Chapter 5
Flux Pinning Phenomena
Abstract The main advantage of superconductors, that these materials can transport
electric current without energy dissipation, is achieved by the mechanism of flux
pinning. Quantized flux lines that contain superconducting structure inside do not
move under interaction with defects in the superconductor, even when the Lorentz
force is present due to the current. As a consequence, no electromotive force appears,
resulting in no energy dissipation. The mechanism of flux pinning is, in principle,
reversible with respect to the motion of flux lines. The observed results are commonly
irreversible, however, as described by the critical state model, which assumes that
there is a balance between the Lorentz force and the irreversible pinning force. In this
Chapter, the summation theory is introduced, which is used to analytically determine
the critical current density, i.e., the maximum non-dissipative current density. The
reason why the resultant electromagnetic phenomena become irreversible is clarified,
even though the fundamental flux pinning mechanism is reversible. The irreversibility
in flux pinning phenomena does not originate from the breaking of time reversal
symmetry, but is of another type, such as friction, that is non-dissipative in stationary
condition, although it causes energy dissipation in motion due to the applied force.
5.1 Flux Pinning Mechanism
The resistivity of superconductors takes on a smaller value in the superconducting
state than in the normal state, as shown by (4.46). This property cannot be utilized,
however, since the normal resistivity ρ n is very much higher than those of conductive
materials such as copper. The only possibility for application is prevention of the
appearance of induced voltage by stopping the flux motion.
The useful mechanism for this purpose is flux pinning. The superconducting
structure of flux lines, as shown in Fig. 4.5, is associated with this mechanism. The
essential point is that the central region is almost in the normal state (( = 0). Equation (4.2) shows us that the energy in this region is higher than that in the surrounding
superconducting region. If the normal core of a flux line meets a normal precipitate
in the superconductor, as illustrated in Fig. 5.1a, it is energetically favorable because
of the smaller volume in which the superconductivity is destroyed than when the
© 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_5
69
Flux Pinning Phenomena
Abstract The main advantage of superconductors, that these materials can transport
electric current without energy dissipation, is achieved by the mechanism of flux
pinning. Quantized flux lines that contain superconducting structure inside do not
move under interaction with defects in the superconductor, even when the Lorentz
force is present due to the current. As a consequence, no electromotive force appears,
resulting in no energy dissipation. The mechanism of flux pinning is, in principle,
reversible with respect to the motion of flux lines. The observed results are commonly
irreversible, however, as described by the critical state model, which assumes that
there is a balance between the Lorentz force and the irreversible pinning force. In this
Chapter, the summation theory is introduced, which is used to analytically determine
the critical current density, i.e., the maximum non-dissipative current density. The
reason why the resultant electromagnetic phenomena become irreversible is clarified,
even though the fundamental flux pinning mechanism is reversible. The irreversibility
in flux pinning phenomena does not originate from the breaking of time reversal
symmetry, but is of another type, such as friction, that is non-dissipative in stationary
condition, although it causes energy dissipation in motion due to the applied force.
5.1 Flux Pinning Mechanism
The resistivity of superconductors takes on a smaller value in the superconducting
state than in the normal state, as shown by (4.46). This property cannot be utilized,
however, since the normal resistivity ρ n is very much higher than those of conductive
materials such as copper. The only possibility for application is prevention of the
appearance of induced voltage by stopping the flux motion.
The useful mechanism for this purpose is flux pinning. The superconducting
structure of flux lines, as shown in Fig. 4.5, is associated with this mechanism. The
essential point is that the central region is almost in the normal state (( = 0). Equation (4.2) shows us that the energy in this region is higher than that in the surrounding
superconducting region. If the normal core of a flux line meets a normal precipitate
in the superconductor, as illustrated in Fig. 5.1a, it is energetically favorable because
of the smaller volume in which the superconductivity is destroyed than when the
© 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_5
69