ANS winter 2010 Conference

[chrismb]

when you break the 3-term sigma function up, you get the 1/E incorporating the bottom of the coulomb barrier term

How does 1/E derive from the Coulomb barrier? Surely the cross-section is an 'E-on-top' type of function.... more energy more probability of fusion, no?

Why is E on the bottom, if this is the Coulomb term?

[TallDave]

In a Polywell, where the ions are contained within the Wiffleball, while any neutrals are free to drift throughout the vacuum chamber. the ions are extremely dominate, so charge exchange and non charge exchange neutral collisions are proportionately much less significant. This requires good vacuum pumping to remove these background neutrals to permit the ion concentration levels to dominate the collisions and to have a useful density of these ions for reasonable fusion rates.

I'm not sure why we would expect the background pumping in Polywells to matter in that respect. Even with the small machines, the densities and energies should be high enough that neutrals are essentially nonexistent in the areas of significant fusion. Bussard was talking usecs for the initial ionization of the interior gas (due to cascading low-energy electrons freed from the initial neutrals). If that's even close to correct, concern regarding pumping neutrals to keep them from fouling up fusion in the core seems a bit like worrying about having enough snowplows for the streets of Hell.

[chrismb]

If that's even close to correct, concern regarding pumping neutrals to keep them from fouling up fusion in the core seems a bit like worrying about having enough snowplows for the streets of Hell.

Not at all, and you are missing the issue. The cross-section for charge exchange is several orders of magnitude more than that of fusion, so whatever happens fusion-wise will happen a million times over for charge-exchange and fast-neutral loss.

Your snow-in-hell analogy is a fine case to draw on. So let's say it is 65C in hell and snow falls. Yeah, it'd melt. The analogy with neutrals 'falling into the fusion zone' is like having snow falling at the rate of 10" per minute. Yeah, it's hot enough for it all to melt, but not straight away and if the rate of snowing is greater than the rate of melting, then it'd build up and Be'elzebab will have to get his snow ploughs out. In this case, the rate of fast neutral loss would be greater than the rate of fusion... and by several orders of magnitude if the neutral density is comparable with the ion density.

In this case, it will be Maxwell that will have to unleash his demon, to shovel all the thermalising particles back into the velocity-space suitable for fusion.

[TallDave]

I think we are talking about essentially the same issue -- energy going into things other than making ions fuse. Sorry, my "fouling up fusion in the core" was probably a bit vague.

In this case, the rate of fast neutral loss would be greater than the rate of fusion... and by several orders of magnitude if the neutral density is comparable with the ion density.

Yes, I agree that would be true in that case. But the densities shouldn't be at all comparable. If the initial cascade takes usecs and converts essentially all of the neutrals within the WB, as Bussard says, it doesn't seem likely enough neutrals could drift all the way into the higher-density core to matter, especially since they have to get through the edge where the ion collisionality is high. It seems a bit like expecting snow on a 400C day in Hell with a sky full of superheated boulders whizzing overhead.

[D Tibbets]

Charge exchange collisions are not necessarily bad. It depends on the speed and directions of the particles. A collision might exchange an electron, but otherwise the collision effects may have similar thermalization effects of two ions colliding. The penalty , at least to a degree would be the collisions occurring outside a small core. With ions these collision near the center are primarily upscattering or down scattering collisions. As the ions are most dense here (with some confluence) these types of scatterings are dominate, but angular momentum (transverse ) increase scattering collisions are small. The neutrals do not have this central density increase, so their effect increases the angular momentum changing collisions. But this is dependent on the relative densities of both types within the Wiffleball. The Wiffleball effect not only increases the ion densities within the magrid, it does so without effecting the neutral density. A 1000X Wiffleball concentrating effect on the ions, means that the collisions between ion and ion is 1 million (density squared) times as frequent. , which by Chrismb's estimate would be similar to the ratio of coulomb collisions and fusion collisions. This means that an ion would be just as likely to collide with another ion and fuse, as it is to collide and scatter or possibly charge exchange with a neutral. Confluence, greater Wiffleball trapping factors, and possibly other considerations (like annealing) may further decrease the significance of these ion neutral collisions.

Dan Tibbets

[TallDave]

Dan -- again, I'm not sure why anything inside the very edge of the WB would encounter a neutral more often than Satan can expect to be hit with a snowball. The first step in lighting the machine is flooding the interior with hot electrons, which then bounce around knocking colder electrons off neutrals, which cascades until we have a population of cold electrons and no neutrals. This happens in usecs, according to Bussard, after which the electrons freed from the ions are heated by the injected electrons so that several usec later we have a well. Is there some reason to doubt this is actually the case?

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). Thus all of the
neutral gas is ionized and the system is filled with low
energy electrons in only a few usec.

