Robthebob wrote:93143 wrote:If a particular ion were at high energy at the edge, it would see the wiffleball effect just like the electrons
I do not understand this. I'm under the impression that the WB effect is just the result of the ballooning effect of electrons at the core of the machine, since the ballooning effect changes the field structure to allow particles to come in easy but leave harder, electrons will effectively relocate themselves to the core.
If you inject fuel into the system when the WB effect is already in place, I can see the ions might go into the core and have a harder time leaving, but I dont see how this have to do with high energy ions at the edge, or something... I'm missing something here.
All I meant is that while the ions are nominally electrostatically confined, the energy spread means that some of them will encounter the magnetic field at the edge of the wiffleball at a substantially nonzero energy. The magnetic field will turn a fuel ion around just as effectively as it will turn an electron around, though it takes more distance because the ions are heavier. So the magnetic confinement works on ions too; just not as well because the ions see larger cusps. In fact, it works on fusion products, though most of the alphas are so high-energy (ie: large gyroradius) that they only get about 1e3 passes before they find a cusp.
Joseph Chikva wrote:93143 wrote:Joseph Chikva wrote:Leakage through the cusps will be observed at beta<1 too.
Of course. With Polywell, beta=1
means the point at which cusp losses are at a minimum, due to the wiffleball effect.
May be. But please provide corresponding reference. Better if that would be the experimental evidence.
Valencia paper, page 9.
You know what the state of play is regarding experimental evidence. I'd point you to the detailed WB-6 final report (not the three-page summary), but it's been withdrawn; it was apparently posted in error...
I am mechanical engineer by my first education.
Good for you. My first two degrees were in mechanical engineering.
Apropos of that, let me point out to all present that when I say "instability", I am using in in the technical dynamic-systems sense. In this context, I mean a mode in which a disturbance grows without bound, until the plasma configuration that gave rise to it is destroyed.
So:
Let’s consider the pressure vessel with several small enough holes allowing some quantity of being there gas to leak and also with several holes for injection of higher pressure gas inside. Let’s inside flow exceeds gas leakage. So, pressure in vessel should be constantly increased. Let’s call beta=1 when gas pressure inside vessel is equal to strength limit of vessel. What will happen with vessel if pressure will reach that limit? Can leakage hole preserve vessel from explosion?
Ever heard of the leak-before-burst design criterion?
Polywell (if I've understood it correctly) is the ultimate leak-before-burst magnetic configuration. The plasma can keep pushing harder and harder on the field, and it will just strengthen to keep pace right up until the surface of the diamagnetic volume passes the magnets themselves.
Of course, by that point, the cusps will have long since been forced wide open by plasma pressure, and losses will be extreme. I don't imagine that the fuel and electron feeds and power supply could drive the system anywhere near such a condition.
And what is beta>1 Not a case when pressure inside exceeds the strength limit.
Nope. In the case of Polywell, it's when the cusps start to open up again.
What feedback you talk about?
After the minimum-loss point (denoted beta=1), plasma pressure starts to open the cusps, and losses increase, so that a slight excess of plasma supply will not result in a plasma disruption, but rather an increase in losses to offset the excess supply.
I did say at one point "if I've understood this correctly". It is possible, as far as I know, that the system exhibits catastrophic hysteresis or some kind of severe nonlinearity that renders it impossible to recover the wiffleball once the cusps have blown out. This would make your objection to the beta=1 run condition correct, though still in my opinion somewhat pedantic. I suspect instinctively that this is not the case, but like everyone here, I await further experimental evidence.
...the geometry makes it immune to certain classes of macroinstability.
Please provide examples from fusion history.
Mirror machines. They aren't subject to some of the classic macroinstabilities that tokamaks have to guard against.
As I also heard these reasonings about advantages of convex fields (minimum beta machines) but we have clear examples that minimum B stellarators have not any advantage vs. TOKAMAK and also suffers macro-instabilities.
A stellarator is not a convex-field machine (this is trivially obvious, since it has no cusps, whereas any machine with uniformly convex fields must as a matter of geometrical necessity have cusps). It does, however, eliminate the risk of current disruptions, since it doesn't need a plasma current to maintain conditional MHD stability like a tokamak does.
kcdodd wrote:KitemanSA wrote:kcdodd wrote:That comes from seeing the results of the solvers Indrek and I made. I am not sure if one could come up with a coils where it would be in equilibrium though.
The graphic that had been at your site is now not available. Can you bring it back?
Hm, I'll have to search for it. Indrek's site is still up though. Here you can see the large variance of magnetic field strength for a spherical wiffleball.
http://www.mare.ee/indrek/ephi/invwb/
All my solver did was find solution of shape for uniform magnetic field pressure on the surface.
Why does the plasma need to be a sphere? Instead of trying to configure the magnets to produce a perfectly spherical wiffleball, why not let the wiffleball decide what shape it wants to be?
If you try to hang a stick horizontally from a string attached to one end, it will not maintain a steady state. The best you can get is pulse mode. Remove the word "horizontally" and Bob's your uncle.