## Resultant particles hitting ion or electron Injectors

Discuss the technical details of an "open source" community-driven design of a polywell reactor.

Moderators: tonybarry, MSimon

chrismb
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MSimon wrote: Care to do the calculations to get some idea of the relative densities (fast neutrals - deuterium permeated walls) that might give rise to the detected neutron counts?
I'd need some more information. For example, and particularly, where were the neutron detectors. If the neutron detectors were bolted to the outside surface of the chamber wall, you can instantly see that you could get a highly elevated reading from a fairly sparse reaction rate. The presumption would've been a 1/r^2 from the centre, but this wouldn't be true if it were a fast neutral/target reaction in the wall. It would lead to a presumption of a 'high rate' at the centre rather than a lower rate at the wall.
MSimon wrote: BTW how do you get the D ions neutralized before they hit the wall with 200 KeV?
There is a given probability of any fast ion either recapturing a free electron, or pulling an electron off of a background neutral. It's a probability that is orders of magnitude higher than fusion, at the drive energies of these devices to date.

I wasn't aware that WB-6, etc., were running 200keV. That's news to me....

MSimon
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More like 50 KeV. With plans to go to 80 KeV in the near future.

Make whatever reasonable assumptions you like (detector close to the wall) and see what comes up.

I usually disagree with you by two orders of magnitude but no matter - we have a baseline for discussion.
Engineering is the art of making what you want from what you can get at a profit.

chrismb
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MSimon wrote: Make whatever reasonable assumptions you like (detector close to the wall) and see what comes up.
Sure. I’m happy to work like that. Throw the numbers in, then see what needs modifying…

Treating the numbers I’ve seen as if they went into a regular fusor, I would say;
1000A means that a total of [1000A/e]*250E-6s = 1.5E18 charged particles have been ‘mobilised’ during the pulse. Now, as both acceleration time and velocity are SQRT(m) dependent, so only one in 60 of those will be deuterons flying around, the rest will be electrons. (That is, at any one time, a given space with one deuteron passing through it will also have one electron in it, but the electron clears that space in 1/60 of the time of the deuteron, so another electron comes to replace it. Total transiting electrons = 60 for each transiting deuteron.)

So we have 2.5E16 deuterons to ‘play’ with.

At @10keV, they’ll be going at 1Mm/s. Cross-section for charge exchange, say = 1E-20m^2 (see Massey, “Atomic Collisions”, if you want anything more accurate.) Take the background pressure as 1E17/m^3. So the rate of charge exchange and fast neutral production will be 1E6[m/s] * 1E-20[m^2] * 1E17[/m^3] = 1000/s per particle.

We have 2.5E16 deuterons, so the fast neutral production rate will be 2.5E19/s.

There will be a chance of re-ionisation for the fast neutral as it makes its way to the wall. The cross-section is about the same as for the charge exchange, at these ~10s of keV energies, but it’s only a chance while it’s on its way – a distance a deuteron covers in a us. So the re-ionisation rate would be a probability of 1000/s * 1E-6 = 0.001. A tenth of one percent re-ionise, which I will therefore ignore.

Take the chamber wall surface area as being 25m^2 (?), so that’d be an irradiation rate of 1E14 fast neutrals/cm^2/s, or 2.5E10/cm^2 for the pulse.

Let’s take the fusion cross-section between a fast neutral and an embedded deuteron to be 1millibarn. The probability of one fast deuteron hitting a single embedded deuterium molecule (2x nucleii) in a cm^2 is therefore 0.001E-24cm^2/1cm^2 = 2 chances in 1E-27. We have 2.5E10 hitting that area in one pulse, so the chance of a single fusion with that lone embedded deuterium molecule is 5E-17.

Now let’s consider the neutron rate seen. I’m going to make this assumption – it was bolted on to the chamber wall, so it will receive a half of all the neutrons from that wall areas, which is probably around 100cm^2. So the neutron detector will see 2.5E-15 neutrons per pulse, per embedded deuterium/cm^2.

