I so appreciate the simulations of Indrek, D.Tibbets and others who have helped me visualize the probability distribution of the electrons that are in the core. Never mind where the positive ions are, I assume they are in a glob in the middle. But when you think about what is being achieved, it is like an atom. You have a core of positive ions surrounded by a cloud of electrons. Except here, we are squishing the electrons by magnetic and electrostatic fields into 'unnatural shapes'.
Going back to the Schrodinger equation, the solution for hydrogen is interesting. I remeber first learning about all the orbitals, and I couldn't understand intuitively why they had such shapes. The solution of the Schrödinger equation (wave equations) for the hydrogen atom uses the fact that the Coulomb potential produced by the nucleus is isotropic (it is radially symmetric in space and only depends on the distance to the nucleus). Not intuitively, we find the resulting energy eigenfunctions (the orbitals) are not necessarily isotropic themselves, but their dependence on the angular coordinates follows generally from this isotropy of the underlying potential.
So, now I come back to the polywell and ask myself the same question-we have an isotropic core and we are generating a simulation of its shape based on external magnetic and electrostatic fields. But why wouldn't the core itself result in anisotropic distributions of electrons?
If we shaped the external magnetic field to be the complement of the intrinsic anistropic electron distribution, these could be made to cancel out resulting in a contained (and higher density core). The goal being to a greater cross section for the fusion reaction.
on the shape of the core
No.
Electron density is highest in the center, with some fade towards the boundaries and a higher density along the cusps axii.
Fuel (+Ion) Density can be simplified to a similar envelope shape like the electrons, however, it should be more or less High on the outer edges (slowing and turnaround), less in the intermediate accel/decel transition zone, and higher towards the center (highest Ion speed, but exponential volumetric decrease convergence that drives up density).
This is how I see it in my mind, and there have been many modeling attempts to understand what it really looks like, with some diverse conclusions.
This is why the primary efforts of WB7 to 7.1 and 8.0 have been plasma and electron distribution diagnostics.
No again.Never mind where the positive ions are, I assume they are in a glob in the middle. But when you think about what is being achieved, it is like an atom. You have a core of positive ions surrounded by a cloud of electrons.
Electron density is highest in the center, with some fade towards the boundaries and a higher density along the cusps axii.
Fuel (+Ion) Density can be simplified to a similar envelope shape like the electrons, however, it should be more or less High on the outer edges (slowing and turnaround), less in the intermediate accel/decel transition zone, and higher towards the center (highest Ion speed, but exponential volumetric decrease convergence that drives up density).
This is how I see it in my mind, and there have been many modeling attempts to understand what it really looks like, with some diverse conclusions.
This is why the primary efforts of WB7 to 7.1 and 8.0 have been plasma and electron distribution diagnostics.
Re: on the shape of the core
Your logic remembered me of the Wendelstein 7-X.bwana wrote:If we shaped the external magnetic field to be the complement of the intrinsic anistropic electron distribution, these could be made to cancel out resulting in a contained (and higher density core). The goal being to a greater cross section for the fusion reaction.
Just in case you do not know the project:
http://www.ipp.mpg.de/ippcms/eng/pr/for ... index.html
I have high hopes for this project to actually deliver some interesting results.
While I admit that there are many subtleties that I do not understand, some gross considerations:
Fussion plasmas are not closely coupled, which means the electrons and positive ions do not spend enough time close together that this local coulomb attraction will dominate over space charge effects. This is pointed out in several plasma physics texts and is the basis of my arguments that bipolar charged particle flows does not occur in the cusps. If this was the case (closely coupled plasma) then A. Carlson's contention that ion containment could not be better than electron containment would be reasonable. He never contested my point- I don't know whether he was stumped, ignored me, or silently laughed at me. He never seemed to make the distinction between neutral and non neutral plasmas.. In any case, a completely coupled plasma (actually a neutral gas) would be atoms. A tightly coupled plasma (cold and dense) is tightly coupled and the local effects will generally dominate over cumulative space charge considerations. A loosely coupled plasma (hot, and not so dense) is the opposite. This does not mean local effects are not present- bremsstrulung would be a good example of that, but that they can be easily (?) overcome. That is why electrons will trail along with the ions to a modest(?) extent, but the reverse is much less prevalent. Due to the mass difference, the ions can effect the momentum of the electrons much more than the reverse. This is why electrons will be pulled inward by ions to form a generally parabolic potential well (as opposed to a square potential well), but ions will not be pulled outward significantly by the escaping electrons because the ions inertia (momentum) is not changed much by the passing electron that spends only a very brief time close enough to the ion that its local electrical field dominates over the space charge, which is generally pulling the ion towards the center.
