The attached paper contains equations/coefficients for the angular and energy distributions of neutrons generated from deuterons incident on a thin target, in the laboratory frame. The data are plotted below. I'm unable to locate the original source of these data: G.J. Csikai, CRC handbook of fast neutron generators, 1987.
https://doi.org/10.1088/17480221/16/10/p10001
DD Fusion Anisotropy Coefficients
 Liam David
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DD Fusion Anisotropy Coefficients
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 MCNP Dose evaluation around DD and DT neutron generators and shielding design.pdf
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Re: DD Fusion Anisotropy Coefficients
Liam, thanks. Interesting.
It took me a few minutes to understand what I think you have given us. Here is a basic description of things I didn't grock immediately. Hope I didn't get this wrong.
The first link is the source of the paper and you already attached the pdf version in the post.
The paper includes two equations for simulating the results. The first gives a relative neutron count at theta. The second gives neutron energy. Each formula has a table of coefficents that are provided for 4 different beam energy levels.
You ran these two equations for the DD case and generated the two angular plots in your message.
I presume the equations were derived by curve fitting the data from actual measurements. That actual data is what you say you haven't been able to find.
Two additional notes:
1) From a simple apparatus diagram in the paper, the beam direction is from 180 toward 0 on the angle scale.
2) The neutron count levels are not absolute, they are scaled relative to the value at 90 deg. Note that in the first plot all the values are 1 at 90 deg. The other values are relative to this.
Let me know if I got any of this wrong.
It took me a few minutes to understand what I think you have given us. Here is a basic description of things I didn't grock immediately. Hope I didn't get this wrong.
The first link is the source of the paper and you already attached the pdf version in the post.
The paper includes two equations for simulating the results. The first gives a relative neutron count at theta. The second gives neutron energy. Each formula has a table of coefficents that are provided for 4 different beam energy levels.
You ran these two equations for the DD case and generated the two angular plots in your message.
I presume the equations were derived by curve fitting the data from actual measurements. That actual data is what you say you haven't been able to find.
Two additional notes:
1) From a simple apparatus diagram in the paper, the beam direction is from 180 toward 0 on the angle scale.
2) The neutron count levels are not absolute, they are scaled relative to the value at 90 deg. Note that in the first plot all the values are 1 at 90 deg. The other values are relative to this.
Let me know if I got any of this wrong.
Rex Allers
 Liam David
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 Real name: Liam David
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Re: DD Fusion Anisotropy Coefficients
Rex, you're completely correct. Thanks for adding the alltooimportant details that I neglected. The beam comes in from the left, from 180 to 0, and the data have been normalized to the 90degree value. The energies and spatial distribution go handinhand in that the forward beam of neutrons will also have higher energies.
These distributions are for a beam impinging on a stationary, thin target, i.e. the region of neutron formation has zero thickness (order of 15um usually). The deuterons quickly lose energy due to the target, and you thus get fusions at energies lower than the incident beam and distributed by depth. I believe the energy range (not the depth) is what leads to the higherorder terms than (cos(theta))^2.
If you have no energy loss, the neutron distribution would be purely a (cos(theta))^2 distribution due to spinorbit coupling (due itself to the deuteron centerofmass and centerofcharge offset) which gives rise to pwave scattering (see https://ir.library.ontariotechu.ca/bits ... sequence=3 and https://link.springer.com/chapter/10.10 ... 458781_6). For those curious, this is because in scattering theory, d(sigma)/d(Omega) = f^2, where the pwave term of f is f ~ P_1(cos(theta)). Here sigma is the crosssection, Omega is the solid angle, and P_1 is the 1st Legendre polynomial P_1(x) = 2x1. The cosine argument gets squared, which is where the distribution arises. Integrate the neutron emission for each "slice" of the target, taking into account the highly nonlinear stopping power of ions in matter (Bragg peak) and I think you'd get the coefficients in that paper. The fact that the A2 terms in table 2 are the largest in magnitude for their rows supports this idea. There's a chance I'm wrong, but it seems to be a pretty solid explanation.
I suspect these measurements were made using a D+ beam on a preloaded titanium or zirconium target. The beam spot size was likely on the order of a few mm to cm, as is the case for most such systems since it helps distribute the heat load and reduce target sputtering. I do not know if these data reflect that finite size, or if they have been altered to represent a point source. My guess is that the measurements were all performed in the farfield, and hence the finite size makes no difference.
A fusor does have areas that behave like thin targets, such as the cathode and endcaps. Beambackground gas fusion is technically not a thin target as the range of D+ and D2+ in D2 gas is on the order of cm, but like with the thin target, one could theoretically integrate the distribution along the appropriate paths to generate the distribution. This would be very complex, as it would require you to have an idea of the spatiallyvarying ion energy distribution.
These distributions are for a beam impinging on a stationary, thin target, i.e. the region of neutron formation has zero thickness (order of 15um usually). The deuterons quickly lose energy due to the target, and you thus get fusions at energies lower than the incident beam and distributed by depth. I believe the energy range (not the depth) is what leads to the higherorder terms than (cos(theta))^2.
If you have no energy loss, the neutron distribution would be purely a (cos(theta))^2 distribution due to spinorbit coupling (due itself to the deuteron centerofmass and centerofcharge offset) which gives rise to pwave scattering (see https://ir.library.ontariotechu.ca/bits ... sequence=3 and https://link.springer.com/chapter/10.10 ... 458781_6). For those curious, this is because in scattering theory, d(sigma)/d(Omega) = f^2, where the pwave term of f is f ~ P_1(cos(theta)). Here sigma is the crosssection, Omega is the solid angle, and P_1 is the 1st Legendre polynomial P_1(x) = 2x1. The cosine argument gets squared, which is where the distribution arises. Integrate the neutron emission for each "slice" of the target, taking into account the highly nonlinear stopping power of ions in matter (Bragg peak) and I think you'd get the coefficients in that paper. The fact that the A2 terms in table 2 are the largest in magnitude for their rows supports this idea. There's a chance I'm wrong, but it seems to be a pretty solid explanation.
I suspect these measurements were made using a D+ beam on a preloaded titanium or zirconium target. The beam spot size was likely on the order of a few mm to cm, as is the case for most such systems since it helps distribute the heat load and reduce target sputtering. I do not know if these data reflect that finite size, or if they have been altered to represent a point source. My guess is that the measurements were all performed in the farfield, and hence the finite size makes no difference.
A fusor does have areas that behave like thin targets, such as the cathode and endcaps. Beambackground gas fusion is technically not a thin target as the range of D+ and D2+ in D2 gas is on the order of cm, but like with the thin target, one could theoretically integrate the distribution along the appropriate paths to generate the distribution. This would be very complex, as it would require you to have an idea of the spatiallyvarying ion energy distribution.
 Richard Hull
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Re: DD Fusion Anisotropy Coefficients
I enjoyed the paper on neutron tube dose. I note that even with no shielding the DD fusion neutron dosage is intrinsically zero at 50kev energies (fusor type operation which is far less efficient and far more isotropic.) It is important to note that all the tables at the end are computed for a B.O.T. tube operated at 200kev and the doses are still not frightening for DD in short exposures at 2 meters. Of course, we all knew this.
A technician forced to operate such a system in a work related environment would need all the shielding he could get.
As systems made in these forums get smaller, with pressures and voltages higher, Xrays remain the #1 issue. Neutrons will always be secondary at normal operational distances up to 100kev. I doubt we will see a lot of operation at this level here.
Thanks for the refs. and paper.
Richard Hull
A technician forced to operate such a system in a work related environment would need all the shielding he could get.
As systems made in these forums get smaller, with pressures and voltages higher, Xrays remain the #1 issue. Neutrons will always be secondary at normal operational distances up to 100kev. I doubt we will see a lot of operation at this level here.
Thanks for the refs. and paper.
Richard Hull
Progress may have been a good thing once, but it just went on too long.  Yogi Berra
Fusion is the energy of the future....and it always will be
Retired now...Doing only what I want and not what I should...every day is a saturday.
Fusion is the energy of the future....and it always will be
Retired now...Doing only what I want and not what I should...every day is a saturday.

