This section you quote of Dr. B is perhaps one of the most confusing I have run across, exemplified by the apparent concretion of two completely different concepts (electron lifetime and ion density ratio) into one variable.TallDave wrote:Not quite. You don't need 1e5 confinement from the cusps, but you do need 1e3 containment.Well here may be where our understandings of the unit depart. It seems that you are looking to the cusps to do some sort of confinement. Not so. The cusps just provide directed leakage and re-entry paths that avoid the MaGrid can. The confinement is the positive charge on the MaGrid.The magnetic fields don't just shield the Magrid. They also provide enough confinement that you have a 1000:1 ratio inside:outside.As previously noted, no Polywell can operate at all if arcing occurs outside the machine, between the walls and the machine, because this destroys the ability of the driving power supplies to produce deep potential wells. Thus the mean free path for ionization outside the machine (inside the container) must be much greater than the external recirculation factor, times the machine-to-wall distance.
Since the mfp for ionization is inversely proportional to the product of the local neutral density and the ionization crosssection, this condition can ALWAYS be satisfied, IF the external neutral gas pressure is made sufficiently small. In order to avoid external arcing, the densities thus required are very much too low to be of interest for fusion, thus the density inside the machine (at its boundary) must be very much higher than that outside. This ratio is the Gmj factor, which is the ratio of electron lifetimes within the machine with B fields on, to that without any B fields.
In contrast, in order to be of interest for fusion, the interior density must be above some numerical value for any given size of machine. Typically this requires electron densities at the interior boundary of order 1E13/cm3, or higher. While the exterior densities (of neutrals able to be ionized) must typically be below 1E10/cm3 or less. Thus a minimum value exists for Gmj (here, typically 1E3), below which no machine can give significant fusion or net power, independent of the unprotected wall loss problem. Both must be solved simultaneously
First and primarily, he defines Gmj as the "ratio of electron lifetimes within the machine with B fields on, to that without any B fields". Now this variable has absolutedly no fundimental connection to population density. If an electron passes thru the grid 10 times before quenching on something when the magnet is OFF and passes thru the grid 10,000 times with the magnet ON, the Gmj is 1000, but the population ratio for the electrons is still 1:1. However, because you can now maintain a decent potential well, the population ratio of ions can be maintained at a much higher value, which is needed to prevent arching.
At least that is how I have come to interpret it.