ANS winter 2010 Conference

[WizWom]

Most of my 'Gut' feeling is due to discrepencies, or rather variations in conclusions from the same lab and others. The D-D fusion has been shown to be greatest (per unit volume) in the center of one of their fusors,

Your understanding is exactly opposite what they reported at the conference, which is their latest and most accurate results.
Really, I've talked with them. Asked questions in their presentations, which were clear, concise, and not at all supporting what you think.
Beam-beam interactions were NOT how Hirsch got his super-high fusion counts per watt.

[WizWom]

As I understand it, I don't know where this 400/200keV stuff has come from.

The Coulomb barrier is quite easy: take the strong force of the nucleons involved; compare to the electric force of coulomb repulsion from the like charges. solve for equality, that's your coulomb barrier. Now modify it slightly for quantum tunneling.

The Coulomb barrier for two deuterons touching is around the 40 MeV range. If two such deuterons came together at that energy, though, they should smash each other up into bits - no fusion.

The coulomb barrier energy is 480keV according to my NE Text, or 211 kEv in CM

http://iopscience.iop.org.libproxy.mst. ... hPage=true

Essentially all nuclear fusion (bar a few parts per million of the multi-sigma outliers in the M-B distribution - which only applies to thermal plasmas mind, not electric fusion) seen in solar and terrestrial fusions is down to quantum tunnelling, as far as I understood it....

Here are the equations;

http://burro.cwru.edu/Academics/Astr221 ... ulomb.html

I see your badly done page, and cite a real article on the subject of fusion.
http://iopscience.iop.org.libproxy.mst. ... hPage=true

In regards whereabouts fusion comes from in an 'electric fusion' device, even if you get piles of hot ions flapping around, the charge-exchange cross-section with backgrounds is so high that one should anticipate that the majority of fusions are fast neutrals into the walls/structures of the device. (Hence why I would want to see this excluded as the source of neutrons in Polywells before I sign away any more credence to the whole scheme.)

There is no reasonable Fe+n or Fe+d reaction that gives n, barring amazingly high energies.

[D Tibbets]

Wizwom, the beam- target fusion Chrismb is referring to is not between D and iron. It is between beam D and D embedded in the surface layer of the vacuum vessel (or grid).

Dan Tibbets

[chrismb]

The Coulomb barrier for two deuterons touching is around the 40 MeV range. If two such deuterons came together at that energy, though, they should smash each other up into bits - no fusion.

The coulomb barrier energy is 480keV according to my NE Text, or 211 kEv in CM

http://iopscience.iop.org.libproxy.mst. ... hPage=true

...

I see your badly done page, and cite a real article on the subject of fusion.
http://iopscience.iop.org.libproxy.mst. ... hPage=true

You will have to screen-print and re-post what you want us to look at. You appear to have the luxury of sitting behind a fully paid-up subscription service, as your links give us a login screen, whereas us mortals have to try to figure stuff out for ourselves and use critical thinking to guide us.

So let us use critical thinking (or is 'education' these days only about some spoon-feeding?).

The equation for electrostatics is F=Q1.Q2/[4.pi.eo.r^2]. If we integrate, wrt r, from infinity to some distance r for two unit charges we get E=~2E-28J.m, or 1.5E-9eV.m. So for a potential of 40MeV this would imply a distance of 1.5E-9/40E6 = 0.04 fm, which appears to be smaller than that quoted for the diameter of nucleii. Whereas your figure of 480 keV implies a distance to the potential peak of 3 fm, which seems more in order.

So I am happy to anticipate adjusting my understanding of this, subject to the answer to a few more points, and withdraw my statement, as you quoted above, on hold pending correction and to establish if I have been mislead by such texts as I linked to....

However, this calculation of the Coulomb barrier cannot be the whole picture, or even half of it, because if we look at the fusion cross-section of DT then it peaks as 64 keV ,and the cross-section keeps going on downwards from there on to 480 keV and beyond. This is similar for DD which peaks around 1.1 MeV. Further, the cross-section for pp isn't the same as that of DD and DT, so what we are looking at is a wholly dissimilar set of 'responses' of unit charges in the range close to the nucleus, and it doesn't seem to be the case that there is some unique point at which the Coulomb barrier is overcome, as per the nugget of the point in this thread.

