Oppenheimer-Phillips, and a guarantee of overcoming Coulomb?

[KitemanSA]

WHY the fusion cross-section does not keep going up indefinitely to the point where 'the majority of particles fuse'

Yes, is not fusion cross-section does not keep going up indefinitely to the point where 'the majority of particles fuse'

But the capability for 'the majority of particles' to fuse is provided by the confinement concept.

Joe,
Would you please try translating this again. The sentance structure you have provided does not make sense in English.

[Joseph Chikva]

Joe,
Would you please try translating this again. The sentance structure you have provided does not make sense in English.

The proposed confinement concept provides for majority of reactant particles capability to fuse.
Is this more clear sentence structure?

[KitemanSA]

Sorry, my bad. I meant the first statement, not the second.

[Joseph Chikva]

WHY the fusion cross-section does not keep going up indefinitely to the point where 'the majority of particles fuse'

Yes, is not fusion cross-section does not keep going up indefinitely to the point where 'the majority of particles fuse'

Yes, that is not well expressed sentence. Sorry.
As I understand, my respectful opponent said the current nonsense that somewhere I have made the statement that fusion cross-section goes to infiniteness and this provides 'the majority of particles fuse'.
I was disagreed.
Not infinitely high cross-section but proposed confinement concept provides such capability.
As fusion cross-section for given reactants depends only on center-of-mass collision energy and on nothing else.

[D Tibbets]

I'm not sure what the basis for argument is here. The conditions and consequences have been hashed out here, and is referenced in many texts. The fusion crosection curves are well accepted . D=T peaks around ~ 60-70 KeV, then falls. there is little reason for pushing to higher energies. I have presented a curve of the DT fusion crosection vs the Coulomb collision crossection. In this case the DT fusion crossection peak corresponds to the best ratio between fusion and scattering collisions at a ratio of ~ 1:10. The Coulomb crossection falls at even higher energies, but the DT- fusion crossection nearly parallels it. No gain, and lots of penalties (bremstrulung, black body radiation,eventually atom smashing instead of fusion, etc).
The fusion crosection curves are derived from experiment, and the difference between them and the theoretical absolute Coulomb barrier math is explained as quantum uncertainty/ tunneling effects. Like much of quantum mechanics it doesn't always make sense, but it does accurately predict results.

If you are talking about DD fusion. purely from the crossection point of view it might make since to push to collision energies of a few MeV. I suspect that the fusion probabilities may actually exceed the Coulomb collision probabilities. But this ignores other losses. The energy gain per fusion goes down (more input energy), the bremsstrulung is much greater ( I believe it goes up as the 1.5 power of the temperature), and of course as chrismb stated the atom smashing effects will reach dominance at some point. This is endothermic (I think) and not only robs energy but scatters any ions as well.

I believe that at ~ 60-80KeV the fusion to Coulomb collision ratio is ~ 1/100 that of DT. (~ 1:1000 ratio). As a few hundred KeV the ratio may be similar to DT at ~ 60-80 KeV. [EDIT- not because the DD fusion crossection is increasing that much, but because the Coulomb collision crossection in continuing to decrease] , but other loss concerns will reach a optimal balance and I doubt it is much above several hundred KeV. I believe Bussard was careful in his calculation (as opposed to me ) and his quotes of ~ 80 KeV for a D-D burning Polywell was the best balance between thermalization issues, other losses, fusion rate, and technical concerns. For P-B11 this is ~ 200 KeV. Additional fusion rates vs scattering could be achieved, but with all of the +/- concerns this is the best balance.

I might add that running at ~ 2 MeV (it doesn't make any since for DT due to the shape of the crossection curve )might make since if you were trying to make nuclear reactions dominate over coulomb scattering reactions. But note that these nuclear reactions is a mix of fusion and smashing, the total exothermic energy delivered is decreasing, the input energy is increasing, the losses are increasing ( the Coulomb losses are not increasing as fast, but they are still increasing) so it is a losing game once you pass some point, which for DD is possible at several hundred KeV. - The fusion crossection graph is still going up slowly, but at a slower rate than the slopes for the losses.
If your purpose is to maximize fuaion and/ or atom smashing, irregardless of the cost then pushing to higher energies makes sence. But from a energy balance situation it does not.

