FAQ - D-D fusion - Energy - Flux - Dose

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Richard Hull
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FAQ - D-D fusion - Energy - Flux - Dose

Post by Richard Hull »

This effort will discuss only amateur deuterium-deuterium fusion. It will discuss energy releases, how to figure flux, discuss does rate versus equivalent dose.

All calculations will be carried out to only the nearest tenth part of any value.

Deuterium-Deuterium fusion data

Two reactions occur with about equal probability.
D + D = T (tritium 1.01 MeV) + P (3.02MeV)
D + D = 3He (.82 MeV) + n (2.45 MeV)

NOTE* There is a third reaction possible, but it only occurs once in every ~50,000 D-D fusions and that is D+D = 4He + gamma ray.....We will not even consider this reaction in any of our work due to its extreme rarity.

Thus D-D fusion is a mixed output of the above two major reactions such that the energy from D-D fusion (7.3 MeV) shakes out to the following fractions of the net ongoing reactions.
T – 13.8%
P - 41.4%
He3 – 11.2%
n – 33.6%

Figuring energy per particle or number of particles per unit energy

The neutron has an energy of 2.45 MeV
1 MeV of kinetic energy is equal to 1.6x10e-6 ergs
A D-D fusion neutron has 2.45 x 1.6 x 10e-6 = 3.9 x 10-6 ergs of energy
There are 10e7 ergs in a joule, thus, there are 10e7/3.9 x 10e-6 = 2.6 x 10e12 D-D neutrons required to represent 1 joule or 1 watt second of energy.
To obtain 1 watt/second of neutrons we must produce 3 watts of D-D fusion.
Countrawise,
1 watt of D-D fusion only contains 0.336 watts of neutrons or .336 x 2.6x10e12 = 8.7 x10e11 neutrons.

Figuring flux

All calculations are based on an assumed point source of fusion (never the case), in order to simplify calulations.
Only one bit of geometry is needed. The surface area of a sphere is A = 4 pi r^2

Flux is generally considered to be the number of particles, (in this case, neutrons), passing through an area of one square centimeter in one second.

Figure the neutron flux from a 1 watt output D-D fusion reaction at a range of 1 meter.

A sphere of 1 meter radius has an area of 4 x pi x 100^2 = 125,664 sq cm
There are 8.7 x10e11 neutron emitted from this reaction
The flux from this reaction at 1 meter would be 8.7 x 10e11 / 125,664 = 7 x10e6 n/sq cm/second.

The difference in dose rate versus total equivalent dose.

Human tissue differs in its absorption of neutrons based on their energy. A plot exists whereby over a span of different neutron energies one might find what flux will produce a given equivalent dose. All dose rates discussed here are once again for the 2.45 MeV D-D fusion neutron and will differ for neutrons of other energies.

Dose rate

Radiation dosage is quantified by the ‘rem’ or Roentgen Equivalent Man. Neutrons of varying energy have varying effects and a correction chart for tissue absorption of neutrons of varying energy shows that for D-D neutrons about 8.4 neutrons per square cm per second is equivalent to a dose rate of 1millirem/hour.

If a neutron rate meter shows a fusor is putting out a dose rate of 10mrem/hr. Then 84 neutrons are passing through each square cm, each second at the location of the detector probe.

Equivalent Dose

The total dose received over a given period of exposure is the dose rate multiplied by time on exposure. If we are at the probe location in the above example for a period of 8 minutes, we will have received a dose of (8/60) X 10 = 1.3 mrem of fast neutrons.

Another method of arriving at absorbed dose per second can be had when we know the flux at a given point. We suspect that we are receiving a high dose of radiation. We know the flux at our location is 10e5 neutrons per sq cm per sec. How much radiation are we receiving each second? (8.4 x 3600) = 30240 neutrons hitting a square cm to receive 1 mrem/second 10e5 / 3 x 10e4 = 3.3 mrem each second. While not deadly even over minutes of time, a wise man would move out to 10 meters and only receive 3.3/10^2 = 33 micro-rem/sec. A wiser man, still, would construct a simple paraffin-boron shield so that he could stay close to his work.

