Even outside the coils you will have a quasineutral plasma.
Huh? That's not my understanding. I was under the impression the ions generally don't make it outside the device. Remember when Nebel said the Larmor radius was essentially infinite for the ions because they almost never see the B field?
So let's run the numbers. At 10 T we have a magnetic pressure of (10^2)/(2*4pi*10^-7) = 4e7 Pa. At beta = 1 and T = 100 keV that's a density of (4e7)/(1.6e-19*1e5) = 2.5e21 m^-3 on the inside. Bussard talks about a density ratio of up to 1e4, so let's take a density of 2.5e17 on the outside. Any fans or blobs are likely to have dimensions on the order of 0.1 m in a meter-scale reactor. If there are no ions, then the Poisson equation says the electrons will produce a potential of about nqd^2/epsilon_0 = 2.5e17*1.6e-19*0.1^2/8.85e-12 = 450 MV. (Check my math!) I think we can agree that we don't want that kind of voltage running around our little reactor, so we had better rather neutralize 99.999% of that charge with ions.
You are not alone in your false impression. I think almost everybody here thinks that there will only be electrons outside the coils. Bussard has encouraged this way of thinking by the way he talks about confinement, although I suspect he knew better himself.
If you can't manage to hold them back electrostaticly
That is the whole game.
Have you been paying attention? Maybe you need to reread my original post, that also deals with this part of the game. The cusps may be small, but directly along the field line through the middle of a cusp, there is no confinement of either electrons or ions. Can you make of sketch of what you think the electric potential looks like along that line, and how you think the electrons and the ions will react to that potential?
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,
this condition can ALWAYS be satisfied, IF the
external neutral gas pressure is made sufficiently small. In
order to avoid external arcing, the densities thus required are
very much too low to be of interest for fusion, thus the
density inside the machine (at its boundary) must be very
much higher than that outside. This ratio is the Gmj factor,
which is the ratio of electron lifetimes within the machine
with B fields on, to that without any B fields.
In contrast, in order to be of interest for fusion, the interior
density must be above some numerical value for any given
size of machine. Typically this requires electron densities at
the interior boundary of order 1E13/cm3, or higher. While
the exterior densities (of neutrals able to be ionized) must
typically be below 1E10/cm3 or less.
If you can't manage to hold them back electrostaticly
That is the whole game.
Have you been paying attention? Maybe you need to reread my original post, that also deals with this part of the game. The cusps may be small, but directly along the field line through the middle of a cusp, there is no confinement of either electrons or ions. Can you make of sketch of what you think the electric potential looks like along that line, and how you think the electrons and the ions will react to that potential?
Sure, but the lucky electron that makes it through sees the Magrid that it loves so much and doesn't like being pushed directly away from it. The ion never makes it this far from the core.
If you can't manage to hold them back electrostaticly
That is the whole game.
Have you been paying attention? Maybe you need to reread my original post, that also deals with this part of the game. The cusps may be small, but directly along the field line through the middle of a cusp, there is no confinement of either electrons or ions. Can you make of sketch of what you think the electric potential looks like along that line, and how you think the electrons and the ions will react to that potential?
You speak about the ExB drift. When looking at the potential gradient:
According to this and the field lines picture before ExB=0. Can you elaborate? Are you saying the recirculation beam will cancel the e-field as such and instead a potential gradient will form within the beam (perpendicular in direction to the beam), causing the ExB drift?
Perhaps I am misunderstanding this discussion, but there are electrostatic fields along the cusp lines. We've measured them with emissive probes. If they weren't there, I don't see how the electrons would enter the device.
If you can't manage to hold them back electrostaticly
That is the whole game.
Have you been paying attention? Maybe you need to reread my original post, that also deals with this part of the game. The cusps may be small, but directly along the field line through the middle of a cusp, there is no confinement of either electrons or ions. Can you make of sketch of what you think the electric potential looks like along that line, and how you think the electrons and the ions will react to that potential?
You know. I do see a magnetic field problem at the cusps. I don't see an electrostatic field problem.
The electric fields lines should be concentric spheres (allowing for actual geometry).
Ions will be repelled. Electrons will be attracted but are deflected by the magnetic field.
Engineering is the art of making what you want from what you can get at a profit.