In a Tokamak, where confinement times and thus losses per ion is less, for DT fusion energy balance and energy density concerns, I think that ~ 20 KeV may be the best compromise.
In a Polywell where confinement time is less and with other issues it makes sense to operate at higher levels. For DT fusion I speculate this may be more in the region of 40-50 KeV.
For systems that have very short confinement times it may make sense to push even higher (at least for DD fusion which has a unique fusion crossection curve), but again at some point you reach a maximum benefit, that MIGHT allow for net positive energy generation. This would definitely not be above the energy level where atom smashing became prevelent compared to the fusion rate.

[EDIT Oppenheimer-Phillips reaction = atom smashing]

And another point- ignoring the atom smashing componet. For DD fusion, at the temperature goes up the scattering of a beam becomes less, but even if this preserves the ions in the reaction space longer, there are other losses. The slope of the DD fusion crossection is shallow above ~ 100 KeV,. The Bremsstrulung goes up a ~ 1.5 rate , the black body radiation goes up at ? rate. If the fusion crossection goes up at a rate below ~ these rates plus the input energy rate, then it is a loss.
Using soem made up numbers. Increasing the input energy from 100 KeV to 1,000 KeV costs 10 units of power. The Bremstrulung losses costs 10^1.5 or ~ 20 units of power. Black body losses costs ~ 1 unit of power (???). Note that this ignores particle containement losses.
If the slope for the DD fusion crossection is ~ 2 over this range then the incresed fusion would be 2 * 10 or ~ 20X. Subtract the losses (~ 31 units of power). The result is a net loss of 11 units of power.
Recovering the energy from some of these losses helps, but is limited, and it penalizes the positive numbers just the seam. Assume steam conversion at 30% for the losses. Now the losses only ad up to ~ 20 units. The fusion gain is ~ 20 units, but converting it to useful power reduces the fusion output to ~ 14 U of useful power. It is still a losing proposition. This is why reactor schemes ideally operate at regions of the fusion crossection curves that are steep. The peak or maximal position on the graph is only desired if you are not concerned with energy balance or Q. There may be some compromising for technical, power density, actual particle confinement time issues, thermalization issues, etc, but there is not a lot of wiggle room.

This is why Joel Rogers used 15,000 KeV as the drive energy for his Polywell simulations a couple of years ago. This is nowhere near the optimal temperature for power density concerns, or even confinement vs fusion rate concerns, or thermalization issues, but it is the steepest part of the graph and maximizes Q at these constrained assumptions.

Dan Tibbets

[Joseph Chikva]

Dan Tibbets

Dan, scattering cross-section curve seems "parallelly" (equidistantly) to fusion cross-section curve only in logarithmtic frame. But that would not be a big problem. We simply can see that by increasing collision energy the ratio between scattering and fusion cross-sections reduces.

Collision energy should be considered only in center-of-mass frame. And for example 3MeV Deutron catching up 2.5MeV Triton can not be smashed. As regardless to that both nuclei have total 5.5MeV KE in our frame of reference, center-of-mass collision energy will have tens keV order.
In each project/experiment where monoenergetic ions are involved their KE should be chosen only on base of expediency.
And dominating reaction for the range of collision energies from 10KeV to up to at least 1000keV will be fusion: scattering or fusion, scattering or fusion and so on.
And my very respectful opponent was wrong.

[D Tibbets]

Joseph Chikva, your first paragraph makes sense if you are limiting the comparison to deuterium fusion.

I'm not certain how fast the Coulomb collisions decrease with increasing temperature. I generally use the 1/square as it is convenient, though the actual relationship may be closer to ~ 1/ (1.5 or 1.75 exponent of delta T).

Assuming that the fusion crossection for D-D fusion increases by a factor of ~ 5 between energies of ~ 100 to 1,000 KeV, and that the Coulomb collision rate drops by ~ 1/square of the energy difference, then the ratio of fusion collisions to Coulomb collisions would change from ~ 1:1000 to ~ 5:10.