If we put in 400 watts to our D-D fusor and, by calculation, find we are producing 10e5 neutrons per second isotropic emission, what is the energy input to actual fusion energy output ratio? (This a realistic case of a successful but not optimally operated fusor - typical example)

We know, from above, that 1 watt of D-D fusion emits 8.7 x 10e11 neutrons isotropically each second. So, we are producing 10e5 / 8.7 x 10e11 = 0.1 microwatt of output energy due to neutrons which we have measured. However, This is only 33% of the total fusion energy. the actual total fusion energy emitted is 3.3 X .1 = .33 microwatt. From this total energy figure we arrive at the requested ratio of 400 / 3.3 x 10 e-7 or 1.2 x10e9
Restated we are putting in more than 1.2 billion times as much energy as we are getting out as fusion energy…Or, for each fusion watt output, we must supply to our fusor 1.2 billion watts of electricity.

We find that even the best fusors are still off by a factor of 200 million to one and the average fusor is in the billion to one range. (Nine orders of magnitude improvement to break-even and 11 orders of magnitude before fusion looks attractive as a power source.

So, we can see that by just using the neutron production as measured from a fusor, we can figure the entire fusion energy produced.

It can't be overemphasized that all the simple calcs above have made specific assumptions designed to make the understanding and order of magnitude calcs easy for the newbie or mathematically handicapped. Any step off the assumptions and the results are skewed and can quickly drift off into fantasy if tight results and data are demanded. Fortunately, in the amateur world, we are not called to task on minutia by overlords looking to hold our feet to the fire. Most are here for the effort and not precision. Still, good scientific investigation, amateur or professional, needs to understand the limits of its data collection accuracy and why those limits exist.

Remember that to work with the simplest of calculations, the number of parameters of an experiment must be limited in number and rigidly fixed and held fixed throughout the experiment. If more parameters are introduced which can change, the complexity of the calculations must increase tremendously to deal these new aspects of the procedure or experiment.

P.S. Thanks to many who helped me make such corrections as needed to all of the above with their comments listed in the posts below. All such corrections are now incorporated above as of 5/22/08.

Richard Hull
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Wilfried Heil »

Thank you for the compilation, I think it will be a helpful FAQ. Here are some cases for comparison:

-A-.
Standing next to a hypothetical 500 W DD fusion neutron source at 1 m distance, you would receive an incapacitating dose of 800 rem within 5-6 SECONDS. This will not kill you immediately, but surely.

Such exposures can and did happen in criticality accidents, e.g. in Tokaimura 1999. The operators noticed a blue flash and received doses between 800-2000 rem in seconds, while the total heat produced was quite small and the fission reaction quenched itself quickly, then restarted again periodically.

-B-.
If one assumes a DD fusion neutron source with just 1 W fusion power, that translates into 10^12 n/s emitted isotropically. The flux at 1 m will be 8x10^6 n/s/cm^2.

1 mrem corresponds to about 30'000 n/cm^2 for 2.45 MeV DD fast neutrons, over an arbitrary time.

Thus with 1W fusion power you will receive 0.3 rem/s at 1 m distance. This exposure would be survivable, if you noticed quickly enough - within minutes - what is happening.

-C-.
Considering the homeopathic fusion rates in todays amateur fusors, even the high powered ones, we can expect a neutron production rate of 1-3x10^6 n/s TIER (total isotropic emission rate) at input power levels of 1KW. A million neutrons per second TIER means 8 n/s/cm^2 at 1 m distance from the fusor's center. This would give the operator or innocent bystanders a dose rate of slightly less than 1 mrem/h. In reality the accumulated dose will be much less, because the fusor is operated for only a few minutes at full power.

In practically all cases, the exposure by x-ray emissions would be several times higher than the neutron dose. Fortunately, these x-rays can be easily shielded.
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Carl Willis »

Hi Richard,

Thanks for the straightforward FAQ on this topic.

