P. M. Grant, (Electric Power Research Institute) Effect of Ferromagnetic Substrates on ac Losses in YBCO Coated Conductors P. M. Grant, (Electric Power Research Institute) N28.002: 8:12 14 March 2001

Coated Conductors Generation II Wire Biaxially Oriented Y-123 Out of Japan, LANL, ORNL DOE/Industry Alliance to Commercialize I H

Cross Section YBCO 1 m I 0.5 m YSZ + CeO2 Nickel H 50 m H 0.5 m

Biot-Savart z B  r z y Jdx’   x -a x’ a x Jdx’ -a a dx’ dBx(x,z) = 0 2 Jz (x-x’)2 + z2 dx’ 0 (x-x’) dx’ - dBz(x,z) = J 2 (x-x’)2 + z2

Field Equations [ ] [ ] ) Bx(x,z) = 0 2 J tan-1 ( x+a z x-a - 1 ln 0 1 Bz(x,z) = J 2 2

Field Distribution a = 2 mm J = 25 A/mm

Hysteresis B BS 2f H > HC ; P = HC BS 0  2f H < HC ; P = H2

Loss HC = 80 Oe BS = 6000 Gauss = 75 P = 0.14 W/m Measured ac Losses Y-123 cc on Hastalloy (non-magnetic) = 0.48 W/m (Ciszek, et al.)

does cost you something Conclusions “Spending a nickel does cost you something even these days”