As I look at the fusion cross-section curve and your statement that the Coulomb barrier is at 480 keV, I see nothing particularly noteworthy to suggest that there are two 'competing' forces here either side of that potential.

That the reactivity of DD and DT drops for energies above the suggested Coulomb barrier, then the logic seems flawed somewhere and doesn't look like it adds up.

So, before throwing around 'absolutes' as quoted from someone's favourite physics texts, I would want to ask a few more questions. As I work far from the physics sector and have no-one knowledgeable to ask questions of, then I would suggest, WizWom, that you could go discuss this with the people you work/study with and figure this out:

Assuming the range at which the strong force dominates over the Coulomb force is a fm or two, why do fusion reactivity cross-sections drop off above the Coulomb barrier energy that this range infers?

There is no reasonable Fe+n or Fe+d reaction that gives n, barring amazingly high energies.

Dealt with.

[chrismb]

chrismb:

Essentially all nuclear fusion ....... seen in solar and terrestrial fusions is down to quantum tunnelling,

Interesting viewpoint. So we can lay the thermonuclear fusion (aka Hydrogen) bomb at the feet of Bohr, Heisenberg and Feynman as their child ... (curie, rutherford and einstein can take a grand-parent role).

You can blame George Gamow for this. I understand that it was he that figured out the missing factor was the tunneling mechanism.

[Tom Ligon]

Yup. Gamow barrier penetration. The standard cross section calculations accepted by the entire fusion field trace back to Miley, et. al. They include this term.

Whatever is going on in LENR (if anything) would be entirely dependent on this quantum tunneling mechanism.

The fact that Miley has been willing to look along those lines should tell us the term ain't trivial.

[WizWom]

The Coulomb barrier for two deuterons touching is around the 40 MeV range. If two such deuterons came together at that energy, though, they should smash each other up into bits - no fusion.

The coulomb barrier energy is 480keV according to my NE Text, or 211 kEv in CM

http://iopscience.iop.org.libproxy.mst. ... hPage=true

...

I see your badly done page, and cite a real article on the subject of fusion.
http://iopscience.iop.org.libproxy.mst. ... hPage=true

You will have to screen-print and re-post what you want us to look at. You appear to have the luxury of sitting behind a fully paid-up subscription service, as your links give us a login screen, whereas us mortals have to try to figure stuff out for ourselves and use critical thinking to guide us.

Sorry about that; I've gotten used to the university library system getting me in to a bunch of journals which charge.

The 480 keV is from using my Introductory text's coulomb barrier first approximation; let me quote the relevant section from that:

The coulombic forces between the incident projectile (charge Zxe) and the target nucleus (charge ZXe), when separated by a distance r is
Fc = Zx*ZX*e^2/(4*pi*eps0*r^2)
where eps0 is the permitivity of free space.

...
Wc = -integral(Fc,dr, infinity, b) = (e^2/4*pi*eps0)*ZxZX/b

.... we may assume, to a first approximation, that b= Rx+RX, where Rx and RX are the radii or the incident projectile and target nucleus, respectively, from Eq. (1.7) we obtain
b = Rx+RX = Ro(Ax^(1/3) + AX(1/3))
thus for an incident particle with a positively charged nucleus to interact with the target nucleus, it must have a kinetic energy to penetrate the coulomb barrier of about [Mayo 1998]
Ecx ~= 1.2*Zx*ZX/(Ax^(1/3)+AX(1/3))

The 1.2 seems magic from this explanation. I can't seem to get it from playing around with e and eps0

The strong force, in this model, is assumed to take hold when the nuclei are in contact, which is reasonably true.

Assuming the range at which the strong force dominates over the Coulomb force is a fm or two, why do fusion reactivity cross-sections drop off above the Coulomb barrier energy that this range infers?

