Another (simple) FAQ - DONE

[KitemanSA]

Here is a fairly simple question. Any takers?

What ion energy is best for deuterium fusion, tritium deuterium fusion, or proton boron 11 fusion?

[WizWom]

http://en.wikipedia.org/wiki/Nuclear_fusion has the pretty table of fusion temperatures:

fuel T [keV] <σv>/T² [m³/s/keV²]
D-T 13.6 1.24×10−24
p-B 123 3.01×10−27

The Temperature IS is the Ion energy. Same thing.

[chrismb]

'fraid you misread that Wizwom. These are the values for the Lawson triple-product criterion for the different reactions in a thermal plasma.

The answer is, roughly, the peak cross-sections. It's not quite the peak cross-sections because as you slide off the peak so you get an increase in velocity quicker than you get a decrease in cross-section (remember, reaction rate is [cross-section].[velocity].[density]), so it is just slightly higher than the peaks, but to all intent and purpose, the peak ion energy for optimum fusion is the peak cross-section.

That being said, this is an answer based on the presumption of either like-nucleii, or a beam-target arrangement for 1+ ions. In theory [and it *really is theory*] the peak driving energy for a H1+ ion and a B5+ ion is some other value I have calculated somewhere in this forum, but forget now as it is essentially irrelevant. Much as you might like to think there will be piles of B5+ ions running around, there won't be 'cos there's lots of electrons and you'll get a distribution of B1+, B2+, etc.. and as such the drive potential to reach peak will depend on that distribution, which cannot be known prior to an actual experimental set-up showing what that distribution is.

I would say that you should bank on 1+ ions, and as such you can pick the peak cross-section and be pretty pleased/confident with that answer.

[D Tibbets]

There is no simple answer. As Chrismb said, there are a lot of variables. Also, it depends on your target. If maximum Q is desired the peak may not be the ideal target. The max Q was ~ [EDIT]15 KeV for D-D in a computer simulation done last year. This was where the fusion crossection curve was steepest. If fusion power is a priority, then higher energies (up to the peak of the curve) are desired. Add other considerations such as non linear losses like bremsstrulung, cost to maintain greater gradients, variations in thermalization times and the picture becomes much more foggy, and there are a lot of options that can hopefully be adjusted to get the best compromise performance.

Also, temperature is a value that does not describe much other than the average kinetic energy of a material. There will be a substantial spread in energies (Maxwell- Boltzman distribution), if the gas/ plasma is thermalized. In Tokamacs the temperature might be [EDIT] 5 KeV, but the majority of fusions will be occuring at the thermal tail of the highest energy ions (perhaps at 15-30,000 KeV). That is why 'monoenergetic' ion populations have such an advantage. All of them are near the ideal energy for fusion. You are not wasting all that energy to maintain most of the ions at less useful lower (but still very hot) energies. Add to that the penalty these lower temperature ions contribute in other ways. Well, why not just raise the average temperature higher? Because it costs more energy, and now the higher energy tail contributes much worse penalties in terms of losses. I don't think that there is disagreement about the advantages of 'monoenergetic' ion populations, or even the ability to produce them. The ability to maintain those ions at the desired energy without intolerable thermalization or intolerable energy costs over the necessary time frames is the bone of contention.

Having said that, I think for a thermalized plasma like in a Tokamac the ideal (or at least reasonable) average temperature is ~ [EDIT] 5 KeV . The Tokamac will have difficulty in reaching even this this level. That is one reason nobody expects it to work with fuels other than deuterium- tritium. The smaller gain and required energies of other fuels precludes the chance for thermalized systems breaking even. Other systems that might work with advanced fuels (like D-D, D-He3, P-B11, etc.) would presumably work exceedingly well with D-T. But there are so many disadvantages with this fuel that it would be a last resort option (except for the Tokamac where it is the only option).
.

From my reading I would hazard a guess that the optimal monoenergetic temperature for the various fuels would ~ be:

[edited to correct units]
D-T 30 KeV
D-D 80 KeV
D-He3 100 KeV
P-B11 200 KeV.

There could be considerable changes to these numbers depending on whether the system is essentially beam-target or beam- beam in nature.


Dan Tibbets

[KitemanSA]

From my reading I would hazard a guess that the optimal monoenergetic temperature for the various fuels would ~ be:
D-T 30,000 KeV
D-D 80,000 KeV
D-He3 100,000 KeV
P-B11 200,000 KeV.

Did you REALLY mean 30MeV for D-T, or was that an example of changing units in mid-type?

Also, would you please edit your posting above into a "quote" block as a FAQ answer? You seem to have a handle on this. That way I can cut and paste without messing things up.

Thanks!

[D Tibbets]

There is no simple answer as there are a lot of variables. Also, it depends on priorities. If maximum Q is desired the peak may not be the ideal target. The max Q was ~ 15 KeV for D-D in a computer simulation done last year. This was where the fusion crossection curve was steepest. If fusion power is a priority, then higher energies (up to the peak of the crossection curve) are desired. Add other considerations such as non linear losses like bremsstrulung, cost to maintain greater gradients, variations in thermalization times and the picture becomes much more foggy. There are a lot of options that can hopefully be adjusted to get the best compromise performance.

Also, temperature is a value that does not describe much other than the average kinetic energy of a material. There will be a substantial spread in energies (Maxwell- Boltzman distribution)if a gas/ plasma is thermalized. In Tokamacs the average temperature might be 5 KeV, but the majority of fusions will be occurring at the thermal tail of the highest energy ions (perhaps at 15-30 KeV). That is why 'monoenergetic' ion populations have such an advantage. All of them are near the selected ideal energy for fusion. You are not wasting energy to maintain most of the ions at lower and less useful (but still very hot) energies. Add to that the penalty these lower temperature ions contribute in other ways. You might ask- why not just raise the average temperature higher? Because it costs more energy, and now the higher energy tail contributes much worse penalties in terms of losses. There isn't disagreement about the advantages of 'monoenergetic' ion populations, or even the ability to produce them in a Polywell type reactor. The ability to maintain those ions at the desired energy without intolerable thermalization or intolerable energy input costs over the necessary time frames is the bone of contention.

