A few questions on Polywell facts and figures.

Discuss how polywell fusion works; share theoretical questions and answers.

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chrismb
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A few questions on Polywell facts and figures.

Post by chrismb »

May I please clarify a few bits of data:

In the Polywell SCIF table, it suggests that the 'fusion reactor' particle density will be 2E20/m3 outside the core. Is this meant to mean that there would be 2E20 ions in that region, or is it also including/anticipating the neutral content of the device?

If it accommodates the neutrals, what is the ionisation ratio expected in the device?

What is the expected electron temperature in the central core?

Bussard was talking about the off-set from neutrality creating very big potentials. I was presuming that, perhaps, you could treat the central electron region as a 'sphere' for the purposes of calculating its capacitance, which works out to be about 1pF for a 1cm radius sphere. So, is it legitimate to say; if I want a 110kV well I would need a central charge of Q=VC=1.1E-7C, or about 7E11 e (well within the Brillouin limit). Is this how Bussard came up with the comment about the small departure from neutrality, and is my calculation/assumption on capacitance OK?

Debye length: For any particle density over about 1E10 charged particles/cm3 and above room temp, the Debye length is less that 10's of microns. So this applies to the central electron region (assuming the above). Is the actual electron charge that pulls the ions in just in the first several microns of the cusp surface, or is it presumed that the full population of electrons somehow acts as a central charge. If the latter, how does it do this. If the former, perhaps the electrons form a shell lining the magnetic surfaces of the cusp region?

I think these are all important matters to detail. I cannot find the answers with the search function, or by internet searching.

best regards,

Chris MB.

TallDave
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Post by TallDave »

Not sure about the neutrals, but Bussard talks about "two-color" electron injection in Valencia, so there might be an answer there. Debye length has come up before; you can do a search here. IIRC, there's some question as to how applicable it would be in a non-LTE environment.

Art Carlson
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Re: A few questions on Polywell facts and figures.

Post by Art Carlson »

chrismb wrote:
If it accommodates the neutrals, what is the ionisation ratio expected in the device?

What is the expected electron temperature in the central core?
I believe that an electron temperature on the order of the well depth - tens or hundreds of keV - is unavoidable, but the polywell orthodoxy seems to be that the electron temperature in the core is significantly lower. But even if T_e were only tens of eV, you would have essentially 100% ionization. (Of course the few neutrals you do have need careful consideration.)
Debye length: For any particle density over about 1E10 charged particles/cm3 and above room temp, the Debye length is less that 10's of microns. So this applies to the central electron region (assuming the above). Is the actual electron charge that pulls the ions in just in the first several microns of the cusp surface, or is it presumed that the full population of electrons somehow acts as a central charge. If the latter, how does it do this. If the former, perhaps the electrons form a shell lining the magnetic surfaces of the cusp region?
I am convinced, for related reasons, that the potential over most of the plasma volume must be nearly flat, with all the electric fields concentrated near the edges. It is not clear to me if that is what Bussard thought or not.

chrismb
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Post by chrismb »

The issue I was thinking was whether the magnetic field is strong enough to hold the electrons against the pull exerted on them by the ions.

If my calculation above is OK, that there are 7E11 free electrons for a 110kV potential, and if they are at 100keV = ~170Mm/s so each electron is held by a force of Bqv=1T*1.6E-19C*170Mm/s=2.6E-11N.

Now, the force on a proton in a 110kV/m field is 1.8E-14N.

So the total number of protons that can be held by these 7E11 electrons in a 1T field is (2.6E-11N/electron)/(1.8E-14N/proton) = 1500 protons for each electron.

In other words, only 1500 * 7E11 = 1E15 protons can be 'held' by a 110kV 1cm radius electron ball in a 1T field before that electron ball is pulled apart by the surrounding ions. This is several orders of magnitude lower than the densities claimed in the data tables.

Where is the error - is it my calculation/understanding, or the data in the table?

Art Carlson
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Post by Art Carlson »

Your way of looking at this problem is highly unconventional, so I'm not sure yet that I understand you. A blackboard would help.

The usual way of looking at this is magnetic pressure. A magnetic field effectively has a pressure equal to B^2/(2mu_0), so it is able to confine a (quasi-neutral) plasma with a total pressure of (3/2)*n_e*kT_e+(3/2)*n_i*kT_i. In addition there are electrostatic forces between the electrons and the ions, but these may be considered internal forces that do not affect pressure balance with the field.

In the case of a polywell, there should be little or no field in the interior, neither magnetic nor electric, so the plasma has a spatially uniform pressure. Just outside the plasma, you have a B-field with constant magnitude such that you have pressure balance between the (external) magnetic pressure and the (interior) plasma pressure. In the boundary layer, the electrons are held back by the magnetic field, while the ions move out a bit farther. This gives you a thin layer with a net positive charge just outside of where the electrons are stopped, but also a deficit of ions in a thin layer just inside of that. This creates an electric field that holds the ions in and pulls the electrons out. Because of their orbits in the magnetic field, the electrons will have a net motion perpendicular to the field. It is through the Lorenz force on this current that the magnetic field interacts with the plasma.