So I do a quick lookup for interstitial hydrogen in steels, and I’ve picked a figure out of those texts of 1ppm. Let’s say the fast deuteron can reach down into the steel by 500 microns, so the total amount of deuterium per cc (per 500 micron depth) is 1E-6 *[8g/cm^3/20]/3.2E-27kg = 1.25E17.

So the neutron rate from fast-neutrals fusing with interstitial deuterium seen by a neutron detector bolted to the wall of one of these devices is, by this estimate, 2.5E-15neutrons/pulse/embedded-deuterium * 1.25E17embedded-deuterium = 312 per pulse.

I do not know if the neutron detectors were sensitive enough to register 3 clicks in response to 300 neutrons passing through them, but there are various points where my own estimates may be up or down, e.g. the background density, and all is proportionate in this calculation.

Whatever the actual variations of assumption that affect the input numbers I’ve used, I’m satisfied I’m looking at the basic mechanism. Therefore, I see no reason to think the idea of fast neutrals being the source of the detected fusion is inconsistent with the neutron count results. In no way does that say this is what happens, but only that there isn’t an immediate reason to think it is an unjustified possibility that, therefore, needs to be otherwise controlled for in the WB experiments.

KitemanSA
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chrismb wrote: I'd need some more information. For example, and particularly, where were the neutron detectors. If the neutron detectors were bolted to the outside surface of the chamber wall, you can instantly see that you could get a highly elevated reading from a fairly sparse reaction rate. The presumption would've been a 1/r^2 from the centre, but this wouldn't be true if it were a fast neutral/target reaction in the wall. It would lead to a presumption of a 'high rate' at the centre rather than a lower rate at the wall.
I don't get this. the overall reaction rate should be the same either way. Yes, you would get a much higher percentage of the real near stuff, but there would be a lot of far away stuff you wouldn't detect. As long as the source is spherical, and inside the detectors, the overall rate detected should remain the same, no?
chrismb wrote: I wasn't aware that WB-6, etc., were running 200keV. That's news to me....
I thought the MaGrid was charged to 12KeV on WB-6. No data on WB-7; and maybe I missed something re 6.

D Tibbets
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chrismb wrote:Make whatever reasonable assumptions you like (detector close to the wall) and see what comes up.
Sure. I’m happy to work like that. Throw the numbers in, then see what needs modifying…........
I'll not contest your numbers except for some questions. Does your electron- ion ratios reflect a random thermalized population or a population of each with thier relative dynamics in a machine where the slow- fast populations of each are opposing each other? Also, will the 1 ppm excess of electrons affect the numbers significantly?

In terms of neutron counts being from neutral wall collisions, two counter arguments. The only information I know of where the neutron production location was measured in a gridded fusor is in the below link. Neutrons came mostly from the core and the central grid, not the walls. Of course the Polywell does not have a central grid, so any wall neutron production may become more significant compared to the total.
http://fti.neep.wisc.edu/iecworkshop/PD ... ashley.pdf

Second, the detection of ~ 3 neutrons in ~ 0.4 ms leading to a prediction of several hundred million isotropic neutrons produced per second at 10,000 eV well depth is much more than is obtained in a gridded fusor (a few thousand at best?). From a neutral atom's standpoint, the only funtional difference in the Polywell is the absence of the physical central cathode grid, so I'm assuming the neutron production occurs in similar areas- the core ( but not impacts on the (absent)grid). The wall bombardment by neutrals would be similar in both a gridded fusor and a Polywell (unless you throw out your ion- neutrals calculations). If that is the dominate neutron production method, the Polywell would produce no detectable neutrons in the brief timespans it was operating in.

Dan Tibbets
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TallDave
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chrismb wrote:
TallDave wrote:Could WB-6, WB-4, and PLZ-1 have gotten the fusion counts they did if the reaction rate was what you claim?
Sure. From fast neutrals bombarding a wall permeated through by deuterium.
That seems extremely unlikely, given the bottom of the well is at the center and the wall is outside the machine entirely. Where are neutrals going to get the energy to fuse? Fast neutral production? That sounds pretty laughable on its face if it takes 2 hours for an accelerated ion to fuse.