For this, we have to get into the Quantum mechanics of the paper I tried to point to, Bosh, H.L., Hale, G.M., Nuc. fusion 32 (1992) which referenced Brennan, J.G. Phys Rev 111 (1958) and Fick, D, Wiess, U., Z. Phys, 265 (1973) for the physics of light nuclei fusion.

as long as the energy available in the centre-of-mass (CM) frame is much smaller than the coulomb barrier, reactions are possible only because of the tunneling effect, and the cross-section is proportional to the tunneling probability
sig ~ exp - 2*pi*Z1*Z2*e^2/(plank*v)
This can be arranged to give
sig ~ exp(-B0/sqrt(E))
where
B0 = pi*alpha*Z1*Z2*sqrt(2*m*c^2)
is the Ganow constant, expressed in terms of the fine structure constant, alpha = e^2/(plank*c) = 1/137.03604, and the reduced mass of the particles in keV. Throughout this paper, E denotes the energy available in the CM frame. For a particle A with mass mA striking a stationary particle B, the simple relation EA = E(mA + mB)/mB holds.

Quantum mechanics shows that the fusion reaction is also proportional to the geometrical factor pi*gamma^2 ~ 1/E, where gamma is the de Broglie wavelength. The strong energy dependences of this factor and the barrier penetrability have prompted the introduction of the astrophysical S-function, defined by writing the cross-section as the product of three factors:
sigma = S(E)*(1/E)*exp(-B0/sqrt(E))
The motivation for doing this is that two well-known, strongly energy dependent factors (which describe the coulombic and phase space parts of the incident channel) are separated, leaving the S-function to represent the presumably slowly varying nuclear part of the fusion reaction probability.
The S-functions of the four functions shown in Fig 1(b) demonstrate very clearly the advantages of using the S-function instread of the cross-section:
- the S-function describes mainly the intrinsic nuclear physics of the reaction and therefore shows clearly the difference between the reactions considered here.
The d+d reactions do not have strong S-wave resonances close to the threshold, resulting in a weak energy dependence, while the other two reactions involve a near-threshold S-wave resonance of the compound system. This is very evident in the S-function, while in the cross-section it is masked by the strong energy dependence of the coulomb barrier penetration.
- In all cases, the S-functions only vary by a factor of 20 over the energy range shown here, instead of by about 14 orders of magnitude. Therefore, it is much easier to not only compare data on a linear scale over a wide range but also to calculate a reasonable fit to the data.

[The figure shows a strong peak for D(t,n)alpha to 28 at ~50 keV, then tapering to a level 0.3; a shallower peak for 3He(d,p)alpha to 16 then tapering to 1.0; and a steadily rising S-function for the d(d,n)3He and d(d,p)t reactions, starting at 6.0 and rising to 28 and 24 respectively by 1000keV]

The peaking in sigma in the d+t and d+3He reactions is caused by the non-linearities of the 1/E, exp(-(B0/sqrt(E))) and S-functions; but the d-d reaction just keeps increasing as the energies increase, until you start dominating by the d(d,d)d elastic reaction above about 4 MeV.

[chrismb]

I'm very familiar with the maths and the parameters that can be used to get an empirical calculation of cross-section.

But it doesn't answer the question. There is a so-called 'astrophysical' factor thrown into an equation to make the thing balanced to that which is measured in experiments. Great! A real 'foundation' of understanding, that is! - a fudge factor, no less!!!....

The equations that can describe empirical cross-sections don't seem to necessitate the inclusion of Coulomb barriers! Funny, that!.......

(see; http://www.kayelaby.npl.co.uk/atomic_an ... 4_7_4.html shows a full empirical breakdown of the astrophysical factor

and; http://www.oup.co.uk/pdf/0-19-856264-0.pdf describes the derivation of the empirical equation)

So it looks to me, unless we're missing something, we are still none the wiser as to the difference that the actual Coulomb barrier makes to fusion cross-section, because it is blurred by this fudge factor that overwhelms such effects.

[D Tibbets]

Most of my 'Gut' feeling is due to discrepencies, or rather variations in conclusions from the same lab and others. The D-D fusion has been shown to be greatest (per unit volume) in the center of one of their fusors,

Your understanding is exactly opposite what they reported at the conference, which is their latest and most accurate results.
Really, I've talked with them. Asked questions in their presentations, which were clear, concise, and not at all supporting what you think.
Beam-beam interactions were NOT how Hirsch got his super-high fusion counts per watt.

