Understanding the Gifford-McMahon Cryocooler Cycle: Single Stage

The main cooling appartus in the Montana Instruments Cryostation system is called a Gifford-McMahon (GM) refrigerator. The figures below provide a simplified description of this mechanism. Figure 1 is a temperature vs entropy diagram of the cycle. Figure 2 shows the configuration of the system components during the cycle (followed top left-right, bottom left-right). 

Figure 1: Temperature vs Entropy Diagram

Figure 2: Configuration of the GM system during a cycle

The displacer is driven by a motor, so at any point through the cycle when the displacer is either at the top or at the bottom of the chamber, the motor has forced this to occur. For simplicity, the rotating valve sometimes used in the description of the GM cooler has been replaced by a high and low pressure port labeled Phigh and Plow, and the cross on the port indicates the closure of a valve, or the closure of a given port. Also, the regenerator is shown as a separate chamber which is in parallel with the chamber holding the displacer (this is again for simplicity, normally the regenerator would be embedded within the displacer). Also, the sample space can be thought of as a heat exchanger in direct thermal contact with the lower chamber below the displacer.

Points 1-2: With the displacer at the bottom, the high pressure inlet is opened and the upper chamber is pressurized. This occurs at a constant temperature.

Points 2-3: With the high pressure inlet open and the exhaust port (low pressure port) closed, the displacer is moved to the top, thus forcing out the gas from the top chamber through the regenerator to the lower chamber. This process cools the gas at a constant pressure. Note: This is only possible due to the process 4-5-1 which has previously cooled the regenerator. 

Points 3-4: With the displacer at the top, the low pressure exhaust port is opened. This process allows the gas in the lower chamber to expand and cool. This expansion displaces some gas out through the exhaust port doing some work. This is the main cooling step in the GM cycle for the gas, and due to the direct thermal contact it will drive heat out of the sample space.

Points 4-5-1: The cooled, low temperature gas is then forced out of the chamber with the displacer moving down. This process cools the regenerator, and thus the gas leaves the low pressure port near ambient temperature.

Notice that in the steps 4-5-1, the cold gas is forced through the regenerator and thus cools it back down for the cooling of the gas in the steps 2-3. This is the role of the regenerator in the GM cryocooler and is very important for the ultimate performance of the system. The above description only describes a single stage system, but the general idea is the same for the multi-stage systems, like the one used in the Cryostation, which has two stages. In principle, there are just lower stages which are “fed” low temperature gas from the previous larger volume stages. In such a system, the displacers would all move in unison, and in principle, one could add many stages to the system due to the simple way the system can be extended in series. 

The system used in the Montana Instruments Cryostation and the Nanoscale Workstation have a first stage base temperature of ~30K and a second stage base temperature of <3K, with a cooling power of 3.0 Watt and ~0.1 Watt on the first and second stages, respectively.

For more information on the GM Cryocooler Cycle, please see:

Gifford-McMahon-Cycle-Paper-1965.pdf.