Collisions till Fusion? - DONE

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

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TallDave
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Post by TallDave »

Kite,

That seems fair. It's possible to come up with an answer only given certain assumptions and conditions. This being the Polywell wiki, you'd probably want to use such assumptions as can be gleaned from Bussard and Nebel, and perhaps mention the more plausible skepticisms. I don't know if I would call anyone an expert; I think it's enough to say there are competing claims.
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.
Confinement for ions or electrons or overall? Those are very different questions.

Polywell orthodoxy is that ion losses are kept very small because we're keeping the mix electron-rich to confine them. IIRC Bussard pretty much ignores them completely and states there are essentially no ion losses, Rick's ITER comparison equation neglected to even include ion pressure (and he found no hotspots on the wall), and Joel's simulation had no ion current. Electrons are a different story.

I haven't seen any support for the idea background neutrals will carry off significant energy; Bussard seems confident ionization times are much too short for this to be possible (it seems intuitively obvious a neutral whose ionization energy is measured in eV won't carry off KeV energy, but maybe I'm missing something). Chacon's paper says ion thermalization can be acceptable.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

chrismb
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Post by chrismb »

TallDave wrote:(it seems intuitively obvious a neutral whose ionization energy is measured in eV won't carry off KeV energy, but maybe I'm missing something).
Yes. You're missing a big chunk of understanding, I fear to say.

This is one of the 'inelastic' collision possbilities, which add up to confound those Coulomb collision numbers above. The most common inelastic collision is the sticky collions called 'charge exchange'. As an ion hits a background, it swipes the electron off of the neutral and leave a cold ion behind in its, now neutral, wake. Thereon impervious to magnetic or electric fields, fast neutrals are a serious loss mechanism if you have background neutrals present (hence my focus on the pumpring requirements). So it's not the neutral that gets to keV energies, it is the same nucleus that was the fast ion, but has picked up an electron.

As one background atom said to another "I think I've lost an electron!". The 2nd atom; "Are you sure". First atom; "yes, I'm positive!".

It is the fast neutrals I have argued *may be* the source of the neutron signature of previous WB efforts. The flux of fast neutrals into the wall will embed themselves or may collide at high energy, thus fusing, with neutrals already there.

TallDave
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Post by TallDave »

You're assuming your conclusion. Why would there be any significant background neutrals in the first place? It's a KeV plasma.

It doesn't seem remotely plausible a neutral can drift into the core unmolested very often. They should be ionized way out at the edge, where ion energies are low.

What is the the likelihood of fast neutrals:

a) being created

b) making it out, from the core, before being knocked back into an ion

at reactor conditions? I'm guessing small enough to ignore, which is why Bussard ignored them. Can you cite something showing otherwise? Can you show a problem with Bussard's usec ionization times?

Again, it seems awfully unlikely you would see this at KeV.
Last edited by TallDave on Tue May 18, 2010 7:12 pm, edited 1 time in total.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

chrismb
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Post by chrismb »

TallDave wrote:You're assuming your conclusion. Why would there be any significant background neutrals in the first place? It's a KeV plasma.
You are responding to someother answer to a question you didn't ask.

You asked why fast neutrals would be produced - that's what I thought you asked.

I'm not aware I made any mention of 'rate'. I don't want any arguments, I'm just trying to help people's understanding of basic atomic collisions.

TallDave
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Post by TallDave »

I'm responding to your claim that background neutrals will carry off enough energy to be a significant loss mechanism. Without a rate, it's hard to see what the objection is.

I'm aware that it's possible. The relevant question is how likely it is.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

chrismb
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Post by chrismb »

TallDave wrote:I'm responding to your claim that background neutrals will carry off enough energy to be a significant loss mechanism. Without a rate, it's hard to see what the objection is.

I'm aware that it's possible. The relevant question is how likely it is.
I did some calcs on exactly this, somewhere. I'm not aware you objected to any of the maths at the time.