I'm not sure for what values of "all of the neutral[s]" this is accurate, but I'm assuming six plus std devs. If anyone has a paper on this sort of thing it'd be appreciated.

Given all that, it doesn't seem reasonable that a neutral drifting in off the edge can survive long enough to affect anything in the core.

As for forming neutrals from ions... even if the electron energy distribution is maxwellian (which it shouldn't be), the tail of electrons below the 15eV ionization energy of deuterium is going to be a very, very small proportion in a 10KV well -- especially at the edge, where electrons are most energetic. And then they have to find one of the small number of ions that also has an energy such that the sum of their combined energies is <15eV, which isn't going to be easy since ions will tend to have some nonzero transverse velocity even at the apogee of their orbit where radial velocity is zero. How often could we really expect that to happen? And if it takes usecs to ionize the whole interior of the WB, how long could they last?

[D Tibbets]

TallDave, your points are valid. My comparison was for a worst case scenario where the neutrals could survive inside the Wiffleball as long as they survive outside (before they are removed by the vacuum pumps). In that case the charge exchange/ neutral ion collision interactions would occur about as frequently as fusion collisions (if you accept Chrismb's estimate of fusion to coulomb collision ratios). Compared to the regular coulomb collisions between ions, the effect on scattering would be ~ 1 million times less. It can be totally ignored.
With the very quick ionization of any neutrals that enter the Wiffleball, and the likelihood that the vast majority of this happens on the edge where annealing of the ions is occurring probably decreases the ion neutral collision effects even more.

In addition, the re-ionization of neutrals that enter the Wiffleball will trap them there, thus removing them from the neutral population within the vacuum vessel. This would decrease the vacuum pumping needs, but, this effect is probably small.

What might be more significant is the occurrence of negative charged ions. Apparently this has been observed in Fusors. These negative ions would be contained within the Wiffleball, so their concentrations may be significantly greater than the neutrals in this region. How this would effect the beam- beam interactions and other dynamics in the system might be interesting, if the concentrations are significant.

Dan Tibbets

[happyjack27]

i haven't done a simulation with a deep well on ion time-scales yet, but from what i've seen so far in addition to being dense, the core is pretty cold, for both electrons and ions, so i wouldn't be very surprised to see a lot of neutrals being formed there.

though once they neutralize, the mag field won't be holding them in place anymore. but that's assuming it's accurate to think of them as one neutral instead of a pair of tightly orbiting point charges. in any case, though, if and when they do get out to some stronger mag fields, i would imagine it's liable to pull them apart, esp. around a high voltage gradient.

[D Tibbets]

happyjack27, The ions in the center are Hot. They may slow some if a large center vertual anod forms, but they will still be much hotter than they are on the edge. Ideally the central electrons will be cold, this may actually inhance ionizations as the cold electrrons have much higher ionization crossections. Read about the secondary cascading of ionization of the neutral gas puffed WB6. As TallDave said, though, any neutral entering the system is unlikely to reach this central region intact. This would be especially true in gass puffing systens there is a dynamic creation of transiant cold electrons near the edge.

As for magnetic fields pulling atoms apart, I'm sure it occurs, but I don't know at what strengths it occurs at. I suspect it is well above the conditions foreseen in Polywells, so the electrostatic based splitting dominates.

Dan Tibbets

[chrismb]

TallDave, your points are valid.

Let's be clear, it is your opinion that his points are valid.

The reason why there will be plenty of neutrals is that electrons and ions will recombine. There is nothing to keep them 'hot'. Sure, in the first few us they might well remain ionised before recombining. But a us of operation is..er... us!

I do not know how to pull such conversations back into the reality of conventional physics. By describing a system in which electrons and ions remain separate, to a high fractional content, what is being described is a very hot plasma. Why does this plasma stay so hot when electrons are being lost to the outer walls? OK, so I have no particular reason to want to disabuse you of a view that claims the first few us of electrons will stay in the centre and keep things hot, but once they get lost after a few ms then this plasma will cool and you'll end up with only a small ionisation fraction.

In such conversations before I always point people towards Saha equations for ionisation fractions, but what I have found is that once we start talking about things already known it is not interesting enough for people to bother with that which is "known", instead they wish to move on with their guesswork.

A ms pulsed operation Polwell will never produce net power. We need to be talking about ionisation fractions of the steady-state system, and for that you can work out the plasma thermal temperature versus ionisation fraction with Saha.

[TallDave]

TallDave, your points are valid. My comparison was for a worst case scenario where the neutrals could survive inside the Wiffleball as long as they survive outside

Fair enough.

What might be more significant is the occurrence of negative charged ions.

An interesting point. I'll have to look into that.

core is pretty cold, for both electrons and ions,

Ions are hot at the center (well, the positive ones anyway). They are cold at the edge. The reverse is true for electrons.

