Collisions till Fusion? - DONE

[D Tibbets]

Some preaching, but no wrestling with numbers to support your position this time.

Where do you people come from?

I gave you numbers above, and everyone else has thrown their own guesses at it. What do you *mean* I haven't given numbers!!!!!!!!!!!!!!!!!!

I am the only one that *HAS* given numbers!!!

Your "mfp"s, &c., are just guesses. The reaction cross-section IS the reaction rate. That's what the ferkin' thing MEANS!!!! Don't you understand the very very most basic of basic elementary simple as simple-can-be concepts of particle physics??!

A typical cross-section for coulomb collisions is around 1E-20/m2 yet for *high yield* fusion event it is around 1E-28/m2. Geez, the best fusion rate there is is DT that peaks at 5E-28/m2 yet the electric size of a deuteron is 7 orders of magnitude bigger.

No matter how much wishful thinking and handwaving you wish to put into this, this is the reality of nuclear fusion - it is a very very unlikely event compared with other nuclear interactions.

A graph of fusion crossections

http://en.wikipedia.org/wiki/Nuclear_fusion

Also, the table or formula used can vary depending on the assumptions such as whether a maxwellian temperature is being used , or the target type, the frame of reference, etc.

http://iopscience.iop.org/0029-5515/32/4/I07


Some pertinent pages of a fusion textbook. See page 47, figure 3.19
One formula describes the Hard Sphere Crossesction as being ~ 10 ^-28 m^2=~1 barn. Note that the units here are in meters squared. The graph of fusion crossections are in meters cubed. I'm not sure how the conversion applies.

I could not find a crossection for coulomb collisions. Are the units in your number M^2 or M^3?

http://books.google.com/books?id=Vyoe88 ... &q&f=false

Just to add to the confusion, here are some additional crossections in cm ^2 units: 50.0 KV crossections for D-D is 2.1x10^-17
Converted to M^2 would be 2.1x 10^-21. This would be consistent with M. Simon's quote of 1/60 collisions being fusions, and Crismb's quote of the coulomb collision rates of ~ 10^-20.

http://nuclearweaponarchive.org/Nwfaq/Nfaq4-4.html

What is a poor layman to think?


One check of your numbers and formulas is to plug them into the results obtained with the Jet Tokamac Are they reasonable? I wonder if your huge orders of magnitude shortfalls would also invalidate the Tokamac results.


And crossection does not determine the fusion rate by itself. it is only a part of the derivation. The density of the reacting ions is perhaps even more important, and the volume also is important. The Sun has a terrible crossection for P-P fusion (~10 ^-45 ) but because of density and volume considerations it manages to do a fair amount of fusion. An atomic bomb does not have a crossection any higher than numbers concidered for fusion reactors, but because the density is so great, most of the aviable fuel fuses within a few nanoseconds.

Dan Tibbets

[chrismb]

A graph of fusion crossections

http://en.wikipedia.org/wiki/Nuclear_fusion

There is no cross-section graph on that page. There is one that shows a reaction rate graph.

The graph of fusion crossections are in meters cubed. I'm not sure how the conversion applies.

Cross-section is always in units of area.

Just to add to the confusion, here are some additional crossections in cm ^2 units: 50.0 KV crossections for D-D is 2.1x10^-17

http://nuclearweaponarchive.org/Nwfaq/Nfaq4-4.html

Well, that certainly is confusing because it is very wrong. DT has a fusion cross-section that peaks at 5E-24cm^2, DD peaks at 1E-25cm^2

What is a poor layman to think?

He is to realise that he should educate himself with a proper text on the subject, before throwing in what he think he knows but can't reference.

For fusion reactions (just an example of a good, free, text);
http://fds.oup.com/www.oup.co.uk/pdf/0-19-856264-0.pdf

For Coulomb scattering, punch some numbers into the helpful little sheet on;
http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html

Please...find youself some good reading...and read....

