## SQUID Magnetometer

The circulating current produced by a flux change in the SQUID can be detected by the use of a measuring current, , as shown in Figure 3.10. This current divides equally between both weak-links if the ring is symmetrical. Whilst the current through the weak-links is small there will be no voltage detected across the ring. As is increased it reaches a critical measuring current, , at which voltages begin to be detected.

The magnitude of the critical measuring current is dependent upon the critical current of the weak-links and the limit of the phase change around the ring being an integral multiple of . For the whole ring to be superconducting the following condition must be met

 (3.31)

where and are the phase changes produced by currents across the weak-links and is the phase change due to the applied magnetic field.

When the measuring current is applied and are no longer equal, although their sum must remain constant. The phase changes can be written as

 (3.32) (3.33)

where is related to the measuring current . Using the relation between current and phase in Equation 3.27 and rearranging to eliminate we obtain an expression for ,

 (3.34)

As cannot be greater than unity we can obtain the critical measuring current, from Equation 3.34 as

 (3.35)

which gives a periodic dependence on the magnitude of the magnetic field, with a maximum when this field is an integer number of fluxons and a minimum at half integer values as shown in Figure 3.11.

Dr John Bland, 15/03/2003