This considerably decreases the Coulomb collision mediated scattering and thermalization issues. But as chrismb likes to point out, smaller angle Coulomb collisions can be much more frequent. The MFP is defined as the distance a particle will travel before it is deflected by 90 degrees. . If you are using 5 degrees of deflection as your measure, then the collisions would be more frequent, though admittedly, the net effect would not be changed (otherwise the MFP would be meaningless for any system that was not limited to only 90 degree deflections).
So, for this example above, at 1000 KeV there would be one fusion collision for every two coulomb collision that resulted in 90 degree deflections (scattering). The question now becomes how much divergence can your opposing beams tolerate- 5 degree dispersion, 20 degree dispersion? Unless the length of travel of your beams is very short, the beams are very thick, and/ or there is some restoring force, the tolorable cumulative deflections are probably small, lets say 10 degrees for arguements sake. Thus the actual significant scattering collisions per fusion collision will be proportionately greater. chrismb calculated this in one thread.
It is not only the MFP to fusion collision probabilities, but the geometry of your system. I think two opposing linier beams would be the least forgiving.
Compare this to the Polywell. With it's nearly spherical geometry, if there is any confluence (focus towards the center - there will always be some, though how much is an open debate). The ions converge towards the center, and because of the resultant increased density near the center, there will be more collisions here. Those collisions that do not result in fusion, will scatter the ions, but since a large portion of these collisions will be occuring near the canter, the angle of deflection relative to the center will effectively approach 180 degrees (depending on just how good the confluence is and the resultant MFP in the center compared to the mantle and edge regions. ie : the MFP is relatively longer in the less dense regions, and at least in the mantle the MFP may be significantly longer than the distance traveled, so large angle deflections (relative to the center become much less frequent. This combined with the high collisionality near the center and that any central deflections are relatively away from the center ( or a shallow angle through the center) at angles approaching 180 degrees. The problem of Coulomb scattering becomes less significant.
At the edge the ions are traveling slow, so the coulomb collisionality crossection goes way up. Here the upscattering and down scattering and angle deflections reach the maximum allowed by Maxwell / Boltzman statistics around the low average temperature.. The key point here is that the Maxwellian distribution occupies a small energy range compared to the energy of the ions once they fave accelerated back down the potential well. I have not seen this resultant effect on the angular scattering being annealed on the edge discussed by Bussard, etel, like the upscattering/ downscattering issue, but it makes sense. Who cares if there is a few hundred eV of transverse motion to the edge ion, then the radial energy imparted to the ion as it falls down the potential well imparts ~ 100 KeV of radial velocity. Upscattering and downscattering from Coulomb collisions is a different issue.

I mentioned that the Bremsstrung radiation may be increasing at rates almost as fast (or faster) than the temperature dependent fusion rate. It might be barely managable with D-D fusion, but with high Z fuels (like P-B11), even if the fusion crossection curve is still positive, the slope is two shallow to keep up with the bremmstrulung.
This assumes that your electron temperatures are ~ same as your ion temperatures. The Polywell again has a claimed mechanism that modifies this process, by having the electrons at low temperatures in the center where the interacting ion density is greatest. I've not seem how this plays out at the edge region where the electron energies are high.
The DPF scheme by Focus Fusion does not have this advantage of the Polywell, instead they use high conversion efficiency of the waste bremsstrulung radiation recovery. Plus quantum mechanical effects that may apply at extremely high B fields that suppresses bremsstrulung.

In short, chrismb's critism may not apply if you keep the center of mass collision energy below some limit (~ 1 MeV?). But the shallow upsloping D-D fusion crossection curve in this range , makes the progressively increasing loss scaling a problem, even without considering containment losses from the admittedly progressively less prevalent Coulomb scattering collisions.


Dan Tibbets

[Joseph Chikva]

Assuming that the fusion crossection for D-D fusion increases by a factor of ~ 5 between energies of ~ 100 to 1,000 KeV, and that the Coulomb collision rate drops by ~ 1/square of the energy difference, then the ratio of fusion collisions to Coulomb collisions would change from ~ 1:1000 to ~ 5:10.

This considerably decreases the Coulomb collision mediated scattering and thermalization issues.

Agreed and here we can stop.

As I disagree with both: what you wrote before quoted phrase.
And with long text written after.
As:
1. It has not a matter how look two curves in different coordinate expression frames. Deuterium or not deuterium.
2. Be sure that scattering cross section permanently decreases by increasing collision energy. This is the reason why for example for TOKAMAKs multimegaampere current can not heat plasma after certain temperature limit. After that limit Bremsstahlung losses will exceed the energy put in plasma by an externally applied field creating current.
3. Scattering cross section is calculated as an integral. You should not consider separetelly 0.5 deg, 45 deg, 90 deg, etc. But all degrees. Also that is true that small angle declinations are more frequent. And at higher collision energies small angle declinations are much more frequent than at lower.

Pardon, I agree also with following:

In short, chrismb's critism may not apply if you keep the center of mass collision energy below some limit (~ 1 MeV?).

Thanks.

[D Tibbets]

Assuming that the fusion crossection for D-D fusion increases by a factor of ~ 5 between energies of ~ 100 to 1,000 KeV, and that the Coulomb collision rate drops by ~ 1/square of the energy difference, then the ratio of fusion collisions to Coulomb collisions would change from ~ 1:1000 to ~ 5:10.

