## F.O. Question to Collision:Fusion Ratios - DONE

Discuss how polywell fusion works; share theoretical questions and answers.

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KitemanSA
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### F.O. Question to Collision:Fusion Ratios - DONE

I have just inserted my previously proposed answer to the Polywell FAQ question on Collision:Fusion ratios. The follow on question to that is:
Related to the above question, wouldn't the ions thermalize after a while of constant collision?
I am looking for actual wording here.
Last edited by KitemanSA on Mon May 31, 2010 3:48 pm, edited 2 times in total.

TallDave
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Rick had a nice answer to why annealling happens a while back. I also like Dan's explanation from earlier.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

WizWom
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A thermal plasma would be one where the ions are reasonably close in energy.
Each collision will tend to have colliding atoms with energies closer together, rather than farther apart. However, the magnetic cycle will accelerate the ions each time they go on a trip outside the core.

In general, the slower ions will be pulled on a trip outside the core faster.
F= qV x B - so the lower V, the less force the magnetic cage has on the ion.

This is why the cage is NOT at thermal distribution. The fastest ions are also affected most by the magnets.
Wandering Kernel of Happiness

D Tibbets
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WizWom wrote:A thermal plasma would be one where the ions are reasonably close in energy.
Each collision will tend to have colliding atoms with energies closer together, rather than farther apart. However, the magnetic cycle will accelerate the ions each time they go on a trip outside the core.

In general, the slower ions will be pulled on a trip outside the core faster.
F= qV x B - so the lower V, the less force the magnetic cage has on the ion.

This is why the cage is NOT at thermal distribution. The fastest ions are also affected most by the magnets.
I think you are confused. A thermal plasma does not have a narrow energy range (often confusingly described as a mono energetic range in the Polywell literature). Without using a mathematical formula, I believe a thermal (Maxwell -Boltzman) plasma can be described as having a slued bell shaped curve over a relatively broad range and this broadening increases as the average energy increases. The higher the average energy, the broader the distribution. One of the critical points is that the Polywell operates outside this condition.
As far as the ions penitrating further into the magnetic field if they have higher energy, while true, is an undesired condition for the ions in the Polywell. In the Polywell the electrons are indeed turned and contained by the magnetic field (except for cross field transport and cusps where unavoidable but tolerable losses occur). But, these electrons then contain the ions electrostatically. Ideally, the ions never interact with the Wiffleball excluded magnetic field.

Important considerations about the 'mono energetic' ion population in the Polywell is that almost all of the ions can be pushed to fusion energy levels without a a significant portion (most) of them being at lower, useless (but costly ) energies. Also, if the majority of the ions are at lower energies their coulomb collision crossections are larger so they contribute to faster thermalization (a double whammy). If ions are at too high an energy (upscattered), they will be effected by the magnetic field and deflect from it at angles that can exclude them from the desirable core. This is bad for two reasons. First, it decreases the central density and thus chances for head on fusion collisions, and two, I suspect it would advance further thermalization. Also, these upscattered ions ( which would be the high energy tail that would actually be contributing most to the fusion in a thermalized system like the Tokamacs- they are apparently unable to heat the average ions to to those temperatures without astounding effort and losses) while not contributing much more to fusion ( too energetic (the fusion crossection curve is flattening out)), will add to losses by heating the electrons (more bremsstrulung) and escaping through cusps with more than minimal energy.

Dan Tibbets

Dan Tibbets
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WizWom
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Yes, my explanation of a Maxwellian thermal distribution was poor.

It would be impossible for ions not to be affected by the magrid. I believe what you meant is the since the ions are from 1836 to 20300 times the mass of the electrons, they will be much more affected by the coulomb force than the magnetic force.

This is because the "well" of electrons will be on the order of 10^5 V in a working machine, you can see that the coulomb force will be many times the magnetic.
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D Tibbets
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WizWom wrote:Yes, my explanation of a Maxwellian thermal distribution was poor.

It would be impossible for ions not to be affected by the magrid. I believe what you meant is the since the ions are from 1836 to 20300 times the mass of the electrons, they will be much more affected by the coulomb force than the magnetic force.

This is because the "well" of electrons will be on the order of 10^5 V in a working machine, you can see that the coulomb force will be many times the magnetic.
At least by the descriptions, the Polywell contains electrons magnetically. They are much easier to contain because of their smaller inertia/ momentum and smaller gyro radii at any given KeV.

The electrons (and ions once introduced?) creates a "Wiffleball". This relatively high density of high energy charged particles pushes out the magrid magnetic fields and creates a central area where there is no magnetic field. This apparently extends outwards far enough that ions introduced or born from neutrals near the top of the potential well, oscillate back and forth in this domain and do not see the magnetic field at all until they are up scattered enough that they climb out of the potential well and enter the magnetic domain. There is not a gradual decrease in the magnetic fields as you approach the center until you reach a null area at the center (the condition before charged particles are introduced). The Wiffleball border is a sharp border presumably ~ 1-2 electron gyro radii wide at the effective electron drive energy. The magnetic fields of the moving charged particles oppose the magrid magnetic field (since the charged particles are moving in net opposite directions (in and out plus any angular thermalization) they effectively neutralize their magnetic fields (while still opposing the magrid fields). At Beta = one conditions this effect is maximized. Any more and the magnetic bubble is overwhelmed, much like inflating a balloon to bursting. This is apparently one of the effects of a near spherical bottle as opposed to a torus where the charged particles may be moving in and out, but most also circulate in one direction around the torus. The circulating charged paticles in a torus push out against the magnets, but because there is a dominate direction that the particles are moving, they have a net magnetic field of their own, so there is no magnetic field free zone in them.
I can see where the borders between the magnetic fields (at right angles to each other?) can have viscosity and terbulance at the border leading to the instability problems that Tokamacs have.