[TallDave]

Good points Dan. I've seen a fair amount of of tripping over this:

Also, the table or formula used can vary depending on the assumptions such as whether a maxwellian temperature is being used , or the target type, the frame of reference, etc.

It's easy to forget not all schemes have the same assumptions.

Re cross section, presumably we all agree on this much:

The reaction cross section σ is a measure of the probability of a fusion reaction as a function of the relative velocity of the two reactant nuclei. If the reactants have a distribution of velocities, e.g. a thermal distribution with thermonuclear fusion, then it is useful to perform an average over the distributions of the product of cross section and velocity. The reaction rate (fusions per volume per time) is <σv> times the product of the reactant number densities:

If a species of nuclei is reacting with itself, such as the DD reaction, then the product n1n2 must be replaced by (1 / 2)n2.

http://en.wikipedia.org/wiki/Nuclear_fusion

Also worth noting:

If the energy to initiate the reaction comes from accelerating one of the nuclei, the process is called beam-target fusion; if both nuclei are accelerated, it is beam-beam fusion

Polywell is beam-beam, not beam-target, in case there was any confusion about that.

Again, if someone wants to run the numbers at the various WB machine conditions under Polywell orthodoxy, that would be interesting (you can do a sanity check given WB-6/7 results are known). If not, I'll probably get around to taking a stab at it someday.

[D Tibbets]

A graph of fusion crossections

http://en.wikipedia.org/wiki/Nuclear_fusion

There is no cross-section graph on that page. There is one that shows a reaction rate graph.

The graph of fusion crossections are in meters cubed. I'm not sure how the conversion applies.

Cross-section is always in units of area.

Just to add to the confusion, here are some additional crossections in cm ^2 units: 50.0 KV crossections for D-D is 2.1x10^-17

http://nuclearweaponarchive.org/Nwfaq/Nfaq4-4.html

Well, that certainly is confusing because it is very wrong. DT has a fusion cross-section that peaks at 5E-24cm^2, DD peaks at 1E-25cm^2

What is a poor layman to think?

He is to realise that he should educate himself with a proper text on the subject, before throwing in what he think he knows but can't reference.

For fusion reactions (just an example of a good, free, text);
http://fds.oup.com/www.oup.co.uk/pdf/0-19-856264-0.pdf

For Coulomb scattering, punch some numbers into the helpful little sheet on;
http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html

Please...find youself some good reading...and read....

I notice you have declined to use your numbers to predict the results from Jet.

As to your dismissal of my points, I repeat that things are not as simple as you imply. Using your reference:
http://fds.oup.com/www.oup.co.uk/pdf/0-19-856264-0.pdf
gives a graph that is similar to the numbers for reaction rate referenced:
http://nuclearweaponarchive.org/Nwfaq/Nfaq4-4.html
The units are cm^3 instead of cm^2, so that is a discrepancy (typographical error ?). This graph on page 18 is for Maxwell averaged fusion reactivities. I don't know how much adjustment would be needed for non Maxwellian plasmas with a narrow ion energy range.

Using your other reference:
http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html
and plugging in numbers Z=1, Atomic Mass = 2 (for deuterium) and a energy of 0.01, 0.05 and 0.2 MeV gave ion-ion scattering crossections of 21,000; 850; and 53 barns respectively. Since the calculation is for beam target interactions I used [EDIT] 0.2 MeV to represents two deuterium ions meeting head on at well depths of 0.1 MeV.

Given that the reaction rate for D-D fusion at ~ 0.1 MeV is approaching 0.1 barns tells me that the fusion to scattering ratio in these conditions is 1/530. I believe mono energetic conditions instead of the maxwellian conditions would shift this ratio closer to the 1/60 ratio quoted by M. Simon. Since the coulomb collision rate drops with increased temperature, by eliminating the large number of nonfusable (or less fusable) ions in the lower energy range of the maxwellian distributed population, the ratio shrinks.

