Bussard's bremsstrahlung calculation

[D Tibbets]

I guess in real life, the electrons injected into the center are actually scraped off of the magrid so that the magrid+wiffleball is electrically neutral. I was just arbitrarily setting the magrid to ground, but it's probably clearer to have ground proportional to 1/2 the charge in the wiffleball.

Some confusion here. I believe that the positive charge on the magrid (deficit of electrons) is derived from the power supply. So long as the magnetic shielding is working there will be no ( or negligable) current flow between the electron guns/ wiffleball and the magrid. The positive magrid provides the potential that accelerates the electrons from the electron gun into the interior of the machine. The ~ 80% potential of the Wiffleball compared to the magrid potential is (my understanding) due to the energy needed to push the electrons through the narrow cusp (like the resistance to water flow in a narrow pipe). Once inside the magrid the electrons no longer see the potential on the magrid. The grid could be grounded while the electron gun has a high enough negative potential to do the same thing, though some other aspects of recirculation may be effected by this. A possibility- with the grid grounded, an escaping electron with a velocity of 1000 eV would see a decelerating potential of only 1000 volts (-1000 volts to 0 volts potential difference) while the charged grid (+10,000 volts) present the escaping electron with a 11,000 volt potential difference to effectively reverse its flight more quickly (shorter time in the domain where any trailing ions could catch up and then see the grid). Of course the now escaped ion would not be acelerated (actually be decelerated some) but I'm guessing (to put it mildly) that when the inertia of the ions and electrons are considered, there may be a different dynamic.

Well, this is an area where I'm still confused, and Art's comment below also impacts this:

you show an inwardly directed electric field over much of the plasma volume. Why do you not expect a radial current to flow, whose divergence would quickly annihilate your excess negative charge?

If we've truly got the ions oscillating within the wiffle-field, rather than across it, then we're relying on some charge in the sphere as the only force that can drive the ions into the center. It makes perfect sense to me that the charge inside the sphere should be annihilated as electrons run away from each other and get stuck in the edge wiffle-field. But if that's the case, then the sphere has no potential difference across it and the ions won't oscillate.

This was why I originally thought that the ions oscillated from the edge of the magrid, through the wiffle-field, and finally to the center of the machine. That way, we know that the voltage between the wiffle-field and the magrid will drive the ions. The problem with this is that lorenz forces on the ions as they traverse the wiffle-field are going to fling them all over the place, resulting in no focus on the center of the machine.

Remember that once any charged particle is inside the magrid it does not see any electric field from it ( actually my understanding is that the field is present, but that the oposite sides tug equally so that the net effective field is zero). The potential on the magrid (see above) serves two purposes, first to accelerate new electrons to the drive potential, and secondly to do the same to any escaping electrons that reach that high so that they are shot back into the machine with (near?) the original energy. This would presumably keep them from remaining traped on magnetic field lines.

Concerning A. Carlson's comments, I have seen elliptical potential wells and square wells (what I guess he is suggesting) in different papers. I postulate that there is indeed current flowing in a sinse. Not current between fixed electrodes (that is the whole purpose of the magnetic shielding), but current between mobile 'electrodes'- the free ions and electrons. They could 'ground' on each other but due to the potential ( kinetic energy) they do not stick, but flow past each other. So long as one of the species are non thermal, the other will also be nonthermal. This is the purpose of the continous resupply of radially directed monoenergetic electrons. This, combined with the excess numbers of electrons and the dynamic speeds of the electrons (fast in the perifery and slow in the center) produces the increased density of electrons in the center that pulls the ions inward to high fusion speeds. The inertia of the nonreacting ions then carry them back up to the top of the potential well to start over. This is what I mean when I say osscilation. The ion could come to a stop in the center due to the build up of an excessive vertual anode, but this is presumably the pount where (as Bussard described it) the potential well is blown out.
The current beween these mobile charged particles may be comparable to an occillation in in a capacitor- resister resonate circuit that decays due to leakage, and it is this leakage (transport losses) that hopefully is small enough to allow net power production. The Wiffle Ball effect and cusp recircuation are what hopefully limits these losses to this level.

