  In this work we study the effect of engineered disorder on the local magnetic
response of proximity coupled superconducting island arrays by comparing
scanning Superconducting Quantum Interference Device (SQUID) susceptibility
measurements to a model in which we treat the system as a network of
one-dimensional (1D) superconductor-normal metal-superconductor (SNS) Josephson
junctions, each with a Josephson coupling energy $E_J$ determined by the
junction length or distance between islands. We find that the disordered arrays
exhibit a spatially inhomogeneous diamagnetic response which, for low local
applied magnetic fields, is well described by this junction network model, and
we discuss these results as they relate to inhomogeneous two-dimensional (2D)
superconductors. Our model of the static magnetic response of the arrays does
not fully capture the onset of nonlinearity and dissipation with increasing
applied field, as these effects are associated with vortex motion due to the
dynamic nature of the scanning SQUID susceptometry measurement. This work
demonstrates a model 2D superconducting system with engineered disorder and
highlights the impact of dissipation on the local magnetic properties of 2D
superconductors and Josephson junction arrays.
