  Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry
simultaneously images the local magnetic fields and susceptibilities above a
sample with sub-micron spatial resolution. Further development of this
technique requires a thorough understanding of the current, voltage, and flux
characteristics of scanning SQUID susceptometers. These sensors often have
striking anomalies in their current-voltage characteristics, which we believe
to be due to electromagnetic resonances. The effect of these resonances on the
performance of these SQUIDs is unknown. To explore the origin and impact of the
resonances, we have developed a model that qualitatively reproduces the
experimentally-determined current-voltage characteristics of our scanning SQUID
susceptometers. We use this model to calculate the noise characteristics of
SQUIDs of different designs. We find that the calculated ultimate flux noise is
better in susceptometers with damping resistors that diminish the resonances
than susceptometers without damping resistors. Such calculations will enable
the optimization of the signal-to-noise characteristics of scanning SQUID
susceptometers.
