Ion injection into a Polywell

[jmc]

I’ve been thinking about the problem of ion injection into a quasi-neutral polywell where the electrons and ions are at roughly equal density. The problem here is as you raise the ion density the region where the well descends in potential (i.e. the region where a radially inward pointing electric field is pointing) gets narrower and narrower this means it gets harder and harder to ionize ions in a region where both, the field pulls them inward and where they are not already at the bottom of this potential well. Let alone to ionize them in a location where they all have the same potential energy. If you ionize them too high up then they are born in a region where the well is parabolic and not spherical and they instantly lose their convergence.

If you inject ions in from the region above the well you come across the second problem that what goes in must come out, in that if the ion enters the well with a finite kinetic energy then after one pass (if the well is perfectly spherical) the will have enough kinetic energy to leave it after one pass and will enter the magnetic field region again and again and again also loosing their convergence. If the equipotentials of well are convex and strongly effected by the field induced by the magrid then you will have the same problem again with convergence.

Yet as you go deeper into the well, the field-lines and thus equipotentials become progressively more spherical as they get weaker and weaker and get pushed around more and more easily by the diamagnetic effects of the isotropic pressure of the plasma inside.

The best and only way that I can think of to inject ions in such a way as to achieve the conditions described by Krall in Physics of fluids B is to inject a focussed neutral beam into the comparatively cold plasma of the polywell.

Far from the polywell you have an ion source, then you have an accelerator that accelerates the ions of the beam to a parallel collimated energy (say 70 keV) then you pass this collimated ion beam through an electrostatic or magnetic lens whose focus is at the centre of the polywell, you then pass the beam ions through a neutralizer, all this is done at a distance from the polywell where the magnetic fields generated by the coils of the polywell are negligible. Now you have a group of monoenergetic beam atoms all on trajectories heading towards a single spot at the centre of the Polywell. Since they are neutral they pass through the magnetic field of the Polywell unperturbed, since the drop in the potential well is so sudden and all the cold ions are at the bottom the fast convergent neutrals pass through this step unperturbed. Now the are at the flat bottom of the potential well (~75keV) travelling at fusion velocities, suddenly all around them is a dense plasma of cool (~5keV) ions which charge exchange onto them and ionize them. They get ionized however, long before they significantly change their energy or trajectory. The electrons start off with a convergent trajectory but soon lose it due to collisions with the isotropic electrons

This results in two populations, a cool isotropic ion population at 5keV and a highly convergent mono-energetic ion population at 70keV that are comfortably trapped inside the well. There is also a cool electron (5keV) population aswell. If the focus of the beam ion population is good enough and indeed if there are enough beamlets all pointing to the same central region, then in spite of the fact that there are much less beam ions then bulk ions, if the convergence ratio is tight enough, say between 100 and 1000, which should be possible with a carefully designed neutral beam and a relatively large machine, then the density of the convergent fast ion population in the core will far exceed the density of the bulk ion population since the density scales with the square of the convergence ratio, this in turn means that for each pass the monoenergetic ions that converge at the centre could make more collisions with fellow fast convergent ions in the core then they do with the slow cooler ions in the bulk. This is due to the strong increase in density with convergence (it increases with at least the square of the convergence ratio and that is not counting a potential peaking slowing the ions down), when the ions collect in the centre at high densities this causes a build up of potential at the centre of the polywell (say 40keV) that sucks in the cold electrons from the bulk to neutralize the ions in accordance with the equation n=n(bulk)exp((e*phi)/kT(e)). This peaking reduces the kinetic energy of the ions which further causes them collide more with each other in the core then they would with cool bulk ions. In the most extreme case of density peaking it might even take an ion longer to collide with a bulk ion then it would to fuse with a core ion.

An interesting aspect of this central potential peaking effect is that it effectively insulates the cool bulk ions from the core of the polywell, they simply do not have the energy to penetrate into the most peaked region, in addition to this the cool electrons, on entering into the peaked region will, paradoxically, heat the monoenergetic convergent ions as the kinetic energy of the electrons shall be 40+5=45keV in the peaked region while the kinetic energy of the ions will be 70-40=30keV, in spite of their high kinetic energy in the core, however, they will not heat the bulk ions as in order to reach the bulk ion population they will have to climb a potential gradient and lose much of their kinetic energy. Thus the neutralising electrons in the reacting region of the Polywell, do not infact heat the bulk ions, this increases the beta of the device aswell as the ability of the central potential peak to suck in electrons (remember the kT(e) in the denominator of the electron density equation.)

So what is the role of these cool bulk ions? To provide electrons that can be sucked into the central potential peak without requiring the electrons be at a ridiculously low temperature, in other words to raise n(bulk).

After passing through the core the convergent mono-energetic population now heads for the edge where they all slow down at exactly the same location, there their cross-sections of collision suddenly balloon and the amount of time they stay their also goes up. This causes the annealing in the edge region. It may be possible for the beam population to be sparse enough for quasi neutrality to be not as much of an issue in the edge as it is in he core. Also because the bulk ions are trapped at a lower potential region without the energy to climb up to the beam ion annealing region, the density of electrons can still be lower in the edge than it is in the bulk, without the potential being lower.

