Another (simple) FAQ - DONE

[TallDave]

Clearly I am very bad at explaining some very basic Polywell theory. The collision cross-section for an ion at low energy is very high, and there are lots of electrons to run into. Did you read how the initial ionization takes place? Under your scenario, the neutrals would all just drift off instead of being ionized in a few usec.

Also, what about the temperature of the electrons? Clearly hot electrons are ionizing. How cold does an electron have to be before it tends to be picked up rather than knock off one already there, and how often do we expect to see such cold electron - cold ion collisions?

[chrismb]

The collision cross-section for an ion at low energy is very high, and there are lots of electrons to run into.

How high is the CS? What is the MFP? So we get a 1+ and it starts accelerating. How far does it take to get enough energy up AND cover its MFP to a 2+. Then how far to a 3+, etc...

Just gimme some numbers, if this is all so easy in TDreamland.

Always treat with suspicion anyone who claims to argue scientifically, but merely comes up with superlatives: When does "high" become "very high", and what is the SI definition for "lots"?

[TallDave]

Heh, well, I gave you Bussard's numbers. Feel free to derive an MFP from Bussard's numbers if you want to know what it is. I'm not sure what CS refers to in this context (cross-section?). The electron density is the same as the ion to within 1/1e6.

If you're looking for more, Valencia is out there, and I believe detail on ionization is given in some other papers as well. I don't know that the calculation has been done (or at least published) for boron ions, but the ionization energies aren't that different so I'm betting it's still going to be usec.

If you're asking exactly how much higher the ion-electron and ion-ion collision cross-sections are at given points on the edge versus the core, I don't think anyone can give a precise answer (except maybe Rick, who may have some density/energy numbers from all those wonderful WB-8 ports by now). Maybe someone can dig up a general reference, for, say, 1KV versus 250KV? It seems to be pretty darn high at the initial ionization conditions, given the usecs to total ionization. Note that Bussard does not appear to depend on ion-ion collisions to produce ionization; even the colder electrons are ionizing.

Maybe out there in ChrisTrolland neutrals hardly ever ionize, but Bussard actually did experiments, and the neutrals didn't just drift off at startup. It's a mildly interesting diversion, but I haven't seen anything that indicates this issue is a significant problem, and it certainly doesn't seem to be in the Polywell canon, which is what the FAQ covers.

Anyways, always be suspicious of people who not only claim to be "scientific" but complain of others' lack in that regard, while they themselves argue with derisive phrases like "wishful thinkers" and "dreamland." Wine and pasta seem more appealing than further barbed banter, so good night all.

I'll leave you with some ionization humor:

So an atom says to another atom "I think i lost an electron". so second the atom asks "Are you sure?" and the first atom replies "I'm positive"

[WizWom]

Bussard studied the ionization issue extensively (it was one reason he built PZLx-1). If you have a paper that suggests Bussard's number is way off, I'd be curious, but it seems safe to ignore this in the FAQ. It seems unlikely neutrals can survive more than usecs.

You really just don't seem to understand, and I am clearly very bad at explaining some very basic nuclear collision theory:

Just because a 1+ ion has accelerated into a 65kV well, it doesn't mean that all the electrons simply jump off the damned thing! ions have to be in collision with something for them to loose any more electrons.

Why would electrons jump off an ion just because it is travelling fast????

Because the Ions aren't all alone in the injection puff, they will bounce off each other.

Plus there is the whole issue of "heat" and "electron orbitals at temperature N" which states that given heat amount "x" the electrons will get enough thermal excitement (photons) to jump ship.

[chrismb]

Heh, well, I gave you Bussard's numbers. Feel free to derive an MFP from Bussard's numbers if you want to know what it is.

I was asking you to do your own homework, but sure, easily done;

So he says "The cascade time e-folds at a rate of
1/(no)(sigmaizn)(veo), where (no) is neutral density,
(sigmaizn) is ionization cross-section for low energy
electrons at speed (veo). Typically, for no = 1E13 /cm3 (i.e.
ptorr = 3E-4 torr), veo = 1E9 cm/sec (Ee = 100 eV), and
sigmaizn = 1E-16 cm2, the cascade e- folds with a time
constant of about 1E-6 sec (one usec)."

The MFP is therefore 1/(no)(sigmaizn), in his parlance, giving an MFP of 10 metres.

Can you, please, now explain how these ions get formed if their MFP to ionisation is 10m, whilst in a device of sub 1 metre scale? Taking the discussion into 'time' and using a linear MFP-type calculation to derive timescale is highly disingenuous because the ions do not undergo linear motion during the usec timescales that derives from the answer to an equation that presumes linear motion.