Art Carlson wrote: If there are no ions, then the Poisson equation says the electrons will produce a potential of about nqd^2/epsilon_0 = 2.5e17*1.6e-19*0.1^2/8.85e-12 = 450 MV. (Check my math!) I think we can agree that we don't want that kind of voltage running around our little reactor, so we had better rather neutralize 99.999% of that charge with ions.
How is that a valid point? There is no drive potential like that anywhere in the device so you would have to violate conservation of energy or the second law of thermodynamics to create a potential such as that, which obviously is not going to happen. The drive potential is fixed, at the magrid and outer wall. If a potential generated from electrons outside gets anywhere near that high it will just push the gradient ever closer to the core keeping more electrons INSIDE making the density ratio higher until the potentials are balanced with kinetic energy. And if there are any ions outside they will go straight toward the wall because of the direction of the elctric field. There is no way to build an ion population outside to begin with. If there is an ion outside it is lost. I just don't understand what you are saying at all.
And if there are any ions outside they will go straight toward the wall because of the direction of the elctric field.
Yes, I was thinking that too. They do not like the Magrid and want to be away from it, so if they somehow did get past it (which they shouldn't) I think they would keep going for the same reason the electrons hew close to the machine.
kcdodd wrote:How is that a valid point? There is no drive potential like that anywhere in the device so you would have to violate conservation of energy or the second law of thermodynamics to create a potential such as that, which obviously is not going to happen. The drive potential is fixed, at the magrid and outer wall. If a potential generated from electrons outside gets anywhere near that high it will just push the gradient ever closer to the core keeping more electrons INSIDE making the density ratio higher until the potentials are balanced with kinetic energy. And if there are any ions outside they will go straight toward the wall because of the direction of the elctric field. There is no way to build an ion population outside to begin with. If there is an ion outside it is lost. I just don't understand what you are saying at all.
Hmm... You may have a point. Remember what Tom Ligon said about cusps being 'plugged' with electrons?
Perhaps the leakage itself helps prevent further leakage. It might be possible for this effect to cap electron losses (those really are small holes) without inducing substantial ion losses, if the ions are generated far enough down the well... or something...
The cusps plugging with low-energy electrons was my interpretation of the behavior of PXL-1 (a closed-box machine) in one particular configuration. Dr. Bussard did not think that was correct, although he was certain some "two-color electron" effects would be important.
Whatever was happening, PXL-1 did drop percipitiously into a low-leakage state, presumably evidence of a wiffle-ball state, where drive current limited to about 50 mA. When the magnetic field was switched off while it was still at high voltage and in this state, all hell broke loose. The effects were similar to accidents I've seen described with electron storage rings. I witnessed very high reverse current in the magnets (blowing a large damper diode open, then arcing past a magnetic blowout contactor) with EMP-like effects damaging other equipment in the lab.
Art Carlson wrote: If there are no ions, then the Poisson equation says the electrons will produce a potential of about nqd^2/epsilon_0 = 2.5e17*1.6e-19*0.1^2/8.85e-12 = 450 MV. (Check my math!) I think we can agree that we don't want that kind of voltage running around our little reactor, so we had better rather neutralize 99.999% of that charge with ions.
How is that a valid point? There is no drive potential like that anywhere in the device so you would have to violate conservation of energy or the second law of thermodynamics to create a potential such as that, which obviously is not going to happen. The drive potential is fixed, at the magrid and outer wall. If a potential generated from electrons outside gets anywhere near that high it will just push the gradient ever closer to the core keeping more electrons INSIDE making the density ratio higher until the potentials are balanced with kinetic energy. And if there are any ions outside they will go straight toward the wall because of the direction of the elctric field. There is no way to build an ion population outside to begin with. If there is an ion outside it is lost. I just don't understand what you are saying at all.
You are absolutely right. (And not just the part about not understanding me.) There is no way there can be multi-MV potentials in the system. I am just pointing out that the picture on the table (pure electron plasma outside the cusps with a significant density) is not consistent. A polywell machine will certainly do something, and that something will certainly be consistent with the laws of physics. I don't think we understand yet what we should expect it to do. And that includes me. (I don't think your scenario is consistent, either, but we can discuss it.)