So it looks to me that you were comparing crossection area to reaction rate without qualifying your conditions (and ignoring the possible significance of maxwellian vs mono energetic conditions). Apparently you were using a temperature of ~0.01MeV for the coulomb scattering calculation where the scattering / fusion numbers are more favorable to your arguement (here the ratio would be ~ 0.005 barns fusion rate / 20,000 barns scattering rate).
Where have I gone wrong? Please explain it to me.

Dan Tibbets

[bcglorf]

I recall Dr. B (or was it Rick?) said that there are 60 collisions per fusion in a pB11 machine (or was it D-D?).

Chris - I'm reluctant to give any credence to the numbers you present because I have seen you exaggerate by several orders of magnitude (in the bad direction) on other questions. i.e. pumping is technically "impossible".

I am dumbfounded [squared] that after so long on the forum I didn't realise how lacking is your understanding of the very basics of this whole bongdoogle; nuclear collisions.

It is an absolute fact that the ratio of the rate of fusing to non-fusing collisions is the ratio of the cross-sections for fusing to non-fusing collisions.

This is why you bother to measure collision reaction rates as 'cross-section' so that you can compare like-for-like - this is the very purpose of that measure!!!!

It is also the case that such numbers for cross-sections are easily and readily available, in the references I have so often repeated yet [it appears] have so often been ignored by people that seem to think physics is 'democratic' so that if enough people wish for a good bit of data then it must exist and so they don't have to bother to go look for it!

Let me start off clarifying that I know nothing about this .

A quick google on fusion cross sections though brings up Nevins critique of Rostoker. The abstract appears to list the comparison between fusion and collision cross sections as 60-1. Does that mean on some level that Chrismb and MSimon are both right? The ratio being the exactly the ratio of the cross-sections, and that ratio for beam-beam interactions is 60-1?

Link follows:

http://www.sciencemag.org/cgi/content/f ... /5375/307a

[D Tibbets]

On my previous post I calculated the fusion to scattering ratios for deuterium.
I have been wondering why Bussard had mentioned ~80-100 KeV wells for a deuterium Polywell reactor. The reaction rate vs temperature is steepest and therefor most efficient at ~15,000 eV (fusion rate vs energy input). I asumed the declining advantages of pushing the voltage was due to tradeoffs in nessisary reactor size, and thus cost needed to reach desired power densities.
But the dropping of the fusion to scattering ratios as the temperature increases would presumably help reduce the forces trying to thermalize the ion population before they have a chance to fuse under the more favorable mono energetic conditions. This would relax the amount of 'annealing' (if it occurs at all) needed.
Mmm...

Dan Tibbbets

[chrismb]

I notice you have declined to use your numbers to predict the results from Jet.

I am not aware I ever declined to calculate for JET. Did you ask, or did I offer?

I broke cover to try to help educate people here, but instead I get pot-shots taken at me whilst trying to help inform. I was told I didn’t help out, yet this is what I always got before, and is what I still get. Nothing changes, so I'll head back to cover and leave you to wallow in your ignorance.

But before I do, I’ll serve you babyfood by the spoonful, seeing as you’ve asked so nicely:

In roundabout numbers, let’s imagine you are a median 20keV deuteron in JET at their working pressure of 0.1Pa.

So your cross-section of fusion with tritons is around 5 barns, that’s 5E-28m2.
And the density is around 1E19/m3
So your mean free path to fusion is, simply, 1/([1E19].[5E-28]) = 2E8m.

Yes, that’s right, a deuteron has to travel a distance equal to half way to the Moon before a typical one will get to a fusion event.

Your speed would be around 1.5Mm/s, so you’ve got to hang around for some 150 seconds before you’ll have coverd that distance and likely fused.

As there are 1E19 deuterons per m3 doing the same thing, so you might expect 6E16 fusions per m3 per second.
Each fusion is worth 14MeV = 14E6 x 1.6E-19 = 2.2E-12J, so 6E16 per second 132,000J of fusion will go on, i.e. 132kW, per cubic metre.