Dan Tibbets

[93143]

No, the main drive current is between the electron emitters and the magrid. Multiply by the drive voltage and you have the drive power.

Magnetic shielding keeps this current from becoming too large.

[TallDave]

No, the main drive current is between the electron emitters and the magrid. Multiply by the drive voltage and you have the drive power.

Magnetic shielding keeps this current from becoming too large.

Yes, that's my understanding as well.

There was some speculation there might be significant current flow to the wall, but Rick has said the hot spots are on the Magrid for what that's worth.

Remember that once any charged particle is inside the magrid it does not see any electric field from it ( actually my understanding is that the field is present, but that the oposite sides tug equally so that the net effective field is zero).

From earlier discussion I gather the Magrid is probably too rough to be a very good Faraday cage. At the center, electrons probably don't see much net force, but at the edge the nearest coil looks like a deep hole.

The charge on the Magrid helps accelerate ions and keeps electrons recirculating (instead of flying out to the wall).

(I was also never 100% clear on whether the Faraday cage effect applies to charges ON the cage itself as opposed to charges outside it. My understanding is that the effect works by rearranging charges on the cage to cancel the field from outside, so I'm thinking it wouldn't -- but if anyone knows better please elucidate).

[TheRadicalModerate]

Remember that once any charged particle is inside the magrid it does not see any electric field from it ( actually my understanding is that the field is present, but that the oposite sides tug equally so that the net effective field is zero). The potential on the magrid (see above) serves two purposes, first to accelerate new electrons to the drive potential, and secondly to do the same to any escaping electrons that reach that high so that they are shot back into the machine with (near?) the original energy. This would presumably keep them from remaining traped on magnetic field lines.

That's not what I'm worried about. I'm worried that, if most of the electrons migrate to the sheath, then, because the sheath electrons are also outside the ions, there are effectively no forces on the ions, so that they won't accelerate into the center of the well.

Concerning A. Carlson's comments, I have seen elliptical potential wells and square wells (what I guess he is suggesting) in different papers. I postulate that there is indeed current flowing in a sinse. Not current between fixed electrodes (that is the whole purpose of the magnetic shielding), but current between mobile 'electrodes'- the free ions and electrons. They could 'ground' on each other but due to the potential ( kinetic energy) they do not stick, but flow past each other. So long as one of the species are non thermal, the other will also be nonthermal. This is the purpose of the continous resupply of radially directed monoenergetic electrons. This, combined with the excess numbers of electrons and the dynamic speeds of the electrons (fast in the perifery and slow in the center) produces the increased density of electrons in the center that pulls the ions inward to high fusion speeds. The inertia of the nonreacting ions then carry them back up to the top of the potential well to start over. This is what I mean when I say osscilation. The ion could come to a stop in the center due to the build up of an excessive vertual anode, but this is presumably the pount where (as Bussard described it) the potential well is blown out.
The current beween these mobile charged particles may be comparable to an occillation in in a capacitor- resister resonate circuit that decays due to leakage, and it is this leakage (transport losses) that hopefully is small enough to allow net power production. The Wiffle Ball effect and cusp recircuation are what hopefully limits these losses to this level.

There's something wrong with this description. You seem to be saying that the electrons in the center are all "newbies"--they've just been injected from the beyond the magrid. But the newbies will only be attracted to the center to the extent that there are already ions concentrated in the center, and ions won't concentrate in the center until there are electrons there. It's a chicken-and-egg problem.

You also seem to be saying that electron injection is needed to generate the potential well, rather than just to replenish electrons that completely escape containment. But if that were the case, wouldn't you wind up with an ever-increasing number of electrons in the sheath? That doesn't sound like a sustainable condition.

I must be misunderstanding something here, because I assume that we actually do get ion acceleration out of real machines. But I'm at a loss to see how. The only thing I can think of is that there is some mechanism that knocks electrons out of the sheath and temporarily into the sphere inside the sheath, but I have no idea what such a mechanism would be.

[TallDave]

The laser fluouroscopy measurements suggest IEC machines have a parabolic well with a dip.

