118
6 Longitudinal Magnetic Field Effect
Fig. 6.4 Dependence of the
AC current loss energy
density in Nb-Ti wires on the
DC longitudinal magnetic
field [3]
(3) Reduction in loss energy due to AC current
The AC current loss energy is the loss energy produced by the self-field of the current.
The loss energy is decreased by applying a longitudinal magnetic field. Figure 6.4
shows the observed loss energy density in Nb-Ti wires that carry AC current of a fixed
amplitude as a function of the longitudinal DC magnetic field [3]. The loss energy
density decreases with increasing longitudinal magnetic field. This can be attributed
to the increase in the critical current density with the longitudinal magnetic field.
(4) Breaking of Josephson’s formula for induced electric field
When the longitudinal and azimuthal electric field components were measured for a
superconducting wire carrying a DC and superposed small AC current in a parallel
magnetic field by the four-probe method and the pick-up coil method, respectively,
the total electric field was found to be directed almost parallel to the DC magnetic
field [4]. Since the magnetic field due to the current was sufficiently smaller than the
applied DC magnetic field, this observation shows that Josephson’s formula (4.41)
does not hold. If this formula holds, the observed electric field must be normal to the
DC magnetic field. Since both (2.49) and (5.34) hold, we have
E = B × v − ∇φ.
(6.1)
This relationship is of the same form as the electric field in materials that are not
superconductors. Note that φ is not an electrostatic potential, since the electric field
including the second term is an electric field induced by the AC magnetic field.
(5) Resistive state
The phenomenon described in (4) applies for a DC current that is lower than the critical current in a superconductor, and hence, that in a resistive state is not included. In
6 Longitudinal Magnetic Field Effect
Fig. 6.4 Dependence of the
AC current loss energy
density in Nb-Ti wires on the
DC longitudinal magnetic
field [3]
(3) Reduction in loss energy due to AC current
The AC current loss energy is the loss energy produced by the self-field of the current.
The loss energy is decreased by applying a longitudinal magnetic field. Figure 6.4
shows the observed loss energy density in Nb-Ti wires that carry AC current of a fixed
amplitude as a function of the longitudinal DC magnetic field [3]. The loss energy
density decreases with increasing longitudinal magnetic field. This can be attributed
to the increase in the critical current density with the longitudinal magnetic field.
(4) Breaking of Josephson’s formula for induced electric field
When the longitudinal and azimuthal electric field components were measured for a
superconducting wire carrying a DC and superposed small AC current in a parallel
magnetic field by the four-probe method and the pick-up coil method, respectively,
the total electric field was found to be directed almost parallel to the DC magnetic
field [4]. Since the magnetic field due to the current was sufficiently smaller than the
applied DC magnetic field, this observation shows that Josephson’s formula (4.41)
does not hold. If this formula holds, the observed electric field must be normal to the
DC magnetic field. Since both (2.49) and (5.34) hold, we have
E = B × v − ∇φ.
(6.1)
This relationship is of the same form as the electric field in materials that are not
superconductors. Note that φ is not an electrostatic potential, since the electric field
including the second term is an electric field induced by the AC magnetic field.
(5) Resistive state
The phenomenon described in (4) applies for a DC current that is lower than the critical current in a superconductor, and hence, that in a resistive state is not included. In