The Physical Basis For The Polywell
We’ve got a problem. We are going to run out of oil. We are going overheat this planet. We are in deep trouble and we know it. Many people are just trying to have fun before the clock runs out. They have given up trying to fix this. We have tried so many outside solutions and they have failed, so why keep trying? In todays’ world money speaks the loudest and the longest, and thus far, the money has been in burning carbon to heat the planet. Not anymore. Not if the polywell works. We are talking about an invention that can run every oil, coal and gas company out of business. This machine can sell energy at a fraction of gas prices. It can produce more energy, in more places than any other invention in the history of the world. Whomever can build the first working Polywell reactor will be the most respected, wealthiest and most powerful organization on the planet, period.
“If the solution is not beautiful, I know it is wrong.” - R. Buckminster Fuller
Where these tubes are placed is important. The location is important for the following reason. The gas is the fuel for the fusion reactor. Once injected, the gas becomes ionized, forming the ions. The ions are what is actually fused. They fuse because there are attracted to a big cloud of electrons in the center. This is like a marble rolling around in a bowl. You can let the marble go in three spots. In the center, where the marble will just sit. On the lip, where the marble will roll from one side to the other side. Or above the bowl. If you let a marble go above a bowl, the marble will crash downward, zip across the center and fly out the other side. The marble is lost! The ions are the marble and the bowl is the voltage drop. If an ion is formed in the wrong place, it will not be caught by the voltage drop. It will have too much energy. It will crash towards the center, zip through the middle and fly out the other side hitting the metal cages. The ion will be lost! Where you form the ions is important. Hence, where you place the emitters is important.
This process ionizes the gas inside WB-6. It increases the number of free electrons and free ions flying around. It separates the material. Ideally, both clouds of electrons and ions have too much energy to recombine. At most it takes 14.9 eV to strip off electrons from deuterium. This is much less than the typical electron energy. Now you can see one reason why the Navy wants to get several 10,000 volt electron guns for their reactor . The higher voltage electrons will ionize the gas much faster. Bussard stated in his Google presentation that the electron voltage for the PZL-1 machine (built in 2003) was 15,000 volts  and the drive voltage was 12,500 volts for WB-6.
The process described here is the “two color” electron start up. Bussard believed that this would be ideal for large machines. The machine would essentially inject a high energy electron population with a low energy electron population which was self-generated. The energies of these two electron populations would merge.
If an electron were to travel from one corner of the cage, what would it experience as it moves into device center? At the start in the corner, it will feel a voltage like being within two parallel plates. This is the voltage valley. The positive charge would be in front of the electron. The electron starts falling down a 12,500 voltage hill towards the center. It feels a Lorentz force, this is shown below.
Inside the voltage valley the electric field dominates this force – the electron falls towards the rings. As it reaches the gas emitters it starts to feel the magnetic field. Over time, the magnetic fields start to dominate the electrons' motion. The electron gets caught by the rings, and recirculates. Lets focus just on the electric field for the moment. When the electron crosses the gas emitters, it enters center zone. There are many ways to model the electron cloud here. For now, we will model it like an infinitesimally small point. This point contains all the electrons. This structure can be modeled like a point charge. The electron sees strong columbic repulsion from the cloud. This spikes as the electron closes in on the center. For this analysis we argue that when the electron reaches dead center, there is no electric field. This would occur if the dead center had uniform charge in all directions. The electron feels the reverse as it comes out the other side of the cage. As it passes the far gas emitter, it once again sees the voltage valley, before reaching the cages edge at 1.70 meters. This electric potential is graphed out below.
The spherical model is probably flawed anyways because these electrons are probably filling in a pocket inside the magnetic fields - and that pocket is not spherical, it is star shaped. If this is the case, the electron cloud would look like a 14 point star. This is shown below. Notice, the points of the star are all the same size. This is because the magnetic fields at the corner and axis are the same. This creates a more uniform containment of the electrons. It is important fact to consider in ring design. Lastly, If the Whiffleball mechanism is real, then that star shape would swell into a sphere with 14 nubs. This would be due to the electrons pushing back the ring fields and pinching off the loss points. These nubs represent remaining holes in containment. The holes are like holes in a real Whiffleball - hence the concepts' name.
Using these distances for each point, we can graph what magnetic field as the rings move apart. This graph is shown below. There is a ton of information contained within this graph. First, the center field should probably not be shown. It is in fact zero. It is shown here – as what it would be for 6 non-interacting ring fields - for comparison. It is the distance to the rings that drives this model. At the joint, the rings close in quicker; this drives the magnetic field up faster, than at the corner. This happens despite the corner accounting for one more ring. The axis field comes from being in the middle of the ring. Therefore the axis moves in tandem with the rings – so the axis field remains constant. The last and most important observation is that the rings are placed where they are, so that the axis and corner fields are the same. Overall, the model predicts what you might expect. As the rings get closer together, the magnetic effects increase in strength.
So if one combines the electric and magnetic fields, you have a total “energy density map” for the system. This is important. It tells you where high energy and low energy locations are. Think of this energy map like the hills and valleys of a mountainous terrain. The high energy spots are the high peaks, the low energy spots are the low valleys. For a particle to occupy a given location, it must have at least this amount of kinetic energy. When the electron turns around, the potential energy is the same as the electrons total energy. This energy map should give you a basic sense of where an ion or an electron can go, if it is injected at a given energy. Indrek already did some preliminary modeling of the electric and magnetic fields, here are images taken from his work .
Because the electron moment is so small the electric field dominates its potential energy. The electric field can be modeled as originating from a spherical cloud in the center. As was stated above, it does not matter what the diameter of this sphere is. Any electron outside a sphere of uniform charge, acts the same, regardless of the diameter of the sphere. The sphere always looks like a point field, which is located at the spheres' center. Improvements to this would incorporate more exotic shapes for the electron cloud – such as the 14 point star or the Whiffle ball. Improved models would have far more complex electric potentials. When the rings are moved away from the center the electric potential energy decreases. The potential energy, shown below, is converted to electron volts and displayed.
Previously,  it was found that the rings could be made from stainless steel. This is modeled as a combination of nickel (10%) and iron (90%). The deuterium gas is treated like hydrogen. This model predicts that sparking between the cage and the rings will occur, as Bussard stated it did.
8. Bussard, Robert W. "The Advent of Clean Nuclear Fusion: Superperformance Space Power and Propulsion." 57th International Astronautical Congress (2006). Web.
25. “The Polywell Blog" Oh, The Possibilities. N.p., 10 Dec. 2011. Web. 18 July 2012.
33. Nevins, William M. "Can Inertial Electrostatic Confinement Work beyond the Ion-ion Collisional Time Scale?" Physics of Plasmas 2.10 (1995): 3804-819. Print.