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Re: DD Fusion Anisotropy Coefficients
Liam, you may be interested in the Los Alamos report LAMS2162 "DD and DT Neutron Source Handbook", Seagrave et al., 1957. Like you mentioned, this is primarily of relevance only for beamontarget work.
https://permalink.lanl.gov/object/tr?wh ... t/LA02162
I have a halfdozen or so references on this as it was relevant to my previous job, if that is of interest I can dig it out of the archives for you. Most of it is older material referenced in the above report, but I believe there were a few newer papers as well.
https://permalink.lanl.gov/object/tr?wh ... t/LA02162
I have a halfdozen or so references on this as it was relevant to my previous job, if that is of interest I can dig it out of the archives for you. Most of it is older material referenced in the above report, but I believe there were a few newer papers as well.
 Liam David
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 Joined: Sat Jan 25, 2014 5:30 pm
 Real name: Liam David
 Location: Arizona
Re: DD Fusion Anisotropy Coefficients
Thanks for the link, Chris. I haven't seen this report before, although I vaguely remember seeing it referenced in other works. I'm definitely interested in whatever else you've got. I've done a lot of searching for papers/reports like this, but especially the older stuff can be really hard to find.

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Re: DD Fusion Anisotropy Coefficients
Sure thing. Archive has been mined, here are the papers.
 Attachments

 1987 Krauss Angular DD.pdf
 (1.45 MiB) Downloaded 49 times

 1966 Theus Angular DD.pdf
 (785.02 KiB) Downloaded 44 times

 1957 Fuller Angular DD.pdf
 (246.45 KiB) Downloaded 41 times

 1955 Chagnon Angular DD.pdf
 (488.44 KiB) Downloaded 41 times

 1954 Preston Angular DD.pdf
 (1.53 MiB) Downloaded 43 times

 1952 Baker Angular DD.pdf
 (200.35 KiB) Downloaded 41 times

 1949 Hunter thesis Angular DD.pdf
 (3 MiB) Downloaded 40 times

 1949 Hunter Angular DD.pdf
 (479.89 KiB) Downloaded 42 times