THE TWISTOR 1325 



The above derivation assumed that the entire circular flux change 

 could be observed externally. Since the magnetic wire must, of necessity, 

 serve as the source of the generated voltage the resultant eddy current 

 flow reduces the observable flux change by a factor of three. Consider Fig. 

 7; assume that the flux reversal takes place in the classical manner and 

 consider the circular component of this flux since it alone contributes 

 to the observable signal. The induced voltage V(r) at any point r is 

 V{r) = F(0)/(/-o — r/ro), where ro is the radius of the wire and F(0) 

 the voltage at r = 0. But V{r), the induced or open-circuit voltage per 

 length of wire I, could only exist if the wire were composed of many con- 

 centric tubes of wall thickness dr, each insulated from one another. In a 

 long wire no radial eddy currents can exist. Therefore the wire of length I 

 can be assumed to be faced by a perfect conductor at both of its ends. 

 It remains to calculate the potential between these ends. The resistance 

 of the tube is R{r) = pl/'Ivr dr, where p is the resistivity in ohm-cm. 

 The resistance of the wire is given by Ro = pl/irvo . These resistances 

 form a voltage divider on the induced voltage in the tube and the total 

 contribution of all tubes is obtained by integration; 



Fohserved - [ V h^ [-J^d 



\pl/2Trrdr J 



*" dr (2) 



ro — r\ 2r 



ro / To- 



F(0) 



Thus, (1) must be modified by (2) with the voltage step-up per memory 

 cell becoming, 



Fobs _ l/d /„v 



long 



6.66 



3.11 Bulk Flux Reversal — - Classical Case 



The switching performance of a magnetic wire under transient condi- 

 tions will now be considered. The speed of magnetization reversal of 

 magnetic materials vmder pulse conditions is best characterized by Su, , 

 the switching coefficient, usually expressed in oersted-microseconds. It 

 is defined as the reciprocal of the slope of the 1/Ts versus H curve where 

 Ts is the time required to reverse the magnetization state and // is the 

 applied magnetic field intensit3^ Onl}'^ eddy current losses will be con- 

 sidered. 



