12. Super conducting transformers
12.2 Power loss in super conductive materials

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As for AC power loss in super conductive materials, there are two kinds ---- Hysteresis loss and Conjunction --- of losses.
Under certain magnetic flux density condition (in the order of 0.05T and above), the flux enters into the materials, and create hysteresis loss.

P_h=(8/3p)fd_fJ_cB_m--- (1)

where, f:frequency(Hz), d_f:filament diameter (m), J_c: critical current density (A/m²), B_m:maximum magnetic flux density (T), and P_h in W/m³.
As smaller the filament diameter is, as lower the loss is. But for extremely small diameter, loss in the stabilizing material between the filaments increases. Actually ca. 0.5 mm is the optimum diameter. See Fig. 12.2.

The conductor of a coil consists of 10 -- 100 thousands of filaments and stabilizing material is filled in between. By the magnetic flux created by the currents in the filaments, conjunction loss P_c is created.

P_C=B_m²(2pf)²t/m₀---(2)
t=(1/2)(m₀/r)(l_p/2p)²

where, t: conjunction time constant, l_p: pitch of twist (m).
For the material, CuNi, the resistance of which is high, is applied. l_p should be less than 1mm. See Fig. 12.3, which shows examples of super conducting conductors for model AC transformers.

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This page is based on Prof. E.Haginomori's lectures in Tokyo Institute of Technology, and edited by Japanese ATP User Group. Copyright (C) Eiichi Haginomori and Japanese ATP User Group.