There are 100 such cubic metres in JET, giving it an approximate fusion output of 13MW.

[D Tibbets]

I notice you have declined to use your numbers to predict the results from Jet.

I am not aware I ever declined to calculate for JET. Did you ask, or did I offer?

I broke cover to try to help educate people here, but instead I get pot-shots taken at me whilst trying to help inform. I was told I didn’t help out, yet this is what I always got before, and is what I still get. Nothing changes, so I'll head back to cover and leave you to wallow in your ignorance.

But before I do, I’ll serve you babyfood by the spoonful, seeing as you’ve asked so nicely:

In roundabout numbers, let’s imagine you are a median 20keV deuteron in JET at their working pressure of 0.1Pa.

So your cross-section of fusion with tritons is around 5 barns, that’s 5E-28m2.
And the density is around 1E19/m3
So your mean free path to fusion is, simply, 1/([1E19].[5E-28]) = 2E8m.

Yes, that’s right, a deuteron has to travel a distance equal to half way to the Moon before a typical one will get to a fusion event.

Your speed would be around 1.5Mm/s, so you’ve got to hang around for some 150 seconds before you’ll have coverd that distance and likely fused.

As there are 1E19 deuterons per m3 doing the same thing, so you might expect 6E16 fusions per m3 per second.
Each fusion is worth 14MeV = 14E6 x 1.6E-19 = 2.2E-12J, so 6E16 per second 132,000J of fusion will go on, i.e. 132kW, per cubic metre.

There are 100 such cubic metres in JET, giving it an approximate fusion output of 13MW.

Yes, I had asked, and thanks for the response. The numbers you gave seems reasonable, and consistent with ion lifetimes to fusion that I have seen.

What I do not understand is how you then turn around and say that similar processes are hopeless in the Polywell. Yes, eight orders of magnitued shortfalls exist at low enough drive energies, and coulumb collisions will thermalize the ions given enough time. But even with thermalization, a Polywell should do no worse than a tokamac- the physics is the same; and if arguments of non maxwellian energy distibutions, wiffleball trapping factor,core convergence are applied the energy density is higher,perhaps as much as ~60,000 times as high, as was mentioned by Dr Nebel-not a neophyte.

As I see it there are three questions, when comparing Polywells to tokamacs.
1) Is the polywell non maxwellian? With a fusion to collision ratio 1/60 at appropiate temperatures (as appartly stated by Nevens (another non neophyte) and the fact that most coulomb ion-ion collisions results in shallow deflections, which means it will take a few collisions to thermalize (perhaps as many as 10) means a combination of edge annealing* and differences in collisionality in the various areas of the potential well do not need to work very hard to delay full thermalization for periods longer than the fusion time.

2) Does the wiffleball effect exist, with the resultant advantage in obtainable plasma densities. And how much confluence is there and how does that effect the collision rate in the core, both coulomb scattering collisions and fusion collisions. According to a published evaluation by one of Bussard, etel papers - coulumb collisions are greater in the core (presumably due to some presumed confluence) but at least the angular momentum collisions have minimal effect as from the center of a sphere all angles are straight out.

3) Confinement issues. Not addressed in this thread. Tokamacs have an advantage as they do not have cusp losses except as instabilities night be considered effectively like temporary cusp openings.
The tokamacs have a disadvantage in that they do not have any electrostatic confinement of ions ( thus the need to go to large sizes to limit the random walk problem), and do not have a capability to recirculate escaped electrons as the Polywell claims to have. Presumably the tokamacs are much better at confining electrons (within limits imposed by quasineutrality throughout the that system), but the recirculation of electrons plus the advantages in ion confinement presumably allows the polywell to improve on the tokamac energy balance.

