Another (simple) FAQ - DONE

[KitemanSA]

... where the crossection goes up at the same rate as temperature, then that would be 45 degrees of slope...

Except that it just struck me that the relavent equation is related to σv not σT, so I would first need to convert to σ vs. v, no? If so, then the slope would be 2 OoM rise to 1 OoM run on the current graph, I think.

[TallDave]

Dan's numbers look good to me, although MSimon has chimed in with something about resonance peaks at a lower p-B11 temp. I want to say it was 90KV. I looked around for a cite but only found this:

The current local temp is .02512 eV

Or maybe that's what the 130 was for.

I don't know if Boron with a Z of 5 might tend to hang onto an electron occasionally. Considering the higher temperature of the P-B11 plasma, I doubt it.

I doubt it matters anyway -- neutrals are unconfined by either electrostatic and magnetic forces and so won't hang around the high-density WB area, (Remember, this isn't a fusor!)

[KitemanSA]

Where exactly is the link to the FAQ you are working on here? I can look up and contribute some numbers and graphs I collected.

There is a "sticky topic" at the front of each of the technical fora that has the FAQ link. But here it is anyway.

http://www.ohiovr.com/polywell-faq/inde ... =Main_Page

[KitemanSA]

AFAIK, a line from one crossing "Order of Magnitude" (say 10E-27,10E2) to the next (10E-26, 10E3) is the "45 degree" slope for the log-log. No?

In a sense, if you are willing to look at the scales, get out your ruler and actually read off the numbers, where the crossection goes up at the same rate as temperature, then that would be 45 degrees of slope if you translated it to symmetrical scales (linear or logarithmic). but that requires work.

I got the numbers by copying a graph from a paper into PowerPoint, placing a "ruler graphic" along the keV axis, striking a slant line from one OoM to the next for the 45degree slope, and laying it against the graphic as best I could. From there I dropped a vertical line down to the axis, read off the ruler value, converted via power of 10 and got the numbers. They are as "approximate" as can be! In some places, the 45 degree line lay along the curve for > 2/10 OoM, quite a spread! The D-D curve was the worst because it has a broad sweeping shape.

I would love to find a decent public domain Xsection curve. Know of one?

[D Tibbets]

Dan's numbers look good to me, although MSimon has chimed in with something about resonance peaks at a lower p-B11 temp. I want to say it was 90KV. I looked around for a cite but only found this:

The current local temp is .02512 eV

Or maybe that's what the 130 was for.

I don't know if Boron with a Z of 5 might tend to hang onto an electron occasionally. Considering the higher temperature of the P-B11 plasma, I doubt it.

I doubt it matters anyway -- neutrals are unconfined by either electrostatic and magnetic forces and so won't hang around the high-density WB area, (Remember, this isn't a fusor!)

No, the 130,000 Volts was a purely made up number, used in an attempt to guess the relative contributions of the borons and the more numerous protons in determining the relative average energy of their beam- beam collisions and matching it to a favorable portion of the crossection curve. I believe the P-B11 resonate crossection peak is ~ 75,000 eV for beam-beam collisions, and 150,000 eV for beam- target collisions. Considering that due to efforts to minimize bremsstrulung, there is an excess of protons in the mixture, so figuring out what effective accelerating electric field would be needed to gain significant advantage from the resonate peak is complicated.

If a single electron stuck to a boron nucleus for awhile it would change it's Z from 5 to 4. It would still be ionized, but undergo less acceleration, and somewhat different dynamics inside the machine. If that electron was in the lowest shell (nearest the nucleus) it might shield the positive nuclear charge slightly and thus increase the fusion rate. But, while this effect is profound with muons, I suspect it is insignificant with electrons (?).

Dan Tibbets

[TallDave]

If a single electron stuck to a boron nucleus for awhile it would change it's Z from 5 to 4. It would still be ionized, but undergo less acceleration, and somewhat different dynamics inside the machine

Ah, true. Duh. Hadn't thought about partial ionization.

I suspect it is insignificant with electrons (?).

Yeah, I'd be curious how the Coulomb force is affected by a partial de-ionization. But like you I also suspect it's moot since the ionization energy (I think it was 630eV for B) is orders of magnitude lower than the fusion energy. Maybe a few on the edge would would momentarily partially de-ionize; hard to see it happening in the core.

