STM-D-0633Paper2008Published and peer-reviewed

Numerical experiments on plasma focus pinch current limitation

S Lee · P Lee · S H Saw · R S Rawat

Abstract and summary · read the original at the source

In one page

A plasma focus fires a capacitor bank through two coaxial electrodes; the current sheet it drives sweeps down the barrel and collapses on the axis into a hot, dense pinch that makes fusion neutrons. Everyone in the field expected that cutting the machine’s stray inductance — the electrical sluggishness of the connections between bank and electrodes — would raise the current and therefore the yield. Sing Lee, Paul Lee, Sor Heoh Saw and Rajdeep Rawat ran the numerical experiments that show it does not. Using the Lee model code fitted to the megajoule PF1000 machine in Warsaw, they lowered the inductance step by step. The peak current in the circuit rose all the way, from 1.66 to more than 4 megaamps. The current that actually reaches the pinch did not: it topped out near 1.05 megaamps and then fell, and the neutron yield followed it. The lesson they draw is that the two currents are different quantities and only the pinch current scales the yield.

Why it matters hereChapter 12 counts on the plasma focus as a compact, buildable fusion machine, and this paper is the design rule for it: there is a best inductance, not a lowest one, and the quantity to engineer for is the current that reaches the pinch. Chapter 9 studies self-compressing plasma structures, and this is the measurement of how much of a machine’s current the structure actually carries.

What it claims

01Below an optimum static inductance the plasma focus stops improving. In the numerical experiments on the megajoule PF1000 at 35 kilovolts in 3.5 torr of deuterium, lowering the static inductance from 100 nanohenries to 5 raised the peak discharge current steadily from 1.66 to 4.37 megaamps with no sign of any ceiling, while the current at the start of the pinch rose only to a broad maximum of 1.05 megaamps around 40 to 30 nanohenries and then fell. Pushed to 1 nanohenry the peak current passed 6 megaamps while the pinch current dropped to about 0.95.Section 4, table 1 and figure 3
Published and peer-reviewed
02Neutron yield follows the pinch current, not the peak current. In the same runs the computed yield traces the same broad maximum, peaking at 3.2 times ten to the eleventh neutrons around 40 to 30 nanohenries and falling to 2.0 times ten to the eleventh at 5 nanohenries, while the ratio of pinch current to peak current falls monotonically from 0.58 at 100 nanohenries to 0.22 at 5.Section 4, table 1
Published and peer-reviewed
03The total discharge current is not the current driving the plasma, and treating them as one is where the field goes wrong. A Rogowski coil around the flange measures the total; only a fraction lifts off the insulator and drives the sheath. In the Stuttgart DPF78 measurements that fraction rose above 0.6 for most of the axial phase, stayed above 0.6 in the radial phase, then dropped to 0.48 at the start of the pinch and towards 0.4 as the pinch progressed. Taking the peak current, or the total current at the dip, as a stand-in for the pinch current would only be defensible if the two waveforms were linearly related, and they are not; yield scaling should be written in terms of the pinch current.Section 2, Distinguishing the total current waveform from the plasma current waveform
Published and peer-reviewed
04The instrument is a fitted model rather than a probe. The Lee model code couples the electrical circuit to the focus dynamics, thermodynamics and radiation across five phases, and is tuned to a machine by fitting the computed total-current trace to the measured one feature by feature — peak amplitude, rising slope, topping profile, roll-over and the current dip — using an axial mass swept-up factor, a current factor and a radial mass factor. For PF1000 at 27 kilovolts the fit gives a static inductance of 33 nanohenries, a stray resistance of 6.3 milliohms, a mass factor of 0.14, current factors of 0.7 and a radial mass factor of 0.35, with a bank of 1332 microfarads and an anode of 11.55 centimetres radius and 60 length. Once the fit is that good, the authors argue, the computed pinch current is as reliable as the measured total current it was fitted to.Section 3 and Section 4, figure 1 and the fitted parameters
Published and peer-reviewed
05The effect is not an artefact of one machine or one damping. Repeating PF1000 at 40 kilovolts with the resistive damping factor lowered from 1.16 to 0.21 still shows the limitation, with a pinch current maximum of 1.59 megaamps and a yield maximum of 8.2 times ten to the eleventh neutrons at 60 nanohenries. A much smaller machine — a 300 microfarad bank at 15 kilovolts in 6 torr of deuterium, with the parameters typically fitted to the NX2 — shows the same shape, a broad pinch-current maximum of 0.455 megaamps between 25 and 15 nanohenries and a yield maximum of 4.4 times ten to the ninth neutrons near 25.Section 4, the repeat experiments at lower damping and smaller capacitance
Published and peer-reviewed
06The design rule, and the next technology. As the static inductance falls from 100 to 1 nanohenries the share of stored inductive energy sitting in the axial section rises from about 47 per cent to about 86 per cent, and the interplay of the physical processes prevents that extra energy from reaching the pinch. So new machines should be designed for the optimum static inductance rather than the lowest attainable one, and getting past the ceiling calls for something else — the authors point to current stepping, the technique Lee proposed in 1984 and Saw studied experimentally in 1991.Section 4, closing paragraphs; Section 5, Conclusions
What to watch

Read it · abstract

Abstract

Contrary to the general expectation that performance of a plasma focus would progressively improve with progressive reduction of its static inductance L o , a recent paper suggests that there is in fact an optimum L o below which although the peak total current increases progressively the pinch current and consequently the neutron yield of that plasma focus would not increase, but instead decreases. This paper describes the numerical experiments and results that led to this conclusion.

S Lee, P Lee, S H Saw and R S Rawat, Plasma Physics and Controlled Fusion 50 (2008) 065012, 8 pages.

(Abstract only — see the rights note above. On this site, Sing Lee and Sor Heoh Saw’s later survey of what the numerical experiments taught them about plasma focus machines is reproduced in full at /library/stm-fbd01b5713, and the Chilean measurement of a pinch in a plasma focus of only tens of joules is at /library/stm-12f5d53acb.)

The way in

https://doi.org/10.1088/0741-3335/50/6/065012Published in Plasma Physics and Controlled Fusion 50 (2008) 065012, received 18 February 2008 and published 11 April 2008, and marked ’© 2008 IOP Publishing Ltd’ with no Creative Commons statement; the aggregator indexes label the DOI open access, but the publisher page is behind a bot challenge and carries no open licence. So this sheet holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The claims are read against the published paper as the authors host it themselves at the Institute for Plasma Focus Studies, and the paper’s own section, table and figure numbering is used in the locators; subscripted symbols are spelled out in words here. Sing Lee writes from the Institute for Plasma Focus Studies in Chadstone, Victoria, from the National Institute of Education at Nanyang Technological University in Singapore, and from INTI International University College in Nilai, Malaysia; Paul Lee and Rajdeep Singh Rawat from the National Institute of Education; Sor Heoh Saw from INTI.

How to cite it

S Lee, P Lee, S H Saw, R S Rawat (2008) Numerical experiments on plasma focus pinch current limitation. doi:10.1088/0741-3335/50/6/065012

Where it sits in the curriculum

Plasmoids, charge clusters and the orbs Lattice confinement fusion