STM-D-0998Paper1989Published and peer-reviewed

Fiber Ablation in the Solid-Deuterium Z Pinch

Irvin R. Lindemuth · Gene H. McCall · Richard A. Nebel

Abstract and summary · read the original at the source

In one page

A Z-pinch is the simplest fusion machine there is: run an enormous current through a thread of material, and the current’s own magnetic field squeezes the resulting plasma into a hot column. In the 1980s the great hope was to start from a frozen deuterium fibre, because a solid fibre cannot suck in cold gas from around it the way earlier gas-embedded pinches did. Irvin Lindemuth, Gene McCall and Richard Nebel of Los Alamos ran the first detailed computer model of what actually happens to such a fibre, solving the equations of magnetohydrodynamics in one dimension from a genuinely cold start. Their answer changed the picture: the current does not flow in the fibre at all. It flows in a thin sheath of hot plasma boiled off the fibre’s surface, while the fibre’s cold interior stays free of magnetic field until it is entirely eaten away — and the instability that ends these experiments may be arriving at exactly that moment.

Why it matters hereChapter 9 is about what dense, self-magnetised plasma columns really do, and this is the calculation that told the field its fibre pinch was a plasma sheath around a shrinking solid core rather than a compressed solid. Chapter 12 keeps the lesson: in every scheme that squeezes fuel with its own current, what carries the current and what holds the fuel are usually not the same material, and the timing between them decides whether you get neutrons or an instability.

What it claims

01In the solid-deuterium-fibre Z pinch the current is carried by hot plasma that has been ablated from the solid fibre, not by the fibre itself. In the computed radial profiles the current flows in essentially fully ionised plasma at relatively low density, a temperature gradient carries heat inward to the cold fibre, and the shock waves that reverberate through the fibre are not enough to raise its conductivity, so the interior of the fibre stays free of magnetic field.Abstract; Figure 1 and the discussion of the radial profiles at 35 nanoseconds
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02The calculation is a one-dimensional magnetohydrodynamic model solved by implicit numerical methods, including thermal conduction and resistive diffusion. Specific internal energy, pressure, average ionisation level and electrical resistivity come from the Los Alamos SESAME tabulated atomic data base, and the thermal conductivity uses essentially the Braginskii formalism. Over a typical run every quantity varies by several orders of magnitude.Paragraph beginning with the report of the first application of the computational capability
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03The cold-start initial condition is the point of the paper. The fibre begins as cryogenic solid deuterium at a thousandth of an electronvolt, at half to full solid density, which is 88 to 176 kilograms per cubic metre, surrounded by a low-density warm halo at one electronvolt. The halo is needed only because the cold high-density fibre is an insulator and something has to conduct the initial current; the authors note that they had modelled electrical breakdown in the gas-embedded pinch but had yet to formulate a model of the breakdown of a solid fibre. Parameter studies show the computed results are insensitive to the halo size.Paragraph on cold-start initial conditions
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04The ablation history has a sharp signature. Heating at the fibre boundary raises a large pressure that drives material outward at about 1.1 centimetres per microsecond and sends shocks inward that reflect from the axis; the on-axis density is compressed by a factor of about four and then falls abruptly by a factor of 400, which is complete ablation of the fibre. After that moment the profiles jump to a similarity solution — uniform temperature, parabolic density fall-off, and the radial velocity of all the material dropping essentially to zero. For the Los Alamos prototype the computed time to complete ablation runs from 40 to 130 nanoseconds and scales with the initial fibre radius and density, and the current-channel radius is always significantly larger than the initial fibre radius.Figures 2, 3 and 4 and the accompanying text
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05Run with the Naval Research Laboratory’s higher current of 500 kiloamperes and its larger initial fibre, the model gives a surprise: the fibre, although reduced to less than half its initial radius, persists for the whole duration of the experiment. The computed current-channel radius tracks the radius measured on the experimental streak photograph, apart from a delay of about 20 nanoseconds, which supports the prediction that the solid fibre survives significantly longer than had been expected — although, as the authors state plainly, experimental techniques to definitively detect the presence or absence of the fibre have not yet been developed.Figure 5 and the paragraph comparing computation with the NRL streak photograph
What to watch
06The paper closes on a conjecture worth testing: that the fibre ablation process may play an important role in the stability of the pinch, and that neutron production may occur at the time of complete fibre ablation. McCall’s model of m equals zero unstable behaviour reproduces the observed scaling of neutron output with current and would not apply until the fibre had totally ablated, and preliminary two-dimensional cold-start computations show the low-density plasma outside the fibre going unstable as early as 10 nanoseconds and speeding the ablation. Los Alamos observations of m equals zero modes at a time comparable to the computed ablation time point the same way.Closing two paragraphs, on the onset of neutron production
What to watch

The way in

https://doi.org/10.1103/physrevlett.62.264Published as Physical Review Letters 62, number 3, page 264, 16 January 1989, received 19 August 1988, under the APS default licence, which does not permit redistribution. TEXT. The article PDF was fetched from the APS harvest full-text endpoint on 2026-09-08 and read in full for the claims below, but it is not reproduced here; the abstract below is the authors’ own as published. UNITS. The scanned PDF loses the micro sign, so micrometre figures are not quoted on this page at all, and the one unit restored by cross-check is the ablation velocity, which is centimetres per microsecond — at the picosecond reading the number would be four orders of magnitude above any plasma expansion velocity. SOURCES FOR THE CLAIMS. Every claim is read from the article itself, and the locators name its own figures and passages. The authors write from the Inertial Fusion and Plasma Theory Group and the Plasma Theory and Computation Group at Los Alamos National Laboratory. SISTER PAGES. The prepulse experiment on a fibre Z-pinch is at /library/stm-06c1a40035, wire-material Z-pinch discharges at /library/stm-02af410435, and the two-wire pinch at /library/stm-704d7be815.

How to cite it

Irvin R. Lindemuth, Gene H. McCall, Richard A. Nebel (1989) Fiber Ablation in the Solid-Deuterium Z Pinch. doi:10.1103/physrevlett.62.264

Where it sits in the curriculum

Plasmoids, charge clusters and the orbs Lattice confinement fusion