  This paper presents experimental and modelling results of an ultra-compact
self-rectifier flux pump energizing a superconducting coil. The device fits
inside a volume of 65x65x50~mm and generates up to 320~A dc through the coil
and a peak output voltage up to 60~mV. We also develop and present a full
electromagnetic effective circuit model of the flux pump and compare its
predictions to the experimental results. We show that our model can reproduce
accurately the charging of the load coil and that it reproduces the systematic
dependence of the maximum load coil current on the input current waveform. The
experiments and modelling together show also the importance of dc-flux offsets
in the transformer core on the final achievable current through the coil. The
miniaturization possible for this class of flux pump and their minimal
heat-leak into the cryogenic environment from thermal conduction make them
attractive for applications with demanding size, weight and power limitations.
Our effective circuit model is a useful tool in the understanding, design and
optimization of such flux pumps which will accelerate their progression from
research devices to their application.
