The Adiabatic Demagnetization Refrigerator:
Temperature and Entropy Cycle

Operating Cycle 1: Brief Description

Here is a quick description of the ADR cycle. We'll go over it in more detail after the temperature-entropy diagram.

Rapid Cooldown

The magnetic field is dropped rapidly. The salt pill cools as the molecular magnetic moments drop out of alignment with the field, absorbing entropy.

Slow Cooling

Once the cooling reaches the desired temperature, the rapid decrease of the magnetic field stops. Heat slowly leaks in from outside. The magnetic field is slowly dropped, to allow the salt pill to absorb the heat without increasing in temperature.

Warmup

When the salt pill has absorbed all the heat it can, the magnetic field is increased again. The salt pill warms as the magnetic moments align and dump their energy.

Dumping Heat

When the salt pill is hotter than the thermal sink, the heat switch is turned on. Heat flows from the salt pill into the thermal sink. Then the heat switch is turned off and the cycle begins again.

Operating Cycle 2: Temperature Entropy Diagram

I have a fairly long description of the following graph for those who'd like a guided tour. I wrote it originally for users with text browsers, then realized that its slightly different approach might be useful to anyone with any type browser. Feel free to read my graph description, or to read this page, or to try both.

This diagram shows how the temperature and entropy of the salt pill vary through the cycle. The vertical axis of the graph is entropy divided by the universal gas constant, R, and is therefore unitless. The horizontal axis is temperature in degrees Kelvin (that is, absolute temperature.)

The green curve near the bottom shows the entropy of the pill at high field. The blue curve higher in the graph shows entropy at zero field. At any temperature, the zero-field entropy is higher than the high field entropy. The zero-field entropy includes both the entropy of random thermal motion (heat energy) as well as the entropy of the disordered magnetic moments. The high field entropy includes only the thermal randomness, since the magnetic moments are all lined up by the field.

The lines between the two curves show ADR cycles, an "ideal" cycle, which is shown as a rectangle, and a "non-ideal" cycle, which extends along a curved line to higher temperatures and which overlaps the full-field curve for some distance. The stages of the ideal cycle are labelled 1 through 4 on the graph. Here are descriptions of those stages:

1. Rapid Cooldown

• Entropy: Constant
• Temperature: Dropping Fast
• Heat Switch: Off
• Magnetic Field: Dropping Fast
• As operators turn down the magnetic field, the magnetic moments disalign. As they disalign, they convert entropy of random thermal vibrations into entropy of random alignments of the magnetic moments. That is, as the moments absorb heat energy and thus cool the salt pill. Because the cooldown is rapid (only a few minutes in the XRS ADR), there is not time for a significant amount of heat to flow into the salt pill. Thus, the entropy of the pill is essentially contstant as the temperature drops.

2. Slow Cooling

• Entropy: Increasing Slowly
• Temperature: Constant
• Heat Switch: Off
• Magnetic Field: Dropping Slowly
• Once the salt pill reaches operating temperature, operators stop the rapid drop of the magnetic field. If they then held the field constant, the salt pill would gradually warm over a period of several hours as heat slowly leaked in from the surroundings. Instead, the operators slowly drop the magnetic field, allowing the molecular magnetic moments to slowly absorb the heat energy that leaks in. In the XRS ADR, this constant temperature, slow cooling phase lasts several hours. (The rapid cooldown only lasts a few minutes.)

3. Warmup

• Entropy: Constant
• Temperature: Increasing Rapidly
• Heat Switch: Off
• Magnetic Field: Increasing Rapidly
• When the magnetic field reaches zero, operators must dump the stored heat. They first increase the magnetic field (rapidly, so as not to waste time.) As the field increases, the molecular magnetic moments fall into alignment with the field. The entropy they stored as randomness of alignment becomes entropy of random thermal motion. That is, as the magnetic moments align, they heat the salt pill by dumping energy into it.

4. Dumping Heat

• Entropy: Decreasing
• Temperature: Constant
• Heat Switch: On
• Magnetic Field: Constant, High
• When the salt pill becomes warmer than the heat sink, operators turn on the heat switch. Heat now flows from the salt pill to the heat sink. (In the XRS ADR, the heat sink is a bath of liquid helium at 1.3 K.) As heat flows from the salt pill, its entropy drops. After dumping heat, the operators turn off the heat switch and start the cycle again.

• Part 1 of the ADR primer
• ADR page
• Cutaway Drawing of the XRS ADR.
• Photo of the XRS ADR.
• Heat Switch
• ADR Intro a less technical ADR discussion, in our Introduction to Cryogenics section.