space charge

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ohiovr
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space charge

Post by ohiovr »

Fusor neutral density is around a millionth of an atmosphere, so per cubic meter you may have about 180 micrograms of fuel ions. If all of that fuel were ionized, you'd have a large fraction of a coulomb (enough to blow it up to smithereens). So I presume only a tiny fraction of the atmosphere is ionized. Am I right?

D Tibbets
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Re: space charge

Post by D Tibbets »

ohiovr wrote:Fusor neutral density is around a millionth of an atmosphere, so per cubic meter you may have about 180 micrograms of fuel ions. If all of that fuel were ionized, you'd have a large fraction of a coulomb (enough to blow it up to smithereens). So I presume only a tiny fraction of the atmosphere is ionized. Am I right?
Lets see.... One mole of deuterium is 2 grams in 22.4 liters at STP, so ~ 50 moles per cubic meter or ~ 100 grams. At 1 millionth of an atmosphere that would be ~ 100 micrograms. The numbers are close, though probably better to talk of molar equivalents rather than mass. With a Z of one and 6.02 * 10^23 particles per 22.4 liters or ~ 3*10^25 particles per cubic meter results in ~ 3 *10^19 particles per cubic meter at 1 millionth of an atmosphere. This number may be ~ 5 times greater in a glow discharge fusor and similar numbers in a good Wiffleball (or perhaps up to 10 times greater depending on the Wiffleball trapping factor and the outside background pressure). This background pressure probably has to be less than ~ 0.0000001 th of an atmosphere. With a Wiffleball trapping factor of ~ 1000, the ions (and electrons) trapped inside the Wiffleball might be as high as ~ 0.00001 atmospheres.

I don't know what percentage of the gas is ionized inside a glow discharge fusor but I have heard that ion- neutral collisions dominate by a factor of ~ 60 over ion-ion collisions. This means the neutral atom/ molecule density is perhaps up to ~ 100 times that of the ions. This would decrease the Coulomb charge pressure accordingly, presuming you only had ions (positive charges) and neutrals in the chamber.

But in a neutral plasma, the negative electrons and positive charged ions cancel each other out. There would be no net space charge, and no space charge Coulomb pressure. Keep in mind that the Wiffleball inflation, increase in Beta is due to the cumulative effects of the kinetic energy of the charged particles (ions and electrons) hitting the magnetic field border, not due to a space charge directly.

In the Polywell, inside the Wiffleball border the ions and electrons may exceed the neutral background atoms by as much as ~ 1000 fold. As such the beam- beam collisions should dominate over beam background collisions. This is important, but does not apply much to this discussion. Inside the Wiffleball the background neutral background atoms may be similar to that outside the magrid, perhaps 0.00000001 to 0.0000001 atmospheres, while the charged particles may be at ~ 0.00001 atmospheres due to selective confinement of the charged particles. This is important as the background pressure outside the Wiffleball region has to be maintained below ~ 1 millionth of an atmosphere to prevent glow discharge/ arcing in this region. This concentrating effect inside the Wiffleball is key to reaching useful fusion generating densities, while avoiding intolerable arcing outside the magrid.

All of this is interesting, at least to me 8) , but doesn't directly address you concern.
What is important here is that a neutral plasma does not have a space charge- there is no charge separation. Coulomb charge pressure is zero. It is when one species exceeds the other that space charge builds up. In a Non Neutral plasma the excess of electrons (in the Polywell) creates the space charge. This is indeed limited by the buildup of space charge Coulomb pressure, and it can theoretically become immense. The Brillion limit applies (I think) but only as applied to the difference in negative and positive charges, not the total. In a Polywell with a internal Wiffleball density of ~ 10^20 charged particles / M^3, the excess of electrons may be ~ 10^14/ M3. The coulomb pressure would be derived from this number, not the total charged particle numbers. There would be 100,000,000,000,000,000,000 positive charges per m^3 and 100,000,100,000,000,000,000 negative charges per M^3. This simple analysis assumes a homogenous mixture of electrons and positively charged ions. There can be local variations while the overall numbers remain the same and this can complicate the picture. Such can apply to the Polywell in various ways- shape of the potential well, POPS like effects, etc.

