I beg to differ!
Having said that I suppose I should read the patent...
Could you provide a link?
The reasons I disagree , based on limited understanding, is some of their statements and images of the plasma. The central three ring magnets, at least in one iteration of their machine has two obvious ring/ line cusps. The additional ring magnets on the ends do modify the pattern of recirculation somewhat. There are also two point cusps , and these feed into two end confinement regions with each again with a ring cusp - that is continous with the central ring cusp, and a point cusp towards the ends of the machine. That the central assembly point cusps feed into another confinement region does not negate the dynamics of charged particles escaping/ transiting between regions, but it does change what happens to them subsequently. Even with out more than the three basic ring magnets, the end point cusps are continuous externally to the two ring/ line cusps. In a simplified view this might be viewed as a contained plasma with embedded magnets. Recirculation of the plasma- electrons and/ or ions is probably more accurate than suggesting they are contained though. With the additional external magnets 'guiding' the recirculation,edge instabilities may become an issue. Provided the plasma in these regions is substantially less dense than in the primary core region, this may be tolerable.
They have mentioned a potential well and that is only possible with electrostatic containment by definition. The potential well is not only a method to accelerate a charged particle, it is a way to contain them, and expel them at the same time. If one is contained- pos. ions, the other must be expelled- neg. electrons. The Polywell tries to expel the excess electrons while electrostatically retaining the ions. There is no way to get around this. But, if you can magnetically confine the electrons, you can avoid this conundrum. The confinement of electrons is magnetic, the ion confinement is electrostatic- and is secondary to the potential well/ electrostatic conditions created by the magnetically confined electrons. You could reverse the process by confining the electrons electrostatically by magnetically confining excess ions. This is of course undesirable for several reasons. First it is the ions that fuse. You want them to be at the bottom of their potential well so that they are fastest in the center and so that the quasi spherical symmetry allows for ion confluence/ density maximum in the center. And, yes, the Lockheed machine is quasi spherical- at least by my understanding. The species that is magnetically contained will of course escape confinement by several means. For electrons this loss is primarily through the cusps. Limiting these cusp loses and / or recirculating the electrons can save considerably on the energy costs needed to inject new / replacement hot electrons. Don't forget that electrons are also lost through ExB transport across the magnetic fields irregardless of other loss mechanisms. If your cusp losses/ recirculation is good enough, the ExB losses can come to dominate the losses. The important point here is that this cross over point for electrons is much different than for ions. The ExB losses are ~ 60 times or less than for ions. The ExB losses are directly proportional to the gyroradius of the particles, and as the ion gyro radius is at least 60 times more... Even excellent ion magnetic cusp and / or recirculation efficiency would lose out to ion ExB losses long before adequate Lawson criterion were met. The only way to avoid this is by going big. This is a primary reason why Tokamaks must be so big. They do not restrict the ExB transport of ions because the ions are not held away from the magnetic field by electrostatic processes. The plasma- ions have to be forced to travel further before fully penetrating the magnetic fields. If you prefer, you can also say the ion gyro radius is small on the magnetic edge because the ions are at the top of their potential well and are cold in this region. Arguements about high Beta creating a sharp transition on the edge and thus limit initial progression of ExB diffusion may play a role, but I suspect it is minor if existent at all. For a Polywell to be small- meters instead of tens of meters, the ions must have only trivial losses through ExB (pronounced E cross B) transport. The only way to do this is to decouple the bulk of ions from the magnetic field and the only way to do this is with an electrostatic field- centrally directed potential well. Electrostatic ion confinement is absolutely essential, unless you are inventing new physics.
Because the ions are electrostatically confined by excess electrons and the electrons have to be magnetically confined to maintain the picture without humongous electron currents being needed. This implies that the escaping charged particles must be primarily electrons and efforts to minimize losses through excellent cusp geometries and recirculation of escaped electrons (or at least recovery of their energy efficiently) is the name of the game. The Lockheed's approach of layering the loss channels may help in this regard. It introduces other questions- like continued ExB electron losses, and unstable magnetic surfaces towards the electrons in some regions. Also, as the electrons must be the dominate species in these non core regions, the density of the electrons must be kept low otherwise the Coulomb repulsion would be unmanageable. This implies that in these outer regions the primarily magnetic confined electron losses are what is being recovered. The ions, with their more efficient electrostatic confinement, are mostly absent from this picture.
If electron are cusp confined for 100,000 passes or more, then escape and are mostly recovered through recirculation, the relative electron currents/ densities in the core (inside the primary magnet rings) is much greater than the external recirculating electrons of new injected electron densities. This allows for maintaining high internal densities that provide for useful fusion rates in relatively small volumes, while minimizing overall ExB losses,and perhaps very importantly minimizing edge instabilities exterior to the core, as the magnetic curvatures cannot be maintained in these outer regions. The much smaller charged particle densities (primarily electrons) in these non fusing external to the core areas help to minimize the losses through these two mechanisms. It is a case of having your cake and eating it too.
Without a potential well and the other basic properties envisioned in the Polywell, I do not see any logic to the Lockheed design.
Basic properties of Polywell are:
1) Quasi spherical geometry
2) Central virtual cathode generated by (tiny) excess of hot electron injection
3) Resultant decoupling of magnetic confinement of ions because of the electrostatic potential well created by the magnetically confined excess electrons
4) Resultant elimination of significant ion ExB losses
5) Electron cusp losses dominating over electron ExB losses, but good enough with or without recirculation to allow for adequate energy balances
6) The above requiring much better cusp confinement than is achievable with typical mirror confinement schemes
7)The above being achieved by high Beta operation which leads to so called Wiffleball operation which not only provides adequate electron magnetic confinement (perhaps with some degree of electron recirculation through the same cusp or adjacent cusps depending on design decisions). This not only allows for adequate electron magnetic confinement, but at densities that not only allows for meeting Lawson criteria, but does so at densities that allows for useful fusion yields in relatively small packages (compared to low Beta machines like Tokamaks).
And finally, not to be depreciated, the important maintenance of favorable B field curvature relative to the bulk of the plasma so that edge instabilities / macro instabilities are of trivial concern, even at the increased densities possible.
Things like recirculation efficiency, electron injection efficiency, bremsstruhlung issues, various engineering concerns are all important or even critical additional considerations.
To error is human... and I'm very human.