This considerably decreases the Coulomb collision mediated scattering and thermalization issues.

Agreed and here we can stop.

As I disagree with both: what you wrote before quoted phrase.
And with long text written after.
As:
1. It has not a matter how look two curves in different coordinate expression frames. Deuterium or not deuterium.
2. Be sure that scattering cross section permanently decreases by increasing collision energy. This is the reason why for example for TOKAMAKs multimegaampere current can not heat plasma after certain temperature limit. After that limit Bremsstahlung losses will exceed the energy put in plasma by an externally applied field creating current.
3. Scattering cross section is calculated as an integral. You should not consider separetelly 0.5 deg, 45 deg, 90 deg, etc. But all degrees. Also that is true that small angle declinations are more frequent. And at higher collision energies small angle declinations are much more frequent than at lower.

Pardon, I agree also with following:

In short, chrismb's critism may not apply if you keep the center of mass collision energy below some limit (~ 1 MeV?).

Thanks.

I think what you say about the temperature dependance and deflection angle considerations are consistent with what I am trying to say. The variable angle collisions have cumulative effects that are predictable and using a standard- the 90 degree deflection that equates to the MFP is thus useful as a predictor. But this applies th creating a thermalize plasma there there is no preferred direction. If your ion beans need to maintain less than say 5 degrees of dispersion before the beam density falls below tolerable levels (the center of mass collision energies fall because of the angle of impact, the fusion power density would be falling, etc) then this is the effective Coulomb collision frequency that applies. Assumeing a ~ linier relation ship (actually I think it is exponential) 90degrees / (5 degrees/2 -the ion can bounce away from the original vector or towards it) results in an increase of the pertinent Coulomb collision frequency of ~ 9X. Using rough calculations this would result in the fusion to Coulomb collision ratio of ~ 1:50 at 1MeV energies using arguements I used in the above posts. . With two opposing beams the Coulomb collisions may be elastic and not represent energy losses directly, but the Coulomb collisions do disperse the beams , even at these energies, and these dispersed ions would eventually hit a wall, and now the energy is lost, while having much smaller chances of a fusion collision before this happens. If you consider the energy yield from a fusion event for D-D fuel. If the input energy of the ions is ~ 1 MeV, and the fusion yield is ~ 3 MeV, then you could tolerate only ~ 3 coulomb collisions that cause the ion to be lost to the beam, before you could come close to breakeven. Based on my arbitrary rough calculation you are still short by a factor of ~ 17. Increasing the KE of the deuterium ions further would perhaps help, but there are several competing processes. The net yield from each fusion collision vs Coulomb scattering collision is decreasing, the Oppenheimer atom smashing reactions are becoming more prevalent, and the Bremsstrulung radiation is increasing. I seriously doubt that breakeven could be achieved with a single pass system. You need recirculation of the ions within the ion beams , which means there needs to be some restoring force that keeps the ions within the beams and the beans themselves may need to recirculated/ reflected without energy loss at least a few times before practical positive Q is achieved.
The Polywell in a good confluence mode is like very like many opposing beams, that recycle the ions hundreds of thousands (or more) times before they are lost, with the resultant confinement energy losses. With just two, or a few beams, the transverely scattered ions are lost to the focus point, and unless they can be recovered at little cost, the loss is tremendous. If your ion beams are so dense that fusion collisions are probable with only a relative few collisions in a short distance, the recirculation needs are reduced. But the space charge dispersion effects and the still dominate Coulomb scattering collisions increases proportionately. without this there has to be very many recirculations to achieve positive energy balances.

