93143 wrote:Density times average outward flow velocity of electrons (proportional to sqrt(drive voltage)) times effective cusp area (proportional to gyroradius^2) times electron specific energy (proportional to drive voltage) times recirculation loss fraction (constant due to geometric similarity).
93143 wrote:I believe drive voltage is an independent parameter unrelated to the scaling laws
93143 wrote:B^2 is plasma density.
(Specifically, gyroradius is inversely proportional to B.)93143 wrote:The gyroradius is going to go down as B goes up.
This stuff is standard plasma physics.
Assumption: Wiffleball trapping works like how it sounds, rather than just having all of the charge collect at the edge in a thin magnetized sheath that directly connects to the cusps via flux tubes. This is necessary in order for the concept of effective cusp area to make sense. The observed virtual well generation efficiency (80%+) seems to me to imply that this is true, and I've already made half a stab at explaining why I think it's physically plausible.
I can't remember why I think the cusp width scales with the gyroradius. It seems logical, and I think Art and Dr. B both thought this, but at this point I can't be bothered to check...
Result: Point cusp leakage is independent of both device size and applied magnetic field. It is similarly easy to show that line cusps leak as B*R, given the same assumptions.
Where's the problem? Except that I noticed a flaw in my analysis halfway through and changed my postulated loss scaling laws as a result - maybe that confused you?