KeithChard wrote:The image technique is a useful qualitative and quantitative tool. which in this case has given a useful insight into a probable structure for the fields inside the wiffleball.
No, the exercise was intended to give the fields OUTSIDE the wiffleball. What it does inside is unphysical.
Inside, the fields will be very small because any magnetic field can be instantly countered with a modification of the electron flow. The internal currents won't arrange themselves into a neat mirror image of the magrid.
or even that there are any internal fields at all.
What would be the basis for thinking that there is zero magnetic field inside a structure such as the wiffle-ball?
How would the electron plasma not carry some kind of field along with it? These would actually be some particularly difficult to achieve formation requirements (initial conditions), would it not?
Well, aside from Bussard, there's the Review of "Cusped Plasma Containment" by Haines (1977):
Plasma formation in high-beta cusp experiments poses a difficult problem in that we wish to establish a hot beta = 1 plasma confined by the cusp magnetic field, which should be excluded from the main volume of plasma. However, during plasma formation, when the electron temperature and conductivity are low, magnetic field diffusion can dominate, resulting in a thickened sheath and unwanted trapped magnetic field. Three methods of plasma formation have had some success in overcoming this problem; firstly injection of a hot plasma from a gun along the spindle axis, secondly ionization of the background gas followed by a rapid rise of the magnetic field (leading to plasma heating by compression), and thirdly rapid ionization and heating of a solid pellet by a laser. ... The main observations of relevant experiments up to a few years ago were that ... the beta was high, e.g. 99% with beta-bar = 83% in Centaur ....(p.839)
Of course the question of the magnitude and form of residual magnetic fields in a polywell is interesting and perhaps important, but it belongs to the relatively large class of problems where, for the sake of argument, I give the polywell the benefit of the doubt.
There was a diagram about Wiffle Ball formation that said that there were two ways to make it happen. The one I remember was ramping the magnetic field.
So I think Bussard confirmed your point.
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Icarus, who originally posted the image idea did so to specifically expose the internal structure of the wiffleball and the features you see are real and physical. I concede that the current solutions with a perfectly spherical wiffleball are simplistic, but the idea that there are currents in the plasma, which are images, probably distorted and fuzzy, but images, nevertheless, of the Magrid coils, with consequent magnetic fields which are probably more effective than the fields outwith the wiffleball at retaining electrons, is a perfectly real and physical phenomenon.
It is also true to say that the internal field lines adjacent to the wiffleball surface are probably the most accurate feature of the current simplistic solution, and it is the shape and strength of this field which will be so effective in confining the electrons.
You're not describing a plausible system. Given electrons and magnetic fields in the same volume, if the electrons can move in such a way as to null out the magnetic fields, they will. Having focused toroidal currents that do not do that is a highly nonequilibrium situation.
This is why everyone who discusses the wiffleball (from Bussard to Carlson) assumes it to be a diamagnetic sphere with no internal magnetic field.
Those image coils are a VERY approximate view of what the internal currents do. Their sole purpose is to produce a spherical surface that the external magnetic fields see as a boundary. This gives a nice idea of the field ON the surface of the wiffleball, but inside is another matter.
Mike Holmes wrote:So, the larger the chamber, the higher the proportion of lines that are short enough to come back without hitting the wall. Yes?Mike
Correct. But the fact that you ask this question makes me fear that you did not read the last paragraph.
Art Carlson wrote:Particles lost through a cusp are expected to be on loops that are so big that they will intersect the wall before returning to another cusp. This is good. You do not want to solve this problem by letting electrons also escape on field lines that make small loops. The hole is big enough already.
I'm not sure what our best numbers are, but simply making the chamber bigger is not a practical way to solve the problem.
I would point out that a simple way to recover electrons is to simple have a set of mirror coils outside your wiffleball coils, which curve all wiffleball field lines back through another face within the chamber. I don't really understand your logic of why any kind of loss is "good". I would argue you want to create recirculation, if for no other reason then to make the system more stable. If you are losing electrons through a cusp at a specific velocity and location, my understanding is that would create instabilities at the cusp as well as in phase space at that location. If you can recirculate the electrons back in so they can equilize then you might prevent such an instability.
kcdodd wrote:I would point out that a simple way to recover electrons is to simple have a set of mirror coils outside your wiffleball coils, which curve all wiffleball field lines back through another face within the chamber.
Folks, we don't need another set of magnets, the positive charge on the MaGrid will return all the electrons we want to keep.
kcdodd wrote:I would point out that a simple way to recover electrons is to simple have a set of mirror coils outside your wiffleball coils, which curve all wiffleball field lines back through another face within the chamber.
Folks, we don't need another set of magnets, the positive charge on the MaGrid will return all the electrons we want to keep.
Why do you not want to keep the ones it doesn't return?
kcdodd wrote:I would point out that a simple way to recover electrons is to simple have a set of mirror coils outside your wiffleball coils, which curve all wiffleball field lines back through another face within the chamber.
Folks, we don't need another set of magnets, the positive charge on the MaGrid will return all the electrons we want to keep.
Why do you not want to keep the ones it doesn't return?
How do you propose to reduce their energy to below the equivalent grid dive voltage in order to return them to the reactor core?
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kcdodd wrote:I would point out that a simple way to recover electrons is to simple have a set of mirror coils outside your wiffleball coils, which curve all wiffleball field lines back through another face within the chamber.
Folks, we don't need another set of magnets, the positive charge on the MaGrid will return all the electrons we want to keep.
Why do you not want to keep the ones it doesn't return?
Basically because they are too energetic and will potentially unbalance the rest of the system, I think, maybe, I'm not totally sure.
Perhaps if we had a way to remove some of the excess energy, they would slow enought to be returned by the MaGrid.
Anyway, the way I have looked at it is that losses of extra energetic electrons is one way to keep the system "annealed".
The way I see it the system will always attempt to fill the higher energy domain whether or not you remove them from the system, which will subtract electrons from the target energy. If you leave the cap on the bottle then you keep everything.
kcdodd wrote:The way I see it the system will always attempt to fill the higher energy domain whether or not you remove them from the system, which will subtract electrons from the target energy. If you leave the cap on the bottle then you keep everything.
You may be right. I wonder what we can do to figure out whether we need the complexity.
Remember, outside the MaGrid is (perhaps) the direct conversion system. Hey, maybe we can use a second set of magnets to turn the electrons around, and turn the alphas enough to seperate into their different energy bands.
93143: In due course of time, experiments, measurements and theoretical developments will tell. In the meantime the image structure will give a more illuminating picture than a sphere with no internal magnetic field, because it is the internal magnetic field that "pushes back" the field of the Magrid.
The image system can also provide interesting global quantites of the wiffleball.
For example, I've been wondering for a while about calculating the magnetic forces on the coils, including for forces due to the image system of a formed wiffle-ball (using some appropriate radius)?
I think it should be greater than without the image system, the extra force being exactly that due to the total electron pressure, pushing back upon the magnetic field, and integrated over the wiffle-ball spherical surface (modelled by the image system singularity forces).
We should be able then to relate wiffle-ball radius and electron pressure in this way.
For example, I've been wondering for a while about calculating the magnetic forces on the coils, including for forces due to the image system of a formed wiffle-ball (using some appropriate radius)?
I think it should be greater than without the image system, the extra force being exactly that due to the total electron pressure, pushing back upon the magnetic field, and integrated over the wiffle-ball spherical surface (modelled by the image system singularity forces).
I don't see how the pressure can be greater than that of the magnetic field alone. But maybe I'm dense. Please explain.
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