If I had a better founding in electomagnetic dynamics I could explain it better.

[EDIT] I should add that the excess number of electrons in the machine is what creates the potential well, and presumably the distribution of these electrons allows the ions introduced or created at the top of the potential well (actually I believe it would be just below the top of the potential well- IE: just below the Wiffleball border) is what keeps the ions confined to this magnetic free region.

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
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My understanding and descriptions are overly simplistic and often evolving (if not plain wrong). A more accurate understanding can be obtained by careful repeated reading of resources like:

Dan Tibbets
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KitemanSA
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### Re: Follow On Question to Collision:Fusion Ratios

Gents,
I would appreciate it if you could take your discussion to another thread. I am still trying to get an answer to my original post:

I have just inserted my previously proposed answer to the Polywell FAQ question on Collision:Fusion ratios. The follow on question to that is:
Related to the above question, wouldn't the ions thermalize after a while of constant collision?
I am looking for actual wording here.

hanelyp
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The collision cross section for ions is much greater at low energies than at higher energies. Thus the ions thermalize much faster at low energies at the edge than at the high energies at the core. Thus the ions assume a narrow energy distribution associated with thermalization at a lower energy.

KitemanSA
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Thank you hanelyp!

That is a nice, succinct statement, and I will include it.

More detail anyone?

chrismb
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KitemanSA wrote:That is a nice, succinct statement, and I will include it.
A nice statement, but incomplete and, ultimately, not a description of a polywell.

Remember; rate of reaction (collision) = [cross-section].[velocity].[density]

For example, the scattering cross-section of two protons with a CoM collision energy of 100keV for a 1millirad scatter is 44kBarn. At 500keV it is 1700Barn. So far so good.

But the protons are going 2.2 times quicker between the two sets of numbers so the rate is closer than the 44/1.7 suggest. More like 44/4, then.

Now we come to density... can someone remind me what the density ratio is supposed to be, between the outer 'annealing' region and the inner core?... Whatever fantastical figure that it, then you also have to weight this into the rate calculation, above.

Remeber;
- rate is in per time
- cross-section is in area
- density is in per volume
- velocity is distance per time

So if you want, for example, a per seconds answer, then you need rate.

Someone'll have to do that density evaluation for Polywell, but I'll wager it'll come out that the Coulomb collision rate (thermalisation rate) will be pretty much equal everywhere.

D Tibbets
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Again, see the two links describing collisions in the core and outside it that I referenced in the earlier thread about fusion vs coulomb collisions. I think some numbers generated referenced three areas of the Polywell. The core, the bulk and the edge. If the bulk had a coulomb collisionality (product of crossection and density) of one, the core was 2 and the edge was 100. Again the core collisions can increase upscatter, but there will be little angular or transverse scattering in that region. The dominate scattering rate in the edge region leads to thermalization in this area much faster than elsewhere. But, again, this thermalization is around a low and narrow energy range because the average ions are at their lowest energy. This dominate collisional area will to a large (or adequate) extent, neutralize any scattering that has built up in the deeper regions, at least over the timescales necessary to reach ion fusion or containment lifetimes. At least that is my understanding of annealing.

Chrismb continues to use smaller and smaller deflection angles to obtain large coulumb cross sections, yet he has not challenged my point that the smaller the deflection angle the less significant is the effect on the thermalization process. If an initially radial ion has to pick up an angular orbit of perhaps 30 degrees before it avoids the desirable core, then one 30 degree collision outside of the core (the bulk area) might do it. If the collision is 1 degree (or even the smaller angular deflection that Chrismb is now quoting) many collisions will be required, with (I guess) ~ same time required for these many small angle collisions to add up to the effect of one large angle collision. If this is grossly wrong then perhaps Chrismb can justify that his many small collisions do not add up to one (or a few) large collisions.
My reasoning is that a coulomb collision will deflect an ion to some degree. If the ion is purely radial, this deflection will always add angular momentum (transverse direction). But if the ion already has some transvere direction the impact may add or subtract to the net angle. Because of this the process is not linear, it is more log rhythmic. Ten 1 degree deflections do not add up to 10 degrees, but perhaps 3-5 (?). I suspect this is burried somewhere in the Maxwell Boltzman calculations and I will stick with this reasoning untill proven otherwise.

Dan Tibbets
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KitemanSA
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chrismb wrote:
KitemanSA wrote:That is a nice, succinct statement, and I will include it.
A nice statement, but incomplete and, ultimately, not a description of a polywell.
Please, don't tell me what is NOT a description, tell me what is. Please be specific. What should the answer say, specifically.

KitemanSA
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Chris and Dan,

Would you too be so kind as to propose specific wording for a "Point, Counter-point" type response to the question? I think that would be a WONDERFUL way to make positive use of both or you talents and passions.

It may seem odd to work together, but I think it would be a good thing for the world. Ok, in a small way, but still good.

hanelyp
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To partly answer Chris' objection: A fast particle sweeps though volume faster. But the slower particle will have more time for collisions as it sweeps through a distance. So the number of collisions is proportional to distance covered * cross section, velocity canceling out.