* I was confused about how increased edge collisionality of ions at the edge of the wiffleball occurred, but thanks to Chrismb's link, I now see that coulomb collisionality increases rapidly as the ion energy drops. At the edge the ions are at the the top of their potential well so are traveling slowly. Due to the increased collisionality they will more quicky thermalize. But, in this region the thermalization is around a low energy level so the maxwellian distribution will be small compared to the velocities/ energy gained as they drop down the potential well.
eg: At ~ 100 eV average energy the maxwellian distribution may have most of the ions at energies between 10-500 eV (made up numbers). As the ions then fall down the well and aquire an energy of perhaps 50,000eV, so the starting thermalized spread on the edge translates into only 50,000 +/_ 500 eV for the nect cycle- thus 'annealing'.


Dan Tibbets

[TallDave]

Dan, I have to say I am impressed by your patience as well as your substance in this thread. Thanks for sharing, this has been educational in a few respects. Definitely one of the better threads we've had here.

But even with thermalization, a Polywell should do no worse than a tokamac-

Assuming they have similar confinement. That's the big question now.

Without thermalization, there's also a question of whether you have to do too much work to maintain a non-Maxwellian distribution, but as you say below there is reason to think some annealing may happen naturally, and Chacon showed large Q values were possible with some relaxation.

Presumably the tokamacs are much better at confining electrons (within limits imposed by quasineutrality throughout the that system), but the recirculation of electrons plus the advantages in ion confinement presumably allows the polywell to improve on the tokamac energy balance.

Yes, I like to think of Polywells as intentionally bleeding electrons in order to avoid having to confine ions magnetically, thus allowing high beta operation.

I was confused about how increased edge collionality of ions at the edge of the wiffleball ocurred, but thanks to Chrismb's link, I now see that coulomb collisionality increases rapidly as the ion energy drops. At the edge the ions are at the the top of their potential well so are traveling slowly. Due to the increased collisionality they will more quicky thermalize. But, in this region the thermalization is around a low energy level so the maxwellian distribution will be small compared to the velocities/ energy gained as they drop down the potential well.
eg: At ~ 100 eV average energy the maxwellian distribution may have most of the ions at energies between 10-500 eV (made up numbers). As the ions then fall down the well and aquire an energy of perhaps 50,000eV, so the starting thermalized spread on the edge translates into only 50,000 +/_ 500 eV for the nect cycle- thus 'annealing'.

Yes, Rick made a similar point a while back. Nicely expressed.

[bcglorf]

But even with thermalization, a Polywell should do no worse than a tokamac- the physics is the same
...
Assuming they have similar confinement. That's the big question now.

I don't think there's any question about containment comparisons between Toks and Polywell. Both Bussard and Nebel seem to agree that containment was magnitudes better in Toks and critics like ChrisMB and Art have most certainly and rightly pointed at containment as one of the major loss mechanisms.


Where I'm seeing Chris at odds with Bussard and Nebel here seems to be, in this thread, on the ratio of fusion to collision events. If your still listening Chris, does a 1/60 ratio change the picture you have much? If 1/60 is flat wrong, can you tell me how I'm misreading the link to Nivens from up thread?

[TallDave]

Right, sorry, that was just an "all else being equal" sort of observation, which probably wasn't really that relevant anyway since Dan is probably talking about power rather than overall reactor performance.

I only meant to allude yet again to the question of whether confinement in Polywells scales more like B^(1/4) or, say, B^(3/2), which I am a bit obsessed with, and which is probably the biggest question mark for the tech. It's not strictly relevant to Dan's point, which I agree with -- given the same conditions, PW fusion power should be at least as good as toks, and better if there's some ion focus, so it's not clear why anyone would insist the same conditions are futile in Polywells but OK in toks.

[chrismb]

Where I'm seeing Chris at odds with Bussard and Nebel here seems to be, in this thread, on the ratio of fusion to collision events. If your still listening Chris, does a 1/60 ratio change the picture you have much? If 1/60 is flat wrong, can you tell me how I'm misreading the link to Nivens from up thread?

Yeah, I'm still listening, and I suppose I'm honour-bound to try to wrap it up while people are still trying their best to understand it.

