Analytical Calculation of the Instantaneous Power in a Current Carrying Superconducting Tube With ${J}_{C}({B})$

To use high-Tc superconductors for alternating current transport, it is important to evaluate AC losses. The influence of
Jc
(
B
) on the self field losses in a superconductive tube fed by a transport current in incomplete penetration is studied for two reasons. First, superconducting power cables have a geometry that resembles a tube and second, for high-temperature superconductors, the variation of
Jc
(
B
) is important especially for low magnetic fields like self field. An analytical calculation of the distribution of the magnetic field
B
(
r
,
t
) by using a linearized law
Jc
(
B
) is presented. From
B
(
r
,
t
) one deduces
J
(
r
,
t
) and
E
(
r
,
t
) . The analytical expressions of those were used to calculate the analytical instantaneous power
p
(
t
). The losses in the superconducting tube are the average value of
p
(
t
) . They are numerically calculated and compared with the measurements taken on a sample whose characteristic
Jc
(
B
) was previously measured. With the linear model, the calculated losses are closer to the measured losses than for the Bean model, but the
Jc
(
B
) identification remains the main problem.