Re: EMC2 has published a polywell preprint on arXiv
Posted: Mon Jun 09, 2014 6:05 am
The electron thermalization process is of course proceeding. The real question is how fast it is proceeding, Increased density speeds it up, increased machine size increases the oppertunity, and increased temperature slows the process. How all three combine, along with probably several other considerations, determines the answer.
Increased opportunity in larger machines is due to increased transit distance. If confinement is defined in number of transits, then the time to complete a transit is the product of average velocity and distance across the machine. At the same transit confinement number, a 1.5 meter machine would have a confinement time ten times greater than a 0.15 meter machine. Note that average velocity is perhaps tricky, as it is a gradient and also depends how radial from the center the motions are.
The only detailed analysis that I know of is a paper by Bussard. I have referenced it before and it .seemed to satisfy Bussard.
As for thermalization in this machine. The measured x-rays came only from electrons with >2000 eV due to the cutoff filter. As the number of relative low energy ions and electrons from the plasma guns was vastly greater than the ~ 7000 eV e- gun electrons (assume a ~ 1,000,000 to 1 ratio), means the average temperature of the total charged particles did not increase much over the lifetime of the test. The e-gun electrons were the only contributor to the X-rays. That the E-guns were operating before the plasma burst, and the increased plateau values were ~ consistent with the density measurements, it is reasonable to assume that the signal came from increased confinement and thus density of the injected high energy electrons. To work the themalization time had to be longer, perhaps much linger than the confinement time. This places a limitation on the injected electron thermalization time minimum possible. How this would extrapolate to other conditions is complex, but this is at least one example of minimal thermalization time of the electrons under these specific conditions.
The temperature of the injected plasma was presumably somewhere between 1000 and 2000 eV. This is suggested by the quantity introduced and the reported ~ 700 MW of power from the plasma gun. Perhaps about 30 to 40 thousands of plasma amps was injected. Compare this to the e- gun current of ~ 2 amps. Assuming much of the E-guns electrons managed to enter the machine, the electron population would be ~ 10^22 at an energy of ~ 1500 eV, and ~ 10^19 would be ~ 7000 eV (at most). Once mixed and thermalized the average temperature would be ~1510 eV. This is well below the x-ray cutoff filter passage window. So thermalization between the two populations of electrons has to be significantly longer. This is of course an over simplified analysis, but I think serves my argument. It does raise questions about the WB6 situation. The high energy electrons ionized the injected gas and the secondary electrons were heated by the hot electrons. This suggests significant thermalization between the two populations. The conditions are much different between these two machines and requires analysis well beyond my pay scale. That is why I have referred to a detailed analysis. Keep in mind the thermalization has two components. The time it takes for the two populations to near a common average energy, and the time it takes the outliers-mostly up scattered high energy tail, to build to their Maxwellian statistic population. This is a slower process as the higher energy electrons have longer MFP and less frequent Coulomb interactions.
Monoenergetic does not have to imply a very narrow energy distribution. But, I think it does have to imply a significant truncation of the high energy Maxwellian tail. The name is perhaps misleading, but I don't know of any better name.
Dan Tibbets
Increased opportunity in larger machines is due to increased transit distance. If confinement is defined in number of transits, then the time to complete a transit is the product of average velocity and distance across the machine. At the same transit confinement number, a 1.5 meter machine would have a confinement time ten times greater than a 0.15 meter machine. Note that average velocity is perhaps tricky, as it is a gradient and also depends how radial from the center the motions are.
The only detailed analysis that I know of is a paper by Bussard. I have referenced it before and it .seemed to satisfy Bussard.
As for thermalization in this machine. The measured x-rays came only from electrons with >2000 eV due to the cutoff filter. As the number of relative low energy ions and electrons from the plasma guns was vastly greater than the ~ 7000 eV e- gun electrons (assume a ~ 1,000,000 to 1 ratio), means the average temperature of the total charged particles did not increase much over the lifetime of the test. The e-gun electrons were the only contributor to the X-rays. That the E-guns were operating before the plasma burst, and the increased plateau values were ~ consistent with the density measurements, it is reasonable to assume that the signal came from increased confinement and thus density of the injected high energy electrons. To work the themalization time had to be longer, perhaps much linger than the confinement time. This places a limitation on the injected electron thermalization time minimum possible. How this would extrapolate to other conditions is complex, but this is at least one example of minimal thermalization time of the electrons under these specific conditions.
The temperature of the injected plasma was presumably somewhere between 1000 and 2000 eV. This is suggested by the quantity introduced and the reported ~ 700 MW of power from the plasma gun. Perhaps about 30 to 40 thousands of plasma amps was injected. Compare this to the e- gun current of ~ 2 amps. Assuming much of the E-guns electrons managed to enter the machine, the electron population would be ~ 10^22 at an energy of ~ 1500 eV, and ~ 10^19 would be ~ 7000 eV (at most). Once mixed and thermalized the average temperature would be ~1510 eV. This is well below the x-ray cutoff filter passage window. So thermalization between the two populations of electrons has to be significantly longer. This is of course an over simplified analysis, but I think serves my argument. It does raise questions about the WB6 situation. The high energy electrons ionized the injected gas and the secondary electrons were heated by the hot electrons. This suggests significant thermalization between the two populations. The conditions are much different between these two machines and requires analysis well beyond my pay scale. That is why I have referred to a detailed analysis. Keep in mind the thermalization has two components. The time it takes for the two populations to near a common average energy, and the time it takes the outliers-mostly up scattered high energy tail, to build to their Maxwellian statistic population. This is a slower process as the higher energy electrons have longer MFP and less frequent Coulomb interactions.
Monoenergetic does not have to imply a very narrow energy distribution. But, I think it does have to imply a significant truncation of the high energy Maxwellian tail. The name is perhaps misleading, but I don't know of any better name.
Dan Tibbets