I've written a lot here, but in practice I'm just talking about firing a focused neutral beam into a (relatively) cool, isotropic plasma.

[MSimon]

If you inject neutral ions into the reaction region at the surface of the grids electron impacts will ionize the neutrals and the magnetic field will sweep the electrons out of the proximity of the grid.

Electron guns or ion guns or neutral ion beams are a loss mechanism in a power producer. You really don't want them in anything other than an experimental unit where the fusion power is low.

Let me add I'm not a big believer in ion renormalization by edge collisions. I think what happens is more like klystron type bunching.

The trouble is our level of ignorance is very high.

[drmike]

Here is what ITER does. It is a very old technique, and it is what I did my thesis on some 25 - 30 years ago. As Simon says - it is a power sink so if we can avoid it for a power plant it would be better - but as ITER shows it may not be possible to avoid this method.

I think we can overcome beam loss using POPS or wakefield acceleration. As Simon's .sig says, engineering is making what you want from what you have - we have electrons, ions and can add some RF. Turn lemons into lemonaid! I'm hoping that's all we need, but boy, it'd be a blast to build neutral beams again!

Now I'll have to actually find my thesis...

[cuddihy]

[quote="jmc"]I’ve been thinking about the problem of ion injection into a quasi-neutral polywell where the electrons and ions are at roughly equal density. The problem here is as you raise the ion density the region where the well descends in potential (i.e. the region where a radially inward pointing electric field is pointing) gets narrower and narrower this means it gets harder and harder to ionize ions in a region where both, the field pulls them inward and where they are not already at the bottom of this potential well. Let alone to ionize them in a location where they all have the same potential energy. If you ionize them too high up then they are born in a region where the well is parabolic and not spherical and they instantly lose their convergence.

/[quote]

I'm missing something here. Isn't injection of neutrals with electron ionization the idea?

Or is there some physical reason that doesn't work?

[jmc]

MSimon:
The neutral beam injector at MAST has a penetration depth of order 30cm or 40cm, that mean neutral atoms produced by it could plough 30 cm through ionized plasma at densities of 4*10^19/m^3 before actually getting ionized themselves, the faster they go and the more energy they have, the further they penetrate. I'm pretty confident most of the neutrals produced by the neutral beam I'm suggesting will penetrate into the zero field flat region at the bottom of the potential well without getting ionized.

You are right about the loss mechanism, today a 70keV neutral beam will have a 40% neutralization efficiency with the remaining ions being diverted by a bend magnet towards a beam dump. However there are schemes to convert the energy of the unneutralized ions back into electricity.

http://www.springerlink.com/content/k7t580217602615w/

Not many people are a big believer, least of all me. But if ion renormalization by edge collissions is possible then all the atoms must slow down to the eV range in exactly the same radial location. And in order to do that they must be born with exactly the same energy. The only way to achieve this that I know of would be with a neutral beam.

I don't believe there has been a single experiment by Bussard that achieved the stringent conditions that might result in ion renormalization

drmike: I think in a polywell it will be even harder to avoid then in a tokamak. How else will you inject mono-energetic ions through a magnetic field and into the device and ensure they will remain trapped in the potential well?

I think MSimon is a littel to obsessed with super-high-q if every bean atom injected has 70keV then if the reaction is D-T, even if only one in ten of them reacts you still have a Q of over 20, asumming 1/3 conversion efficiency you get six watts of electricity out for every watt you out in.

The beam I'm suggesting will be more complicated then the ITER beam in one sense, that it needs to be highly mono energetic and focused to a very sharp point and less demanding than the ITER beam in another, that because a Polywell is smaller the current can be lower, also it does not need to penetrate through so much plasma to get where it want to go.

[jmc]

I'm missing something here. Isn't injection of neutrals with electron ionization the idea?

Or is there some physical reason that doesn't work?

If you want the beam to be mono-energetic then you have to ionize the atoms in almost identical potential locations, something that will prove virtually impossible as the device become more quasi-neutral and the potential step becomes more square-like.

If you ionize slow gas at the bottom of the well then it will have no energy.

[MSimon]

jmc,

I'm thinking of alpha impingement. A neutral beam injector of even 1% efficiency would not be a serious loss mechanism.

The problem is where do you locate the injector in a machine that uses a decelerator (1 to 2 Meters deep) for power generation so that alphas do not over heat it?

Or suppose you have a thermal machine. You still have a 1 meter traverse to get into the reaction space.

Injecting gas at the inner face of the grids will give you ions due to alpha collisions with no extra loss mechanisms, in fact there would be a slight reduction of losses.

[jmc]

If your injecting neutrals, they should pass through the decelerator region of the device without perturbation (what with not having a net charge and all) so long as the densities are low enough not to ionize them, and if there are only fusin alphas in this decellerator region I imagine the densities will be pretty low.

Again 1 metre is fine so long as the vacuum outside reaction space is good enough.

With regards to gas, if creates electrons in the region of strong magnetic field, drawing the whole potential well into this region, this will contribute to making the equipotential surfaces less spherical, ruining convergence as Joel pointed out. Again I mention the near impossibility of a mono-energetic ion distribution function be puffing gas in.

