STM-D-0990Paper2017On the bench now

Increasing plasma parameters using sheared flow stabilization of a Z-pinch

U. Shumlak · B. A. Nelson · E. L. Claveau · E. G. Forbes · R. P. Golingo · M. C. Hughes · R. J. Oberto · M. P. Ross · T. R. Weber

Abstract and summary · read the original at the source · none found

In one page

A Z-pinch is the simplest fusion machine there is: send a large current straight down a column of plasma and the current’s own magnetic field squeezes the column. It has always had one fatal habit, which is that the column kinks and necks itself apart within nanoseconds. Shumlak’s group at the University of Washington report that giving the plasma a sheared axial flow — fast along the middle, slower at the rim — holds the column still, and keeps holding it as the column is compressed. Their two machines, ZaP and the three-electrode ZaP-HD, run quiet for tens of microseconds where the theoretical growth time for the kink is twenty nanoseconds, stay smooth along the whole metre of their length, and reach a pinch three millimetres across carrying an 8.5 tesla field, an electron density around one hundredth that of ordinary air, and an electron temperature of one thousand electron volts — about eleven million degrees. No coils, no applied field: the flow does the work.

Why it matters hereChapter 12 needs a small source of very large energy, and this is the least complicated route anyone has to one — a metre of pipe, two capacitor banks, no magnet coils and no externally applied field, with the scaling running the right way, so more current means a smaller and hotter machine. Chapter 9 is about plasma that organises and holds itself, and a column kept azimuthally symmetric and axially uniform for tens of microseconds by nothing but its own velocity profile is that subject at its clearest.

What it claims

01The Bennett relation and the adiabatic approximation give scaling laws in which, at fixed linear density, raising the plasma current raises the temperature and the density while shrinking the pinch radius — so high-energy-density and possibly thermonuclear conditions are reached by making the device smaller rather than larger, provided the plasma can be kept stable.Section II, Equations 5, 7, 9 and 10; Figure 1
Published and peer-reviewed
02Sheared axial flow leaves the radial force balance untouched, so it stabilises the column without reducing the average beta, without magnetic field coils and without the parallel heat loss an embedded axial field brings; theory sets the kink threshold at a flow shear above one tenth of the axial wavenumber times the Alfvén speed, and the experiments show quiescent periods of tens of microseconds where the theoretical kink growth time for the measured parameters is twenty nanoseconds.Section III, opening paragraphs and the threshold quoted from Ref. 32; Figure 4, quiescent period from 28 to 55 microseconds
Published and peer-reviewed
03The measured flow profile is explained by anisotropic ion viscosity: viscosity peaks at the axis, where the azimuthal magnetic field vanishes, flattening the profile there, and is low near the pinch radius, where the shear concentrates — and the resulting viscous damping distance of over 200 centimetres for ZaP parameters is what sets the design constraint on how long a sheared-flow-stabilised Z-pinch may be.Section III A, Equation 15 and the viscous damping distance calculation
Published and peer-reviewed
04Magnetic probes every five centimetres show the field variation along a 126 centimetre assembly region falling from more than 30 percent before the quiescent period to mostly under 10 percent during it, and in ZaP-HD — whose third coaxial electrode lets one capacitor bank control acceleration and a second control compression — the kink fluctuation stays low simultaneously at nine axial stations for 24 to 72 microseconds, so the column is azimuthally symmetric and axially uniform at the same time.Section III A, Figure 5; Section III B, Figures 6 and 8
Published and peer-reviewed
05With acceleration and compression controlled separately, a digital holographic interferometer measures an electron density peaking near two times ten to the seventeen per cubic centimetre at a pinch radius of about 0.3 centimetres; Ampère’s law applied to that profile gives a peak azimuthal field of 8.5 tesla at the pinch radius, and radial force balance gives an electron temperature peaking at one kiloelectronvolt on axis, held stable for many Alfvén times.Section IV, Equations 16 to 18; Figures 10, 11, 12 and 13
On the bench now
06Scaling relations built on this work indicate that scientific breakeven may be possible at a plasma current of 650 kiloamperes provided the plasma remains stable; the named open questions are the polytropic index during formation, since shocks may spoil the adiabatic assumption, and whether drift instabilities appear as higher currents raise the drift speed.Section V, Discussion
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Abstract

The ZaP and ZaP-HD Flow Z-pinch experiments at the University of Washington have successfully demonstrated that sheared plasma flows can be used as a stabilization mechanism over a range of parameters that has not previously been accessible to long-lived Z-pinch configurations. The stabilization is effective even when the plasma column is compressed to small radii, producing predicted increases in magnetic field and electron temperature. The flow shear value, extent, and duration are shown to be consistent with theoretical models of the plasma viscosity, which places a design constraint on the maximum axial length of a sheared flow stabilized Z-pinch. Measurements of the magnetic field topology indicate simultaneous azimuthal symmetry and axial uniformity along the entire 100 cm length of the Z-pinch plasma. Separate control of plasma acceleration and compression has increased the accessible plasma parameters and has generated stable plasmas with radii of 0.3 cm, as measured with a high resolution digital holographic interferometer. Compressing the plasma with higher pinch currents has produced high magnetic fields (8.5 T) and electron temperatures (1 keV) with an electron density of 2×10¹⁷ cm⁻³, while maintaining plasma stability for many Alfvén times (approximately 50 μs). The results suggest that sheared flow stabilization can be applied to extend Z-pinch plasma parameters to high energy densities.

The way in

https://doi.org/10.1063/1.4977468Published as Physics of Plasmas volume 24, article 055702, 2017, copyright AIP Publishing, with no Creative Commons statement on the record. The Department of Energy’s DOE PAGES service holds the authors’ accepted manuscript, OSTI 1465207, dated 25 January 2017, which is free to read but does not change the copyright in the published article, so this sheet stays abstract-only. The abstract below is the publisher’s, verbatim, with its exponents rendered as typographic superscripts. The summary and every claim were written from that accepted manuscript, retrieved and read in full on 2026-09-08, and each locator points to a numbered section, equation or figure of it; the accepted manuscript’s text matches the published abstract sentence for sentence. The work was done in the Aerospace and Energetics Research Program at the University of Washington in Seattle and funded by ARPA-E, the National Nuclear Security Administration and the Department of Energy. Author initials are left as the published record gives them. Companion sheets: the earlier ZaP stabilization experiments at /library/stm-d1e9e565b8, the programme’s later statement at /library/stm-d90424cb8a, sustained neutron production from the same configuration at /library/stm-751d0ee864, and Zap Energy’s repetitive system at /library/stm-49324933a9.

How to cite it

U. Shumlak, B. A. Nelson, E. L. Claveau, E. G. Forbes, R. P. Golingo, M. C. Hughes, R. J. Oberto, M. P. Ross, T. R. Weber (2017) Increasing plasma parameters using sheared flow stabilization of a Z-pinch. doi:10.1063/1.4977468

Where it sits in the curriculum

Lattice confinement fusion Plasmoids, charge clusters and the orbs