THE TWISTOR 1327 



dieted from (9) but generally possesses considerable curvature at low- 

 drives. Equation (9) satisfactorily predicts the slope of the switching 

 curve in the high drive region, but Ho must be determined experimen- 

 tally. In Section 3.12, flux reversal by wall motion is treated as it is a 

 possible switching mechanism at low drives. 



The switching coefficient s^, for the case in which the magnetization is 

 purely axial will now be treated. As above, the flux density will change 

 from —Bs to -{-Bs uniformly in time Ts . The eddy currents, which are 

 circular, result from an induced voltage V{r) where V(r) = [V{ro){r/rof], 

 and 7(^o) is given by F(ro) = [(25./r,)W]10"'. Thus, E{r) = V{r)/2Tr, 

 and E{r) = {Bsr/Ts)lO~ . Following the procedure used above, the in- 

 ternally dissipated energy density is 



Sav/cm3 = — . / zirr dr, 



Ecjuating this expression to (8) yields 



s. = (H - H,m = "^^fl^ , (11) 



p cos 02 



where 6-2 is defined as the angle between the applied field and the switch- 

 ing flux now assumed axial. 



The helical flux vector in a twist or can be resolved into a circular and 

 an axial component. Fortunately, since the dissipated energy is pro- 

 portional to the eddy current density squared, and the axial and cir- 

 cular current density vectors are perpendicular to each other, it is 

 possible to write 



£av/cm 3 (helical) = 8av/cm3(axial) + Sav/cm 3 (circular). (12) 



It follows, for a 45 degree pitch angle, that 



^.(helical) = ^-(axial) + ..(circular) ^^^^ 



where the factor "2" is a consequence of the flux density components 

 being smaller by l/\/2 than their resultant. Substitution of (9) and (11) 

 into (13) gives the desired switching coefficient 



..(helical) = {H - Horn = ^ ^.^0^10' ^4) 



18 p cos d 