Why does this plasma stay so hot when electrons are being lost to the outer walls?

I'm not sure what system you're describing. Are you still talking about Polywells? In a PW, electrons will generally flow to the anode in the system, the Magrid. The system stays "hot" because it has a hot electron drive, which dominates the energy inputs.

In such conversations before I always point people towards Saha equations for ionisation fractions,

Isn't Saha intended for weakly ionized plasmas?

I haven't yet seen any reason to doubt Bussard's claim of fast ionization at startup, so I'll treat it as valid. As I said before, I would be interested in any papers on the subject. (The closest thing I stumbled across so far was an IEEE paper claiming full ionization of deuterium plasma at avg energy of only 50eV.)

[chrismb]

Should be for all plasmas. Type in "Saha's equation" into a search engine and let us know what you find out. I don't really feel like my word is taken for much here, so at least follow some of the directions I offer to independent references over what I am talking about.

As I said, I have no objection to accepting highly ionised conditions in the first few us. But the idea that an electron drive can maintain those conditions... well, best you show me the number crunch on that rather than taking someone's word for it.

[TallDave]

Well, the famous classroom example is that if you take the Saha ionization fraction of the Sun, you find it is only 75% ionized. Doh! But here's the wiki fwiw.

http://en.wikipedia.org/wiki/Saha_ionization_equation

the Saha equation only holds for weakly ionized plasmas for which the Debye length is large.

But I'm not 100% sure how to parse that. Either way I'd still be curious what ionization fraction one gets plugging in Rick's ITER comparison numbers (I think that's 10K eV, 1e22 density, deuterium). Maybe we can all run that over Thanksgiving just for fun.

Your other statement seems to imply the plasma could be less ionized after startup (at avg temp of KeVs) than at startup (at 100eV), which seems counterintuitive at least.

[chrismb]

My gut reaction is that it is probably like that. As you flick the switch you will likely get an initial rush of particle trapping in the mag fields at the centre, but then as that space charge builds, more charged particles will just expand that trapping until you get losses, and when you get losses to the outer chamber surfaces neutralisations may occur that would 'pollute' the thermal mix such that if you are trying to pump the ion trapping with electrons then they'll have to work pretty hard.

I've said similar before, but the way I see it is that even if you can start off with a perfect vacuum and lose one ion to neutralisation, then that'll start causing non-radial scattering, with further neutralisation, etc..

This is just my feeling about it, mind. I can't say I've crunched the numbers either, but that's mainly because I don't really see how it is going to avoid thermal [ion] losses to the chamber. I might be surprised yet, it might still all work out beautifully as planned.

[D Tibbets]

chrismb, it seems to me (hopefully my impression is acurate) that you are talking about the initial conditions of a static system. As it runs down, you would expect what you say. But Bussard repeatedly stressed that this is a dynamic system. Of course electrons are leaving the system as they fly to the walls or diffuse across the magnetic fields. That is why you need to continuously (dynamically) inject new hot electrons. The problem is that this dynamic feeding of the machine has always cost way too much energy. The cusp squeezing and recirculation apparently changes this shortcoming. Also, keep in mind that ions are also leaving the system. Hopefully with good relative fuel ion containment in a net positive energy machine, most of these escaping ions will be fusion produced ions. This changes the dynamics a small to moderate amount. This fits with what Bussard said about injection of electrons may be minimized by the lingering left behind electrons in a gas puffed system, especially with high Z fuels. I have no idea how this would effect the energy of these secondary electrons

Saying that, the visible spectrum light you see in these machines is probably almost all from recombinations. A comparison of this recombination glow intensity that is observed to that expected if almost all of the plasma was participating would be interesting. Is this glow coming from 1 recombination/ trillions of ions, 1/ million ions, 1/ 100 ions, 1/ 768,480,900,020,000,000,000 ions, etc. I'm guessing this is significantly smaller than the glows seen in glow discharge fusors (or the WB7 demo picture) as this can be easily recorded with a CCD camera, while a photomultiplier tube was used with WB6 measurements

The WB7 picture doesn't count as the machine was arcing and (I think) overloaded with helium gas.

The only comparison that I can think of would be with pictures of the glow in Tokamaks. Is the densities similar? Perhaps, at least in WB6. Is the recombination glow intensity similar? What does this glow in Tokamaks represent compared to the ratios above?
A visible glow (if not florescence) implies there is some recombinations occurring, at least on the edge. But this does not give much information about the proportions. One other element is to consider the Pashin glow morphology in fusors or glow discharge tubes and figure out what is occuring and relating it to Polywells.

As for the Polywell working as a pulsed machine, it all depends on the length of the pulses, and the energy required to reset the system, and possibly on the amount of excess positive Q you have if the machine was steady state.

Dan Tibbets