I have been arguing that the electrons and ions will stream out the cusps together and these beams/fans will extend to the wall. This is a result of the quasi-neutrality required by the densities, geometry, and potentials of relevance here and does not require the fluxes to be ambipolar. These beams, however, attach the central plasma ball to the wall electrically through the Debye sheath, so that the relative potential is determined by the current. Specifically (within a factor of 2 or so),
In addition there will be a "pre-sheath" voltage drop that accelerates the ions to the speed of sound. If the current is controlled by the sources (i.e. the electron beam), then the voltage of the plasma ball is fixed. When the current is near zero, the power loss will be minimized, which sounds like a good idea.I = n*e*sqrt(kT/m_i)*A*exp( (V_1-V_2) / (kT_e/e) )
What about the potential of the magrid? The plasma will react with a surface charge density to patch together the potential it wants to have internally with what the magrid and other structures want to have externally, i.e. in the vaccum regions. You might want to use the voltage on the magrid as part of your electron gun, but you don't have to. It is irrelevant for confinement of the ions for the same reason I give to (almost) every question about plasma physics: quasi-neutrality. If you manage to (magnetically) confine the electrons, the ions will not have any choice but to stick around in their neighborhood.
The density and temperature within the plasma ball and cusp beams will be roughly constant. There will be about a factor of 2 drop in the density from the center to the wall.
I believe this picture is self-consistent and that a real polywell will not look too much different. If anyone can find inconsistencies I would appreciate hearing about them.
Rick Nebel, if he ever shows up again, will say that's all wrong because it assumes a thermalized plasma. In other threads I have calculated the thermalization rate and shown that draining off and re-injecting the electrons at a rate sufficient to maintain a non-Maxwellian distribution will require an unbelievably efficient machinery (>99.96%), and even given perfect engineering there are probably physics reasons why that cannot be achieved. On top of that, Rick has never explained just how a non-Maxwellian distribution will change anything in its essence. Sometimes it does, but often it doesn't. Until somebody shows why it matters and how the power balance works out, I'm sticking to the straightforward conclusion that the plasma is very nearly Maxwellian.