Time for a possibly absurbly optimistic prediction

[93143]

I thought the issue with concave magnetic fields was that they 'blow out'; that is, the field gets weaker as it expands outwards under plasma pressure. In a Polywell, the field configuration is naturally convex in the absence of plasma pressure, so concavity due to electron pressure shouldn't matter; the field still gets stronger as you push on it. Am I wrong?

[TallDave]

That was more or less my argument as well.

[D Tibbets]

I thought the issue with concave magnetic fields was that they 'blow out'; that is, the field gets weaker as it expands outwards under plasma pressure. In a Polywell, the field configuration is naturally convex in the absence of plasma pressure, so concavity due to electron pressure shouldn't matter; the field still gets stronger as you push on it. Am I wrong?

At least up to the Beta=1 condition? Beyond that does the magnetic field at the midpoints between the cusps become spherical, then concave twoards the center?

Concerning electrostatic versus magnetic confinement. Though not stressed, I wander how much compromise there is between the two and how much this contributes to performance.
Certainly the initial electrons injected are contained magnetically progressively more efficiently as Beta = 1 is approached. Once ions are injected they are contained by the electrostatic field of the excess electrons. But, as highlighted by Nebel's comment about high energy alphas being contained magnetically for ~ 1000 passes, while the potential well will only slow them on their outward bound journy by perhaps 1% (eg:30KeV potential well / 3MeV kinetic energy). If the fuel ions are contained for ~ 100,000 passes, then the electrostatic/ magnetic containment ratios are reversed.
Is this ~ 1 percent ratio trivial, or is there some synergestic effect that multiplies the effective containment, border conditions, annealing, etc, etc ? Also, does the regions (distance from center) where the ions are stoped by the electrostatic field, versus the distance the electrons are stoped by the magnetic field effect border conditions (I'm thinking in terms of why there would not be ambipolar flow in the cusps)?


Dan Tibbets

[TallDave]

The electrons are contained for 100K passes. I'm not sure I've seen any estimate of the ions -- but Bussard claims the only losses are electron losses, so he apparently figured they never got out in any siginficant quantity.

Ion upscatter is not believed to be a big problem in these machines. Nebel said he talked this over with Luis Chacon and described the issue as "a red herring."

(I'm thinking in terms of why there would not be ambipolar flow in the cusps)? ?

Yep. We know a Polywell isn't ambipolar -- it's going to be spitting out MW of electrons and essentially no ions, according to theory.

Rick asked once what such a quasineutral flow (ions and electrons) would look like. As best I can figure it doesn't jibe with what we can guess are the measured results, because you would see big ion losses, like Bussard saw when he tried repeller plates at the cusps. Presumably the reviewers would not be pushing forward if that were the case.

[D Tibbets]

The electrons are contained for 100K passes. I'm not sure I've seen any estimate of the ions -- but Bussard claims the only losses are electron losses, so he apparently figured they never got out in any siginficant quantity.....

My understanding is that ions are lost at some acceptable rate, but they are at the top of thier potential well, so the energy lost per ion lost is trivial. The limit on acceptable ion losses are primarily dependant on concerns about ions accumulating / neutralizing at a rate that the density outside the magrid builds till arcing can occur between the positively charged magrid casing and other structures outside the magrid - emitters, deceleration grids, supports, vacuum vessel wall etc. I use 100,000 passes for the ion lifetimes because I'm assuming that they escape slower than the electrons. I suspect the real ion lifetimes are significantly higher than this, though admittedly I don't recall seing any actual numbers . It should be derivable from electron and ion gun currents, but again I don't know the numbers. Reports on WB6 could give some rough ratio, but I don't know how many gas molecules were delivered and ionized.


Dan Tibbets

[TallDave]

My understanding is that ions are lost at some acceptable rate, but they are at the top of thier potential well, so the energy lost per ion lost is trivial.

An ion that escapes has gained enough energy to get out of the well, so they're the most energetic ions in the system.

They probably don't drag a whole lot of energy out with them relative to the well depth, considering when they leave they aren't much higher than where they started. But ions are a thousand times heavier than electrons, so with even a small gain they take a lot of energy with them when they leave.

(An ion would have the least potential energy at the bottom of the well. To take out the least energetic ions we would have to pull out ions at rest from the bottom of the well; they would have the least potential and kinetic energy. Think of them as rocks bouncing around in a valley and it makes more intuitive sense.)

My understanding is that ions are lost at some acceptable rate,

Well, again, Bussard says only electron losses.

Assuming the use of super-conductors for the magnetic field drive coils, the electron losses are the only major system losses.

If there's upscatter, it's too small to be significant -- let's say 1% of electron losses. And ions are a thousand times heavier than an electron, so they must be confined 1000x better than electrons for them to be equal, 1000/.01 = 100,000x better to give 1% losses. I don't know how to translate that into the number of transits because I don't know the ratio of electron speeds to ion speeds.

