Talk:Aneutronic fusion/Archive 1

message: :1) I suppose you are right about the plasma frequency. I would like to read about it. Could you supply a reference? I find the calculation of maximum beta useful anyway. I would want to put it back in, with mention of any appropriate restrictions.
::try any standard textbook. The calcuation is not at all valid.68.39.247.3 02:47, 28 June 2006 (UTC)
replies: text: The criterion \omega_p>\omega_c/2; is equivalent to nkT/(B^2/2\mu_0)>kT/(2m_ec^2)=kT/(1\,\mbox{MeV}). Is it possible you meant \omega_p^2>\omega_c^2/2? That is what would make sense looking at the dispersion relation of the X wave (or the L wave). Either way, a substantial, but not obviously prohibitive beta would be required. Although this restriction might be somewhat more severe for aneutronic fusion because it generally requires a higher temperature, I think it is rather too detailed - and difficult to get the details right - to include on this page. Maybe I can put it under Electron cyclotron resonance, but even then... --Art Carlson 09:00, 29 June 2006 (UTC)
replies: text: Your formulas are entirely wrong. Please refer to a text-book for the correct ones. What is right is that the magnetic field energy per electron is 1 Mev.  kT can be anything.Elerner 01:05, 5 July 2006 (UTC)
replies: text: Should I make an equally helpful contribution to this discussion? You are entirely wrong. Go read an (unspecified) elementary text book. (See below for a less emotional response.) --Art Carlson 09:05, 5 July 2006 (UTC)
replies: text: 1 MeV per electron is a really interesting number, too. In a perfect system, you first supply magnetic energy of 6 MeV for each p-B11 pair (one electron for p and 5 for B), plus a bit for thermal energy. When they fuse - and let's assume they all do -- each pair releases 8.7 MeV in the form of fast alphas. Now you have about 15 MeV of energy, partly in the form of magnetic fields and partly in the form of fast particles. This energy has to be extracted, converted to electricity, and reinserted with an total efficiency of 6/15 =  40% to break even. That includes the efficiency of the direct convertor, the efficiency of the capacitor banks and magnetic coils, the production of the plasmoid, bremsstrahlung losses, and losses due to heat conduction and instabilities. Oh, and I almost forgot, we want to have a little bit of electricity left over to sell! --Art Carlson 09:27, 6 July 2006 (UTC)
thread_title:  Cyclotron radiation (1) 

message: :2) The statement \omega_p>\omega_c/2; is mathematically equivalent to nkT/(B^2/2\mu_0)>kT/(2m_ec^2)=kT/(1\,\mbox{MeV}). If you can't do the math yourself, you have disqualified yourself as a physicist.
::According to the NRL plasma formulary, p.29, the ratio of electron plasma frequency to gyrofrequency is proportional to n^1/2/B. You have asserted, in your addition to this article, that the ratio is that of plasma pressure to magnetic field pressure, which is proportional to nT/B^2. Your error is that you have introduced a factor of T which does not belong there.Elerner 00:38, 6 July 2006 (UTC)
replies: text: Look again. I also have a factor of T on the right hand side. Your mistake. --Art Carlson 07:49, 6 July 2006 (UTC)
replies: text: Right, you can introduce T into any equation by multiplying both sides of the equation by T. We all learned this in high school. But that does not miraculously create a real physical dependence on T. If you take T back out, you can see that the criteria depends on the plasma density, not the plasma pressure. Different physical quantity. In dimensionless terms, the ratio is the square root of the ratio of the rest energy density of the plasma to the magnetic energy density.Elerner 00:21, 7 July 2006 (UTC)
replies: text: I found it helpful to express the relation in terms of β and T. For some purposes, using n and B as the variables is more useful. The physics is always the same no matter what set of variables are chosen. You seem to realize that now, although before you refered to my "error" and wrote, Your formulas are entirely wrong. I don't expect it, and I won't hold a grudge, but a simple "I'm sorry I called you stupid" would seem appropriate here. --Art Carlson 07:55, 7 July 2006 (UTC)
thread_title:  Cyclotron radiation (2)