I have been considering the idea of bowing the magrid until the ends of the grids meet at the top and the bottom. Start with a WB6 truncated cube. Discard the top and bottom grids. Lengthen the side grids till they are ~ 2 times as tall as wide.* Then bow them inward until they almost meet at the top and bottom. You end up with a 4 sided near sphere shape. The advantages is that you only have 4 magnets instead of 6. It is more spherical. And, there are fewer cusps. There are 4 point cusps instead of 6. These point cusps may be larger, but I don't think they would exceed the area of the original 6 point cusps. There would be two corner cusps instead of 8. The resultant individual corner cusp area may be modestly larger (or not). But the number advantage would be significant. The side 'funny' cusps would be longer individually, but the total would (I think) be the same. So, I think you would have a ~ 4 X advantage in corner cusp losses, while the other cusp losses would be unchanged. I Think this might result is and ~ 4 x advantage in the cusp confinement dominated Wiffleball trapping facter ( the corner cusps are the most significant for losses).This may translate into a 4X density advantage and a 16X fusion rate advantage. Multiply that by the 3-5X advantage Bussard expected from a more spherical shape and the net gain might be ~ 45- 75X.
You would need perhaps two connecting nubs on each side of the magnets- one perhaps neat each end of the grid, but the total nubs in this case would be 8, compared to 12 in WB6. This represents a 1.5X gain in the exposed metal considerations, With separate stand off supports, the number of legs might be 16, instead of the 24 in a WB6 truncated cube design(4 per magnet)- the same gain.
With the two (top and bottom) corner cusps dominating the cusp losses (IE: the alpha escape routes), there may be advantage in designing a conversion system for a P-B11 reactor.
* I say ~ 2X the height for the prebent grids, because as the ends approach each other on the top and bottom, the opposing fields may displace each other to a degree. In order to get a near spherical shape to the internal B-field edge, the physical magrid shape may need to be elongated somewhat ( or perhaps even shortened a bit, depending on how close together they approach each other and the angles involved) . Perhaps as much as 1.5 times as tall as wide for the bowed physical grids would be required.
This closure angle and overall height (vs width) may be adjusted somewhat to maximize alpha collection advantages (make the end cusps more leaky) . This would compromise containment advantages somewhat, but if my estimates are real, you are starting with an ~ 4X advantage, so there is some wiggle room. If your priority is to maximize alpha (or other charged fusion ion) flows through the ends of the device (like in a rocket engine- use one side for direct conversion, and the other end for thrust) you could trade off size for this polar flow advantage. Even for stationary reactors this might give enough direct conversion engineering advantages that it is worth the larger size (especially as that would also ease other engineering concerns).
[EDIT] I don't think bowing the sides would have to result in concave towards the center magnetic fields. Though this concern might require the the prebowed length be be a little longer to prevent the deformations of the opposing fields on the ends resulting in this problem . Or instead of increased length, a shallower closure angle (say each side bowed inward ~ 88 degrees instead of 90 degrees); or a combination of both might be used.
As mentioned above, and as emphasized by
concern for the shape of the magnetic fields on the top and bottom of the grid might be addressed by varying the geometry as mentioned above and as shown in the illustrations. The red shading hopefully illustrates the magnetic field geometry and that the distortion of the face point cusps may not be as great as it might seem from the grids themselves. The magnetic field shapes in the other illustration shows an estimate of the correction needed to restore Wiffleball surfaces to near spherical geometry (instead of convex towards the center) on the top and bottom corner cusps regions.icarus wrote:The whole idea of bowing the coils to arc around a sphere is suspect in my consideration, unless I see a good simulation (or an experiment god forbid) of why it would help.
It seems at first glance to be creating the situation of having a field gradient away from the center of the device, exactly the opposite of what you want for stability of the plasma.