Historical research guide · 0990 · 2017
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
In one minute
A Z-pinch sends a large current down a plasma column, whose own magnetic field squeezes it. Its limiting problem is instability: the column kinks and necks apart on nanosecond time scales. Shumlak’s University of Washington group reports that sheared axial flow — faster near the centre and slower near the edge — can stabilize and compress the column. Their ZaP and three-electrode ZaP-HD experiments remain quiet for tens of microseconds, despite a theoretical kink growth time of about twenty nanoseconds. They measure a 0.3-centimetre pinch, an 8.5-tesla azimuthal field, electron density near 2 × 10¹⁷ cm⁻³ and electron temperature near 1 keV. The paper reports a laboratory plasma configuration and scaling calculations, not a fusion-power result.
Connection
Chapter 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.
From the source
The 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
Sheared 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
The 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
Magnetic 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
With 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
Scaling 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
The way in
https://doi.org/10.1063/1.4977468How 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