LPPFusion Mechanical Engineer Rudy Fritsch, with the help of Chief Scientist Lerner and suggestions from Research Scientist Syed Hassan, has completed the redesign of the anode stalk, based on extensive thermal and mechanical simulations. The key to the redesign was in optimizing the thickness of the anode wall, or equivalently the radius of the hole in the end of the anode.
Previous work (see last report) had shown that the most likely source of heating of the anode’s inner wall is the relatively cool background plasma, shocked by the arrival of the current sheath. “Relatively” cool still means around 10 million C°—but that is cool relative to the more than 2 billion C° in the plasmoid where fusion reactions occur, see figure 4. Lerner’s calculations showed that as the radius of the hole is increased in alternative designs, the magnetic field in the hole decreases. This in turn leads to a decrease in the density of the plasma in the hole and a big decrease in the X-ray radiation released. The net result is that increasing the radius of the hole by 50% decreased the intensity of the radiation by more than a factor of 3. (see Fig. 4)
Figure 4. Current filaments converging within the anode’s hole at the tip of the anode. X-ray radiation from plasma compressed by the rapidly moving filaments heats the anode hole surface.
Reducing the X-ray radiation reduced the temperature that the surface of the anode is heated to by the low-energy X-rays from the plasma, which are absorbed in the outer few microns of the anode’s surface. This in turn reduces the mechanical stress that comes from the sudden expansion of the heated metal. Of course, widening the hole reduces the thickness of the anode wall. But the simulations showed that stress continued to decrease as the thickness of the wall decreased to about half what we started with.
As Fritsch pointed out, stress did not seriously increase until the wall was thin enough for compression waves to spread across the wall during the time the heating was still being applied. With heating only lasting about 0.2 microseconds, the compression wave moves only 0.26 cm even at beryllium’s speed of sound—13 km/s. This is a lot less than the optimal wall thickness of around 0.6 cm. The four-fold reduction in maximum stress is shown in the simulations in Figure 5.
Figure 5. Thermo-Mechanical simulation shows maximum stresses on a half-cross section of anode. Left figure shows stress (in psi) for existing anode design, while right figure shows maximum stress for new optimized design. By moving the anode wall further from the axis, stresses are greatly reduced. The maximum stress (note different scales) falls by a factor of four. The distortions in shape of the anode are exaggerated by 1,000 times to make them visible. In reality the maximum motions are only around 3 microns or 1/10,000 of an inch. The yield strength of beryllium is around 35,000 psi.
Based on this work, we have now sent new drawings to the manufacturer and expect to get the anode in February or so. The reduction in stress in the simulations of the design makes us confident that the anode will survive the enhanced stresses produced by the increase to 1.7 MA currents that we expect in the coming experiments with the new switches. This first series will be carried out with only eight capacitors attached, as were the experiments last year. When we go to the full 12 capacitors, and increase current further up to perhaps 2.4 MA, more study may be needed. But we intend to monitor the vibrations with a remote, laser-based vibrometer which will give us data as to the actual stresses the anode is undergoing.