Dan Tibbets
To error is human... and I'm very human.

ohiovr
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Re: space charge

Post by ohiovr »

Thanks Dan this clears a lot of things up.

I think it is pretty reasonable to say that the neutral gas outnumbers the ions by at least 60 (I'd guess more than 100). I looked at how many coulombs were involved and it was pretty scary looking.

I understand all that about neutral plasmas and the potential benefit to the polywell concept over pure ions. I do now having thought about it recently.

Its a little ironic in a twisted way that my recent inspiration for a new geometry came out of research dealing with making electrodes transparent for eliminating space charge. But.. the problem is, space charge limits the density of my idea! Since as Hanlyp said, power output is the square of the density.... well looks pretty grim Well its dumb but at least I can laugh about it.

I have other ideas. Muahaha

ohiovr
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Re: space charge

Post by ohiovr »

BTW,

I bought a book recommended to me called Inertial Electrostatic Confinement Fusion. Great book. But unfortunately their index is really very poor. I could not find anything on density or space charge. The three things they said were the biggest impediments to IEC fusion power were (paraphrasing)

Collisions with the grid
Charge Exchange (collisions with neutrals I think?)
upscattering

They didn't mention in the same page or near the same page how much density has such a huge role. I guess people far more educated than myself, would realize these things already. But it would be nice to see in ink at any rate.

D Tibbets
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Re: space charge

Post by D Tibbets »

PS: Speaking of the Brillion limit, I think, without bothering to look it up again, that the excess charge limis is ~ 10 ^13 charges per CC, or ~ 10^19 per cubic meter. Beyond that the Coulomb pressure rises very rapidly, which means the voltage increases proportionately. Even below that the associated voltage can be high, but still in the neighborhood of less than a million volts- thus obtainable in a reasonable machine.

I assume in a Polywell with an overall charged particle (positive and negative) density of ~ 10^22 per M^3, the excess electron density would be ~ 10^16 per M^3. Low enough that the Brillion limit is not a problem at voltages of up to a few hundred thousands of volts. Pushing much past this imbalance density though might become intolerable. This may be why Polywells with it's desired ~ 1 part per million excess of electrons is limited to overall densities of ~ 10 ^22 charged particles per M^3. At this combination of total balanced charge density plus the excess electron density, a useful potential well can be maintained, and a useful fusion generating density can be maintained, without without run away Coulomb pressure buildup. The ~ 1 part per million excess of energetic electrons produces the desired deep potential well, with the Brillion limit concerns minimized to acceptable levels.

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
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Joined: Thu Jun 26, 2008 6:52 am

Re: space charge

Post by D Tibbets »

ohiovr wrote:BTW,

I bought a book recommended to me called Inertial Electrostatic Confinement Fusion. Great book. But unfortunately their index is really very poor. I could not find anything on density or space charge. The three things they said were the biggest impediments to IEC fusion power were (paraphrasing)

Collisions with the grid
Charge Exchange (collisions with neutrals I think?)
upscattering

They didn't mention in the same page or near the same page how much density has such a huge role. I guess people far more educated than myself, would realize these things already. But it would be nice to see in ink at any rate.
Darn it :evil: my post was lost. Oh well, it spares the reader. I'll try again in a much condensed manner...

The virtual grid advantage is obvious. Passes are not limited to ~ 20 passes at best, but by many thousands at least.

Collisions between hot ions and cold neutrals (weather they charge exchange or not) leading to hotter neutrals flying to walls loses energy without contributing much to fusion possibilities. It also cools the ions if the collisions happens in the core.

Upscattering of ions through collisions results in the ion escaping the potential well created by the real or virtual cathode and smacking into the walls. I don't know how much this contributes in a fsuor relative to smacking into the grid, but with a virtual grid, the upscattering of ions becomes relatively much more important. Conditions that permit ion annealing in a Polywell becomes increasingly attractive.