But anyways, back to your original point: the electrostatic confinement is good enough that the magnetic confinement probably doesn't even matter. But if you're getting alphas (moving at MeVs, mind you!) to make 1000 passes, if there was any upscatter the odd fuel ion that washed up to the magnetic fields would very likely get bounced around and fall back down.

[D Tibbets]

My understanding is that ions are lost at some acceptable rate, but they are at the top of thier potential well, so the energy lost per ion lost is trivial.

An ion that escapes has gained enough energy to get out of the well, so they're the most energetic ions in the system.

They probably don't drag a whole lot of energy out with them relative to the well depth, considering when they leave they aren't much higher than where they started. But ions are a thousand times heavier than electrons, so with even a small gain they take a lot of energy with them when they leave.

(An ion would have the least potential energy at the bottom of the well. To take out the least energetic ions we would have to pull out ions at rest from the bottom of the well; they would have the least potential and kinetic energy. Think of them as rocks bouncing around in a valley and it makes more intuitive sense.)

My understanding is that ions are lost at some acceptable rate,

Well, again, Bussard says only electron losses.

Assuming the use of super-conductors for the magnetic field drive coils, the electron losses are the only major system losses.

If there's upscatter, it's too small to be significant -- let's say 1% of electron losses. And ions are a thousand times heavier than an electron, so they must be confined 1000x better than electrons for them to be equal, 1000/.01 = 100,000x better to give 1% losses. I don't know how to translate that into the number of transits because I don't know the ratio of electron speeds to ion speeds.

But anyways, back to your original point: the electrostatic confinement is good enough that the magnetic confinement probably doesn't even matter. But if you're getting alphas (moving at MeVs, mind you!) to make 1000 passes, if there was any upscatter the odd fuel ion that washed up to the magnetic fields would very likely get bounced around and fall back down.

It's true that the most energetic ions are the most likely to climb high enough in a cusp against the electrostatic potential well and escape. But while they start out fast with alot of potential energy, this is bled off till thier outward velocity drops to zero (no kinetic energy- or the ion is bounced off the mafnetic field, if not at a cusp, with no energy loss), or some hopefully small residual velocity/ kinetic energy that allows them to escape. But, its position at this represents potential energy. Most or all of it's kinetic energy has been returned to the potential well. Because of the positively charged magrid now inside of this escaped ion, the electron potential well is effectively neutralized and the ion drifts along on its inertia, perhaps gaining some kinetic energy from the positively charged magrid, but not much as the electron potential well is almost as strong. I've wondered how much energy the escaped ion would pick up from the positive magrid. With (eg) the magrid being charged to 12 KV and the potential well being 10 KV it seems the ion would pick up ~ 2 KeV of energy. A substantial amount. How this fits into the picture, I don't know. Geometry of the magrids probably plays a role - summation of electric field vectors and all that. If, more than a small amout of energy is lost in this manner, the ion lifetimes would need to be perhaps an order or two of magnitude greater to make the energy loss trivial, but I doubt that a 1000 fold difference would be needed(?).

Also, remember that while the ion is much heavier than the electron the kinetic energy is the same as the electron. One volt will accelerate an ion or electron to the same eV of kinetic energy. A 10,000 eV electron has as much kinetic energy as a 10,000 eV ion. The energy is 1/2 MV^2. The 10,000 eV electron is traveling ~ 10 million meters per second, while the heavier ion (proton) is traveling ~ 2 million meters per second. The velocities are different but the KE's (mass times the velocity squared) are not.

That raises the question - why does a magnetic field contain an electron better than an ion if they both have the same kinetic energy. I think it might be because the kinetic energy is not the same as the inertia (anyone know the formula for calculating inertia?), at least where magnetic fields are concerned. That is why the gyroradius is different. I'm foggy in this area, any enlightenment?

Those ions that are down scattered so they stay near the center spend all of their time in this ion dense area and are sitting ducks for upscattering collisions from fast ions . And since they are near the center they are more likely to be bounced in a more radial direction rather than a transverse direction. This isn't 'annealing' as I understand it , but it would tend to limit the low energy tail of the ions so long as there is a significant population of average or high energy ions that are on mostly radial paths. The periferal 'annealing' of low kinetic energy ions decrease transverse motions in this area, thus preserving the near radial orbits of the average ion. By this convoluted reasoning I can see the edge annealing not only helping to slow down transverse thermalization, but also slowing radial thermalization- at least on the low side and possibly also on the high side as the upscattered (but still contained) ions that approach the dense central reigon is more likely to hit a low energy ion that spends alot of time in this area rather than an average ion that speends less time in the dense center. Also, consider the potential anode, if too many ions are tightly focused to the center or lazy low energy ions accumulate in the center they will repell each other, so it's not quite like rocks in the bottom of a well, more like a bowl that has a small hump in the center and which is being constantly bombarded with marbles from the edge.
Enough rambling!

ps: An ion that escapes carries a positive charge with it. That is one less electron that needs to be replaced with a new high energy electron, provided that the electron that is left behind has not thermalized yet, so that may match the loss of the ion accelerating outward outside of the magrid.
Or, if escaping ions tend to drag free electrons along with them as they traverse the cusp (As A. Carlson believes), once the pair are outside the grid, and the charge on the magrid is seen the pair seperate- the electron is accelerated back into the Wiffleball , effectively balancing the ion's outward acceleration- a net zero balance. In that case the cusps would be ambipolar within the magrid, but outside the charges would seperate and overall the cusp would not be ambipolar (due to electron recirculation).
Now, I'm really done rambling.

