Explaining the self-field AC loss behaviour of silver-clad (Bi,Pb)-2223 tapes for power engineering applications

Transport ac loss in a long cylinder with a hard superconducting core and normal conducting shell

“…In recent years, (Bi, Pb) 2 Sr 2 Ca 2 Cu 3 O x (Bi-2223) hightemperature superconducting tapes prepared by the powderin-silver (Ag) tube technique have been extensively studied. For such tapes, low-frequency ac loss per cycle per unit length is shown roughly consistent with the hysteretic loss calculated from the critical state model [1][2][3][4]. Since the volume fraction of Ag is quite high (typically about 0.7) and its resistivity at 77 K is quite low, ρ = 3 × 10 −9 m [5], there also could be an appreciable loss resulting from the normal currents flowing through the Ag matrix when the frequency is increased.…”

“…Without giving its derivation in [5], it is difficult to guess the exact reason for this difference. The concept of eddy current seems to have been used when deriving the formula, since there is a factor of (d /dt) 2 for the flux within the normal conducting sheath, assuming I m /I c 1 so that no flux in the core is effective and using the field at the border as the average in the sheath. The feature of a transport current seems also to have been considered, since the longitudinal conductance of the entire sheath is used as the second factor.…”

“…To show the frequency dependence, we choose the highcurrent limit (i = 1) to calculate. In figures 4(a) and (b) and figures 5(a) and (b), we give the normalized field and current density in the shell as functions of r/r 0 for i = 1 and θ 2 = 0.1, 1, 10 and 100. θ 2 = 0 and with increasing θ 2 it increases and becomes progressively proportional to (I m /I c ) 2 . From the positions of symbols corresponding to each pair of i and θ 2 values, we see that I m /I c ≈ i if θ 2 is less than 0.1.…”

Transport ac loss in a rectangular thin strip with power-law E(J) relation

“…(1)-(3) [5][6][7][8][9][10][11][12][13][14][15], which means that the CS model is basically valid for such tapes. However, this comparison between experimental and modeling results is somewhat ambiguous, since the relations between current density J and electrical field E in the actual HTS tapes and in the CS model are significantly different.…”

Alternating current loss in rectangular superconducting bars with a constant critical-current density

“…Both formulae have been widely used in the experimental research of ac losses of high-temperature superconductors and are popularly known as the Norris formulae for ellipse and strip [5][6][7][8][9][10].…”