You really need to read what people write. If I wrote " fast neutrals are a serious loss mechanism if you have background neutrals present", as I did, then surely I am NOT saying it is a loss mechanism if there are no backgrounds present. I am clearly not intending to imply that it'd be a serious loss mechanism if, say, you had 3 neutral atoms present!!

It is often best to read and take time to inwardly digest, before engaing auto-response mechanism.....

TallDave
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Post by TallDave »

I haven't seen those calcs that I can remember. Did you really calculate the likelihood of neutrals going into the core and coming out again, and get a number that suggested this was a significant loss mechanism at expected PW pressures? It just seems really unlikely. Maybe you meant if there are pumping problems?
You really need to read what people write. If I wrote " fast neutrals are a serious loss mechanism if you have background neutrals present", as I did, then surely I am NOT saying it is a loss mechanism if there are no backgrounds present.
Heh, well you really need to remember what you've written in this thread. This was your response to Bussard's ionization assumption:
(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!)
Are you really making a serious argument there, or just trolling a bit? You call this assumption a "dreamland," then claim you aren't looking for an argument, then appear to say you never claimed there would actually be significant background neutrals but just used it as a hypothetical situation. Are you claiming they are a significant loss mechanism, or not? It's a little hard to tell.

That argument seems more appropriate to a fusor, creating some ions from a grid in a neutral background, rather than a PW where electrons bounce around inside a magnetic enclosure (who wants to calculate mean time to ionization?). I think where your assumptions are tripped up is that the post-startup ionization in PWs is tending to happen in low-ion-energy areas as neutrals drift in at the edge, not in a random distribution across the plasma. But maybe you aren't making that argument at all, in which case we can ignore this both as a loss mechanism and in terms of affecting the length-to-fusion.
Last edited by TallDave on Tue May 18, 2010 8:32 pm, edited 3 times in total.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

KitemanSA
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Post by KitemanSA »

Folks,
Is there a way I can improve my FAQ response?
If the 1E8 is for 10s of keV, is there a better number that I can quote that is for the ~550keV pB11? Please?

I am a total neo at this, I am just trying to put together a useful FAQ. Please help!

TallDave
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Post by TallDave »

Are you sure you are not thinking of charge exchange reactions? If, so, remember that background neutrals will be in a small minority by a factor of ~ 1000- based on what Bussard claimed for the wiffleball traping factor which can maintain this ratio within the magrid- but only for charged particles, neutrals float freely throughout the system and need to be pumped out to maintain this ratio. This deficit of neutrals would severely limit recombinations [EDIT- sorry, I should have said charge exchange reactions] and their subsequent relative effects on ion flows.
Also a good point. In fact, Bussard says >1e4 is achievable. It's hard to see how a neutral drifting in ever gets into a high-energy region. The ones that aren't ionized should tend to bounce out of the region of 1e4x higher pressure inside the Magrid anyway. It seems exceedingly unlikely very many will make it to the region of ion focus where pressure is highest and ion energies are high. Additionally, the collision cross-section is highest at the edge.

Yes, handwaving, but all in all a hard road to hoe for a fast neutral.

Kiteman -- jmho: too many unknowns for a p-B11 length. We don't really have a good idea how much brem we're losing. But my hands are tired from all the waving.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

D Tibbets
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Post by D Tibbets »

KitemanSA wrote:Folks,
Is there a way I can improve my FAQ response?
If the 1E8 is for 10s of keV, is there a better number that I can quote that is for the ~550keV pB11? Please?

I am a total neo at this, I am just trying to put together a useful FAQ. Please help!

Using fusion rates taken from the graph from page 12 here:

http://fds.oup.com/www.oup.co.uk/pdf/0-19-856264-0.pdf

Keep in mind that these are beam target rates, for beam- beam rates the KeVs should be two times the potential well (in volts)

And, coulomb collision rates calculated from here:

http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html

Again, KeV twice that of the potential well should be used (at least early on in the thermalization process where all of the ions have near radial velocities) the ratio is easily calculated for D-D mono energetic ions. Also P-B11 collisions are shown.

