The nitty gritty, the mathematics of it all

[madhatter]

New here, hello all.

I wanted to know if this group covers the actual mathematics of fusion. I do have enough of a background in QED to follow them, and was wondering if there are those in the group who have designed their fusors around them?

If it's a non-disclosure issue I fully understand. When I came across this site after doing some further research on Farnsworths work I was struck with enthusiasm and honest work going into the development and testing of fusors here. I read thru Farnsworths patent and then referencing it with electrostatic optics and particle physics it was clear just how much goes into the design before the power switch is flipped.

Going on only what I know, it would be akin to shooting in the dark if you just thru a containment field together and ran up/down the KV potentials to see what works.Noting that Farnsworth had the cathode and anode shaped and sized to the electron probability location based on charge potential to increase and re-enforce the field and pressure gradient, I wondered if that was a given place everyone starts at? not to mention his choice of materials was based upon the desired result as well.

If the math is covered somewhere just point me there and I can share what I know and any ideas.

thanks

[Carl Willis]

The highest math needed to get a fusor built and making detectable fusion is algebra.

University courses in the relevant subjects--electrodynamics, plasma physics, nuclear physics--are usually taught with the aid of a wider suite of mathematical tools such as vector calculus, linear algebra, and differential equations, and while those tools add insight and a deeper understanding to some aspects of what we might get involved with as amateur fusion experimentalists, they clearly aren't necessary to get in the game, nor will you find a particularly deep exercise of mathematics anywhere on this site.

Should you want to advance the theory of fusion, we have a separate forum for that in the hope that, one day, something particularly useful or well-informed might get put there. History has demonstrated (to me at least) that the theoretical contributions seldom meet the prevailing standards of utility, factual accuracy, and attention to detail found in the experimental forums, probably because generally no physical or monetary commitment is tied up in a pipedream. But the day may come...

-Carl

[madhatter]

Ahh, OK.

It doesn't have to be a pipe dream though. As an engineer myself without the proper fundamental tools I can't bring my ideas to life. The biggest obstacle is the cost of manufacturing.

I look forward to more in depth discourse in the future.

[Chris Bradley]

In regards what ions and electrons do at the 'first order' approximation, this scenario is mathematically trivial because there is an applied electrical field such that + charges experience a Eq force in and are accelerated to fusionable energies, - experience a Eq force out. If it were more complicated than that then it'd likely not be do-able with such basic kit.

It is, of course, more complicated because charges don't just move individually but interact en masse (and, ultimately, interact with the structure of the reactor, of course). However, the fusion event itself is always a more intimate, particle-on-particle, event.

Some 'blame' the former for the fusion rate of a fusor being limited, e.g. saying 'if only the grid could be replaced by a virtual grid, then the rate would go up'. However, I contest that and offer you equation (2) of the attachment in;

viewtopic.php?f=15&t=7183#p51021

as a demonstration of why it is in the very nature of a 'passive beam-fusion' process, as in a fusor, that means there is a limit to its fusion rate.

(Of course, there are many sources of losses in a fusor, but just because there are losses does not, per se, mean there would be a limit to the possible rate. The maths in that attachment, equation (2) proposes why there *is* a limit to the possible rate.)

To overcome it, move on to equation (3), describing where you can get to if you can keep fusion fuel ions 'in contention', feeding back lost scattering energy and avoiding 'Maxwellian-isation' (which will always require entropy to be removed, viz. an 'active' process that can do work on the ions is required, to overcome the fundamental limitation of equation (2)).

Please feel free to do as much maths as you like on the proposition in that thread; download_thread.php?site=fusor&bn=fusor ... 1227208869 . I look forward to your own maths on this!

It may be useful to look at Appendix E [particularly E2.2] of Todd Rider's thesis in conjuction with that thread of mine.

[Brian McDermott]

You beat me to it. Rider's thesis has all the math anyone could ever want regarding IEC systems, and all the justification anyone could ever (not) want for why they will never generate net power.

[Chris Bradley]

Brian McDermott wrote:
> Rider's thesis has ... all the justification anyone could ever (not) want for why they will never generate net power.


Not exactly. He was rather specifically looking at one particular device in his general critique (that did not have any clear ways of extracting entropy), but recognised there may be other classes of device that might remove entropy actively, that he only got to describe in generalities.

Check out his Appendix E.

[madhatter]

thanks guys,
I'll go thru this in the next couple days, day job has a deadline right now.

[Dan Tibbets]

Rider's thesis may have all the math needed, or perhaps not. some of the defense against Rider's conclusions is a different approach to analysis using Fokker Planck modeling by Chacon.

http://pop.aip.org/resource/1/phpaen/v7 ... horized=no

Dan Tibbets

[Steven Sesselmann]

On the subject of calculations...

I have read that it was once calculated that no rocket could ever make it into orbit, against the force of gravity, because the energy required to lift the mass of the fuel would always be more than the fuel contained.

Easy to prove mathematically, but mathematics does not account for lateral thinking.

