An analytical model for pulse shape and electrothermal stabilityin two-body transition-edge sensor microcalorimeters

High-resolution superconducting gamma-ray sensors show potential for the more accurate analysis of nuclear material. These devices are part of a larger class of microcalorimeters and bolometers based on transition edge sensors (TESs) that have two distinct thermal bodies. We derive the time domain behavior of the current and temperature for compound TES devices in the small signal limit and demonstrate the utility of these equations for device design and characterization. In particular, we use the model to fit pulses from our gamma-ray microcalorimeters and demonstrate how critical damping and electrothermal stability can be predicted.