[TallDave]

Heh, I thought of that more as your homework, given that you're raising the issue. I think you're neglecting that the cascaded electrons are doing most of the ionization -- the first hot electron breeds more electrons at ionizing energies.

I'm not sure how to calculate an ionizing MFP in an electron cascade, though I'm pretty sure they don't travel 10m in a few usecs. I'm not sure how much sense MFP even really makes in this context, given that the neutrals can just sit there getting ionized by the cascading electrons around them.

And electron temp is the problem with post-startup neutral formation, too: in order to get a neutral, you need a collision between an electron and ion for which the combined energy is below 671eV. That's a tiny proportion of both populations -- and worse yet, the well goes in opposite directions: where ions are slow, electrons are fast and vice versa. So, as they say, "never the twain shall meet," or at least too rarely to matter.

Doesn't appear to be an issue. Maybe if I'll get time I'll calculate exactly how rare such a collision would be at reactor conditions. It might just barely be possible near a coil casing.

[TallDave]

Sorry Kite, got a little sidetracked there.

What's the parenthetical term in your chart there? I started to make a version with a drive power column added in but I was confused by that.

Other than that, for the text portion I would humbly suggest the following edit:

The word “best” implies an optimization which immediately raises the counter question, “optimized for what?”

The polywell is hypothesized to be a mono-energetic (or at least only partially relaxed) beam-beam process. For such processes, the equation for fusion rate (two reactants) is:
ƒ = n1n2 (σv)
where then “n”s are the densities of the reactants, “σ” is the cross section of the reaction and “v” is the center of mass velocity. It is important to remember that “σ” is a complex function of “v”.

Many, perhaps most, people think of the optimum as being where “σ” is at its global (or a local) maximum. But where power to weight is important, it may be where the term (σv) is at a global or local maximum. This happens on the down-slope past the “σ” maximum. Conversely, some think the “optimum” is where the rate of increase in the term (σv) has reached its maximum.

For advanced fuel mixes like p-B11, due to efforts to minimize bremsstrahlung there will probably be an excess of protons in the mixture, so figuring out what effective accelerating electric field would be needed to gain significant advantage from the resonate peak is complicated.

So there is no simple answer as there are a lot of variables.

[chrismb]

I'm not sure how to calculate an ionizing MFP in an electron cascade, though I'm pretty sure they don't travel 10m in a few usecs.

If a boron neutral is gonna ionise to a 5+ in the first few cms of the outer edge, then why does that mean anything other than indicating the electrons there will have a potential of over 600eV and a density of over 10^21/m3 [which is definitely not the picture of 'low energy' nor 'low density' electrons that reside in the outer edge of a Polywell that folks have alluded to]?

[MSimon]

can you, please, now explain how these ions get formed if their MFP to ionisation is 10m, whilst in a device of sub 1 metre scale?

They bounce around.

[MSimon]

I'm not sure how to calculate an ionizing MFP in an electron cascade, though I'm pretty sure they don't travel 10m in a few usecs.

If a boron neutral is gonna ionise to a 5+ in the first few cms of the outer edge, then why does that mean anything other than indicating the electrons there will have a potential of over 600eV and a density of over 10^21/m3 [which is definitely not the picture of 'low energy' nor 'low density' electrons that reside in the outer edge of a Polywell that folks have alluded to]?

Ions are at high density and low energy near the grids.

[chrismb]

can you, please, now explain how these ions get formed if their MFP to ionisation is 10m, whilst in a device of sub 1 metre scale?

They bounce around.

But I've been told their motion is raidal. So are you saying they bounce around, but somehow only radially?

[chrismb]

Ions are at high density and low energy near the grids.

You'd better get this straight between yourself and TD, 'cos it don't look like it makes much sense from here.

[MSimon]

can you, please, now explain how these ions get formed if their MFP to ionisation is 10m, whilst in a device of sub 1 metre scale?

They bounce around.

But I've been told their motion is raidal. So are you saying they bounce around, but somehow only radially?

So they bounce around radially? As long as they hit other particles during the bouncing they will most likely get further ionized.

[MSimon]

Ions are at high density and low energy near the grids.

You'd better get this straight between yourself and TD, 'cos it don't look like it makes much sense from here.

Let me see if I can explain it. Near the most positive potential in the system the positively charged ions will be the slowest.

[KitemanSA]

Sorry Kite, got a little sidetracked there.

What's the parenthetical term in your chart there? I started to make a version with a drive power column added in but I was confused by that.

In the cross-section graph I have the p11B reaction has a sharp peak before the main hump, and the graph flattening out after it. When I used the "45 degree" rule, I ran into the front peak at 130keV. With the -45 rule, I couldn't reach a max til past the end of the graph at 10MeV.

Since the 130keV seems so different than other values mentioned, I am wondering if I have used a bogus data set.