Dan Tibbets
To error is human... and I'm very human.

ohiovr
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Re: space charge

Post by ohiovr »

D Tibbets wrote:PS: Speaking of the Brillion limit, I think, without bothering to look it up again, that the excess charge limis is ~ 10 ^13 charges per CC, or ~ 10^19 per cubic meter.
Dan Tibbets
Are you sure? That would be more than a coulomb per cubic meter. I hope you are sure cause this is great news heh heh.... :twisted:

ohiovr
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Re: space charge

Post by ohiovr »

ohiovr wrote:
D Tibbets wrote:PS: Speaking of the Brillion limit, I think, without bothering to look it up again, that the excess charge limis is ~ 10 ^13 charges per CC, or ~ 10^19 per cubic meter.
Dan Tibbets
Are you sure? That would be more than a coulomb per cubic meter. I hope you are sure cause this is great news heh heh.... :twisted:
I think I don't understand. Does this mean it is technologically possible to stuff a coulomb of ions into a box 1 cubic meter in size some how? What does the Brillouin limit mean?

ohiovr
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Re: space charge

Post by ohiovr »

Ha! That's still only 33.4 micrograms per cubic meter. A lot smaller than mr ITER.

D Tibbets
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Re: space charge

Post by D Tibbets »

This was discussed some in an earlier thread. Perhaps it will help:

viewtopic.php?f=3&t=956
/Chrismb

The Brillouin limit defines the maximum number of particles in non-neutrality conditions, viz. Polywell's central core of electrons.

{L Brillouin, Phys. Rev. 67, 260 (1945)}

This is n=B2/(2umc2) [n:particle count, B: mag field, u:permeability]

For a 1T field, as per the 'fusion reactor' in http://www.askmar.com/Fusion_files/Poly ... oncept.pdf, you get n = 4.8E18, which means in the central core of radius 1cm there would be a maximum total population of 1.5E13 electrons at any one time.

Presumably, then, the total population of ions within the device cannot exceed this 1.5E13 else total charge in the device would go positive, rather than negative, thus stifling any further ion generation.

Is the Polywell designed to exceed the Brillouin limit for electron confinement, and if so what makes it special that it can do so?

best regards,

Chris MB.
I think this is where I think my perception that ~ 1*10^13 particles per cubic centimeter comes from. In the quote though there are several misconceptions (in my opinion). It is not the number of total charged particles, but the total excess of one species of charged particles, ie: difference in electron numbers and single positively charged ion numbers. This separation of charge density is the quoted number.
Also, note this calculated number was at 1 Tesla. At 10 Tesla the number would be 100 times higher.
What this quoted analysis does not consider is several things.

First is the dwell time of electrons at any given radius based volume (cc) based on their local speed as they transit the system in their potential well. I'm unsure of how to apply this except that it would presumably modify the picture.

Secondly, the number refers to the charge imbalance, not the absolute numbers of any one species. At the often quoted Polywell conditions of a non neutral plasma with an excess of ~ 1 electron for each 1 million electron/ ion pairs, the charge imbalance for a total plasma density of 10^13 charged particles / c c would be 10^ 7 /cc excess of electrons/ cc. This is well below the Brillouin limit. At the Brillouin limit for unbalanced charge of 10^13/ cc (electron excess), the total plasma density would be 10^19 charged particles / cc. Even at these modest B field strengths the density converted to meters cubed would be 10^25 total charged particles / M^3. This is well above the predicted density targets in a Polywel of ~ 10^22 total charged particles / M^3l, so the consideration is not a concern. At least that is my impression.
At 10^22/ M^3 the unbalanced electron excess numbers would be 10^16 / M^2 or 10^10/ cc. This is ~ 1000 times less than the Brillouin limit. Also, I think this represents ~ 0.001 Coulombs of unbalanced charge.


Further down the thread there are some links that might give further insight, though it is complicated by various geometries and confinement systems.

Dan Tibbets
To error is human... and I'm very human.

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