Historical research guide · 0908 · 2010
Numerical Experiments Providing New Insights into Plasma Focus Fusion Devices
Sing Lee · Sor Heoh Saw
In one minute
A plasma focus is a capacitor bank fired into a coaxial electrode: the current sheet sweeps down the tube, collapses onto the axis, and for a few billionths of a second makes a pinch hot and dense enough to fuse deuterium. Sing Lee and Sor Heoh Saw ran thousands of simulations with the Lee model code, which is tuned to each machine by fitting its computed current waveform to the measured one, and report four findings. Lowering a machine's fixed circuit inductance raises the peak current without limit, but the current that actually reaches the pinch peaks and then falls — so peak current is not a proxy for pinch current. Neutron and soft X-ray yields scale as steep powers of the pinch current. And the long-standing worry that neutron output saturates above a few hundred kilojoules has a cause they name: the moving current sheet acts as a fixed resistance of about seven milliohms, which caps the current once the bank impedance drops below it. Their prescription is to raise the voltage instead.
Connection
Chapter 12 needs devices that make fusion happen in a compact, repeatable machine rather than a reactor hall, and the plasma focus is the oldest of them; chapter 9 is about self-organised plasma structures, and the focus pinch is the laboratory's most studied one. This paper matters because it replaces a discouraging empirical wall with a circuit quantity you can engineer around.
From the source
Reducing a plasma focus device's static inductance raises the peak circuit current without limit, but the pinch current reaches a broad maximum and then falls: for PF1000 at 35 kV in 3.5 torr deuterium the peak current rose from 1.66 to 4.37 megamperes as static inductance fell from 100 to 5 nanohenries, while the pinch current peaked at 1.05 megamperes near 40 to 30 nanohenries and then declined.Section 3 and Section 3.1, Table 1 and Figure 7
Over storage energies from about 8.5 kilojoules to 24.5 megajoules the computed neutron yield scales as the pinch current to the power 4.5 and as the peak current to the power 3.8, and the pinch-current scaling holds with less scatter than the peak-current scaling when machines with mixed parameters are added.Section 4.2, Figures 8 and 9
Neon soft X-ray yield over 0.2 kilojoules to 1 megajoule scales as the pinch current to the power 3.6 and as the peak current to the power 3.2, and only the pinch-current index survives unchanged when the circuit and model parameters of real machines are substituted.Section 5.2, Figure 11 and the summarising equations
Because the moving current sheet makes the tube inductance change with time, half of that rate of change acts as a genuine resistance — the dynamic resistance — and for deuterium at the universal end-axial speed of about 10 centimetres per microsecond it takes a near-constant value of about 7 milliohms in the axial phase.Section 6.2, Equations 5 to 7; validated numerically in Section 2.3 against Figure 4j
That fixed 7 milliohms is the cause of the apparent neutron saturation: as the bank capacitance grows, the surge impedance falls below the dynamic resistance, the peak current tends to the asymptote of charging voltage divided by dynamic resistance, and the steep yield scaling turns a current ceiling into a neutron ceiling.Section 6.2, Table 3 and Figure 14
The authors propose escaping that ceiling by raising the operating voltage rather than the stored energy: the saturation level is proportional to voltage, and at 1 megavolt with parallel Blumleins matched to the radial-phase dynamic resistance they estimate peak currents beyond 15 megamperes and pinch currents above 6 megamperes, combined with krypton doping and current-stepping.Section 6.3
The way in
https://doi.org/10.3390/en3040711How to cite it
Sing Lee, Sor Heoh Saw (2010) Numerical Experiments Providing New Insights into Plasma Focus Fusion Devices doi:10.3390/en3040711