This sounds vaguely like the calculation you are trying to do, but not quite. The number of ions and electrons will be very nearly equal globally, and their densities will be very nearly equal locally, except in the surface layer, which, depending on details, may be a Debye length thick or a Larmor radius thick.

That that get you any farther?

chrismb
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Post by chrismb »

I need to clarify. In this calculation I am assuming the ions and electrons in the central core are quasi-neutral, with just the 7E11e = 1.1E-7C worth of charge forming the 110kV electrostatic potential well. I'm not questioning that, in this post.

But outside this core, in the rest of the device, there are a pile more ions waiting in the electric field, just poised, or on their way in, to dive into that potential well.

All these ions outside the central core cannot exceed 1E15 in number, else they would pull the central core apart. The magnetic field of 1T is not strong enough to maintain this potential well with just 7E11 100keV electrons if there are more than 1E15 protons outside of that core in this potential field.

Art Carlson
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Post by Art Carlson »

chrismb wrote:I need to clarify. In this calculation I am assuming the ions and electrons in the central core are quasi-neutral, with just the 7E11e = 1.1E-7C worth of charge forming the 110kV electrostatic potential well. I'm not questioning that, in this post.

But outside this core, in the rest of the device, there are a pile more ions waiting in the electric field, just poised, or on their way in, to dive into that potential well.

All these ions outside the central core cannot exceed 1E15 in number, else they would pull the central core apart. The magnetic field of 1T is not strong enough to maintain this potential well with just 7E11 100keV electrons if there are more than 1E15 protons outside of that core in this potential field.
What radial build are you assuming? I am thinking of a uniform, quasineutral plasma out to some radius (say, 10 cm). Then a thin layer with interesting physics (say, 1 mm thick). Then a region with no plasma, vacuum magnetic fields, and a nearly radial electric field out to the radius of the coils (at say, 15 cm).

You seem to be thinking of a much smaller "core", surrounded by a thcik layer with a significant net ion density. Is that right? You also write, "All these ions outside the central core cannot exceed 1E15 in number, else they would pull the central core apart." How can a shell of ions pull anything apart? The electric field inside a spherical shell of charge vanishes.

chrismb
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Post by chrismb »

I'm referring to the table fo data in http://www.askmar.com/Fusion_files/Poly ... oncept.pdf

Core radius, rc (m) = 1E-2

But still I do not understand you. Are we talking about the same device?

AC: "The electric field inside a spherical shell of charge vanishes."

So where are the fuel ions that are being accelerated into the core, if they are not outside the core, how many are there and, if there is no electric field, how do they accelerate?

AC: "How can a shell of ions pull anything apart?"

If there is no force on the electrons, then there is no force on the ions. What pulls and accelerated them in, otherwise?

Electric fields do not just 'exist' to accelerate charged particles, there has to be an inertial reaction somewhere. In a Polywell, an ion gains momentum by being accelerated towards electrons that hold up the electric field. Those electrons are held by a magnetic field, so ultimately the ion's momentum change (the force on it) is being reacted through to the magnets, but the electrons are intermediaries, the forces on which cannot exceed the forces that the magnets can apply.

The electrons on one side of the core pull in ions on that side of the core, the electrons on the other side of the core pull in ions on the other side of the core, and those electrons are being held together within a magnetic field. No magnetic field, no force can be applied to the electrons thus no force can be applied to the ions to accelerate them.

With no magnetic field in place, the electrons would high-tail it towards the nearest build-up of charge, which would be the ions on that electron's side of the device. With insufficient magnetic field, the same thing would happen, just at a slighly slower rate.

These are elementary force-reaction considerations. No manner of ingenious words can talk away the basic need for there to be an inertial reaction to pull ions inwards, and so there will always be an equal force applied to the component that is the source of that force.

SuperMan might well be able to lift up a building whilst standing on a table, but the table won't hold up SuperMan holding a building!! So it is also that the electrons rely on the magnetic field, which appears to be insufficient to hold in the (2E20*pi*1^2=) 6E20 particles that the above paper appears to suggest would be reciprocating through the core.

TallDave
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Post by TallDave »

Chris,

I'm not sure you're thinking about the same geometry as the rest of us. There is a positively charged magnetic grid on the outside. The field confines electrons, which would otherwise stream into the grid. The ions are confined by the electrons.

The ion focus at the core is caused by the fact that is where the well is deepest (there is some debate as to whether the focus would happen in a reactor-sized device, and whether it would even be necessary, but the well has been observed in experimental devices with laser fluoroscopy).

chrismb
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Post by chrismb »

I am of the understanding that there are meant to be electrons that are confined in a cusp like magnetic field which creates a potential well that accelerates ions from the periphery into the focus at the centre.

Is this in error?

