That link shows several important features. First, that the magnetic field strength change gradient is very much slower or larger than the gyroradius of the charged particle at typical energies. This is a common consideration of plasmas as it is more simple to describe. From the gyroradius perspective the field is almost constant, so gyro orbit is almost circular. This is much different where the magnetic field strength is varying at rates similar to or shorter than the gyroradius at the given test point within the field. In this case the gyro orbit is prolonged, mildly to extremely elliptical. In the Polywell, especially at the Wiffleball border this applies. The gyroradius is short on the outside of the orbit but long on the inside. This allows the charged particle to complete ~ 1/2 of the highly elliptical orbit and then travel towards the center of the machine. Most of the gyro orbit is so long that the width of the machine is exceeded before the single orbit is completed. This results in this inner plasma being effectively non magnetic. It is not trapped on a field line. That is - it is turned/ reversed by the magnetic field, but subsequent behavior is highly dominated by other processes,such as collisions. There are U tube videos that show electrons mirroring (bouncing) back and forth along field lines. This is misleading inside the machine because this behavior would only be seen by particles that have penetrated well past the Wiffleball border (Magnetic field strength is not changing as fast as at the border). This is why an analogy like the "Wiffle Ball " toy is more descriptive of what is going on inside the machine rather than charged particles mirroring back and forth on field lines. Getting electrons into and leaking out of the cusps is somewhat different. Here more classical mirroring perspectives may be more useful.
http://farside.ph.utexas.edu/teaching/p ... mlLikewise
... the gyroradii of such particles are much smaller than the typical variation length-scale of the magnetospheric magnetic field. Under these circumstances, we expect the magnetic moment to be a conserved quantity: i.e., we expect the magnetic moment to be a good adiabatic invariant. It immediately follows that any MeV energy protons and electrons in the inner magnetosphere which have a sufficiently large magnetic moment are trapped on the dipolar field-lines of the Earth's magnetic field, bouncing back and forth between mirror points located just above the Earth's poles.
Magnetic fields do not stop charged particles, they turn them, and this behavior is dependent on the field strength locally, which has to be considered at every position of the charged particle as it moves. For the Earth, and to a lesser extent even a Tokamak, the plasma charged particles will have more circular orbits. That and the dominate magnetic field created by the moving charged particles themselves determines a lot of the observed behavior. The Polywell plasma is considered as non magnetic for the most part, while the Tokamak plasma is magnetic for the most part. They are different beasts.
Secondly, ExB diffusion or collision driven movement of charged particles within a dominate magnetic field results in particles traveling through a magnetic field. This limits containment based on the particle gyro radius in the magnetic field (here assumed to be constant for convenience) and the total distance the particle has to travel to transverse the field. The Earth's magnetic field is extremely wide relative to the gyroradius, so it takes an extremely large number of collisions before the trapped particle penetrates to the atmosphere. This allows for good containment and is one of the things that drives Tokamaks to such large sizes. A small narrow magnetic field might contain charged particles very well also, but this is because the density of charged particles is very low, so the ExB driving collisions are very rare. Penning traps that are used to contain antiparticles, etc. fall into this category.
The loss of particles to the atmosphere at the poles is a different process, and is essentially what happens at the cusps in the Polywell. A Tokamak does not have cusps so it does not suffer this problem. Ignoring extremely important instabilities in the Tokamak, the magnetic containment is due solely to ExB diffusion/ drift issues. In the Polywell, mostly due to the decoupling of ion containment from magnetic electron containment, the picture is changed. ExB drift becomes much more manageable at smaller scales, mostly because onye electron ExB needs to be considered and this is a much slower process than it would be for ions. This allows for temperature and density inputs to be greater at a given B field strenth without the need to grow the machine size as much. This allows Polywells to have a fusion energy density much greater than Tokamaks, ie smaller machines at the same fusion output.
The plasma containment in a Polywell is much worse than in a Tokamak (perhaps 10s of milliseconds vs 100s of seconds) but this has to be compared to the relative density , temperatures and resultant fusion rates. A few milliseconds of containment in the Polywell is sufficient.
Very importantly, the fusion rate versus the loss rate still the same (Lawson criterion met), but the fate of the fusion products is different. At higher temperatures (MeVs) the fusion products have much slower collision rates than the fuel ions. In the Tokamak, the long confinement times at the relative densities still allows for these energetic particles to reach thermodynamic equalibrium with the rest of the plasma. The fusion products heat the plasma, often called ignition once the fusion ions contributes more heat to the plasma than that input needed to make up for losses . The Polywell with it's much worse losses through cusps allows for these fusion ions to leave before reaching thermodynamic equalibrium with the fuel ions. In an ignition machine, once this condition is reached, no additional power needs to be input and it will continue to run until the fuel is depleted (or other things terminates the burn), It the Polywell, which is not an ignition machine, the fusion continues until the input power is shut off, then, the fusion stops very quickly. Bussard described the Polywell as an amplifier for this reason. This is a fundamental difference in the machine design. It also allows for the fusion ions with most of their KE intact to deposit their energy well outside the reaction space. This allows for direct conversion of much of the output energy, In an ignition machine this is not possible because most, if not almost all of the fusion energy is needed to continue to directly heat the plasma. The maintained heat eventually is transferred into the walls and this drives a thermal conversion plant. This can be done with a Polywell (or DPF, and perhaps other schemes) but direct conversion can enhance the yields in terms of final useful energy (electricity).
Dan Tibbets