Liquid helium - Siemens-cycle only?

[liketotalk]

Why can't I reach 4K with the Siemens-cycle?

 

[Astronuc]

http://kryolab.fysik.lu.se/dokument/e_techn.html

The Hampson-Linde cycle ( independently patented by W. Hampson and C. von Linde 1895) is very similar to the Siemens cycle, except that the expansion-machine is replaced by a Joule-Thomson orifice in [D]. First a few words about the Joule-Thomson effect. A gas could be cooled by letting it expand freely against the atmosphere. This could be explained by that the gas was doing a work against the atmosphere by lifting and/or heating it, and thereby loosing energy in form of heat. 1852 Joule and Thomson did some experiments to observe a gas, expanding without any work to be done. They let the gas flow through a pipe with a porous plug to restrict the flow. To their surprise the gas was cooled by passing the plug. This could first be explained twenty years later by van der Waals. The gas was not doing an external work, but an internal against the forces between the molecules. What Hampson and von Linde did was to combine Siemens cooling machine with Joules and Thomsons expansion plug, and put together a complete gas liquefication cycle.

It appears that He liquification systems use the Siemens cycle upfront in the high temperature range, and the last stage is Hampson-Linde cycle.

It would be worthwhile to find the original patents - Siemens cooling cycle (patented by W. Siemens 1857) and the Hampson-Linde Patent.