Ice, steam, thread and a needle were added to make an sensitive instrument. It has a vortex chamber at the injection point and a throttle valve on the hot end. It can achieve -60 celcius temperatures . They apparently were used to cool lathe tools during use. Scientific American has a good starting plan.
Real ones are commercially available somewhere.
Compressors are usually inefficient unless you can power them for free. Heat pipes are another oddity currently used to cool lathe tool tips. These conduct more heat than Diamond OR Silver and are trivial to construct, in Copper or stainless steel. I saw a free pump in a 1970's Popular Mechanics. Your pump has a bit missing.