Re-thinking Some of Dr Rider Work

[mattman]

Hello,

I realized today that I had been thinking incorrectly about Rider’s basic arguments against the polywell. I think I have found a better way to explain his work.

Rider basically argues that if you have a “blob” of hot fusing plasma, you cannot expect to get net power.

What is a “blob”? A blob of plasma has the following properties:

1. Quasineutral: All the (+) and (-) are equally mixed together.

2. Isentropic: The plasma looks the same, in every direction.

3. Thermalized: The energy distribution is a bell curve. Both the electrons and ions have the same distribution.

4. Uniform: The density and fuel mix of the plasma is basically uniform everywhere.

5. Unstructured: there is no structure. No concentration of (+) or (-), no “virtual anode” no “edge annealing effect” no “14 point star” or “whiffle ball effect”, ect…

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Anything about the Polywell plasma, which removes it from the “blob” should improve the performance.

1. If the cloud has ANY structure: (whiffle ball, virtual anode, edge annealing effect, 14 point star, ect…)

2. If the cloud has ANY energy distribution which is not a bell curve: (bimodal, tri-modal, ect…)

3. If the electrons and ions can have different energy distributions.

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Here is the first part of Riders analysis. He start by assuming the polywell has a “blob” in it. He then models this cloud, using general plasma equations from Lyman J Spitzer’s book “The physics of fully ionized gases”. It is all statistics, over large particle populations with assumptions. He calculates:

1. The volumetric fusion rate.



2. The time it takes for an ion to fuse



3. The energy transfer rate between two ion clouds



Can one ion group be kept hot against another colder group? To solve this, Rider separates the clouds into two. These are “hot” ions and “cold” ions. He first finds two equations:

4. The ion to ion heating rate.



5. The ion to ion cooling rate. This is solely due to the replacement of hot fused ions with cold ions coming in from outside.



Rider sets these rates equal to one another and finds the temperature of one of the ion populations.



Using this math, Rider argues you cannot keep one ion population at two different temperatures. He examines two cases for this. In the first case, some ions are kept cold by swapping fused hot ions with fresh cold ones. Using the equation above, he argues, that this will only allow a 5% variation in temperature.

In the second case, some ions are kept cold by refrigeration. To solve this he estimates average velocity of an ion.

6. The average speed of an ion:



He uses this speed to estimate how fast cold ions transfer energy to hot ions. This equation is divided by the fusion rate and he comes up with this expression.



In his paper he throws in some numbers for boron fusion and shows the ratio to be 1.4. This means the machine would need more energy than it could make. I am not sure he explored all situations, to see if this equation could ever be less than one.

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Based on these calculations Rider will, from now on, assume all clouds of ions have the same average temperature. It is these kinds of calculations that form part of the argument against the polywell. They would not hold up against actual data from a working machine.

[D Tibbets]

Hello,

I realized today that I had been thinking incorrectly about Rider’s basic arguments against the polywell. I think I have found a better way to explain his work.

Rider basically argues that if you have a “blob” of hot fusing plasma, you cannot expect to get net power.

What is a “blob”? A blob of plasma has the following properties:

1. Quasineutral: All the (+) and (-) are equally mixed together.

2. Isentropic: The plasma looks the same, in every direction.

3. Thermalized: The energy distribution is a bell curve. Both the electrons and ions have the same distribution.

4. Uniform: The density and fuel mix of the plasma is basically uniform everywhere.

5. Unstructured: there is no structure. No concentration of (+) or (-), no “virtual anode” no “edge annealing effect” no “14 point star” or “whiffle ball effect”, ect…

Your interpretation of Rider's assumptions shows the gulf between the thermalized plasma, neutral/ quasi-neutral blobs of plasma view point and the far different assumptions of an optimistic Polywell approach. Plasmas may follow Riders assumptions, but it is not mandated. There have been many papers describing potential wells, virtual anodes, etc. This by itself differentiates the expectations. The thermal distribution of ions (and electrons) and the energy distributions inside the machine are also much different. A (proven) potential well implies a definite differential structure to the plasma energy distribution. The magnitude and duration of this imbalance and the effort to maintain it are open questions. But the existence is not.

In general, it seems that all five of the assumptions are inconsistent with stated conditions in the Polywell. The question becomes what is the validity of the Polywell claims. The conclusions of Rider are moot or at least vague if any of the assumptions are challenged. That is the role of experimentation, and alternate theory / claims such as those of Dolan's.

Taking the Boron proton reaction, I accept that riders calculations are valid, but only with the assumptions he uses. The potential well consequences plays a role in Bremmstruhlung. But, even ignoring that, the dilution of boron with excess protons in the reaction mixture, changes the Bremmstruhlung contribution. There is not only wiggle room in the theory assumptions, but also in the practical assumptions.

I do agree that maintaining a separate population of cold and hot ions (or electrons) can not be maintained for reasonable periods of time. But this operates under the assumption that the hot and cold species are mixed together in a homogenous reaction space- your blob of plasma. But hot and cold species are not mixed together. They are separated in space depending on their radius from the center. Of course this is not a complete separation, but it is a relative one based on the shape of the potential well, restoring forces (annealing) and related central confluence/ focus. Again, only experiment can demonstrate the degree of these segregating interactions, or more precisely how much energy input is needed to maintain these separations for adequate periods of time.

It is interesting to note that Nebel stated that even without central ion confluence, and a thermalized plasma -a blob of plasma, a D-D Polywell could exceed a Q of 1. In this case, I think that the only Rider assumption that would not apply is the neutrality of the plasma. The excess electrons is an essential component of the Polywell that is needed to confine the ions electrostatically, thus avoiding much of the ion ExB drift/ diffusion issues that would otherwise render the small Polywells impossible. I think even Rider conceded that a D-D Polywell might exceed breakeven by a modest amount (using all of his assumptions).

And, failing D-D breakeven, that still leaves D-T fusion which is ~ 100 times easier. It would be interesting to see how a D-T burning Polywell would function. The General Fusion and other approaches may give some insight.

D Tibbets