Historical research guide · 0895 · 2002

Ion and electron acceleration in the field-reversed configuration with an odd-parity rotating magnetic field

Alan H. Glasser · Samuel A. Cohen

In one minute

A field-reversed configuration is a smoke-ring of plasma that carries and closes its own magnetic field. It is compact, it uses its magnetic field efficiently, and it is the shape most small fusion companies are built around — but it has long lacked a proven way to heat its particles and keep its ring current running. Alan Glasser and Samuel Cohen propose one and test it in software. Their tool is a rotating magnetic field of the odd-parity kind, applied at the frequency at which ions naturally gyrate, and shaped so that the two ends of the machine see opposite signs. They follow individual particles by integrating the equations of motion for very long runs, and the answer is strong: ions climb to thermonuclear energies in less than a tenth of a millisecond in a modest-sized device. The heating is not a clean resonance, because the field strength varies too much across the machine, but the orbits turn chaotic and chaos heats efficiently. Electrons heat too, by a different route entirely.

Connection

Chapter 12 treats fusion as the first door the vacuum programme walks through, and aneutronic fusion needs a machine that heats ions hard in a small volume — which is exactly what this paper argues an odd-parity rotating field does. Chapter 9 treats the self-organised plasma object as a real engineering target, and the field-reversed configuration is that object, built on purpose and driven from outside.

From the source

The proposal is a heating and current-drive method for the field-reversed configuration: odd-parity rotating magnetic fields applied in the ion-cyclotron range of frequencies. Odd parity means the applied field is antisymmetric about the midplane, so the two halves of the machine see opposite senses — a different animal from the even-parity rotating fields long used to drive current in these devices.Published abstract, first sentence
The evidence is computational and the method is stated as such: the approach is based on long, accurate numerical integration of Hamilton’s equations for single-particle orbits. The companion report shows what that means in practice — an adaptive integrator carrying six coupled nonlinear equations for a particle in a Solov’ev field-reversed equilibrium with the rotating field added, checked by a conserved transformed Hamiltonian that also turns out to control which flux surface the particle ends up on.Published abstract, second sentence; companion report PPPL-3554, equations 1 to 4
The headline ion result: rapid ion heating to thermonuclear conditions occurs in less than 0.1 milliseconds in a modest-sized field-reversed configuration. Read it precisely — this is the energy single ions reach in the simulated orbits, on a timescale far shorter than the confinement time, not a measured bulk temperature.Published abstract, third sentence
The heating mechanism is stochastic rather than resonant, and that is a feature. Strong variation of the magnetic-field strength over the confinement region prevents a true cyclotron resonance, so the drive never locks to a single particle for long; heating proceeds anyway, and effectively. Lyapunov exponents are computed to demonstrate that the orbits are genuinely chaotic, which is the quantitative statement behind the word.Published abstract, fourth and fifth sentences
Electrons are heated too, in the same frequency band, far below their own cyclotron frequency, primarily by a mechanism involving trapping in the wells of the azimuthal electric field. The companion report works this half out in detail on a reference machine with a 10 centimetre separatrix radius, elongation 5 and a 2 tesla axis field: with a 20 gauss rotating field, electrons starting at 100 electronvolts reach several kilovolts and, for the reversed rotation sense, tens of kilovolts, scattering off the sharp field curvature at the ends in what the authors call Speiser collisions.Published abstract, sixth sentence; companion report PPPL-3554, figures 1 to 4 and the summary paragraph
What to watch: the closing conclusion is that odd-parity rotating magnetic field promotes oppositely directed ion and electron motion near the minor axis — appropriate for supporting the plasma current. Heating and current drive from one antenna, on the magnetic axis where nothing else reaches. That prediction is what the Princeton Field-Reversed Configuration experiments were built to test, and the measurement that settles it is a device sustaining its own current with an odd-parity drive and showing the ion energies these orbits promise.Published abstract, closing sentence

The way in

https://doi.org/10.1063/1.1459456

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

LICENCE. Published as Physics of Plasmas, volume 9, issue 5, pages 2093 to 2102, May 2002, under the American Institute of Physics copyright; Crossref deposits no licence at all for the DOI, and OpenAlex and Unpaywall both report the record closed with no repository copy on 2026-09-08. No text of the published article is reproduced here. SOURCES READ. Two things could be read on 2026-09-08 and this sheet is written from them. First, the authors’ complete published abstract, deposited with Crossref, which states the method, the ion result, the heating mechanism and the current-drive conclusion in order. Second, the authors’ own companion Princeton Plasma Physics Laboratory report PPPL-3554, Electron Acceleration in the Field-reversed Configuration by Slowly Rotating Odd-parity Magnetic Fields, April 2001, prepared under U.S. Department of Energy contract DE-AC02-76CH03073 and posted openly by the DOE Office of Scientific and Technical Information — that report was downloaded and read in full, and it carries the same two authors, the same RMF1.13 orbit code and the same reference machine as the published paper. Locators say which of the two a statement comes from. AUTHORS. The registry record for this sheet named Samuel A. Cohen alone; Crossref gives both authors and the given names above are taken from the PPPL report title page — Alan H. Glasser wrote from Los Alamos National Laboratory, Samuel A. Cohen from the Princeton Plasma Physics Laboratory.

How to cite it

Alan H. Glasser, Samuel A. Cohen (2002) Ion and electron acceleration in the field-reversed configuration with an odd-parity rotating magnetic field doi:10.1063/1.1459456

Where it sits in the curriculum

Fusion machines: pinches, focus devices and inertial drivers