When the "hot" electrons are injected, they fly around inside the B fields, bouncing around trying to get to the Magrid casing. For them, the center is the top of the hill, so they're slowest there, so a virtual cathode develops very very fast. Ions see the bottom of the virtual well at the center, and head for it. They're fastest at the center, so the virtual anode is small (just a dip in the gradient). They're slowest at their edge, so they tend to collide more and thermalize at the same velocity there.

Electrons are always thermalizing and leaving the system via cross-field transport and unshielded surfaces, but as long as you have new hot electrons replacing them, there will still be a well.

That's my understanding anyway. There's probably a paper somewhere with a better description than this.

[D Tibbets]

Yes the magrid or the vacuum vessel wall , or other grounded structures like supports would serve as the anode. With the configuration where the magrid is at high positive potential and the electron gun/emitter is a low voltage the grid provides the accelerative force on the electrons. But, in an ideal machine the electrons would never contact the magrid, the final neutralizing structure would be the vacuum vessel wall. Of course that is not possible, but good enough isolation will work- according to Bussard less than ~ 0.01 percent of the surface of the magrid structures can be vulnerable. With reported hot spots on the magrid interconnects there are obviously electrons reaching there. This is probably excessive based on R Nebel's comments (or at least an area where significant improvements would be profitable). But this does not rule out that most electrons are grounding on the vessel wall or other structures (a lot more area so significantly less heating per unit of surface). The key may be that the electrons that are grounding on the grid interconnects are at least in part electrons that could still be recirculated. The electrons escaping to the vessel walls are at the end of any usefulness. A wordy ramble... perhaps a useful analogy might be an old TV tube. The electron gun in the back provides low energy electrons which are acellerated by ring (or parallel plate) anodes, the electrons fly past them and hit the phosphor screen (ground). So the driving potential is provided by the anode, but the current flow is past the anode to the grounded screen. In the TV the high potential may be on the electron gun while the anodes only have enough potential to guide the electrons, but the idea is the same (this would match the other method of providing the drive energy to the electrons that Bussard mentioned).

Concerning how the electrons reach the center of the machine. Again it is due to the drive potential. The electrons are accelerated to (eg 12,000v). This gives them an energy of ~ 10,000 eV (some resistance to the electrons getting through the cusp, initial scattering etc.) Bussard reported that this resulted in a speed of ~ 1 billion cm per second. As the electrons approach the center they encounter additionalelectrons that are bouncing back and forth inside the machine. This convergence results in the electrons repelling each other- they slow to a stop near the center, then reverse and accelerate to the magnetic field border where they reverse and start over again. The length of time they do this is dependent on energy losses (they won't reach as close to the center), scattering, and final entrapment at the Wiffleball border and/or escape through a cusp. Those that escape past the magrid border, might recirculate- be reincarnated as an appropriately high speed electron (helping to maintain a more mono energetic population of electrons. It is the inertia of the electrons that create the potential well and this is what then accelerates the introduced ions to high speeds in the center. Ideally, the magrid has no direct effect on the ions at all (though there may be some significant ion interactions at the Wiffleball border). The faster the radial electrons are traveling (higher eV) the closer they will come to the center, the more concentrated they will be in this region, and the deeper the potential well will become. The keys are how tight and how long this condition can be maintained through various mechanisms. The new electrons (or reincarnated electrons) that are mono energetic and radial help to maintain acceptable conditions for the average lifetime of the electrons (~100,000 transits in the machine). Thus a compromise. That the low energy electrons that accumulate near the Wiffleball border and then escape (I don't know how this occurs) and the excessively energetic electrons that escape is good as it helps to impede the thermalization of the electrons in total (thanks to replacement mono energetic electrons). The balance between the input energy needed to provide mono energetic replacement electrons for the essential leakage rate (needed to allow the machine to work at all, ie- if the thermalizing electrons are not removed, there would be no room to fit new mono energetic electrons in) and the hoped for fusion rates is the question.
And this is without delving much into what may be effecting the ions side of the machine.

Dan Tibbets

[TheRadicalModerate]

This convergence results in the electrons repelling each other- they slow to a stop near the center, then reverse and accelerate to the magnetic field border where they reverse and start over again.

