only in superconductors with the pinning effect, and new phenomena that have not been considered in
electromagnetism can be seen.
6.1 Experimental Results
The magnetic field produced by a current is usually normal to the current, and electromagnetic phenomena in superconductors are determined by the balance between
the Lorentz force on flux lines and the pinning force, as described by the critical state
model. Such a magnetic field is called a transverse magnetic field.
When a magnetic field is applied along the length of a superconducting wire or
slab, and then, a current is applied, as shown in Fig. 6.1, electromagnetic phenomena
completely different from those in transverse magnetic fields are observed. Since
such a magnetic field is called a longitudinal magnetic field, these phenomena are
classed together as the longitudinal magnetic field effect. The main phenomena are
introduced here.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
T. Matsushita, Superconductivity and Electromagnetism, Springer Series
in Solid-State Sciences 195, https://doi.org/10.1007/978-3-030-67568-4_6
115