. .... but, what if.....


Dan Tibbets

[TallDave]

But, its position at this represents potential energy. Most or all of it's kinetic energy has been returned to the potential well

Yep, except for what it borrowed from other ions to get out.

The velocities are different but the KE's (mass times the velocity squared) are not.

Yeah, that's why it's a little easier just to work with overall energy loss.

That raises the question - why does a magnetic field contain an electron better than an ion if they both have the same kinetic energy.

Kinetic energy is 1/2mv^2, momentum is mv. So an electron has to be ~1e3 times as fast to be as hard to deflect as an ion.

[D Tibbets]

But, its position at this represents potential energy. Most or all of it's kinetic energy has been returned to the potential well

Yep, except for what it borrowed from other ions to get out.

The velocities are different but the KE's (mass times the velocity squared) are not.

Yeah, that's why it's a little easier just to work with overall energy loss.

That raises the question - why does a magnetic field contain an electron better than an ion if they both have the same kinetic energy.

Kinetic energy is 1/2mv^2, momentum is mv.

Ah, I see your point about the escaped upscattered ions stealing energy from the rest of the ion population. It is all a matter or degree, or the spread in the energy of an upscattered ion before, on average, it finds a cusp. At least some of the high end thermalization would be dampened by this (at the cost of the average ion energy). Obvously the longer the ion lifetime the better (so long as they remain nonthermalized). A thousand fold longer lifetime than the electrons? Actually, I have no idea, but keeping them nonthermalized for that time would mean efficient annealing would be essential.

And, thanks for the momentum formula, the fog has lifted a little.

Dan Tibbets

[Art Carlson]

Why are you only worried about up-scattered ions? If an ion gets down-scattered significantly it will no longer be able to participate in a fusion reaction but will continue to take up pressure and contribute to bremsstrahlung. And what about the ions that undergo energy-conserving scattering? They can also spoil your picture.

[TallDave]

IIRC the Chacon paper tended to suggest they would gain energy from collisions.

And what about the ions that undergo energy-conserving scattering?

Are we talking about transverse momentum? Ions that gain transverse momentum should tend to lose it and gain radial momentum while at the top of their orbits, where the collision cross-section is greater.

[MSimon]

Msimon probably has something like it already and I am preaching to the choir I bet.

Even a simple spreadsheet overseeing the whole agreed upon framework? I know a few have been done before on one issue at hand or another.

I do my work with spreadsheets. Better than BOE. Not as good as interactive.

[TallDave]

Msimon probably has something like it already and I am preaching to the choir I bet.

Even a simple spreadsheet overseeing the whole agreed upon framework? I know a few have been done before on one issue at hand or another.

I do my work with spreadsheets. Better than BOE. Not as good as interactive.

I've got a couple bouncing around too, probably very simplistic compared to Simon's.

It's hard to do something elaborate without access to the WB-X data and a strong physics background. I imagine EMC2 has some nice simulations though.

[D Tibbets]

Why are you only worried about up-scattered ions? If an ion gets down-scattered significantly it will no longer be able to participate in a fusion reaction but will continue to take up pressure and contribute to bremsstrahlung. And what about the ions that undergo energy-conserving scattering? They can also spoil your picture.

Art, my rambling in an earlier post about impeading radial motion thermalization of ions ...
"Those ions that are down scattered so they stay near the center spend all of their time in this ion dense area and are sitting ducks for upscattering collisions from fast ions . And since they are near the center they are more likely to be bounced in a more radial direction rather than a transverse direction. This isn't 'annealing' as I understand it , but it would tend to limit the low energy tail of the ions so long as there is a significant population of average or high energy ions that are on mostly radial paths. The periferal 'edge annealing' of low kinetic energy ions (at the top of thier potential well) decrease transverse motions in this area, thus preserving the near radial orbits of the average ion. By this convoluted reasoning I can see the edge annealing not only helping to slow down transverse thermalization, but also slowing radial thermalization- at least on the low side and possibly also on the high side as the upscattered (but still contained) ions that approach the dense central reigon is more likely to hit a low energy ion that spends alot of time in this area rather than an average ion that speends less time in the dense center."...
At least from a hand waving perspective, does this make sense, or is it nonsense?


Dan Tibbets