If there was not some lose coupling the ions would be accelerated past the ~ shell of electrons, and accumulate towards the center till mutual repulsion stops and reverses them for the next cycle. I'm uncertain if this would be sustainable. In this case a true virtual anode would form in the center (net positive charge). Bussard stated something to the effect, that if the positive charge accumulation achieved ~ 80% (?) of the potential well depth, the potential well would be 'blown out'.
Because of the lose coupling and some partial dragging of the electrons towards the center this does not occur. A relative central anode can form, but it can be managed to levels of ~ 20-30% of the potential well depth. The virtual anode is relative because the charge is still negative, but less so. This allows for greater ion confluence while still remaining within tolerances.
The dynamics in the Polywell is a complex blend of interactions based on the negative space charge provided by the excess electrons, the momentum differences between the ions and electrons, and the position within the Wiffleball. With a thermalized neutral plasma, any location within the plasma volume will have similar properties. In the near spherical geometry of the Polywell, the properties are much different in the outer margins, the 'mantle' region, and the core.
Also, though I am not certain, I suspect that there may not be much electron concentration in the cusps. Certainly, in a magnetic concave surface between magnets (like in a Tokamak), I could see electrons accumulating (provided it was a negative plasma) but with the non concave open cusps in a Polywell, these are holes that the electrons will quickly transit and exit without impediment. Once outside the magnets the electrostatic charge can reverse them so there would be a bidirectional flow, but this is the same over the rest of the Wiffleball surface also. The only difference is that here the magnetic fields reverse the electrons. Magnetic mirroring effects in the cusps may modify this some , but with the negative space charge inside, I speculate that this would be minimized.
If the Gauss law effects are not complete (there is some leakage due to the size of the holes in the ' magrid sphere', I could see a low energy electron oscillating back and forth at the border between the negative space charge dominated region and the positive magrid dominate region. But, two considerations would impede this. First, collisions with other electrons at different energies would destabilize this balance. Secondly the internal negative space charge (potential well) is about 15-20% weaker than the potential on the magrid. This bias would essentially give the magrid potential a ~ 20% advantage. If an electron reached this border with a tiny outward velocity it would meet a reversing force at least 20% greater than the outward force. So in this tiny distance it might oscillate back and forth a few times but the greater inward velocity gain on each orbit would push the electron deep enough into the potential well until on the rebound it reached high enough that it was exposed to the full accelerating potential on the magrid, and was shot back deep into the magrid (recirculated). This ignores the collisions mentioned above. Also, the collisions would not only disrupt the energy balance, but lead to cross field transport so these electons would ground more quickly on the magnet surface- certainly if there is a greater density of electrons in this area. I'm not saying that there may be a tendency for electrons to accumulate here, but that there are several competing effects that would minimize or eliminate this. This might (pure speculation) be part of the reason efforts to provide active cusp plugging didn't work. IE: Using reverse logic, placing electron repellers in the cusps, led to electron accumulations in the cusps and this led to unacceptable ion loses . While this was not a problem in WB6 where the open cusp losses (counteracted by recirculation) prevented this negative space charge accumulation in the cusps. This fits the weakly coupled considerations above. Between the weak coupling of the ions to the electrons, the presence of an increased negative space charge in the cusps would allow the ions to climb higher against the relatively weakened internal space charge (inverse square law considerations) so that it reaches outside the midline of the magrid (or perhaps not quite so high if there is some leakage) and sees the positive charge and is accelerated to the walls. This may be a fairly delicate balance as WB5 work presumably tried a range of settings to try to find a happy medium.