If I were to add anything, it might be to simply emphasize to readers (these assumptions are already explained, but I know some people will neglect them!) that the 8.4 n / cm^2 / sec / mrem / hr is specific to ~2.5 MeV monoenergetic neutrons, and the flux- and dose-at-a-distance calculations assume an isotropic distribution of products particles. Deviations from the assumptions mean those simplifications no longer apply.

Also a minor semantics correction: what you've labeled the "absorbed dose" should be called the "equivalent dose" (absorbed dose is measured in rads or Gray).

-Carl
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Richard Hull »

Thanks to Carl and Wilifried. All corrections are now included. The proper terminology is important for us all.

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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Steven Sesselmann »

Richard,

Thanks for another informative FAQ, which will be very useful for the many newbies that have joined lately.

Although I agree with your calculations, I hope you don't mind if I pick on the semantics a bit.

Reading your post it comes across to me, that Q (input vs. output energy) depends on the neutron energy only. If this were the case then 66% of the D+D reaction energy would disappear into nowhere.

One must of course consider the full 7.3 Mev per two fusions, when calculating efficiency.

It makes the figures look just a little less depressing..

Steven
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Richard Hull »

Thanks for the correction. I refigured to the total fusion energy, which was the actual question posed. This was an important correction. Thanks.

I personally fail to see how one is at all bouyed by the 3X correction. as the 9 order magnitude remains to breakeven and 11 order to electrical grid attraction. 3 times nothing is just a bit more of nothing.

I have acknowledged the corrections and added a date of the corrected FAQ

Richard Hull
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Wilfried Heil »

A few more words on the dose definition might be in order. This can be a tricky matter, also due to the number of historical radiation units, which adds to the confusion.

"Absorbed dose" here is the amount of energy deposited in matter by ionizing radiation. (1Gy=1J/kg)
"Equivalent dose" is the absorbed dose multiplied by a quality factor to reflect the biological effect, depending on the type of radiation. Fast neutrons are the most damaging of all.

dose rate = dose per time unit (e.g. Gy/h)
dose = dose rate x time (e.g. Gy)
equivalent dose = dose x quality factor Q, depending upon radiation. (e.g Sv, mrem)

So we can compare absorbed dose rate and equivalent dose rate, but not vs. equivalent dose.
That's like comparing speed to distance.

For fast neutrons of 2.45 MeV, Q is somewhere between 10 and 20.

The actual biological effectiveness is smaller and difficult to measure. Q is defined for radiation protection purposes, so it is exaggerated on the safe side.
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Richard Hull »

I, not being a professional member of the physics community nor writing professional papers for publication within it, do hereby refuse to use SI units. I was born and raised a CGS guy and so I will perish as one.

I hated MKS, but have found a particularly acute loathing deep within myself for SI. There is but one SI unit that I will speak in, if forced, and that is the very reasonable, Becquerel. How such a tiny, logical and reasonable unit made the SI cut I can't imagine. Some one asleep at the switch, I guess.

My beef is one of scale and seemingly constant and needless revisionism. We work in a laboratory of sorts, both pros and amateurs. Such facilities are people sized and project components within them mostly are of the order of the human hand as a median size. Really tiny experiments can go to atoms and large stuff we can handle or guide and control go to many meters in size.

CGS covers the median, laboratory sized stuff.

MKS was designed for some sort of great out of doors laboratory. (falling safes and pianos, lobing artillary shells and designing rockets.

SI seems to look at a unit magnetic field greater than most any permenant magnet air gap can achieve and other larger than lab or even life units. Admittedly, a number of the old MKS stuff moved over, some with the names changed to confuse the innocent.

I realize that, slowly with each old fossils death, SI will become the norm...................Or will it?.......Will Phd. Carl Willis be forced, at 57, to adapt to the OUS (Otovian Units System)?!!

Don't chuckle too hard. In college I had to deal with one physics class that still talked english in poundals and slugs and then hit a Chemistry and Electrical math class that spoke only in CGS. While picking up additional classes later at the Univesity of Florida in the late 60's, it was all MKS. Now it is SI. Welcome to a world where your units are like the shifting sands and light bulbs forever seem to go off in the heads of the annointed that wind up keeping the confusion gas jet turned up full blast.