What I am talking about in this thread is that these ions in the periphery also pull on those electrons, equal and opposite to how much those electrons pull on the ions.

I have calculated the maximum number of ions in the periphery by means of calculating how much force each of the free negative charges (electrons) there are in the centre of this spherical potential well.

What I am showing is that the ions would pull so hard on the electrons that the whole electric field would 'unpeel' as the electrons are pulled out of the core.

There HAS to be a polarisation of charge between the periphery and the core else a) there would be no e-field and ions would not be motivated to accelerate to the centre, and b) otherwise you are talking about the magnetic confinement of a thermalised plasma and this wouldn't be an IEC device.

If it is the latter, then it is absolutely clear that the microscopic Debye lengths involved would totally compromise the mechanism proposed. You would have to maintain radial polarisation to maintain motion of ions. Just putting a positive charge around a magnetically confined plasma, which is what I think you are trying to get at as a description, just doesn't work, if I understand this is what you are saying.

Art Carlson
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Post by Art Carlson »

chrismb wrote:What I am talking about in this thread is that these ions in the periphery also pull on those electrons, equal and opposite to how much those electrons pull on the ions.
This is incorrect. As I pointed out before, the electric field inside a spherical shell of charge is zero. The ions do not pull out on the electrons, or at least the ions on one side pull just as hard as the ions on the other side, but in the opposite direction. If the electron happens to be off-center, so it is nearer to one bunch of ions, the force is still balanced because the number of ions on the other side is greater.

What you do have is that the electrons repel each other. The other electrons, and not the ions, is what tends to cause a ball of electrons to explode.
chrismb wrote:There HAS to be a polarisation of charge between the periphery and the core else a) there would be no e-field and ions would not be motivated to accelerate to the centre, and b) otherwise you are talking about the magnetic confinement of a thermalised plasma and this wouldn't be an IEC device.
(a) I agree that the polywell advocates have not presented a self-consistent picture of how this is all supposed to work, in particular, the replacement of electrons and ions.
(b) I, for one, am talking about "magnetic confinement of a thermalised plasma". I don't think there is any other way this can come close to working.

Aero
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Post by Aero »

Art Carlson wrote:the electric field inside a spherical shell of charge is zero.
Art - This is true, but does it relate to the polywell? For the moment, let the polywell be considered to be spherical. But is it really a shell. Might it not be more like a charged solid of uniform density, like this.
http://answers.yahoo.com/question/index ... 448AAcLcJn
I agree that at the exact center point the charge will be zero as for a spherical shell.
Aero

chrismb
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Post by chrismb »

Art Carlson wrote: (b) I, for one, am talking about "magnetic confinement of a thermalised plasma". I don't think there is any other way this can come close to working.
I am..stunned... I don't know how to come back on that.

You are saying that this will be a 6 billion Celsius thermalised plasma, with a central core at 1/10th of atmospheric pressure, and all this is to be held together with some cusping magnetic fields.

I'm not one for emoticons, but the only thing I can say is :shock:

The radiative inelastic collisions, (recombination, brems, etc..) in this setup will be simply ENORMOUS! What do you think would be the power loss from such a configuration? I can't remotely see any mechanism for keeping enough energy in this to maintain any nuclear processes.

It must shine like a lighthouse!! It might even have a useful application as a very high power UV light.

TallDave
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Post by TallDave »

It's probably going to operate in a partially relaxed state. There are some ways brem can be mitigated.
You are saying that this will be a 6 billion Celsius thermalised plasma, with a central core at 1/10th of atmospheric pressure, and all this is to be held together with some cusping magnetic fields.
That's the advantage of IEC: electrons are light and easily confined with magnets.
I can't remotely see any mechanism for keeping enough energy in this to maintain any nuclear processes.
That's why the wiffle-ball effect and electron recirculation are so important.
What do you think would be the power loss from such a configuration?
I believe a 100MW reactor is expected to have continuous power input of 5MW.

Net-power fusion is a very tough cookie, and doing it in a way that has a reasonable plant power density (so that it's economically sensible) will be even tougher. Anything that can do that will of necessity have some eye-popping properties.

I'm not sure what you're referring to with "recombination."

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Post by MSimon »

If most of the particles are monoenergetic the concept of temperature loses some of its normal meaning. This kind of confusion comes up a lot with those new to the study of the device.

But yes - if you operate the machine using D-D with a 50 KV well (60 to 80KV drive depending) the collision temperature (head on) would be equivalent to 11,605 * 200,000. Roughly 2.3 billion degrees. Pretty slick huh?

The cross section for D-D at that velocity is about .1 barns.

Now if it is really a colliding beam machine - during most of the cycle there would be no radiation. So you only get significant radiation when you are producing fusions. Net energy possible? It remains to be seen.

Let me add that one of the reasons I love this device is that the engineering problems are both interesting and hellacious. So I'm really hoping the physics pans out.
Engineering is the art of making what you want from what you can get at a profit.

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