Also, iirc PLZ-1 was a closed box. Neutrals can't be hitting the wall and fusing because they don't get out.

IEC wasn't invented yesterday, you know. They've been measuring neutron counts like these for decades. And most of those were in systems where accelerated ions were constantly hitting the grids. You've either just falsified the entire field or you're badly mistaken.
Last edited by TallDave on Wed Jul 01, 2009 4:29 pm, edited 3 times in total.

D Tibbets
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chrismb wrote:
D Tibbets wrote: You have the reaction rate droping as the density increases because the density is in the denominator. There has to be some other consideration or it doesn't make sense , at least not to me. How would your calculation fit with the reported results of JET?
I've no idea what you're talking about here, Dan. Sorry, this isn't what I've said at all. The definition of 'cross-section of some event' involved the average distance 'to some event' and the density of the reactants involved in that event. Look again at the way I've done the calc. The reaction rate is only done in the very last line, long after I've dealt with MFP to fusion, and density. By then, by the end of the calc, the numbers that you think you're looking at have effectively ended up upside down.

Why you think I need to reconsider *my* objective figures just because the conclusion doesn't come out as someone else's subjective presumption is an odd logic to follow.
I'll abandon my other weak arguments. But, while your numbers are real, I feel they are only a part of what is going on. Your 'mean distance to a fusion event' and the derived seconds to a fusion event is from the first person perspective of a single deuteron (at least that is my understanding). Forget the hydrogen in the Sun analogy, instead look at radioactive decay half lifes. My intrepretation is that your number is equivalent to the half life of the deuterium (or full life, in anycase ~ the time the deuteron could expect to survive in the system). The radiation (power) level, though is dependent upon the half life and the number of molecules in the sample. A uranium 235 isotope may last a billion years, but I wouldn't recomend sleeping on a pillow made of the stuff.
In your example there are 10e20 deuterons in the 1 meter machine*.
So, the net fusion rate would be 1 fusion / 7000s per deuteron X number of deuterons = ~ 10e16 fusions per second (provided the burnt fuel is continually replaced).
That should generate ~ 10,000 Watts of power.

*Ignoring things like convergence/ focus or higher effective density that might decrease the 'half life'.

Dan Tibbets
Last edited by D Tibbets on Wed Jul 01, 2009 4:24 pm, edited 2 times in total.
To error is human... and I'm very human.

chrismb
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TallDave wrote:Could WB-6, WB-4, and PLZ-1 have gotten the fusion counts they did if the reaction rate was what you claim?
chrismb wrote:Sure. From fast neutrals bombarding a wall permeated through by deuterium.
TallDave wrote:
That seems extremely unlikely, given the bottom of the well is at the center and the wall is outside the machine entirely. Where are neutrals going to get the energy to fuse? Fast neutral production?
Not sure I understand you. D'you understand what a fast neutral is? A fast ion picks up an electron and becomes a fast neutral (with pretty much the same energy). It'd be happening all over the reaction volume, all of the time.
TallDave wrote: That sounds pretty laughable on its face if it takes 2 hours for an accelerated ion to fuse.
yeah. Pretty laughable. But that's the score. Under the conditions above, the mean time to a fusion event is 2 hours. Any neutron production in a ms pulse would be done by the multi-sigma statistical 'tail-end' of ions that just happen to fuse very quick.
TallDave wrote:IEC wasn't invented yesterday, you know. They've been measuring neutron counts like these for decades. And most of those were in systems where accelerated ions were constantly hitting the grids. You've either just falsified the entire field or you're badly mistaken.
In what way have I falisified it? It is well known that fast neutrals lead to a significant amount of fusion in IEC devices, the proportion is, obviously, going to depend on the type of device. I have not made any specific claims regarding polywell, merely that it is a mechanism that must be understood and controlled for, it can't just be ignored as you seem to be choosing to do.