I understand your points but will not include the SI units in my posting. Folks that chose to handle the finer points of radiation physics in SI need to get a modern textbook and study it. This effort was a quick rinse for newbs looking for easy speak.

I mentioned in the post above that the neutron flux selected came from a neutron energy flux to tissue dose conversion plot to create a rem value for a specific flux at a specific energy. I have already spoken to the biological effectiveness rating multipliers in a previous radiation FAQ.

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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Chris Bradley »

I do tend to agree - I like to use centimetres, but then usually confuse myself throughly by combining it with kg!!!

Depends on the exercise, I guess. I always used to build virtual computer RF models using units of imperial feet. The reason; the speed of light = 1 foot/ns (near enough). Very convenient!
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Chris Bradley »

Good point on X-rays. Could/should this FAQ also cover X-ray emissions? When most likely, dose, most appropriate protection for a given dose (and/or best value? - lead's getting pricey these days!), etc..

best regards,

Chris MB.
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Wilfried Heil »

The field of radiation measurement has been particularly beaten by multiple definitions and redefinitions of the same units. This can make it difficult for someone just getting started in this area. The particular system is not important, but one has to know which is which - a dose, a rate or an equivalent dose and so on.

You will notice that I'm only using the units "mrem" and for pressures "mbar" here, for consistency and because I don't find most of the SI units well adapted for our purposes. I grew up with pressures in bar, activities in Curie and cars with horsepower "HP" or rather "PS".

If someone should come to the point where we measure exposures in Sievert he'll be in trouble anyway.

One Pascal for pressure would fit nicely (run the fusor at about 1 Pa = 10E-3 mbar and it'll be in the operating range) but this is still a rather odd unit for the weather forecast. Who on earth would measure pressures in Pascal? An ant maybe, or a plasma physicist.
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Richard Hull »

This discussion is drifting and needs a new thread if what you have to say is not directly related to the above titled posted FAQ.

The efficiency part of my original posting was posed as an exercise, a mathematical problem to solve and not a lead in to a discussion.

Thanks all.

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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Carl Willis »

Chris,

A search on "shielding" or "x-rays" in the Radiation Detection and Measurement forum is likely to provide the answers you seek.

-Carl
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Re: tritium dose.

Post by Frank Sanns »

I don't think you have to worry about T in any of our fusors or even one producing 10E10 n/s for two reasons.

First, 10E10 sounds like a huge quantity but when you consider 3 grams of T is 6e23 atoms, then that is only 3E-13 atoms of T/sec. One curie of T is around 2e19 atoms so 10E10n/second translates to tens of microcuries/sec. This is not trivial but it is not a raging quantity and it assumed 10E10 n/sec and nobody here is within 3 orders of magnitude of that.

Secondly, T will not stick around. It is light and at RT it will have a velocity that will keep it escaping every but a sealed vessle. The reason there is no H or Helium on the earth is because it will reach escape velocity just from themal surroundings and it will be lost to space.

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Re: tritium dose.

Post by Steven Sesselmann »

Chris,

I am with Frank on this one, Tritium is a hydrogen gas and will quickly float up to your ceiling and escape.

A much more serious helth hazard are the oil vapors from the roughing pump, wich typically runs all day when you are in your lab. I have solved this problem by connecting a plastic hose to the pump exhaust, and feeding it out through a hole in the wall, incidentally this would solve the trituim problem too (if there ever was one).

Tritium is a problem when it is in the form of tritiated water or "Tritium Oxide", tritiated water can hang around in the air as water vapour and it can also be absorbed by the skin and become an internal radiation hazard.

Heavy water (D2O) becomes tritiated when it is used as a neutron moderator around the neutron emitting cores in nuclear reactors, needless to say this tritiated water also becomes hot and steamy, so I imagine that special ventilation is needed in these reactor buildings.

In a full scale energy producing fusion reactor of the future, one would probably want to try and keep the valuable tritium and Helium3 fusion products, so there is an opportunity for someone to invent a way to separate these gases from the vacuum exhaust.

Further down the track...