[drmike]

Not many people are a big believer, least of all me. But if ion renormalization by edge collissions is possible then all the atoms must slow down to the eV range in exactly the same radial location. And in order to do that they must be born with exactly the same energy. The only way to achieve this that I know of would be with a neutral beam.

I think another way to achieve radial uniformity in velocity distribution is to use wakefield acceleration. By structuring waves in the electron distribution we can force radial pumping of ions. So I don't think neutral beams are the only method. It will be interesting to see the overall energy balance and fuel requirements though - neutral beam injection may well be exceptionally useful to maintain fuel levels and radial velocity distributions.

[hanelyp]

Unless experiment shows otherwise, injection of low energy neutrals from the inner face of the magrid should work fine. I.e. a puff of gas, very distinct from high energy neutral beam such as sometimes used to heat a tokomak. For best time response, injector valves squeezed in the magrid may help.

[MSimon]

Unless experiment shows otherwise, injection of low energy neutrals from the inner face of the magrid should work fine. I.e. a puff of gas, very distinct from high energy neutral beam such as sometimes used to heat a tokomak. For best time response, injector valves squeezed in the magrid may help.

Hanley,

I did some work on this at the IEC Fusion Technology blog. The conclusion I came to was that the valve needed to be magnetically operated to get the travel required (about .1 mm or less, i.e. .004" or less). That means either incorporating the valve as part of the grid magnetic structure (difficult) or locating it in one of the stalks supporting a grid (easier). Response times of the valve could be on the order of .3 mS. Add in a delay of about 1 ms for the feed tube and you get a total servo response of under 2 mS. Given the rate of burn, volume, and gas flow in a test reactor this should be more than adequate. In a full size reactor a response time in the 10 to 100mS range should be workable.

The biggest problem is getting adequate response time from the pressure measuring system. I have a design for that (at the same blog) that should also help with controlling the POPS (or other beam enhancement) frequency. Some guy at NASA Space flight thought my idea for the electronics was pretty good. Something he had not seen commercially or otherwise.

It is all here:

http://iecfusiontech.blogspot.com/

root around.

[cuddihy]

I'm missing something here. Isn't injection of neutrals with electron ionization the idea?

Or is there some physical reason that doesn't work?

If you want the beam to be mono-energetic then you have to ionize the atoms in almost identical potential locations, something that will prove virtually impossible as the device become more quasi-neutral and the potential step becomes more square-like.

If you ionize slow gas at the bottom of the well then it will have no energy.

What makes the machine become more neutral over time? I would think that by the time this gets to be a problem your pressure would be sufficient to choke off the reaction anyway?

[jmc]

I mean as you approach power densities required for a realistic powerplant.

The laser wakefield stuff sounds sublte and difficult to achieve. Maybe in the future it might be more economic then a neutral beam in the long run, but I still say a neutral beam is the most straightforward way to achieve the desired results.

Why should injecting neutrals from the inner magrid work-fine? What if the gas makes its way to the bottom of the potential well before it gets ionized? what if it gets ionized in a region which still has magnetic field and its trajectory departs significantly from being radially convergent? What if the gas atoms get ionized at different positions in the potential well so the initial distribution is not mono-energetic?

Why do you think, even ignoring the engineering issues that from a physics point of view, ionisation sound work fine. Incidentally apart from the afforementioned issues ionization of neutral gas tends to cancel out any electric field it is ionized inside, that is why in tokamak phyics it inhibits the H-mode. Puffing in neutral will create electrons in the poorly confined adiabatic region where their presence may allow heat to be conducted away from the core.

Why do people think that gas puff is fine and has no problems associated with it?

[MSimon]

jmc,

It is not a laser wakefield. It is an electrostatic wakefield due to the oscillating beams.

Of course there will be problems. However, in an operating machine with long electron and ion lifetimes using alpha particles to ionize the gas flow should work fine. Assuming the engineering details can be worked out.

The mechanism for start up need only be turned on for a few milliseconds at most. Assuming the decelerator is also charged up at start up that means injecting ~2MeV electrons into the machine to get it going. Then you turn off the e-beams and let alpha production do the rest.

At least that would be my preferred design. As much empty space as possible. Because nothing is the cheapest material you can use and it eliminates the heating problem from alpha loading.

If you are squirting gas in through the decelerator section you are fighting ionization from alphas headed in the other direction.

BTW I don't anticipate gas puffing. Steady flows based on pressure/density feedback is the way to go. Gas puffing was used because it was quick and dirty and solved the immediate problem.

[jmc]

Are you sure alpha particles are that good at ionizing? I think the fact that they are moving so fast actually reduces their cross-section of collission and ability to ionize. I also thought there was relatively few of them around and that even in a reactor their density would be far lower then he plasma. I still don't understand how this spontaneous ionization

This oscillating electrostatic wakefield, is it created by oscillating the voltage at the thermionic electron emitters at the cusp?

Empty space? Cheap? Evacuated volume is extremely expensive and should be used sparingly and efficiently.