Some great lateral thinker came up with the three stage rocket, and made waste paper out of the calculations.

Steven

[Edward Miller]

Great point Steven!

I think this is a great video on the topic of trying to figure everything out in math: http://www.ted.com/talks/tim_harford.html

[Steven Sesselmann]

Edward,

Great talk, thanks for posting...

Which brings me back to an earlier post of mine called Fusion reactors by energy quotient

I think my post was seriously misunderstood by most of the readers. The objective was NOT to create a competition, but to collect data on which configurations resulted in a better Q.

Many fusor builders never properly reported their neutron output under this post for the fear of coming in at the bottom of the list. Yet their data would have become an important factor in determining the best design.

At fusor.net dozens of neutron producing fusors have been built, yet we do not have the slightest clue, what the optimum grid size, chamber size, chamber shape etc. is.

Every newbee starts out fresh and makes the same mistakes as others did before, and that's a waste of time and resources.

Steven

[Doug Coulter]

Steven, it's precisely this thinking that has driven our Standard Counter project - the ability to compare results across labs. If everyone has a different detector setup, it becomes very difficult to do in any reasonable way - does this guy's calculation of absolute sensitivity have a different (potentially large) error in it than that other guy's? I've seen that one change within a single lab here as various mistakes were found and corrected. And it's a fact that in the neutron metrology game, absolute numbers are admittedly pretty hard to get and trust - this from the "pros" in many papers.

For the purposes of Q, you don't really care about the absolute number anyway, just relative will do if it's stable and repeatable. When you're a million away from actual net energy output, a 20% error doesn't mean that much. When we get closer, a thermocouple/calorimeter will do fine and have little chance of error on an absolute scale.

I think it would also help if the few that have running fusors put up some specs and some pictures of their rigs. I know a few seconds of peering into Richards through the window, not even running on D, helped get me going more than all the words in a few websites did. Where any instability or intermittent behavior is present (often it seems) a movie on a place like youtube and linked back from would also help any newbs quite a bit.

To my mind, raw data is often better over time than interpreted data. A new understanding can be back-checked against the former, but not the latter. Pictures and computer based data aq can really help preserve the raw data -- you might not know what's important till later on!

[Steven Sesselmann]

That's right, throw in the raw data, too much is better than too little, time of day, temperature in the lab, what you had for dinner and more importantly, how many beers you had with it

The bubble detector is not perfect, but it is a reasonable comparison especially if you use two and take the average.

In any case, more data is needed, so if someone has a scrap book with accurate notes from their past experiments, it's not too late to post.

Steven

[Doug Coulter]

Well, BTI results might be accepted here, but about a year ago Bill bought us two new ones, since expired (another ~$300 bites the dust, again). We put them side by side about 1" outside the fusor shell. The readings diverged 3::1 between them. Thinking no way they could be that bad, and maybe we were seeing something weird like neutron beaming, we did another run, this time with them turned 90 degrees. Same result.

If that kind of thing is acceptable, along with the short life for that money, go for it, man. I'm only rich, not wealthy, and 3::1 variance between two new BTI's is WAY not good enough for me. If I'd bought one, and then the other, I'd have thought I'd made a 3x improvement, or lost one. Maybe they didn't label them right? I have no way to know, but averaging numbers that far apart isn't really going to make me believe in them - if I'd had three, I'd maybe use the median and assume two were bad. Not great odds. Could be a quirk - out of the 6 or so we've had here (all now failed) most seemed to agree fairly well. I won't waste another dime on one. A thousand bucks buys a lot of other fusor gear, and stuff that lasts a lot longer in the bargain.

Meanwhile, silver seems to do a more consistent job, and it doesn't wear out.

[Richard Hull]

Doug is right, Activation (silver in our case) is a final and flawless arbiter. This is, provided the exact same setup, distance, and moderator is used, though math, if one wishes to twist in the wind with it, can allow for some variations. This is for fusors producing over 250,000 neuts/sec or so though and the budding fusioneer really needs something other than activation.

Activation as a Q indicator will shine only if the silver is of known purity, thickness and form, baked in a standardized oven, of sorts, at a fixed distance from a fusor that is producing 250K neuts per second or more and the detector/counter setup is the same machine to machine in a fixed counting environment. All of this can be achived and mechanized rather inexpensively.

If we are serious about all of this, we would do well to establish this normalized, silver activation environment. This would involve a bit of cost effective design engineering.
I will do a bit of musing over this idea. Any future postings on this from me might be in the radiation detection forum, as this topic is drifting laterally now.

Richard Hull

[Chris Bradley]

I think the thread has drifted too far. Energy quotients, wrt set-up, and neutron counting accuracy/statistics are worthy topics in need of being captured in their own threads so info is not 'buried' so deep from the titles.

[Richard Hull]

First pass at the silver activation assembly is located in the Radiation forum.

The original posting probably should have been in the Theory forum and not construction forum anyway as any attempt at mathematical modeling of a fusor is really a theoretical adventure.

Richard Hull