Robthebob wrote:wait what? how is skunks machine using diamagnetic effect to counteract B field in order to get it to a condition that increase electron confinement by reducing escaping through cusps?
In plasma experiments I have done the shape of the plasma is very similar to that of the Skunk Works plasma (once the permanent magnets I have used are adjusted for). In the experements and from the magnetic field illustration the shape of the plasma matches that in a opposing magnet mirror machine.
The advantage of inserting a third magnet in the center helps moderatly to greatly, depending on how you model the system.
If you use mathematical lines to represent your magnets the overall confinement gain is greater than 2. This is due to the inverse square law of electromagnetism. Cusps are defined by the magnetic field strength fall off past some level. Simple inverse law considerations implies that if you halve the distance between the magnets, then the field strength is 4 times greater. This means the line cusp width is 1/4th. There are two line cusps now though, so the net gain would be two. This simple comparison is not accurate though. The cusp walls are defined not only the inverse square law and the opposing field drop off which I think scales as the separation from the mid line of the cusp to the 2nd power to the 4th power as you get closer to the cusp center or else the separation to the 2nd power *up to 2 as the cusp is approached. I'm not sure which applies, but it is obvious that the B field drop off accelerates as the cusp midline is approached. The B field lines show this in the illustration (and many others also show this). The net effect from the magnet separation distance is the product of these two processes. That is why I used 2 as the minimum gain. The actual gain may be mildly to greatly greater (say as much as 3--8 fold gain).
This simple line modeling of the magnets is flawed though, just like it was flawed in the Polywell modeling. The magnets must have a real physical thickness (not an infinitely thin line) and this changes things considerably, just as in the WB6 considerations.
With real magnets the B field at the center of the magnet can is irrelevant. What is important is the magnetic field strength you can generate at the surface of the can.
Take an example. With line magnets you have 1 Tesla fields with a biconic cusp mirror machine where the magnet separation is 1 meter. The midline of the line cusp would be at 0.5 meters from either magnet, and the cusp walls would be defined as the field strength near this mid line, for simplification assume it is the midline. Thus using only the inverse square law, the cusp width would be a value, set here as 10 cm.
Adding a third opposing magnet in the center (one of the end magnets need to be flipped) halves the distance from the lines representing the magnets and this means the field strength would be four times as strong midway between the either pair of magnets.
Now consider real magnets. In this example the can thickness is 20 cm (radius of 10 cm). The magnet mid line separation of the end magnets remains the same at 1 meter, but now the can surface separation is 0.8 meters. Half of that is 0. 4 M and applying the inverse square law results in field strength close to the midline (my defined cusp border) as 1/0.16 instead of the 1/0.25 obtained by using the simplistic line magnet representation above.
This means the cusp would be ~ 6/4 or ~ 1.5 times smaller in width in the real system. This multiplied by the gain of the simple model results in a gain of ~ 6 instead of 4. Since there are now two line cusps the net gain would be 3 fold. This would be a minimum gain due to the deficiency of my B field drop off calculation (using only the inverse square law). By playing with the thickness of the magnet cans and and the separation of the mid line (mid plane) of the magnets, the line cusps could be made to be extreamly thin so that the losses here could approach or improve on the losses of the end point cusps (just as in the Polywell). There is a tradeoff though on the resultant central volume. What would be the best balance requires much more involved modeling.
An alternative is to make the magnet can surfaces closer together by increasing the width of the central magnet relative to the end magnets. There are probably limits, but my modeling suggests the the central magnet might have a minor radius can diameter of up to 1.5 to 2 times that of the end magnets. With appropriate strengths of the central and end magnets I think the central volume may be preserved (or at least not reduced as much) while the magnet separation is comparable to the few mm of the EB6 design.* If this is the case the losses could be considerably less as the 8 corner cusps of the Polywell would be equivalent to the two narrow cusps og the three ring design, while the point cusps are reduced from 6 to 2 (or even less if ring assemblies are stacked together. The net comparison is uncertain though as I don't know how the central volume would compare, and it is the ratio of the central reaction volume to the losses that is important.
I think though that the 3 ring design could at least approach the performance of the Polywell if not exceed it. It should at least significantly outperform the biconic opposed mirror machine. Other considerations such as direct conversion and focusing output for rocket thrust may also favor the three ring design.
*By varying the B field strengths of the end versus the central, the 3 ring arrangement could be adjusted for a central quasi spherical focus or to a hourglass shape along the line of symmetry (the horizontal x axis in the illustration) to a torus shape at a given radius from the axis of symmetry. What varying this condition at various time scales would do to the dynamics in the machine is anyone's guess, but it gives another knob to play with.
Dan Tibbets
To error is human... and I'm very human.
