Modern technology calls increasingly for provision of cooling at cryogenic temperatures: super-conductivity research; imaging equipment for search-and-rescue; contemporary diagnostic medicine (MRI - magnetic resonance imaging); space exploration; advanced computer hardware; and, military defence systems. Where it is desirable to generate the cooling effect close to the point of heat removal, electrically powered Stirling and pulse-tube machines offer advantages over traditional, passive systems (Leidenfrost and Joule-Thomson). Until now there has been no agreed approach to the thermodynamic design of either type. In particular, the choice of regenerator packing has remained a matter for time-consuming - and thus expensive - trial-and-error development. There has been no way of knowing whether an existing 'fully developed' unit is performing to the limit of its thermodynamic potential. "Stirling and Pulse-tube Cryo-coolers" addresses these problems. The features include: an ideal cycle for the pulse-tube yielding heat, mass-flow and work; previously unseen phenomena of real gas behaviour; pictorial reliefs of pressure wave interactions; multiple wave reflections in graphic perspective; first solution of the 'regenerator problem ' by a full, unsteady gas dynamics treatment; first ever depiction of pulse-tube boundary-layer events (heat conduction, 'streaming') driven by interacting left-and right-running pressure waves; first analysis of the graded regenerator and optimisation of gas path design; and, embryonic 'cook-book' method of ab initio cooler design based on dynamic similarity and thermodynamic scaling. "Stirling and Pulse-tube Cryo-coolers" raises the threshold from which first-principles design of regenerative cryo-coolers may start. Those wishing to extend their study of the subject beyond the well-trodden, ideal gas/quasi-steady-state rationalisations will require this book.