Several points. The ions on the edge are not spun up. You could induce this angular momentum in a Wiffleball toy, but this is not what occurs in a Polywell. IF there was a spin up- ions tacking along the Wiffleball edge with a preferred transverse (axial) motion, the plasma would have a dominate flow direction, and this would result in a magnatized plasma, repeatedly denied for the Polywell. Individual ions may assume a high degree of axial motion - approaching a circular orbit instead of a highly parabolic orbit), but these individual axial motions may be in any direction. There is not a preferred direction of rotation. Thus the individual magnetic fields of each ion is cancelled out by ions traveling in the opposite direction.The net plasma induced magnetic field is zero. Compare this to a Tokamak where there is a preferred direction of rotation about the torus and thus a strong and significant magnetic field throughout the plasma.happyjack27 wrote:ya, no. you said nothing there to explain why ions would prefer one set of radial energies over another; one apsis over another.
The ions preferred motion is governed at the simplest level by the potential well. As they fall towards the center- bottom of the potential well, their potential energy in the system is converted to kinetic energy. The ions are fast in the center/ core, intermediate in the mantle and slowing to a stop in the radial vector at the edge. The near spherical geometry has significance. So long as there is some radial component to the ion orbit and there will always be some, then the ion concentration per unit volume will increase towards the center, this is central focus or confluence. The extent of radial contributions is the big argument . Annealing doesn't set the average ion speed at any given radii. The important point of annealing is straight forward thermalization rates that increase rapidly as the average velocity drops in a local area and also includes density considerations. The average radial speed of the ion is determined by the potential well. Annealing is a consequence of normal thermalization (in both radial and angular momentum/ transverse or axial) about a low average speed. The speed will be an average with a bell shaped curve distribution of thermalized energies about this slow speed and this spread might be plus or minus ~ 1000% (as an example). But with an average KE of say 1 eV means that the thermalized KE would be plus or minus 10 eV in this case. This assumes that the ions spend enough time in this edge region that full thermalization occurs. The residence time is greater than the thermalization time. This local condition would always be met if the ions are purely radial, without much thermalization deeper in the machine. Transverse/ axial motion is not effected by the potential well so they would not slow to a stop on the edge due to the potential well, but if their total motion (KE )is small enough in this region they will also fully participate in edge thermalization so their deviation from the average energy spread would also be reduced in the axial direction as well as the radial. The greater the component of axial motion for the ion the less likely it will fully thermalize on each pass through the edge region, thus axial annealing is less absolute than radial annealing. Collisions in the core, mantle and edge are all interrelated. Perhaps the saving grace for the Polywell concerning angular momentum is the spherical geometry with always some radial component (hopefully large component). The collisions will be the greatest in the core because the density is greatest* at least relative to the mantle region. Here angular momentum generating collisions are least significant- all directions from the center is radial. This allows for tailoring of the machine density and energy so that reasonable fusion rates are obtained while the restoring forces of annealing and preferential loss of up scattered ions prevent full ion thermalization in the bulk of the machine, except in the edge region where the average ion energy is modest (sum of radial and transverse KE) with resultant high Coulomb collisionality leading to Maxwellian distributions about a low average energy. This Maxwellian energy spread is proportionately a small fraction of the potential well induced ion energies in the core, thus with each transit from the edge to the core and back again the ion energy is reset to a small energy spread (relative to core energies).
Coulomb collisionality, energy, density and machine size all contribute and gradual thermalization occurs throughout the machine but this is a time dependant process. The edge annealing does not stop global thermalization, but it may slow it so that the ions are lost from containment and/ or fuse first. There is some energy spread but it is much (?) less, especially the problamatic high energy tail.
As I said, the thermalization (radial and axial) of the electrons is a foggier issue, but there may be restoring forces (delaying factors) as well. These are possibly ion tugging towards the center, preferential losses of up scattered electrons and average lifetimes short enough. Here recirculation plays a double dividend. The setup allows for average and upscattered electrons to leave faster than you would otherwise need for energy balance, but because of Magrid direct conversion the energy cost of this shorter confinement time is minimized.
* Coulomb collisionaliy scales as the inverse 1.75 power of the temperature/ KE. This means that at an average energy of say 10 eV at the edge compared to an average energy of 10.000 eV in the core means that Coulomb collisions at the same density occurs 1000^1.75 power more rapidly. That is ~ 60,000 times more rapid, or conversely the MFP is ~ 60,000 times shorter. This needs to be factored with the relative density in the regions as Coulomb collisionality also scales with the density squared. The final result incorporates both. The core may be more dense, but not by a factor of ~ 240, thus if full Maxwellian thermalization occurs anywhere on one pass, it will be in the edge region. This degree of thermalization per pass is the key, so long as the edge thermalization dominates, full ion thermalization deeper in the machine cannot occur.
Um.. to add more considerations, consider that the lifetime of the ion is ended with either escape from confinement or fusion. Fusion results in high energy particles which have KE of perhaps 30 times the KE of the fuel ions. This means the Coulomb collisionality of these fusion ions are 30^1.75 or ~ 500 times less- the MFP is ~ 500 times greater. This means these fusion ions partake in Coulomb collisions much less frequently, they do not share their energy with the fuel ions much before they complete enough passes to find a cusp and escape. This is why a Polywell does not have an ignition condition. The fusion products do not contribute (much) to collisional heating of the plasma They also do not partake in annealing as their speed at the Wiffleball edge is slowed only marginally (like from ~ 3 MeV to 2.9 MeV) by the potential well. Their MFP remains very high and Coulomb collisionality remains very, very small compared to the inter fuel ion collisionality on the potential well edge (or even in the core).
Dan Tibbets