ABSTRACT
For an alternating field of frequency / the average power loss is obtained by
multiplying the loss per cycle by / .
6.2. Effect of a D C Transport Current
The effect of a fixed dc transport current on the hysteresis loss caused by a cyclic
in-plane applied magnetic field depends on whether full penetration is achieved at
some time during the ac cycle. For simplicity, the dc current per unit width is taken
to be less than the critical value Jc. It is assumed that the dc current wi l l be pushed
to the middle or the sheet as in Figure 6.1, and until full penetration is reached
the dc current has no effect on the loss. Consequently, for partial penetration the
instantaneous power loss is again given by Eq . (6.1). However, full penetration in
this case is reached when the moving boundaries touch the boundaries of the dc
current. At this point the upper moving boundary in Figure 6.1, in effect, moves
discontinuously to meet the lower moving boundary, and the electric field also
redistributes itself. Thus the loss for full penetration applies over the remainder
of the half-cycle, where a single fixed boundary exists. The boundaries of the dc
current are at ±J/2j,, and full penetration occurs when y>\ = J/2 jc (for the signs
chosen in Figure 6.1). Beyond full penetration the single remaining boundary is
located at —J/2jc. If HQ is the peak value of HA and the start of the half-cycle of
interest, then before full penetration it follows from (5.42) that
A C Loss and Macroscopic Theory of Superconductors 71
Results that were obtained 2 from a rather long calculation for this case are given
in the Summary section,
6.5. Loss Due to a Field Applied Normal to a Strip
For the case of an infinite sheet, it is meaningless to consider a magnetic field
applied normal to the plane of the sheet. However, one can examine this case for
a long strip with rather narrow width W, which nevertheless is large compared
with the thickness. In Bean approximation, with no net transport current, the
problem becomes very simple for the case where the applied magnetic field is large
compared with the field required for full penetration. Consider the result (6.5) for
a large in-plane applied magnetic field in a sheet where 2yojc is substituted for
Jc. For this large applied-field case the magnetic field due to the internal currents
is neglected. Thus one can imagine cutting out a thin slice of cross-section of the
sheet, normal to the applied magnetic field, to form a strip in a normal applied field.
