ohiovr wrote:Fusor neutral density is around a millionth of an atmosphere, so per cubic meter you may have about 180 micrograms of fuel ions. If all of that fuel were ionized, you'd have a large fraction of a coulomb (enough to blow it up to smithereens). So I presume only a tiny fraction of the atmosphere is ionized. Am I right?
Lets see.... One mole of deuterium is 2 grams in 22.4 liters at STP, so ~ 50 moles per cubic meter or ~ 100 grams. At 1 millionth of an atmosphere that would be ~ 100 micrograms. The numbers are close, though probably better to talk of molar equivalents rather than mass. With a Z of one and 6.02 * 10^23 particles per 22.4 liters or ~ 3*10^25 particles per cubic meter results in ~ 3 *10^19 particles per cubic meter at 1 millionth of an atmosphere. This number may be ~ 5 times greater in a glow discharge fusor and similar numbers in a good Wiffleball (or perhaps up to 10 times greater depending on the Wiffleball trapping factor and the outside background pressure). This background pressure probably has to be less than ~ 0.0000001 th of an atmosphere. With a Wiffleball trapping factor of ~ 1000, the ions (and electrons) trapped inside the Wiffleball might be as high as ~ 0.00001 atmospheres.
I don't know what percentage of the gas is ionized inside a glow discharge fusor but I have heard that ion- neutral collisions dominate by a factor of ~ 60 over ion-ion collisions. This means the neutral atom/ molecule density is perhaps up to ~ 100 times that of the ions. This would decrease the Coulomb charge pressure accordingly, presuming you only had ions (positive charges) and neutrals in the chamber.
But in a neutral plasma, the negative electrons and positive charged ions cancel each other out. There would be no net space charge, and no space charge Coulomb pressure. Keep in mind that the Wiffleball inflation, increase in Beta is due to the cumulative effects of the kinetic energy of the charged particles (ions and electrons) hitting the magnetic field border, not due to a space charge directly.
In the Polywell, inside the Wiffleball border the ions and electrons may exceed the neutral background atoms by as much as ~ 1000 fold. As such the beam- beam collisions should dominate over beam background collisions. This is important, but does not apply much to this discussion. Inside the Wiffleball the background neutral background atoms may be similar to that outside the magrid, perhaps 0.00000001 to 0.0000001 atmospheres, while the charged particles may be at ~ 0.00001 atmospheres due to selective confinement of the charged particles. This is important as the background pressure outside the Wiffleball region has to be maintained below ~ 1 millionth of an atmosphere to prevent glow discharge/ arcing in this region. This concentrating effect inside the Wiffleball is key to reaching useful fusion generating densities, while avoiding intolerable arcing outside the magrid.
All of this is interesting, at least to me
, but doesn't directly address you concern.
What is important here is that a neutral plasma does not have a space charge- there is no charge separation. Coulomb charge pressure is zero. It is when one species exceeds the other that space charge builds up. In a Non Neutral plasma the excess of electrons (in the Polywell) creates the space charge. This is indeed limited by the buildup of space charge Coulomb pressure, and it can theoretically become immense. The Brillion limit applies (I think) but only as applied to the difference in negative and positive charges, not the total. In a Polywell with a internal Wiffleball density of ~ 10^20 charged particles / M^3, the excess of electrons may be ~ 10^14/ M3. The coulomb pressure would be derived from this number, not the total charged particle numbers. There would be 100,000,000,000,000,000,000 positive charges per m^3 and 100,000,100,000,000,000,000 negative charges per M^3. This simple analysis assumes a homogenous mixture of electrons and positively charged ions. There can be local variations while the overall numbers remain the same and this can complicate the picture. Such can apply to the Polywell in various ways- shape of the potential well, POPS like effects, etc.
Dan Tibbets