[EDIT] My formatting was lost so it is difficult to interpret the numbers.
The first numbers xxx/xxx are for fusion crosssection in Barns divided by coulomb crossection in Barns with beam- target conditions. The second xxx/xxx numbers in the line is for beam- beam conditions

For Beam- target collisions For Beam- Beam collisions (KeV used for calculation is doubled)

Fusion crossection /
Coulomb crossection (Barns)

D-D fuel
10 KeV ~ 0.0005 / 21000 ~ 0.002 / 5300
50 KeV ~ 0.005 / 850 ~ 0.05 / 212
100 KeV ~ 0.09 / 212 ~ 0.1 / 53
200 KeV ~ 0.1 / 53 ~0.1 / 13


P-B11 fuel
100 KeV ~ 0.001 / 5300 ~ 0.02 / 1330
200 KeV ~ 0.02 / 1330 ~ 1.0 / 330
400 KeV ~ 1.0 / 330 ~ 1.1 / 83
(the P-B11 fusion resonance peak is ignored)


And , to answer a question I had about why the alpha particals produced in the P-B11 reaction
could bounce around a thousand times inside the Polywell before escaping and yet not have
significant coulomb collisions with the fuel ions-
The Coulomb crossection for ~ 3 MeV alpha particals is only ~ 6 Barns.

So, when Chrismb says the ratio of fusion collisions to coulomb collisions is ~ 10^-8 for potential wells of ~ 10-50 KeV, he actually means it is that for a beam- target system at 10 KeV only. For beam- beam conditions at 10 KeV drive energies the ratio is actually ~ 10^-6. At the 50 KeV range the ratios would be ~ 10^-5 for beam- target and ~ 10^-4 for beam- beam conditions.

All of this ignores the effects of convergence and varying speeds in the core, bulk and edges of the machines that persist so long as thermalization is limited to some degree over the fusion and/or containment lifetimes of the ions.

PS: The coulomb collision crossection in the edge region where the deuterium ions have a presumed energy of ~ 500 eV is a whopping ~ 8 million. At room temperature (~ 0.001 eV) the coulomb crossection is ~ 20 million. This assumes the model is accurate over this broad range of energies .


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

chrismb
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Post by chrismb »

D Tibbets wrote:Using fusion rates taken from the graph from page 12 here:
NO.NO.NO!!!

Fusion cross-section is measured in units of area. Fusion rate is measured in [velocity].[cross-section].[density], i.e. it is measured in units of frequency.

Just look at the darned units of measurement!!

Is your 'confusion' over this just a wind-up?
D Tibbets wrote: Keep in mind that these are beam target rates, for beam- beam rates the KeVs should be two times the potential well (in volts)
No it isn't. It clearly stated 'centre of mass', which means it is the total energy available for the collision. A beam-target requires twice the drive voltage to achieve a given CoM, whereas a beam-beam requires half to achieve the CoM energy. Your end-point is right but for the wrong reasons.
D Tibbets wrote:And, coulomb collision rates calculated from here:

http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html
You still don't seem to understand that you are using a particular scattering angle, not an integration over all possible scattering angles. (Have you foung the 'angle' box on that spreadsheet yet?)

FYI: The loss of energy for a given particle when it deflected by the 10 degree deflection you are using for your measurements is 3% per collision. So it could only collide 33 time before it would've lost all its energy (let alone dropped below a possible fusion collision).

If you are using the 10degree deflection cross-section for your calculation then you have to show that it is *this* cross-section that is in ratio to fusion by 33:1 to demonstrate net-energy.

I'm bored repeating myself with the aim of educating you on this. Your numbers are within an order of magnitude correct, and using 10degree angle it is easy to then say you need 33:1 ratio between scattering to fusing rate.

