The collisionless limit is actually where turbulence is the most likely to dominate. In fluids, for instance, viscosity is what damps turbulence. The drivers are anything nonlinear. In fluids, that's usually convection. In plasmas, there are many nonlinearities. Any nonlinearity will cascade the turbulence to shorter wavelengths where it can be dissipated. The most likely candidate for generating turbulence in Polywells is the lower Hybrid Drift instability.
With all due respect, a lot of what has been written above is sweeping generalisations and extending into misleading gross speculation. I could take it apart line by line but almost each one would be a new topic in itself.
I hope this has been a "hand-wavvy lapse" by Dr. Nebel and not the usual order of business for Polywell research or else I wouldn't be holding out much hope for success.
Give me non-peer-reviewed technical reports with hard numbers, facts and results over paragraphs of pontification and circumlocution any day.
...what?
I've studied both turbulence and gas kinetics as part of my Ph.D. coursework, and I see nothing wrong with what he's said (unless it be an objection to the use of the word "turbulence" to describe a phenomenon in the collisionless regime - but then I'm not a plasma physicist).
Also, he doesn't seem to be trying to prove anything with that statement, so I don't see what your problem is...
Lower Hybrid drift modes have been reported in earlier cusp experiments (Dolan's paper has some references), but they haven't been looked for in Polywells. I think the earlier machines were line cusp devices. Krall has stated that it is consistent with the observed "Magrid" scaling, but I wouldn't hang my hat on it. I think it's an open question.
Wouldn't Paschen arcing depend on both? Without sufficient electrons, there's nothing to arc. (I'm assuming we are talking about the cloud of exterior electrons arcing to the wall, not the Magrid arcing to the wall).
I think your assumption doesn't make sense. An arc generally has to be driven by a power supply. You can't possibly pack enough electrons into a cloud to sustain an arc. Maybe Rick can give us a definitive answer on this one before we bash each others' heads in.
TallDave wrote:
Without so much as a mention of the loss mechanism???
This part is a summary. He mentions mechanisms earlier:
1. Direct MG transport through the B-shielded surfaces,
2. Electron losses to poorly shielded or unshielded
metal surfaces, and
3. Losses due to local arcing.
He claims they have an empirically-derived model for #1.
This says where (in Bussard's mind) the transport occurs, not how. How does he determine experimentally that the major loss channel is through the surface area? How can he possibly rule out that the (purely) empirical electron flux depends on the size of the machine in some way?
Art Carlson wrote:Jboily, the power loss does not necessarily scale with R^2. A bigger radius, of course, implies a bigger area, but the energy flux per unit area may go down if the transport is diffusive, because the gradient scale length may also be proportional to the radius. If you have line cusps, the loss area is proportional to R (times the width of the cusp), not R^2, and the loss area of point cusps is not directly related to R at all.
Art, this is true, the line losses, would scale at ~R. However, there are other losses that scales at ~R^2, like the electrons and Ions diffusion trough the field. I think Dr. Bussard was saying these losses were at the same order of magnitude of the line losses for small devices . The R^2 scaling would indicate these will be more important then the line losses for larger machine, this is why I started with the r^2 scaling losses, wich seems to be the wordt case.
For a specific Magnetic field and configuration, there would be a radius were these two losses are of equal importance. It may very well be that one of the losses become insignificant at larger fields.
Art Carlson wrote:Jboily, the power loss does not necessarily scale with R^2. A bigger radius, of course, implies a bigger area, but the energy flux per unit area may go down if the transport is diffusive, because the gradient scale length may also be proportional to the radius. If you have line cusps, the loss area is proportional to R (times the width of the cusp), not R^2, and the loss area of point cusps is not directly related to R at all.
Art, this is true, the line losses, would scale at ~R. However, there are other losses that scales at ~R^2, like the electrons and Ions diffusion trough the field. I think Dr. Bussard was saying these losses were at the same order of magnitude of the line losses for small devices . The R^2 scaling would indicate these will be more important then the line losses for larger machine, this is why I started with the r^2 scaling losses, wich seems to be the wordt case.
For a specific Magnetic field and configuration, there would be a radius were these two losses are of equal importance. It may very well be that one of the losses become insignificant at larger fields.
OK. although I can think of several plausible models with a scaling weaker than R^2, I can't think of any with a stronger scaling, so we can take it as a worst case. The scaling could well be that bad, but probably not any worse.
The scaling with B is less clear theoretically, but is in principle able to be determined in a single machine.
There could be important scaling with the energy, but I am assuming (probably not accurately) that small scale experiments run at full reactor potential. (Of course, that makes the electric fields bigger. What effect can that have?)
And we are assuming that the geometry of the machine is not changed.
I think your assumption doesn't make sense. An arc generally has to be driven by a power supply. You can't possibly pack enough electrons into a cloud to sustain an arc. Maybe Rick can give us a definitive answer on this one before we bash each others' heads in.
Hrm, true. He does seem to mean machine-to-wall.
As previously noted, no Polywell can operate at all if arcing
occurs outside the machine, between the walls and the
machine, because this destroys the ability of the driving
power supplies to produce deep potential wells.
OK, re-reading that whole graf I think maybe I see what Bussard meant:
As previously noted, no Polywell can operate at all if arcing occurs outside the machine, between the walls and the machine, because this destroys the ability of the driving power supplies to produce deep potential wells. Thus the mean free path for ionization outside the machine (inside the container) must be much greater than the external recirculation factor, times the machine-to-wall distance. Since the mfp for ionization is inversely proportional to the product of the local neutral density and the ionization crosssection,
Maybe he means the electron density is important because of how it affects the ionization of the neutrals?
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
Gosh, I thought he meant that the electron density was important because when to dense, the electrons provide a discharge path between the machine and the wall.
I wouldn't recommend doing a lot of modelling of the arcing right now. We've been looking at it, and it's complicated. It's not just a Paschen breakdown to the chamber wall. However, rather than sticking my foot in my mouth (by saying something that's not correct) let me say that we don't understand all of it right now, but we are working on it.
Is the arcing related in any way to actual fusion events?
Since,
1) The fusion events should all occur at the very center of the polywell.
2) The density of ions may be higher near the center of the polywell.
3) Any alphas produced by fusion would have plenty of kinetic energy.
Is it possible that those alphas are colliding with deuterium ions and kicking them out of the polywell? Would this contribute to arcing?
Maybe a better question would be what is the mean free path of a fusion product that is produced at the center of the polywell?
If that mean free path is short, that could be a problem.
If that mean free path is very long, then that may not be a loss mechanism or at least not a very significant one.
Arching doesn't have to do with fusion events, but it can. It has to do with the sheath region creating an avalanch of particle motion. It doesn't take a whole lot of noise to create a runaway condition, and it doesn't need to have a very high probability because the plasma sheath is a non-linear system. If you think plasmas all by them selves are complicated, wait till you try to analyze a sheath!! Especially in a magnetic field.
I think Rick calling it "complicated" is a nice understatement.
rnebel wrote:I wouldn't recommend doing a lot of modelling of the arcing right now. We've been looking at it, and it's complicated. It's not just a Paschen breakdown to the chamber wall. However, rather than sticking my foot in my mouth (by saying something that's not correct) let me say that we don't understand all of it right now, but we are working on it.