On the plus side, they don't get to carry off any energy.

[chrismb]

I dunno why I've bothered telling you guys anything, as it seems widely ignored.

That's why the last time I told you where to look for cross-sections, I put it in colourful capitals and a "grrr" face.

http://talk-polywell.org/bb/viewtopic.php?p=35968#35968

As that was about the 10th time I've pointed to that website, I have to admit defeat and give up trying to provide any info.

There is a small resonant peak for p11B at ~148keV. The broader peak is around 580keV.

[TallDave]

Isn't that beam-target chris?

I think MSimon may have done something a little more involved, but I can't recall for sure. Maybe if I get some time I'll dig around.

[chrismb]

Isn't that beam-target chris?

I think MSimon may have done something a little more involved, but I can't recall for sure. Maybe if I get some time I'll dig around.

No. That's CoM, as far as I am aware. For a 'big' nucleus like 11B compared with a p, so the energy needed for the p is only a little more than the 148keV to achieve the CoM, even in a beam-target. To achieve 148keV with a stationary 11B, the p needs only be at 161keV.

[KitemanSA]

I dunno why I've bothered telling you guys anything, as it seems widely ignored.

As that was about the 10th time I've pointed to that website, I have to admit defeat and give up trying to provide any info.

And you have to be a nucular psycist to figure it out.

Your told me about it 10 times and 10 times I gotten a headache trying to figure it out.

[KitemanSA]

This is my draft answer. Comments?
===============
The word “best” implies an optimization which immediately raises the counter question, “optimized for what?”

The polywell is hypothetically a mono-energetic beam-beam process. For such processes, the equation for fusion rate (two reactants) is:
ƒ = n1n2 (σv)
where then “n”s are the densities of the reactants, “σ” is the cross section of the reaction and “v” is the center of mass velocity. It is important to remember that “σ” is a complex function of “v”.

Many, perhaps most, people think of the optimum as being where “σ” is at its global (or a local) maximum. But where power to weight is important, it may be where the term (σv) is at a global or local maximum. This happens on the down-slope past the “σ” maximum. Conversely, some think the “optimum” is where the rate of increase in the term (σv) has reached its maximum.

So obviously there is no simple answer as there are a lot of variables.

A ball park estimate for the optimal monoenergetic temperatures in keV for the various fuels and different optimizations would be:

Code: Select all

          d(σv)  	     σ                (σv)
DT    ~    50           63                 78
D3He  ~   205          245                300
p11B  ~   555          560  (130)         565 (10,000+)
DD    ~    83         1150             10,000+

[chrismb]

There is no such complexity in beam-based electrostatic acceleration methods.

As I have said before, fusion rate is [velocity].[density].[cross-section]. It is a much simpler bit of maths for beam methods, the sigma relates to the nature of thermal plasmas and doesn't apply in non-thermal scenarios.

[KitemanSA]

The paper to which I generally refer labels cross-section as sigma (σ). It further defines reactivity as a function that integrates cross-section and velocity across a temperature function and denotes it <σV>. I was putting f as density*density*cross-section*velocity. Is that wrong?

[MSimon]

Dan's numbers look good to me, although MSimon has chimed in with something about resonance peaks at a lower p-B11 temp. I want to say it was 90KV. I looked around for a cite but only found this:

The current local temp is .02512 eV

Or maybe that's what the 130 was for.

I don't know if Boron with a Z of 5 might tend to hang onto an electron occasionally. Considering the higher temperature of the P-B11 plasma, I doubt it.

I doubt it matters anyway -- neutrals are unconfined by either electrostatic and magnetic forces and so won't hang around the high-density WB area, (Remember, this isn't a fusor!)

The nominal number for the resonance peak is 50 KV. With well formation and other "losses" I figure 65 KV. For an experimental reactor I'd design a 75 KV max. power supply.

BTW the "current local temperature" was outdoor temperature in eV. i.e. a nerd joke.

[hanelyp]

For "Best" I'd favor best Q, which given major losses vs. reaction rate would be at somewhat short of the energy for max cross section.