What is the mechanism for this reversal and re-acceleration back towards the center? As far as I can tell, this will only happen if an electron is repelled from the center directly at a cusp, allowing it to follow a conservative path around the B-field line, past the magrid, and then back in through a cusp. Even then, though, those electrons as more likely to follow a field line through the sheath than they are to make it back to the center of the machine.

But the bulk of the electrons won't even do this--they'll get repelled back so that they strike one of the perpendicular portions of the B-field. They'll then mirror back and forth between cusps lots of times, losing energy through scattering, until they finally escape through a cusp. If they've lost enough energy, they won't make it back to the wiffle-field. They'll just oscillate back and forth along the field lines to either side of the magrid, until they eventually ground themselves on the magrid. But they're useless as contributors to the electrostatic acceleration of the ions, since they live outside the radius of ion oscillation.

So it seems to me that the wiffle-field isn't helping at all. It almost seems as if we'd be better merely magnetically shielding the magrid and encouraging the cusps to be as large as possible, rather than wiffling them closed. Then at least you'd be assured of the electrons following conservative paths until they thermalized.

[TallDave]

What is the mechanism for this reversal and re-acceleration back towards the center?

Same reason the ions head back out to the edge: inertia. The electrons bounce off the B field adiabatically.

The more energy they lose, the more they get stuck near the Magrid (too tired to climb up the well) and aren't helping us with an interior well as much.

That's why they flood the Pollywell with "hot" electrons, so they have enough energy to bounce around. That's also why Polywells need a constant supply of energy to replace tired electrons with hot ones.

As far as I can tell, this will only happen if an electron is repelled from the center directly at a cusp, allowing it to follow a conservative path around the B-field line, past the magrid, and then back in through a cusp.

This probably doesn't happen much. Most electrons that get out probably oscillate inside the cusps, with only a small number making it to the exterior. This is consistent with Bussard's claim the ratio of interior to exterior density should be at least 1000:1, and can be tens of thousands to one.

So it seems to me that the wiffle-field isn't helping at all. It almost seems as if we'd be better merely magnetically shielding the magrid and encouraging the cusps to be as large as possible, rather than wiffling them closed.

Then you would reduce your achievable interior density by several orders of magnitude. The only thing keeping the electrons inside is the B field (and maybe cusp plugging as a result of WB geometry).

[D Tibbets]

This convergence results in the electrons repelling each other- they slow to a stop near the center, then reverse and accelerate to the magnetic field border where they reverse and start over again.

What is the mechanism for this reversal and re-acceleration back towards the center? As far as I can tell, this will only happen if an electron is repelled from the center directly at a cusp, allowing it to follow a conservative path around the B-field line, past the magrid, and then back in through a cusp. Even then, though, those electrons as more likely to follow a field line through the sheath than they are to make it back to the center of the machine.

But the bulk of the electrons won't even do this--they'll get repelled back so that they strike one of the perpendicular portions of the B-field. They'll then mirror back and forth between cusps lots of times, losing energy through scattering, until they finally escape through a cusp. If they've lost enough energy, they won't make it back to the wiffle-field. They'll just oscillate back and forth along the field lines to either side of the magrid, until they eventually ground themselves on the magrid. But they're useless as contributors to the electrostatic acceleration of the ions, since they live outside the radius of ion oscillation.

So it seems to me that the wiffle-field isn't helping at all. It almost seems as if we'd be better merely magnetically shielding the magrid and encouraging the cusps to be as large as possible, rather than wiffling them closed. Then at least you'd be assured of the electrons following conservative paths until they thermalized.

