#10H.  The Motion of Magnetically
            Trapped Particles -- History

Going in circles

The particles inside the Tevatron at Fermilab in Illinois need a diameter of about a mile, and a much bigger machine, the SSC or "Superconducting Super-Collider", was started in Texas but left unfinished when its funds were cut off. The Fermilab magnet is shaped like a huge ring whose cross-section resembles the letter "c". Inside the "c", where the magnetic field is strong, is the pipe in which protons (and antiprotons) are accelerated (the "c" cradles it the way the rim of a bicycle wheel cradles the inner tube). That pipe also forms a ring about a mile across, with a vacuum on the inside. The magnet is really an electromagnet, and as the accelerated protons gain speed and energy, its electric current is gradually increased, strengthening the magnetic field in a way that keeps the orbits of the protons within the pipe.

Adiabatic invariance

At this point Albert Einstein called attention to the drawn-up pendulum: its "adiabatic invariant", the product E times T, was almost constant. Could it be, he suggested, that similar quantities were associated with atomic systems, and that they determined stability--when they had certain values, they were exactly conserved, and the atom then could not run down.

Such general adiabatic invariants were soon found by Paul Ehrenfest, and their use led to the early quantum theory of Bohr and Sommerfeld. That theory worked quite well for the states of hydrogen, but with larger atoms it hit a dead end. The successful "wave mechanics" theory of Schroedinger, Heisenberg and Born, which replaced it in 1925-6, used a completely different approach.

Adiabatic invariance again surfaced decades later, in the study of ions and electrons moving in space. As the story of Birkeland and Stoermer shows, this area held special interest to Scandinavian scientists seeking to understand the aurora. One of them was Hannes Alfven (1970 Nobel prize) who in his 1950 book "Cosmical Electrodynamics" showed that for appropriate conditions a certain mathematical combination of the properties of ions and electrons was almost a constant.

He apparently did not realize that this was an adiabatic invariant of the sort defined by Ehrenfest: this was pointed out at about the same time by the Russian physicists Lev Landau (Nobel, 1962) and Solomon Lifshitz, as a worked-out example for the student in their textbook on the theory of fields.

A "second" adiabatic invariant, also important in the theory of radiation trapped in the Earth's field, was derived by Grad, Longmire and Rosenbluth while studying the confinement of laboratory plasma, and a related "third" invariant was introduced shortly afterwards by Northrop and Teller.