Having said that, for a thermalized plasma like in a Tokamac the ideal (or at least reasonable) average temperature is ~ 5 KeV. The Tokamac will have difficulty in reaching even this this level. That is one reason nobody expects it to work with fuels other than deuterium- tritium. The smaller gain and required energies of other fuels precludes the chance for thermalized systems breaking even. Other systems that might work with advanced fuels (like D-D, D-He3, P-B11) would presumably work exceedingly well with D-T. But there are so many disadvantages with this fuel that it would be a last resort option (except for the Tokamac where it is the only option).


A ball park estimate for the optimal monoenergetic temperature for the various fuels would be:
D-T 20-30 KeV
D-D 80-100 KeV
D-He3 100-120 KeV
P-B11 200-400 KeV.

There could be considerable changes to these numbers depending on whether the systems' fusion collisions are primarily beam-target or beam- beam in nature.

[WizWom]

So, essentially you are saying somehow these ions are not fully ionizing, despite having so much energy that they are way above the full ionization temperature?

Dr. Bussard though differently, assuming that the ions would be fully ionized within 1 cm or so (per his paper on scale-up).

[D Tibbets]

So, essentially you are saying somehow these ions are not fully ionizing, despite having so much energy that they are way above the full ionization temperature?

Dr. Bussard though differently, assuming that the ions would be fully ionized within 1 cm or so (per his paper on scale-up).

I'm not sure what your asking in relation to what I posted above.
My assumptions are that ~ 99.9% or more of the fuel is ionized. This would be the minimum possible if you are to maintain a 1000 X Wiffleball trapping factor and arcing limits discussed in several papers. I don't know if Boron with a Z of 5 might tend to hang onto an electron occasionally. Considering the higher temperature of the P-B11 plasma, I doubt it.
The numbers are a compilation of my impressions from various statements by Bussard and others, combined with an arbitrary target energy where the crossection curves are nearing their peak, but still have significant steepness to the fusion crossection curves (the D-T value I used may be a little hotter than it needs to be). Again, these are values assuming non Maxwellian conditions.

I admit to some confusion about the boron with a Z of 5. A potential well of 100,000 Volts would give it as much energy as 500,000 Volts would give to protons. Add to that the desired beam- beam conditions, and the actual potential well needed to accelerate a mixture of ~ 8-10 protons per one boron ion to a effective beam - beam kinetic energy of 200 KeV might be in the neighborhood of ~40,000 volts(?). If you allow the boron to have 200KeV and the protons to have a corresponding 40 KeV (beam beam collisions would be at a net 240KeV. The voltage needed to do this would be ~ 40,000 volts. This ignores any thermalizing collisions. This effect of Z on the energy gained by an ion in an electrical field is one of the considerations used in determining the mixture (P-B11) and compromise voltage that is used to minimize bremsstrulung (along with considerations about the electron energy in various parts of the machine (hopefully cold near the center).

Dan Tibbets

[KitemanSA]

FYI
Peak of XSect graph vs CoM energy in keV:

Code: Select all

            Peak               45 Slope         -45 Slope
DT    ~   63                     50                 78
D3He  ~  245                    205                300
p11B  ~  560  (130)             555                560 (10,000+)
DD    ~ 1150                     83             10,000+

[D Tibbets]

FYI
Peak of XSect graph vs CoM energy in keV:

Code: Select all

DT    ~   63
D3He  ~  245
p11B  ~  560  (130)
DD    ~ 1150

Thanks, it is nice to have some actual numbers rather than eyeballing a small graph.

If the slope is still positive, but the slope is less than +45 degrees on a graph with linear scales (difficult to determine with a logarithmic scale) then the fusion yield (crossection) will still be increasing, but the input energy is increasing faster. Add to this other losses like bremsstrulung and some drive energy well below the peak will probably offer the greatest effective gain/ power advantage.


Dan Tibbets

[KitemanSA]

Won't the location of a 45 degree slope on a rectilinear plot be at the same location with a 45 degree slope (OOM to OOM) on a log-log plot?

[D Tibbets]

Won't the location of a 45 degree slope on a rectilinear plot be at the same location with a 45 degree slope (OOM to OOM) on a log-log plot?

Well, yes, I guess so, provided the log scales are the same on each axis.
Using the graph from the Wiipedia page:

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

The graph covers 6 orders of magnitude on the vertical axis, and 3 orders of magnitude on the horizontal axis- not the same logrithmic scales on both axis. Some head scratching could allow a correction, but I don't know my trigonometry well enough to be certain. Would the slope have to be +30 degrees degrees in this example?

Dan Tibbets

[KitemanSA]

AFAIK, a line from one crossing "Order of Magnitude" (say 10E-27,10E2) to the next (10E-26, 10E3) is the "45 degree" slope for the log-log. No?

[D Tibbets]

AFAIK, a line from one crossing "Order of Magnitude" (say 10E-27,10E2) to the next (10E-26, 10E3) is the "45 degree" slope for the log-log. No?

In a sense, if you are willing to look at the scales, get out your ruler and actually read off the numbers, where the crossection goes up at the same rate as temperature, then that would be 45 degrees of slope if you translated it to symmetrical scales (linear or logarithmic). but that requires work.

Dan Tibbets