a miniature pulse tube cryocooler such as is described in the article titled u201c a study of a miniature in line pulse tube cryocooler u201d published in cryocoolers vol 16 pp 87 95 2010 by the present applicants and another the cryocooler operates at approximately 100 hz and requires a filling pressure of 40 bar and a pressure ratio of 1 3 the effective mean volume of the cryocooler is about 0 7 cc assuming a 12 mm diameter compression piston with 1 mm stroke the mean compression volume increases up to 0 76 cc and according to equation 1 the gas spring constant becomes 113 n mm pure water was used for the amplifying system liquid in this experimental compressor since it possesses relatively high bulk modulus and is bio and chemically friendly the relatively high viscosity of the water has a minor effect on the system dynamics because of the very small strokes the fluid volume was minimized in order to increase the hydraulic spring constant according to equation 2 selection of the a1 piston diameter is restricted by the pzt parameters and the hydraulic pressure since the dynamic operation of the pzt stack actuator must be accompanied by application of a specific preload on the piezoelectric stack according to recommendations of the manufacturer of the stack used the mean preload should result in half the maximum allowable pzt shrinkage which is about 30 u03bcm in the case of the selected element assuming a mean hydraulic pressure of 50 bar a 28 mm diameter a1 piston was used in contrast to the a1 piston selection of the.