The Thermoacoustic Stirling Heat Engine(TASHE) designed by Backhaus, a device without moving parts which operates at a frequency of 85 Hz with an average pressure of 3 MPa that is capable of using sustainable energies, is applied to run an Inertance Pulse Tube Refrigerator(IPTR) with 1 W cooling power at 90 K. The coupling of these devices caused to eliminate all moving parts as well as miniaturizing the refrigerator to use for cooling superconducting magnets for MRI systems. A new method for the design of the IPTR performed by using numerical simulation of REGEN3.3. Moreover, to have a better vision of the overall configuration of IPTR and verify the Results of REGEN3.3, DeltaEC is used as an auxiliary software. Fortunately, both software results matched perfectly, and the performance of the IPTR was acoustically and thermodynamically ideal.