STM-D-0774Paper2014Published and peer-reviewed

Plasma Focus Radiative Model: Review of the Lee Model Code

S. Lee

Summary and citation · read the original at the source

In one page

The plasma focus is one of the most elegant machines in fusion research: a coaxial electrode gun that drives a sheet of current down its length, then collapses it onto the axis into a short-lived pinch so dense and so hot that it throws off neutrons, soft X-rays and fast ion beams. Sing Lee has spent three decades building a computer model of that machine, and this review is the first complete published description of it. The Lee model code couples the machine’s electrical circuit to the plasma’s motion, its thermodynamics and its radiation, and it is built to keep energy, charge and mass consistent throughout. The recipe is simple enough to be striking: fit the computed current trace to the measured one, and the model then hands back the pinch radius, the temperature and density, the radiation and neutron yields and the ion beam fluence. Lee notes the code has no formal source reference except plasmafocus.net, where he posts it free.

Why it matters hereChapter 9 is about self-organised plasma structures — how a current sheet becomes a compact, luminous, radiating object — and the plasma focus is the cheapest laboratory in the world for making one and measuring it. Chapter 12 gets the fusion side: this is the reference tool that laboratories from Chile to Poland use to turn a single current trace into pinch temperatures, densities, ion beams and neutron yields, which is what makes small-machine results comparable across the field.

What it claims

01The code couples the electrical circuit with plasma focus dynamics, thermodynamics and radiation. It is energy-, charge- and mass-consistent and accounts for the effects of transit times of small disturbances and plasma self-absorption. That combination is the point: nothing is bolted on, and the machine and the plasma are solved together.Abstract, page 319
Published and peer-reviewed
02Five phases describe a Mather-type plasma focus — the axial snowplough phase, the radial inward shock, the reflected shock, the slow compression radiative pinch and the expanded axial phase — and the whole model is tuned by two pairs of mass and current factors, one pair for the axial phase and one for the radial. Lee reports that fitting the computed current waveform to the measured waveform of each low-inductance machine is enough to set them.Section: The Five Phases of the Plasma Focus, pages 321 onward; Conclusion, page 334
Published and peer-reviewed
03The commonly accepted picture today is that mechanisms within the focus pinch — micro- and MHD instabilities, acceleration by turbulence and anomalous plasma resistance — are important to plasma focus behaviour, and that the emitted neutrons do not originate from thermonuclear reactions. The pinch is doing something more interesting than simply getting hot.Introduction, pages 319 to 320
Settled physics
04Neutron yield is computed as two terms. The thermonuclear term uses the thermalised reaction rate at the pinch temperature; the beam-target term models a beam of fast deuterons produced by diode action in a thin layer close to the anode, driven by the high voltages of plasma disruption, striking the hot dense pinch column. Combining all available experimental data gives a measured fit of neutron yield equal to nine times ten to the tenth multiplied by the pinch current in megaamps raised to the power 3.8, over the range 0.1 to 1 megaamp, and the code is calibrated to it at 0.5 megaamps and seven times ten to the ninth neutrons.Section: Neutron Yield, page 329
Settled physics
05In one respect the five-phase code is found wanting. High-inductance machines, which Lee calls Type 2, show an extended dip in the measured current that the five-phase computation cannot fit; an extended sixth phase dominated by anomalous resistance completes the fit, and Lee argues that this is precisely what makes the current trace a way of measuring the anomalous resistivity of the plasma focus.Abstract, page 319; Conclusion, page 334
What to watch
06Once fitted, the code outputs realistic axial and radial dynamics, pinch length and minimum pinch radius, temperatures and densities, bremsstrahlung and line radiation yields, thermonuclear and beam-target neutron yields, fast ion beam flux and fluence, energy flux and fluence, power flow and damage factors. Lee reports that all tests to date of computed against measured quantities have shown good agreement, across machines from sub-kilojoule devices to the megajoule class.Conclusion, page 334; Introduction, pages 320 to 321
Published and peer-reviewed

The way in

https://doi.org/10.1007/s10894-014-9683-8Published as Journal of Fusion Energy volume 33, pages 319 to 335 (2014). The Springer version of record is closed access and Unpaywall, OpenAlex and Crossref all report no open deposit. Lee posts the paper and the model code itself openly through the Institute for Plasma Focus Studies at plasmafocus.net, and that author-posted copy is the one read for this sheet on 2026-09-08; it carries no licence permitting redistribution, so no text of the paper is reproduced here. Every claim below is drawn from the paper as read and located to its own abstract, sections and page numbers.

How to cite it

S. Lee (2014) Plasma Focus Radiative Model: Review of the Lee Model Code. doi:10.1007/s10894-014-9683-8

Where it sits in the curriculum

Plasmoids, charge clusters and the orbs Lattice confinement fusion