Simply, there is a number in the Nevins' reponse saying something about an effective cross-section from multiple small deflections. I don't really see where this comes from, but it is true that at particular particle energies the ratio to a *particular* deflection angle is this, or less. So where DanT has posted up some numbers, these are based on deflections of 10 degrees of the projectile particle. There is an angle box on that page and you adjust that to get different angles. So, for example, it is 53 barns in his example *for a 10 degree deflection* but for a 1 degree deflection it'd become 5300 barns. The deeper the deflection, the bigger the cross-section (i.e. the more likely such a low angle deflection is).

So if you really wanted to know how many deflections a median projectile particle will undergo before a fusion then you have to integrate all the Coulomb scattering cross-sections for all 'impact parameters' [this is the posh term for how far away the projectile's path is from the target]. You have to double-integrate the Rutherford scattering equation across a 2D surface, not forgetting the Jacobian (which I did the first time I tried the calculation - how silly of me!).

However, at the higher energies, at >10keV, you'll find other non-conservative collisions are going on and you need to take the 'total' cross-sections for these interactions which aren't just Coulombic.

I didn't want to confuse you on all of this, but basically the Coulomb scattering consideration alone tends to rule out the prospect of these types of devices. At very high energies, these things do begin to look a bit more manageable but then you have to start looking seriously at the electron-ion collisions which become dominant energy loss mechanisms, as Rider has well published on.

If you can recover these collisional losses then fusion looks possible for a very limted set of reactions. So, if the fabled 'annealing' does happen then that would mitigate this discussion on collision ratios because the total collisional *losses* can be made to be lower than the fusion energy gains *providing* the projectile particles remain mono-energetic. Again, even Rider has stated this is a potential route for these types of devices (see his appendix 'E' of his thesis), but you have to be able to prevent thermalising diffusion through velocity-space.

I don't think there's any question about containment comparisons between Toks and Polywell. Both Bussard and Nebel seem to agree that containment was magnitudes better in Toks and critics like ChrisMB and Art have most certainly and rightly pointed at containment as one of the major loss mechanisms.

At this time, there is no public information that shows confinement capability of Polywell, neither directly nor indirectly. The principle of electrons' space-charge acting to confine ions has also been tried out in the Elmore-Tuck-Watson device, and also in the Penning fusion experiment, and neither have shown any 'confinement', as such. Based on these actual experiments, the prospective outcomes don't, exactly, look 'solid'.

[D Tibbets]

...
Assuming they have similar confinement. That's the big question now.

Without thermalization, there's also a question of whether you have to do too much work to maintain a non-Maxwellian distribution, but as you say below there is reason to think some annealing may happen naturally, and Chacon showed large Q values were possible with some relaxation.

Presumably the tokamacs are much better at confining electrons (within limits imposed by quasineutrality throughout the that system), but the recirculation of electrons plus the advantages in ion confinement presumably allows the polywell to improve on the tokamac energy balance.

Yes, I like to think of Polywells as intentionally bleeding electrons in order to avoid having to confine ions magnetically, thus allowing high beta operation.

I had not emphasized losses. Chrismb's point that a Tokamac needs to contain ions for hundreds of seconds (with distance traveled to fusion being many thousands of kilometers) to produce useful fusion is pertinate. To do this they have to have relatively excellent confinement. My impression is that the Polywell does not even come close to this. But because of the necessary conditions of non Maxwellian distributions (almost all of the contained ions are at potential fusion energies instead of a few percent) and the much higher densities achievable due to the Wiffleball trapping factor, and some degree of confluence in the ion flows (requires maintaining non Maxwellian conditions just long enough and at acceptable energy costs) the confinement time only needs to be a small fraction of a second to reach the nessisary distance traveled to a likely fusion event for the ions.

From a fusion power production stand point the Polywell wins because as the density increases the distance to fusion decreases (or time to fusion). If the Polywell can have a density ~ 100- 1000 times as great as a Tokamac and the percentage of ions at sufficient energy to have a certain probability of fusing is ~ 10 times as great, and that is combined with some mild confluence of the ions to increase the effective density even further, then the power density advantage of ~ 60,000 seems reasonable.

