D+D Cross section?

[Steven Sesselmann]

Richard speaks obout fusion reaction cross section charts in his FAQ post. I
tried searching for charts, but was unable to find any.

Would any of you have charts or formula's for the most common fusion
reactions, that you could post here?

I am interested in finding the maximum cross section for these reactions.

Steven

[Carl Willis]

Steven,

I use the CSISRS database (used to be EXFOR) at the National Nuclear Data Center (nndc.bnl.gov). Cross-sections for most of the common reactions can be plotted right off the Web. Some data has to be downloaded and imported into a little tool called XVview or something like that, also freely available, in order to get a plot.

-Carl

[Steven Sesselmann]

Carl,

I looked at the web site that you recommended, and it has a vast amount of information, some of which I do not have enough knowledge yet to understand.

I downloaded some pdf charts showing various cross sections for DD - DT - TT etc., but I dont think I am reading them properly.

What I specifically am interested in knowing, is at how many ev one reaches the maximum cross section for...

D+D

D+T

D+HE3

Would anyone happen to know this?

Steven

[Edward Miller]

I'm also interested in this data. Both for ionized and non-ionized D atoms.

[Steven Sesselmann]

Attrached are some charts I downloaded from a website..

Would someone here in the group be able to pass some comment on what they mean?

PS: I should give credit to the person who created this file, but I can't find my way back to the site. Sorry!

Steven

[Raymond Jimenez]

There are multiple formulas and tables available in the NRL Plasma Formulary (http://wwwppd.nrl.navy.mil/nrlformulary/), on pages 43-44.

[Alex Aitken]

The maximum cross section does not corrispond to the maximum power output, or the maximum reaction rate, so on their own, I'm not convinced they help much.

DT fusion cross section peaks about 100kev deuteron energy. DD peaks about 2 Mev.

Carl,
When I search for H-2 d,* in ENDF the only results are d,inl and d,p. What gives, is it censored now? I get better results from a Japanese site.

[Carl Willis]

I can't really comment fully on everything in these graphs with the time I have now, Steven, but here's a starter:

Elastic cross-section: the rate at which the nuclei just bounce off one another in an elastic collision and do not "react." Obviously it's very much higher than any other nuclear reaction cross-section. This is due to coulomb repulsion. Real reactions involve a tunneling process to overcome the coulomb barrier, so the probability is much lower.

The heating cross-section is mainly relevant where one wants to figure out the locally deposited energy in some medium: dosage. Or, in extreme cases, how much of a heat-removal problem you will have on a target.

There are some other charts in there that show angular cross-section data for threshold (i.e. endothermic) reactions that are not accessible at energies found in fusors, and some charts that break down the heating cross-section into contributions from various energetic product particles. Such data might only conceivably apply to high-power fusion research devices and to H-bomb designers.

The only of these graphs that would be potentially useful for you really is the first heating cross-section, showing low-energy heating up to 10 MeV. The shape of the curve will largely track that of the D(d,n) + D(d,p) fusion reactions which predominate at these energies. You can in principle use the graph to figure out how much total fusion power you expect to produce with your fusor as a function of accelerating voltage, although in practice this calculation is complicated.

-Carl

[Carl Willis]

Marvin,

ENDF is principally a library of neutron reaction data. D(d,n) is probably not there, although the people using codes that come with this library like MCNP and MCNPX would probably put a high priority on getting some of the light fusion reactions. Use EXFOR (now called CSISRS).

-Carl

[Steven Sesselmann]

Carl,

So if I understand you correctly, the chart is saying that there is almost a linear ralationship between fusor voltage and fusion reaction, if one ignores the amps.

Steven

[Carl Willis]

(1). Go to www.nndc.bnl.gov (national nuclear data center website).
(2). Click on Nuclear Reaction Databases, then CSISRS
(3). Enter "H-2" as the target, "D,N" as the reaction, "CS" as the quantity, and the energy range of interest. Hit submit.
(4). Look through the list for interesting data (consider energy range, number of data points, and date). Select the box next to the data set(s) of interest. At the top of the screen you will have the option of getting a GIF plot. EXFOR format will give you a table of data. Not every data set has a GIF. If it doesn't have a GIF and you want one, you have to download the EXFOR table and import it into ZVView, which you also must download.

See attached (from CSISRS, the D(d,n) cross section between 10 keV and 150 keV, one set of recent data). I plotted it on linear scales. If you say that part of this cross-section relationship is linear with respect to energy, you have to be specific about which part, because on the whole it has numerous ups and downs (resonances). In the range of 10 keV - 50 keV, it has upward monotonicity and is probably better fit by an exponential. Above that, indeed it does look pretty linear for a while.

Now how meaningful is this data? It does not tell you what your reaction rate will be in a practical device, it only tells you what the reaction rate will be between monoenergetic reactant particles and stationary non-ionized target particles and presumes that the target is thin (does not consider reactions that occur after scattering). In a Hirsch fusor device, one would expect a continuum of deuteron energies ranging from 0 eV up to the full energy of the field. You will also have D2+ present in significant fractions. You will have charged-charged collisions and charged-neutral collisions. You have a thick target where a lot of Coulomb scattering is going on. The cross-section does tell you that more voltage is good and suggests that better efficiency can be expected for a given power input if you raise the voltage rather than the current. In no way does it give you a reaction rate quantity that would be expected to be anywhere near an accurate reflection of the reality.

This cross-section data would help give a highly realistic calculation of rate if it were used in a Monte-Carlo simulation that accounts for the factors described above. Another approach would be to invoke heavy math that has a 99% chance of just causing your head to repeatedly slam into a brick wall and hence is discouraged.

-Carl

[Todd Massure]

Here is a curve showing plasma energy required vs. containment time for thermonuclear reactions. Note that this is coming from the angle of confining a bulk of plasma at a high temp for a certain time (Lawson Criterion) like in a stellerator etc. which is not what a collider reactor like a fusor does, but I think that a power producing fusor or other type of collider reactor would have to meet the Lawson Criterion in it's own way.
The left side is the density, or number of ions contained in a given volume per unit time.
Above the curve you are in power production territory.
Also note that there is a sweet spot (bottom of the curve) where at a certain energy less containment time and density are needed. In other words reaction rates drop off when energy levels are higher or lower than at the bottom of the curves. I had previously thought that the fusor had the same sweet spot of energies between 50 - 100 keV, but it sounds like it's actually much higher.
I'll be interested to hear if others think that this has much bearing on what we are doing.

Todd Massure

[Steven Sesselmann]

Carl,

Thanks for the detailed instructions...I needed every bit of it.

The data was very helpful, and it looks good, roughly speaking, the cross section goes up with the voltage, which is good, as I am working on a new design that will draw very little amps, so I will be able to go past 100KV.

Thanks again...

Steven

[Steven Sesselmann]

Raymond,

There were lots of useful formula in your attachment. I plotted some of the data found on page 44.

The reaction rates for the various reactions differ significantly, however if a fusion reactor was cooking away for long enough, one could expect that there would be a whole lot of reactions happening ,so I included a line for the average rate. (Yes Richard I realize that this would take an awful long time with a table top Fusor).

See attached image...

Steven

[George Schmermund]

I thought I'd make an offering here in order to add to the confusion. The source is 'Accelerator Nuclear Physics' published by High Voltage Engineering Corp. (1970). The subtitle is Fundamental Experiments With A Van De Graaff Accelerator. Applying a little bit of imagination one might see the D+D curve in here.

[DaveC]

Neat, George.

Thanks for sharing that.

Dave Cooper