Remember this is only for Coulomb collisions, not for all collisions.

D Tibbets
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Post by D Tibbets »

chrismb wrote:
D Tibbets wrote:Using fusion rates taken from the graph from page 12 here:
NO.NO.NO!!!

Fusion cross-section is measured in units of area. Fusion rate is measured in [velocity].[cross-section].[density], i.e. it is measured in units of frequency.

Just look at the darned units of measurement!!

Is your 'confusion' over this just a wind-up?
D Tibbets wrote: Keep in mind that these are beam target rates, for beam- beam rates the KeVs should be two times the potential well (in volts)
No it isn't. It clearly stated 'centre of mass', which means it is the total energy available for the collision. A beam-target requires twice the drive voltage to achieve a given CoM, whereas a beam-beam requires half to achieve the CoM energy. Your end-point is right but for the wrong reasons.
D Tibbets wrote:And, coulomb collision rates calculated from here:

http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html
You still don't seem to understand that you are using a particular scattering angle, not an integration over all possible scattering angles. (Have you foung the 'angle' box on that spreadsheet yet?)

FYI: The loss of energy for a given particle when it deflected by the 10 degree deflection you are using for your measurements is 3% per collision. So it could only collide 33 time before it would've lost all its energy (let alone dropped below a possible fusion collision).

If you are using the 10degree deflection cross-section for your calculation then you have to show that it is *this* cross-section that is in ratio to fusion by 33:1 to demonstrate net-energy.

I'm bored repeating myself with the aim of educating you on this. Your numbers are within an order of magnitude correct, and using 10degree angle it is easy to then say you need 33:1 ratio between scattering to fusing rate.

Remember this is only for Coulomb collisions, not for all collisions.
I did look at the units of measurement (did you?) and used the first reference,

http://fds.oup.com/www.oup.co.uk/pdf/0-19-856264-0.pdf

Figure discription from page 12 "Fusion cross sections versus
centre-of-mass energy for reactions of interest to controlled fusion energy. The curve labelled DD represents the sum of the cross sections of the various branches of the reaction."

instead of the graph on the Wikipedia article because it used Barns as the units on the Y- axis, so that I would be considering apples to apples.

The units for the Coulomb collision crossections are also in barns and, I believe, represents beam target conditions.

http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html

The graph in the first reference is center of mass measurements. The resonance peak at ~ 150 KeV for P-B11 supports my interpretation that this represents beam- target conditions, as I have seen graphs with this peak at ~ 75 KeV (which would represent Beam- Beam conditions. Am I wrong?


The numbers I gave are crossections for a single collision, irregardless of the resultant angles of deflection of the particals. Your rant about the angles imparted from coulomb collisions are indeed important and I believe is incorporated in one of the Bussard papers linked below. But, by ignoring these considerations, my numbers represent the worse case scenario, ie one collision fully thermalizing the particle in the angular direction (to the extent that it no longer transits the core (some central volume of significant size, not some tiny theoretical volume that could not be obtained anyway due to limits on the central vertual anode height that can be tolerated)). If it takes two or more collisions to reach this limit, then my numbers are actually pessimistic. And, again, this is ignoring the significance of where in the machine these collisions take place.


Some links that discuss scattering collisions in the Polywell ( both upscattering, and angular scattering) are below. If you wish to attack them, feel free, but if you do, please do it in detail, referencing how the various numbers and formula are in error. Please don't use the the method that A. Carlson used, saying that he (Bussard, etel) was wrong and was a fool, without giving detailed justification for his conclusions.
eg: His calculation for the potential well depth needed to contain upscattered ions of several million volts is intimidating, but not justified by comparing his methods to those used by Bussard, etel (plus he did not respond to why his number was so much higher than even Riders numbers).



