Joseph Chikva wrote:
Previous work based on fluid models suggested that the electron-electron two-steam instability would become unstable when the well depth of the virtual cathode was 14% of the applied voltage
If so, I think that feasible number density will be defined not by beta (ratio of magnetic pressure to kinetic pressure) but by this factor: "14% of the applied voltage"
Regarding annealing I think that is certain process making the temperature (measure of thermalization) isotropic in all points of volume occupied by plasma. Temperature is the same anywhere but its value defined by collision intensity, scattering cross-section, etc. And temperature will permanently grow till enery input by electric field will not become equal to energy losses mainly via Bremstahlung. I do not see any other mechanism limiting thermalization.
The reference- admittedly only an abstract, stated that the 14% value was accepted by previous studies, but that their analysis did not support this claimed limit.
I'm not sure what you are saying. Annealing at the edge (I repeat- the edge) of the plasma results in the vast majority of ions in this edge region only, to be moving in randome motions- ie: isotropic. Any angular momentum that has accumulated in the mantle (region between the central core area and the edge area) is anneled out in the edge. This is due to the extreamly high collisionality/ very short MFP of the low energy ions (perhaps ~10 eV +/- 50 50 eV (or what ever the Maxwell distribution would be for a plasma with an average of 10 eV. The electrons have collided so many time that the motions are random, fully thermalized in this defined region. Being fully thermalized, means the velocities are within well defined limits, and the directions are fully randomized.
The entire machine certainly does not have a cloud of ions at the same temperature (not if it works with advanced fuels) Each position within a defined set of radial shells will have a different temperature (KE), possibly significantly different densities (if there is any confluence) with corresponding differences is MFP. As often pointed out in the past, the spherical geometry means any ions that collide in the center- and with confluence most of the collisions will occur near the center, can up and down scatter, but the angular momentum collisions are less profound as the possibble angles of deflection relative to the center decreases as the center is approached.
I'm uncertain on this point, but I believe the 10^22 density often quoted is the average density within the Wiffleball. If there is more than minimal confluence towards the center, the densities will vary . A little to a lot more dense in the core, less dense in the mantle, and more dense again on the edge. This assumes certain competitive considerations. In the core the ions are traveling fastest in the amallest volume, so the transit times will be less, and this will reduce the relative density. The central confluence/ focus will have to overcome this interaction befor pressure will start building in the core. At some defined region volumes, there may be a balance point where the number of ions in each region may be equal. But the volume of the core is much less than the volume of the mantle, and the edge is also probably smaller than the mantle. Since the core would have the same number of ions during a time slice confined to a smaller volume, the effective density is larger. If this core density is the 10^22 or more value quoted, then the mantle where most angular momentum changing collisions would occur in a steady density assumption, may be mildly to extremely relaxed due to these dynamic considerations. Also, with a virtual anode forming in the center ( less negative ) has to form if there is any confluence at all. This will be slowing the ions in the core by perhaps as much as ~ 20% (number that has been used) this will increase the density in the core even further due to slower ion speed/ transit times. The fusion rate/ Coulomb collision rate may change , it depends on the balance between the temperature dependent consecrations and density dependent rates. This is another 'knob' to consider.. Any virtual anode effects in the core would not effect the mantle, because the anode effects cancel out as the ions aproach , then depart the core region.
Dan Tibbets
To error is human... and I'm very human.