In addition to what TallDave said, consider the Wiffle ball as a solid near spherical ball with very small holes in it (the cusps). The electrons that have a speed high enough that thier gyroradius is much larger than the magnetic field gradient see the border effectively as a solid wall that it bounces off of elastically. While the actual Wiffleball border has to be slightly convex to the center (apparently for plasma stability reasons), this curvature is small enough that the reflected electrons head back at no more than a few degrees off center for the majority of the wiffleball surface. That is were the term quasispherical comes in. Consider the Wiffleball border where the magnetic field strength goes from zero to several Teslas over a distance of perhaps 0.1 mm (pure guess). If an electron traveling at 10,000 eV has a gyroradius of 2 mm (again a pure guess) it will be turned/ reversed by the magnetic field, that is zero on inside of the electrons potential orbit and several Teslas on the outside of the potential orbit, not captured. Compare it to a rocket approaching Jupiter, the speeds and angles involved precludes the rocket from being captured into an orbit, but the direction is changed in a hyperbolic trajectory (gravity boost). As the speed drops the hyperbolic trajectory eventually will become parabolic and the rocket (or electron/ion) is traped.

Also, electrons that are approaching the Wiffleball border at shallower angles (wether from scattering, prevous shallower deflections of the Wiffleball border due to the electron approaching the the capture speed as they lose energy, or those prevously deflected from areas near the cusps where the convexity is greater) will be more likely to be captured, thus preferentially capturing electrons that have lost thier radial purity- another possible mechanism for slowing electron thermalization within the Wiffleball volume.

Dan Tibbets

[D Tibbets]

My prevous post describing electrons bouncing off the Wiffleball borders with only a few degree off center deflection is fine for a few bounces, but in just a few passes the deflection could become close to 90 degrees from center. But, considering it , the multilobed curved surface, while being convex everywhere will deflect these wandering electrons back twoards the center eventually thanks to bank shots like in billiards, so long as the electron does not hit a cusp (pocket). Now all I need to worry about is considering interactions when more than one particle is present.

Dan Tibbets

[TheRadicalModerate]

In addition to what TallDave said, consider the Wiffle ball as a solid near spherical ball with very small holes in it (the cusps). The electrons that have a speed high enough that thier gyroradius is much larger than the magnetic field gradient see the border effectively as a solid wall that it bounces off of elastically.

That's what I was missing.

So the only quibble I'd have with your analysis is that, given that the B-field doesn't just end abruptly inside some critical radius, is that the electrons will have a slightly more complex geometry to their bounces--one where angle of reflection is slightly less than than angle of incidence.

P.S.: I'll be intrigued to see what search engines make of the term "radial purity" when they apply misspelling algorithms. Who knows: you may be responsible for a whole generation of neo-nazi plasma physics enthusiasts. Maybe they'll start a magazine and call it "Fusion"...

[93143]

...given that the B-field doesn't just end abruptly inside some critical radius, is that the electrons will have a slightly more complex geometry to their bounces--one where angle of reflection is slightly less than than angle of incidence.

Why? The path may not be a perfect semicircle, but it should still be symmetric (barring collisions, of course)...

[Roger]

I have never heard R. Nebel chime in with his opinion.

Dr Nebel told me that in the my video Fusion for Dummies, the electron paths of one cusp to the other cusp was wrong. I would then put Dr Nebel in the same cusp group.

[TallDave]

I have never heard R. Nebel chime in with his opinion.

Dr Nebel told me that in the my video Fusion for Dummies, the electron paths of one cusp to the other cusp was wrong. I would then put Dr Nebel in the same cusp group.

That's interesting, I didn't know that he had expressed an opinion. Thanks for sharing that.

Looking over Valenica for the billionth time the other day, I belatedly realized Bussard never actually states (afaict) that "recirculation along field lines" means they go around, so I'm not sure if that was his error or ours. We may have all just wrongly assumed that was what he meant. (I'm trying to remember if there was some graphic that implied that somewhere in the Google Tech Talk, but I don't really want to sit through it again.)

FWIW, it's also occurred to me a few times when my eyes happened to wander over the WB-7 machine in the pic on my desktop that it appears to have been built without any expectation there would be "going around" recirc, based on how close the coils are to the walls (although distances are difficult to estimate from the angle of the picture).

[MSimon]

Looking over Valenica for the billionth time the other day, I belatedly realized Bussard never actually states (afaict) that "recirculation along field lines" means they go around. We may have all just wrongly assumed that was what he meant.

I was never in that camp. Go back to NASA Spaceflight and have a look.

I never liked the word - recirculation. I preferred oscillation or something similar.