http://www.askmar.com/Fusion_files/EMC2 ... %20Ion.pdf


http://oai.dtic.mil/oai/oai?verb=getRec ... =ADA257642
(an abstract, I have the article, but could not find a web link to the entire article)


http://www.askmar.com/Fusion_files/EMC2 ... %20Ion.pdf


http://www.askmar.com/Fusion_files/EMC2 ... etimes.pdf


http://www.askmar.com/Fusion_files/Some ... ations.pdf


http://www.askmar.com/Fusion_files/EMC2 ... ration.pdf

[EDIT]
PS: Center of mass collisions are indeed implied from both of the references I used. That is obvious. But, your implication that this represents the energy imparted by a potential well is the same or less for a beam-beam interaction and a Beam-target interaction is wrong. In beam- beam the ions are both accelerated to the potential well voltage, so when they hit (head on) they have twice the kinetic energy of the potential well voltage. In beam- target collisions one of the 'ions' is stationary, so only the 'beam ion' has any kinetic energy (provided by the potential well), so the collision energy equals the potential well energy. You said this above , but in context you then implied that my numbers for beam- beam energies should be half of the beam- target numbers.


D. Tibbets
Last edited by D Tibbets on Wed May 19, 2010 7:49 pm, edited 2 times in total.
To error is human... and I'm very human.

chrismb
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Post by chrismb »

D Tibbets wrote:The numbers I gave are crossections for a single collision, irregardless of the resultant angles of deflection of the particals.
I have no idea what you think you are saying, here. There is a cross-section that can be calculated which is the frequency (given by v.rho.cs) that the beam particles will be deflected by the target particles at or less than the chosen angle. The chosen angle you are quoting for is 10 degrees. Why are you choosing 10 degrees, other than the fact that it is the default entry in the web page I showed you? Why not put in 1 degree (which'd result in a cross section x100 bigger)? Or a deflection angle of 0.1 degree (which'd be x10000)?

Why are you picking a 10 degree deflection angle for your numbers?

D Tibbets
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Post by D Tibbets »

chrismb wrote:
D Tibbets wrote:The numbers I gave are crossections for a single collision, irregardless of the resultant angles of deflection of the particals.
I have no idea what you think you are saying, here. There is a cross-section that can be calculated which is the frequency (given by v.rho.cs) that the beam particles will be deflected by the target particles at or less than the chosen angle. The chosen angle you are quoting for is 10 degrees. Why are you choosing 10 degrees, other than the fact that it is the default entry in the web page I showed you? Why not put in 1 degree (which'd result in a cross section x100 bigger)? Or a deflection angle of 0.1 degree (which'd be x10000)?

Why are you picking a 10 degree deflection angle for your numbers?
I indeed left the deflection angle at the default number, because in my ignorance I assume that this is an angle that is reasonable for coulomb collisions (I assume the authors assumed the same). The collision crossection goes up if shallower collisions are assumed, as you say, but to get the same cumulative effect, more collisions are required. I don't know how the net deflection angles would work out over say 100 collisions at 1 degree deflection per collision (+/_ 1 degree change in previous deflection angle) vs 1 collision at 10 degree deflection (I'm guessing they would be similar).
The important consideration is how many deflecting collisions (large or small) are required to result in the ion being lost to the core. Also, if a significant number of these collisions occur near the center of the machine, their contribution to angular deviation from radial paths will be lessened.

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

TallDave
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Post by TallDave »

The Coulomb crossection for ~ 3 MeV alpha particals is only ~ 6 Barns.
Yep. Rick didn't share his number for the alpha energy loss, but he seemed to indicate it would be small over the expected average 1000 transits.
PS: The coulomb collision crossection in the edge region where the deuterium ions have a presumed energy of ~ 500 eV is a whopping ~ 8 million.
You can just about hear them clanging off each other.

Another fun calculation: given 1000 passes for an alpha at 3Mev, how often does an ion at 500eV make it out? You can see why Nebel and Chacon call upscatter a red herring in this kind of machine.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

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