mattman wrote:Hello,
I am starting to do research on the Whiffle Ball. A few months ago, someone on this forum (I think it was Dan Tibbets), said they had proven the Whiffle ball effect in Japan.
Do you have a paper, or author, or group name, for this research?
I think I may have found a mistake in Rider's Work having to do with the mirror ratio. I need to get more details on this. I have seen several definitions of the mirror ratio - here is one definition below:
Mirror Ratio = Weakest Magnetic field strength/Strongest Magnetic Field Strength
If the whiffle ball effect is happening, I am trying determine how high the mirror ratio would be. From this, I think it is a safe bet Rider significantly underestimated the mirror ratio in his paper.
Concerning the mirror ratio, I assume this is equivalent to the number of passes before escape. In the EMC patent/ patent application 2008, the ratio of an optimized(?) opposing magnet mirror machine was ~ 5-8 passes. The 'cusp' confinement of the Polywell ('14 all point like cusps' replacing the two polar point cusps and equatorial line cusp of a typical mirror machine) was ~ 60 passes, and with Wiffleball inflation, the passes before loss increased to 'many thousands'.
In a sense this is better confinement, but it is similar to mirror point cusp losses, except in the truncated cube these cusps are increased to 14 from two. This total point cusp loss area is worse than the mirror point cusp losses, but eliminates the vast majority of the horrendous equatorial line cusp losses. Thus the ~ 10 fold improvement in 'cusp' confinement. The Wiffleball effect is improving confinement further, but it could also be considered as not changing the cusp loss areas much if any. What it does do is increase the relative volume that is contained, and in doing so it increases the surface area of the contained plasma 'balloon' so that the chances of a charged particle hitting the surface and rebounding is proportionately greater than the chances of hitting a cusp. The resultant angles into the cusp proper may also be changing- effectively decreasing the loss area, but this is more complicated than the simple Wiffleball analogy. Apparently this inflation adds up to the ~ 1000 fold advantage over simple mirror confinement (or ~ 100 times better than simple ' point cusp' confinement?).
To calculate the wiffleball effect you would need to know the effective volume of the spiky ball of plasma confined by the 14 point like cusps at low Beta. Then compare this to the inflated plasma ball volume/ surface area with Wiffleball inflation. The cusp holes/ loss cones could be considered unchanged (I think). How these two volumes would be determined is uncertain, but the ratio between them should be directly proportional to the B field strength.
EG: The 'cusp' contained volume in a 1 Tesla B field might be ~ 1 cubic meter, under 10 Tesla, this area may be 0.001 cubic meters. And, because of the increased B field strength the Cusp surface areas may be 100 times less (1/B^2). This doesn't look good (assuming I'm not completely off track). But, while the plasma area is 1000 times less, the resultant surface area is 100 times less. It is a wash, the confinement is less, but so is the effective confined volume. The ratio of plasma surface area to cusp hole loss area would be unchanged so the density at any given input rate would be unchanged. As the volume is decreased another order of magnitude, the number of confined charged particles would actually be 10 times less- not good.
Now enters the effect of increased charged particle populations (essentially electrons). These increased density of electrons is driven by input rates greater than cusp losses. As this progresses, the electrons push out against the magnetic fields (comparable to gas pressure pushing outward against a balloon). Up to a limit this will inflate the internal volume under constant B-field strength. This is limited by the available radius / starting plasma radius within the machine. This equates to the Beta= one condition- the maximum size allowed. This limits the volume gain- surface area gain over cusp loss hole size to this contained radius proportion. In this constant B condition the volume is increased while the density and loss rate is unchanged. This would scale as r^3 within the constraints of the available radius change.
But the B field can be varied also. By increasing B strength by 10X, the volume could be unchanged if the density is increased 100 fold. This is dependent on the loss hole size being 100 X (10^2) times smaller with the same volume/ surface area of the plasma sphere.
This is the B^2 density effect.
Various combinations of these competing effects are possible.
In the example of WB100, the radius in increased 10X, the resulting area 1000X, the resulting surface area 100X, while the B field is increased 100X with resulting cusp hole size decreasing by 10,000 * ratio of plasma sphere surface area / loss hole surface area. The increased plasma sphere surface area multiplies this ratio by 100, while the increased distances between the magnets divides this ratio by 100. The net effect is that cusp hole size to plasma sphere surface area remains at a ratio of 10,000. (B^2). This total surface area divided by the B field strength induced cusp hole size cancels out so the only concern is the B- field strength in determining the ratio.Thus, again the B^2 density scaling.
As the fusion rate scales ad the density squared, this gives the final B^4 fusion rate scaling.
The result is (10,000 improved density)^2 * 1000 increased volume = 100,000,000,000 times increased fusion., or ~ 100 MW of fusion power.
The loss scaling is based on the this surface area ratio, which ends up being ~ r^2. This ignores some magnetic loss scaling (B^0.25 I think)), but this is modest compared to the radius loss scaling.
I understand that the power output scaling is well understood and difficult to argue against (this ignores ion confluence which would magnify the advantages?)
The loss scaling is more uncertain. The relative shrinking of the cusp hole loss cones seems straight forward, but there is disagreements. Other losses such as electron injection efficiency through the tighter cusps, Bremsstrulung, etc are additional input energy loss concerns.
Dan Tibbets