It is the latest and perhaps most accurate results for that particular design. But, in other designs the central fusion dominance (not beam- target) has been demonstrated. I'm not contesting their results, I am cautious about their conclusions, as it seems to be directly contrary to other findings in their and others labs. For that matter I have not seen a discussion of why beam- target (grid) fusion of D-He3 seemed to dominate (considering the areas involved) in their glow discharge fusor, while central (suggesting Beam- beam fusion) dominated with D- D fusion in the same fusor (see the presentations from the 2009 conference.

PS,: Another possible variable influencing their results is the recirculation factor. In a typical gridded fusor an ion is expected to make 10-20 passes before it hits the grid. . If beam- beam fusion dominates, then this means that there are ~ 10-20 core collisions (beam- beam) that might lead to fusion. With beam, target fusion, especially if the target (neutral deuterium gas or surface embedded deuteron is near the center where the beam deuteron has its highest velocity in a central cathode grid fusor, then the beam target may dominate if the density of the target deuterium is high enough. In the ion gun version like Hirsch's model I speculate that the ion achieves it's greatest velocity at the negative shell surrounding the core. It then drifts across the core, perhaps slowing as it approaches the center (like a vertual anode in a Polywell), then speeding up again as it approaches the opposite side. In this case, beam target (or beam- background neutral) can dominate over confluent central beam - beam collisions if the densities of these non beam densities are high enough or the areas are large enough. It boils down to which is more likely a beam ion finding another beam ion to fuse with in the center at a given density in that area and a lifetime of 10 passes, of a beam ion finding a deuterium to fuse with in the wall on it;s one pass. Keep in mind that if there is a window in the shell that the ion beam passes through that allows for several recirculations, it is not hitting the shell during that time. But if the beam is defocused, more of the ions will fall outside this window and hit the shell (or embedded deuterons in the shell). This is a double whammy against the beam - beam fusion. It is increasing the likelihood of fusion on the shell, and decreasing the ions aviable for recirculation and thus beam -beam fusion. Also, if the negative shell is less transparent than the above mentioned central grid, the ion will recirculate fewer times. This would favor beam - target fusion with embedded deuterons in this shell and handicap central convergent fusion. Even if focused beams pass through windows and are recirculated more, you would of course expect this to happen less if the beams are not focused. From that aspect, the conclusions only illustrate the importance of the setup on results. In many ways, this description is consistent with what ChrisMB has said about glow discharge fusors. The interfering background neutrals (or the grid, intermediate walls) prevents the beam - beam collisions from dominating, because of the satistics of the process. Anything that interferes with the particles maintaining their energy till it fuses, will penalize the fusion rate. It doesn't necessarily imply conflicting physics, just conditions that gives a competitive edge to one of the processes.
In that case, the results are consistent and possibly positive as opposed to discouraging. Does anyone believe that Beam target fusion is always dominate over beam - beam fusion. The energy advantage of beam - beam fusion is obvious. What is not certain is the relative densities and volumes/ areas of the reacting particles.

Another point, if this beam- target fusion is dominate in this machine, what is the explanation for it's superior performance over a gridded fusor? Is it all attributed to better vacuums and therefor fewer neutrals to get in the way, charge exchange with and otherwise mess with the energy of the neutrals. How is that different from a wall messing with the ions energy. Well, I can see the neutrals interferring with ions achieving the full energy that is aviable from a potential well, but, I don't know how this dynamic process would work out.

Sorry for this rambling post. I formed my arguments as I wrote.

Dan Tibbets

[D Tibbets]

chrismb:

Essentially all nuclear fusion ....... seen in solar and terrestrial fusions is down to quantum tunnelling,

Interesting viewpoint. So we can lay the thermonuclear fusion (aka Hydrogen) bomb at the feet of Bohr, Heisenberg and Feynman as their child ... (curie, rutherford and einstein can take a grand-parent role).