If the containment in the Polywell came anywhere close to Tokamacs the input energy needed would be relatively tiny compared to claimed levels.
As it is, the energy input necessary in an appropriate volume sized machine is small enough and the subsequent power/ cost scaling is great enough that the Polywell has a hugh advantage.

Of course, this is based on acceptance of the claimed performance estimates, and assumption of predicted scaling laws. And, the Tokamac has it's own set of problems and hand waving.

The smaller scale and thus costs of pursueing the Polywell approach (and some other alternative approaches) in terms of dollars and time has tremendous advantages over the stupendously costly and plodding Tokamac approach, even when you factor in greater risks.
Also, keep in mind that none of these approaches exist in isolation. The sharing of data, methods, and theories have cross applicability. For instance, it seems that Penning traps are a dead end for profitable fusion power, but it has contributed much applicable to Polywells, as have Tokamacs, other forms of magnetic confinement, and even efforts by Farnsworth, Hirsch, Elmore, Tuck, Watson, Nebel (POPS work), and many others have contributed to the evolution of the Polywell, which hopefully is nearing the holy grail within a few years (instead of a few decades or more).

Even if Polywell works, it may lose out to other methods in the economic battlefield, if other systems also work- such as DPF or RFC systems alone or as fusion/fission hybrids. From my limited understanding, even if Tokamacs work, they will potentially be economically nonviable, if any other approach works even moderately well.


Dan Tibbets

[KitemanSA]

Having let the dust settle a bit, I am getting the impression that there is no simple answer. My proposed response is:

There is no simple answer to this question, answers being dependant on the assumptions made when answering it. Experts have provided answers from as low as 60 [1] to as high as 1E8 [2] for pB11 at ~550keV. The lower presumes an effective cross section that produces a 90 degree RMS scattering, while the larger includes each and every glancing interaction.

[1] http://www.sciencemag.org/cgi/content/f ... /5375/307a
[2] viewtopic.php?p=40472&highlight=#40472

Comments?

[chrismb]

Ah! Now you get around to being specific! There is an 'average-equivalent' Coulomb scattering cross-section, and at 550keV I'd hazard a guess (it's a good guess, based on my memory of previous calculations) it's around 3000 barns. As I mentioned above, all you have to do (!) is integrate the Rutherford cross-section in the two dimensions of impact parameter.

Now *in the Polywell theory*, ionisation is 100% and that ions don't thermalise with the electrons. (It won't be, but, hey, while we're taking a wander through dreamland you can still do maths, right? And maybe when you wake up someone will have invented a miracle to which your maths applies!)

So with those assumption in place, namely that there are no inelastic electron collisions and the fusion cross-section is around a barn, then you'd be at around the 3000 Culomb-collisions-per-fusion mark. I'd mark a small wager that this is about right for that much energy. Remember my 1E8 refers to 'normal fusor operation' (say 10 to 50keV).

(Best you also check out what is called the 'Colulomb Logarithm' if you want the full tech spec on this, in addition to running the integration I mention above.)

Interestingly, on Coulomb collisions alone, these collisions will be loosing on average around 15eV per collision. So after 3000 collisions you'll have a proton with around 400keV in it. That probably isn't enough because you'll have dropped to some 20,000 collisions per fusion by then, and so the proton ends up in a death-spiral of getting colder and colder. But if there is some process by which you can artificially dial back into the proton the 15eV, for each collision at 550keV and so keeping it 'on the boil' so to speak, then you'll only spend 150keV plus the 550keV of the proton, total = 700keV, yet get back out of it 8.68MeV. Success!! Net power!! Q=10!!

This idea relies on the concept of making sure the proton stays at 550keV, so you need a process to keep it there. This is why I keep banging on about this 'annealing' process and whether there is any chance of it, because it is probably a show-stopper without it. (notwithstanding all the other issues).