Let me remind you that there has NEVER been any fast-fast, or even fast-background, neutrons demonstrated out of an IEC system that uses an electron cloud as a virtual cathode. Only gridded fusors have ever produced neutrons.

TallDave
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So you're seriously arguing that all IEC devices only produce fusion by hitting the grid?

Sorry, no. If that were true, "star mode" fusors which deliberately avoid the grid would produce less fusion rather than more.

chrismb
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D Tibbets wrote:The wall bombardment by neutrals would be similar in both a gridded fusor and a Polywell
yes, I completely agree. And if you chuck 1000A into a fusor, on top of the other fast-background fusions, i suggest you'd get the same rate of neutral-wall fusions I've calculated. In the Polywell, I'm suggesting you should consider that you're seeing ONLY the equivalent neutral-wall fusions, because there aren't any fast ion-X fusions.

chrismb
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TallDave wrote:So you're seriously arguing that all IEC devices only produce fusion by hitting the grid?
eh? I've not come close to suggesting that. In a gridded DD fusor, the most significant rate of fusion is between the fast ions and background nucleii. As far as I understand, UniW have worked with D3He and they've identified that a significant fraction is, as you say, by [ion] collision with the inner grid (and embedded nucleii therein].

TallDave
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At @10keV, they’ll be going at 1Mm/s. Cross-section for charge exchange, say = 1E-20m^2 (see Massey, “Atomic Collisions”, if you want anything more accurate.) Take the background pressure as 1E17/m^3. So the rate of charge exchange and fast neutral production will be 1E6[m/s] * 1E-20[m^2] * 1E17[/m^3] = 1000/s per particle.
OK, but you're assuming all the ions are going 10keV, when that's only the speed of the fraction that are at the core at a given point in time. You also appear to assume that all the fast neutrals get exactly the right angle to fuse and don't hit anything on their way out (such as the shell of slower ions outside the core).

chrismb
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TallDave wrote:
At @10keV, they’ll be going at 1Mm/s. Cross-section for charge exchange, say = 1E-20m^2 (see Massey, “Atomic Collisions”, if you want anything more accurate.) Take the background pressure as 1E17/m^3. So the rate of charge exchange and fast neutral production will be 1E6[m/s] * 1E-20[m^2] * 1E17[/m^3] = 1000/s per particle.
OK, but you're assuming all the ions are going 10keV, when that's only the speed of the fraction that are at the core at a given point in time. You also appear to assume that all the fast neutrals get exactly the right angle to fuse and don't hit anything on their way out (such as the shell of slower ions outside the core).
There are all manner of assumptions in what I've calculated. I've not claimed otherwise.

I am only suggesting that what I have put is sufficient to flag up that neutral-wall fusions need to be tallied up and accounted for, one way or the other, and that they cannot be ignored. If you want to adapt the maths so that neutral-wall fusions 'disappear', then feel free. Doesn't make it right to do so. I'm flagging up a possibility, not a claim that this is what happens.

TallDave
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chrismb wrote:
TallDave wrote:So you're seriously arguing that all IEC devices only produce fusion by hitting the grid?
eh? I've not come close to suggesting that. In a gridded DD fusor, the most significant rate of fusion is between the fast ions and background nucleii. As far as I understand, UniW have worked with D3He and they've identified that a significant fraction is, as you say, by [ion] collision with the inner grid (and embedded nucleii therein].
OK, that makes more sense. But the fast neutral fusions still sound pretty ignorable.

TallDave
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chrismb wrote:I am only suggesting that what I have put is sufficient to flag up that neutral-wall fusions need to be tallied up and accounted for, one way or the other, and that they cannot be ignored. If you want to adapt the maths so that neutral-wall fusions 'disappear', then feel free. Doesn't make it right to do so. I'm flagging up a possibility, not a claim that this is what happens.
Fair enough.

I think we'll know for sure from WB-8, since the scaling from .002 watts to 8 watts would look very different if a significant portion of that .002 watts is from fast neutrals hitting the wall rather than ion-ion collisions.