In a word - Yes!. Actually, it depends on the temperature of the fission/ fusion plasma formed in the bomb.
Some to almost all of the fusion may come through quantum mechanics effects.
See the illustration taken from page 49 of the same text I referenced earlier. The graph is for D-T fusion, I believe.

PLASMA PHYSICS AND
FUSION ENERGY
Jeffrey P. Freidberg
Massachusetts Institute of Technology 2007




Dan Tibbets

[WizWom]

I'm very familiar with the maths and the parameters that can be used to get an empirical calculation of cross-section.

But it doesn't answer the question. There is a so-called 'astrophysical' factor thrown into an equation to make the thing balanced to that which is measured in experiments. Great! A real 'foundation' of understanding, that is! - a fudge factor, no less!!!....

The equations that can describe empirical cross-sections don't seem to necessitate the inclusion of Coulomb barriers! Funny, that!.......

(see; http://www.kayelaby.npl.co.uk/atomic_an ... 4_7_4.html shows a full empirical breakdown of the astrophysical factor

Um... this page references the paper I quoted from, which I have in front of me here. I'm glad you were able to find a source you could understand.

and; http://www.oup.co.uk/pdf/0-19-856264-0.pdf describes the derivation of the empirical equation)

This goes into the quantum-mechanical basis for the geometric factor, that is, the time-dependent Schroedinger equation.

So it looks to me, unless we're missing something, we are still none the wiser as to the difference that the actual Coulomb barrier makes to fusion cross-section, because it is blurred by this fudge factor that overwhelms such effects.

well... yeah. If it was classical, or even just classical and quantum mechanical, we would be seeing less than 1/20th the d-d fusion at high energy, and so forth. The magnitude of the S(e) term is very disturbing from a theoretical physics standpoint. As an engineer, we take the actual data and work with it, why it is what it is isn't terribly important.

[chrismb]

The magnitude of the S(e) term is very disturbing from a theoretical physics standpoint. As an engineer, we take the actual data and work with it, why it is what it is isn't terribly important.

I think that means we are now in agreement that whatever the actual Coulomb barrier energy is, it pales into insignificance when compared with the reality of the actual physical nature of the fusion tunneling and nuclear resonances?

[WizWom]

The magnitude of the S(e) term is very disturbing from a theoretical physics standpoint. As an engineer, we take the actual data and work with it, why it is what it is isn't terribly important.

I think that means we are now in agreement that whatever the actual Coulomb barrier energy is, it pales into insignificance when compared with the reality of the actual physical nature of the fusion tunneling and nuclear resonances?

No.
The "nuclear resonances" I think you are talking about are the strong force stability characteristics of the nucleus; that is, they are the likelihood that the compound nucleus will integrate, rather than undergo an elastic collision.
The "fusion tunneling" is easily quantifiable; that is what the "geometric" term is quantifying.

There seems to be no theoretical reason behind the S(E) term; it's included to make the formula of the other two terms come out to match the data. It's a kludge of the worst sort.

[chrismb]

I think that means we are now in agreement that whatever the actual Coulomb barrier energy is, it pales into insignificance when compared with the reality of the actual physical nature of the fusion tunneling and nuclear resonances?

No.

So, you're saying that the Coulomb barrier IS a dominant term, compared with tunneling and astrophysical factor?

Is it a dominant term, or isn't it? I was just saying I don't see it appear, so I think it must be insignificant. What is the 'No' in reference to?

[WizWom]

I think that means we are now in agreement that whatever the actual Coulomb barrier energy is, it pales into insignificance when compared with the reality of the actual physical nature of the fusion tunneling and nuclear resonances?

No.

So, you're saying that the Coulomb barrier IS a dominant term, compared with tunneling and astrophysical factor?

Is it a dominant term, or isn't it? I was just saying I don't see it appear, so I think it must be insignificant. What is the 'No' in reference to?

OK, when you break the 3-term sigma function up, you get the 1/E incorporating the bottom of the coulomb barrier term, the top gets subsumed in the S(E) but ISN'T the whole of the S(E). Which is why I said it's a kludge of the worst sort - it mixes parts of an equation into other parts of equations, and still leaves you with a curve-fitting for something that seems to have a theoretical underpinning, but does not.