I anticipate that dense well focused opposing ion beams would approach the performance of beam target fusion. The target is a stationary chunk of deuterium, with the ion bean hitting it. After the beam ions speed is increased to compensate so that the center of mass closing velocities are the same, then the fusion rate/ ion flux in the beam would be similar. I'm uncertain, but I suspect the mechanisms would be the same. These methods have been used many times for study purposes, but the energy balance is millions of times short of breakeven. Despite the high velocity of the ion beam, the vast majority of the beam energy is converted to waste heat. Now, if you had some way to convert that waste heat to useful power at efficiencies of ~99.99...% efficiencies, you may be able to produce useful positive power. In otherwords, if two one pass opposing beam systems would work, even at high energies, I would think that beam target systems which are also single pass systems would have solved the problem long ago.
This waste energy recovery at high efficiencies is essentially what the high recirculation efficiency of the ions within Tokamaks, etc. does. While the Polywell is less confinement efficient on a constant time frame, it makes up for the difference due to beam- beam advantages (not absolutely essential according to Nebel) , monoenergetic advantages and density advantages.
The density advantage is important. If you consider the density difference on the mean time to fusion, the hundreds of seconds confinement times to Tokamaks at ~ 10^19 ion/ M^3 densities to the less than a second ion confinement times of Polywells, with densities of ~ 10^22 ions/ M^3, the confinement times necessary for equal probabilities of a fusion event is comparable- actually significantly favoring the Polywell as the fusion rate scales as the square of the density (though tha actual important measure is the energy confinement time, which in a Polywell is apparently dependent on the electron lifetimes, as they are the dominate loss path for the energy expenditure necessary to maintain the ion containment. This is on the order of milliseconds, even with electron recirculation. The net ratio of energy confinement time to fusion rate is now similar between the Tokamak and the Polywell. The triple product considerations are inescapable. The density advantage obtainable with the Polywell balances the relative loss rates. There are other advantages- like smaller size for the same fusion output. A Polywell operating at densities similar to Tokamaks could produce just as much fusion/ unit volume, or perhaps an order of magnitude greater fusion rates due to monoenergetic advantages. The disadvantage would be it would have to be the same size as the Tokamak. Of course a Polywell operating in this manner would not work, because it needs the higher densities of charged particles to create the Wiffleball effect which creates the high Beta condition that improves the electron containment by a factor of ~ 100 over cusp confinement. Without this effect breakeven would probably never be reached even in huge machines.

I don't know how you accommodate this recirculation need in your system. As stated above, if this was not extremely important, them beam target systems should also be capable of positive Q's. Unless your beam ion density is much higher than that in solid targets (approaching nuclear bomb densities) I think the losses would be too great to break even.

Just to add to the rambling length of this thread,: Concerning the difficulty of heating the plasma in a Tokamak, no doubt various factors apply, though I have generally considered that the difficult to match heat losses were due to the large surface area of the plasma leading to painful levels of black body radiation. Bremsstrulung radiation, cyclotron radiation, and bursts of hot plasma escaping through macro instabilities also contribute. Since increasing the Beta apparently disproportionately effects macroinstabilities, you are limited to how fast you can pump in hot plasma, which means you have to use smaller quantities of hotter plasma and use addition heating of the plasma in order to reach temperatures without overstuffing the system. The large volumes also means the current must also be large in order to reach the best balance. The Tokamack community have struggled mightily to reach the minimal 5,000 eV level, I don't know how confidant they are that they can reach the ~ target temperature of ~ 20,000 eV.

In this regard, Polywells , IEC in general, or your preferred colliding beam scheme have a tremendous advantage in this area. Tokamaks cannot reach temperatures where significant decreases in Coulomb collision corssections can approach within a few orders of magnitude of the fusion crossections, so this debate about modification of thermalization times, scattering loss magnitudes, significance of restoring forces (like annealing) are nearly irrelevant or even anathema to them. This doesn't mean your scheme (or the Polywell) would work, but it does mean that you have to look at the competing elements in detain to form a valid judgement. Blanket statements that Coulomb collisions are millions of times more prevalent than fusion collisions is inappropriate as this only applies to temperatures anticipated for the rather feeble (in terms of the average particle energies) Tokamak systems.


Dan Tibbets

[Joseph Chikva]

If your ion beans need to maintain less than say 5 degrees of dispersion before the beam density falls below tolerable levels

“My” ion beams will recover particles deflecting at any angle including 90 deg.
Ions will return back to the axis immediately after each scattering event ideally with no losses of energy. But in real they will pass some (little part) of that acquiring radial momentums to electron gas (fraction) and so thermalizing that. But thanks to magnetic attraction of unidirectional currents most of radial momentum again converts to axial.

If you are comparing my Concept with Polywell, my Concept is more monoenergetic and suffers less thermalization. As in Polywell "angular" momentum and corresponding KE aquiring as result of scattering event directly participates in thermalization. In my case only little part of radial momentum participates and most part returns to right direction. So, at given number density and collision energy we will have less energy losses per each scattering event than in Polywell and consequently lower thermalization intensity.

Number density in cyclic design is easily achievable to up to 10^23-10^24 /m3 and for given relativistic factors of electrons and ions' coherent motion velocities depends only on electron and ion currents' ratio.
And unlike Polywell those densities are achievable without very strong 10Tesla magnets.
Unlike my concept 10^22 density for Polywell causes a big doubt. As Polywell as such is an ordinary magnetic trap with declaring and not real monoenergetism.