Steven

PS: Chris, it is generally not a good idea to rename the subject line of an old thread, better to start a new one. It confuses everyone.
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Re: tritium dose.

Post by Richard Hull »

Frank re-iterated math already done on all three of our websites over the past decade by myself and others on this subject. Tritium, at even 10e6 neutrons/sec, is a total non-issue. Only two here have verified claims of such emissions and on short runs only. I know we would all like 10e9 n/sec, but it is safe to rule this out of our range, completely.

Steven is right, also. Please don't rename a reply's subject line. If your question is that big a deal and not immediately related to the topic to the point of forcing you to consider renaming the subject line, start a new thread.

Tritiated water can be in the form of HTO or DTO but only very rarely T2O. T tends to replace only one molecule of liquid water. Such contaminants, we need not worry about either.

There are plenty of things to "nervous nelly" about around a fusor, Neutron radiation or nuclear waste gases are not among them.

In operation, only electrocution should be considered a prime and ever present danger. In the highest end operation, above 30 KV, x-rays might be addressed as a weaker secondary consideration. X-rays only become a major issue above 50kv at which point, the shell goes rather transparent to the pesky rays.

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Re: tritium dose.

Post by Chris Bradley »

Sure. I hear what you're saying but it wasn't really the maths of the tritium that I was thinking about, but if there were any physical reasons it might 'linger'. The second maths question is different and is clearly a matter of academic interest wrt fusor technology - at what point would it become an issue?
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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Jboily »

Wilfried,

Thank you for the information and corrections.

There is something I do not understand in your calculation. The 500 W DD fusion would produce 168 watts of neutron. At 1 meter distance, somebody would absorb at the most 1.34 mRad per sec. (that is if the the energy absorbed within the first cm cube of Skin, less if the energy is distributed across a deper region). This would be 1.07 mRad in 8 a seconds exposure, similar to the exposure from a medical XRay.

How would a 500 watts reactor produce 800-2000 rem (a letal dose)! Unless it was overloaded in the 10 MW range.

What is the conversion ratio for Rad to Rem at 2.45 MeV?

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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Jboily »

I just answered my question, a RAD is 100000 J/gram, a factor of 10^5. Then you multiply by a Q of about 10 to get to Rem.

Everything then seem to fit. Sorry for the confusion.
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Re: tritium dose.

Post by Richard Hull »

The answer to your question is simply tritium production and environmental contamination about a fusor occurs at a point so distant that none of us could ever reach it. Period.

We talk in isiotopic emission of n/sec. The big boys talk in flux of n/sqcm/sec

I doubt if 10e12 n/sec, isotropic, from a fusor would produce a tritium level that would be worrisome based on our operational times. Again, the x-rays and neuts, themselves, would be the major worry at this level. (Which we could never attain)

Based on Frank's 10e19 atoms per curie, the fusor at 10e12 n/sec would produce only 0.1uCi per second. Not to worry.

The body sheds T quickly, again, a big plus.

Unless you stick your pump's exhaust pipe in your mouth at 10e12n/sec you need fear naught.

I don't know about others, but I vent my pump system to the great out of doors. This is mostly to avoid oil mists. T outside is a non issue, of course.

Dearest creator, will we ever be free of tritium issues constantly popping up as being useful fuel in a running fusor, (which it is not), or creating an imminent danger to ourselves and our beloved pets? (which it is not) Alas, I fear we shall forever be lashed to the wheel of both false joy and false fear due to the tritium issue.

Mathematical machinations will tell the tale, but many would rather cry and wail. For numbers great and small are oft something heard as a distant call. Reason and logic are hoped to abound, but alas, they are rarely found.

Radiation, asbestos and lead are the current demons in our head. To rid them of our space we toil with the result, our lives we foil.

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Re: FAQ - D-D fusion - Energy - Flux - Dose

Post by Brian_Gage »

Excellent! This is the kind of simplified presentation that gives me some idea of what is going on in a fusor. More, it answers my questions about shielding and exposure. I might never build a fusor, but everything I read about this topic is facinating, and one can't help but admire the skills required to build and operate even a demo unit.
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