Dan Tibbets
Fussion plasmas are not closely coupled, which means the electrons and positive ions do not spend enough time close together that this local coulomb attraction will dominate over space charge effects. This is pointed out in several plasma physics texts and is the basis of my arguments that bipolar charged particle flows does not occur in the cusps. If this was the case (closely coupled plasma) then A. Carlson's contention that ion containment could not be better than electron containment would be reasonable. He never contested my point- I don't know whether he was stumped, ignored me, or silently laughed at me. He never seemed to make the distinction between neutral and non neutral plasmas.. In any case, a completely coupled plasma (actually a neutral gas) would be atoms. A tightly coupled plasma (cold and dense) is tightly coupled and the local effects will generally dominate over cumulative space charge considerations. A loosely coupled plasma (hot, and not so dense) is the opposite. This does not mean local effects are not present- bremsstrulung would be a good example of that, but that they can be easily (?) overcome. That is why electrons will trail along with the ions to a modest(?) extent, but the reverse is much less prevalent. Due to the mass difference, the ions can effect the momentum of the electrons much more than the reverse. This is why electrons will be pulled inward by ions to form a generally parabolic potential well (as opposed to a square potential well), but ions will not be pulled outward significantly by the escaping electrons because the ions inertia (momentum) is not changed much by the passing electron that spends only a very brief time close enough to the ion that its local electrical field dominates over the space charge, which is generally pulling the ion towards the center.
If there was not some lose coupling the ions would be accelerated past the ~ shell of electrons, and accumulate towards the center till mutual repulsion stops and reverses them for the next cycle. I'm uncertain if this would be sustainable. In this case a true virtual anode would form in the center (net positive charge). Bussard stated something to the effect, that if the positive charge accumulation achieved ~ 80% (?) of the potential well depth, the potential well would be 'blown out'.
Because of the lose coupling and some partial dragging of the electrons towards the center this does not occur. A relative central anode can form, but it can be managed to levels of ~ 20-30% of the potential well depth. The virtual anode is relative because the charge is still negative, but less so. This allows for greater ion confluence while still remaining within tolerances.
The dynamics in the Polywell is a complex blend of interactions based on the negative space charge provided by the excess electrons, the momentum differences between the ions and electrons, and the position within the Wiffleball. With a thermalized neutral plasma, any location within the plasma volume will have similar properties. In the near spherical geometry of the Polywell, the properties are much different in the outer margins, the 'mantle' region, and the core.
Also, though I am not certain, I suspect that there may not be much electron concentration in the cusps. Certainly, in a magnetic concave surface between magnets (like in a Tokamak), I could see electrons accumulating (provided it was a negative plasma) but with the non concave open cusps in a Polywell, these are holes that the electrons will quickly transit and exit without impediment. Once outside the magnets the electrostatic charge can reverse them so there would be a bidirectional flow, but this is the same over the rest of the Wiffleball surface also. The only difference is that here the magnetic fields reverse the electrons. Magnetic mirroring effects in the cusps may modify this some , but with the negative space charge inside, I speculate that this would be minimized.
If the Gauss law effects are not complete (there is some leakage due to the size of the holes in the ' magrid sphere', I could see a low energy electron oscillating back and forth at the border between the negative space charge dominated region and the positive magrid dominate region. But, two considerations would impede this. First, collisions with other electrons at different energies would destabilize this balance. Secondly the internal negative space charge (potential well) is about 15-20% weaker than the potential on the magrid. This bias would essentially give the magrid potential a ~ 20% advantage. If an electron reached this border with a tiny outward velocity it would meet a reversing force at least 20% greater than the outward force. So in this tiny distance it might oscillate back and forth a few times but the greater inward velocity gain on each orbit would push the electron deep enough into the potential well until on the rebound it reached high enough that it was exposed to the full accelerating potential on the magrid, and was shot back deep into the magrid (recirculated). This ignores the collisions mentioned above. Also, the collisions would not only disrupt the energy balance, but lead to cross field transport so these electons would ground more quickly on the magnet surface- certainly if there is a greater density of electrons in this area. I'm not saying that there may be a tendency for electrons to accumulate here, but that there are several competing effects that would minimize or eliminate this. This might (pure speculation) be part of the reason efforts to provide active cusp plugging didn't work. IE: Using reverse logic, placing electron repellers in the cusps, led to electron accumulations in the cusps and this led to unacceptable ion loses . While this was not a problem in WB6 where the open cusp losses (counteracted by recirculation) prevented this negative space charge accumulation in the cusps. This fits the weakly coupled considerations above. Between the weak coupling of the ions to the electrons, the presence of an increased negative space charge in the cusps would allow the ions to climb higher against the relatively weakened internal space charge (inverse square law considerations) so that it reaches outside the midline of the magrid (or perhaps not quite so high if there is some leakage) and sees the positive charge and is accelerated to the walls. This may be a fairly delicate balance as WB5 work presumably tried a range of settings to try to find a happy medium.
Dan Tibbets
To error is human... and I'm very human.