A method for optimizing the design (shape of the displacer) of low power Stirling cryocoolers relative to the power required to operate the systems is described. A variational calculation which includes static conduction, shuttle and radiation losses, as well as regenerator inefficiency, was completed for coolers operating in the 300 K to 10 K range. While the calculations apply to tapered displacer machines, comparison of the results with stepped displacer cryocoolers indicates reasonable agreement
