Solo wrote:I should have gone ahead and quoted him:
Dolan wrote:there will probably be about an order of magnitude density ratio between the anode region and the central plasma
n/n_0 ~ 0.1.
The ratio would probably be lowest for cases with a large volume of field-free plasma, narrow anode gaps and low neutral gas pressure; and it could be near unity for cases with spindle cusp magnetic field, wide anode gaps and high neutral gas pressure. Values inferred from data in a variety of experimental conditions range from 0.01 to 1.
Dolan wrote:Moir et al [76] showed that the electron density in the gaps is lower than the magnetically penetrating density n_p by
a factor n/n_p = exp(y) erfc(y^(-1/2)) where y=phi /T_ion, and erfc is the complementary error function. For values of y from 3-6, n/n_p is 0.29-0.22.
[Where n_p = density of electrons that are able to penetrate into the magnetic cusps by geometry and mirror considerations]
Thanks, but I'm still not sure what's he's talking about. Probably I'll just have to sit down and read it again. Aside from not having the time, my electronic version is damaged and unreadable and I don't seem to have a paper copy.
Solo wrote:
Art_Carlson wrote:But before they have time to do that, they flow along the field lines out the cusps.
That's where I'm getting stuck. What happens then? If recirculation happens by electrostatic field, those electrons are not lost and are returned to the plasma, and the diffusion continues until ... well, I think the actual WB machines probably limit this because the electrons are lost in the coil corners (the center of the line cusp). Somehow they have to be lost though, either they are lost to the wall as you say (ie, recirculation doesn't happen) or else they'll diffuse till they hit the magrid. Do you agree?
Typically, the cross-field transport will depend on the density gradient. For simple diffusion it is proportional, but for turbulent transport it can be a higher power. If the particles cannot drain off parallel, then, like you say, they build up, making the sheath thicker. This both increases the parallel transport (through more area and/or density) and decreases the perpendicular transport (through the smaller gradient). Eventually a new equilibrium is reached. As long as you have free-streaming in the parallel direction, the situation should be relatively tractable, and you land at a minimum sheath thickness between rho_e and sqrt(rho_e*rho_i). If you actually have significant recycling plugging the field lines, then you would have to consider the broadening of the sheath to get a reliable estimate of the net loss rate.
I find myself being very puzzled by physicists, who I am sure know much more about plasmas than I do, making statements that are in total conflict with physics that I understand. Please forgive me and put me right if the following is nonsense, but knowing how easy it is for familiarity with a complex and difficult subject to encourage one to produce hypotheses that do not conform with fundamentals, I feel that I must state things as I see them and thereby, hopefully, get clarity.
My main concern is with the mechanism of "push-back" of the magnetic field of the Magrid to form the wiffleball. This is often talked of as if plasma pressure can act directly on the field lines.
As I see it the magnetic field lines of the Magrid can only be modified by adding another magnetic field within the wiffleball. The two magnetic fields can then be added together to form a new magnetic field structure which has a boundary that is the periphery of the familiar wiffleball.
To do this it is necessary that there should be a magnetic field inside the wiffleball and it also implies that there are coherent electric currents within the wiffleball that produce this magnetic field. The currents in the Magrid produce a force on the Magrid coils and the currents in the plasma produce a pressure on the plasma boundary which, integrated over the area of the plasma boundary, is equal to the force on the magrid coils. So the plasma pressure is linked to the "push-back" of the Magrid field, but only by being a consequence of the electric currents and associated magnetic fields within the plasma.
To my mind these considerations make it much easier to accept that the method of images produces a useful first approximation to the internal structure of the wiffleball. They also show that some of the assumptions that are being made to facilitate BOE calculations are unnecessary and, in some cases, incorrect. Careful examination of Indrek's calculations and visualisations will be much more accurate and productive.
It is also hard to believe that some of the alarming results of BOE calculations are consistent with the experimental results produced by EMC2. These experimental results may, or may not, be good enough for ultimate success but they do not appear to be the disaster zones of these BOE calculations. The doubts about effectiveness of recirculation appear to me not to be substatiated by either the experimental results (sparse as our current knowledge of them is) or by the probable effects of the internal magnetic fields of the wiffleball on confining electrons within the wiffleball. I also suggest that the internal magnetic field may invalidate the idea that plasma pressure will be uniform at the boundary.
As an engineer I have stuck my neck out here. I hope this is useful.
It is certainly not necessary that there be a magnetic field inside the plasma. How can I convince you of this? Surface currents, which interact with the external field, are sufficient. Maybe it would help to think of the Meissner effect that expels all magnetic fields from the interior of superconductors.
Another view is to look at back emf. Every time you try to push current against a field, the field pushes back on the current. In a plasma, you can do that to the point where all the current is on the surface and all the field is on the surface too. The plasma inside doesn't see any external field because the surface currents exactly cancel it out. That's a natural balance point, but real viscosity and friction will not really get you perfection. But it can be "close enough".
I've always pictured it as the electrons zipping back and forth across the well, bouncing off the field and pushing it back by those rebounds. Is that basically right or horribly wrong?
KitemanSA wrote:I've always pictured it as the electrons zipping back and forth across the well, bouncing off the field and pushing it back by those rebounds. Is that basically right or horribly wrong?
Tom Ligon told me essentially the same thing when I was animating the Fusion for Dummies Video. At a certain point I made the cusps smaller (Mag field lines squeezed together) as the electrons push back from the well. And I think the Electron push back comes from the high electron population in the well, not fronm zipping back and forth, but you knew that.
I like the p-B11 resonance peak at 50 KV acceleration. In2 years we'll know.
Roger wrote:Tom Ligon told me essentially the same thing when I was animating the Fusion for Dummies Video. At a certain point I made the cusps smaller (Mag field lines squeezed together) as the electrons push back from the well. And I think the Electron push back comes from the high electron population in the well, not fronm zipping back and forth, but you knew that.
Actually, I didn't, and I am not quite sure I agree. I am under the impression that the "zipping back and forth" is what creates the very high population of electrons in the center of the sphere making the density of the ions follow suit. Is that not the whole reason for the concern about sphericity? Don't we really want the electrons to move as close to perfectly radially as is possible to make them? Why else would Dr. B expect a 3-5 fold increase from a dodecahedral unit if it isn't due to improved sphericity and thus ion density at the core of the machine?