2004 II 1
From QED
Ion-ion collisions follow the same physics as the electron-electron collisions (i.e., pitch angle scattering in the center of mass frame). The e-e collision frequency is approximately the electron-ion collision frequency, which goes like . Thus to get the i-i collision frequency, we simply replace the electron mass with the ion mass:
It may also depend on Zeff.
The electron-ion energy exchange rate is that of the slowest component, ions slowing on electrons, νie. Therefore:
The drift velocity is . The bounce frequency is vtε1 / 2 / qR. The banana width is thus Λj˜vD / ωb˜vtq / ε1 / 2Ω˜ρq / ε1 / 2. Since q = εBt / Bp, this is Λj˜ρε1 / 2BT / Bp. ε is the aspect ration r / R0.
The magnetic field must increase to , because of the frozen-in condition. The total energy density is proportional to , and the total energy is this times the area. Since the total energy must be conserved:
This means that the new energy density is:
This page was recovered in October 2009 from the Plasmagicians page on Generals_2004_II_1 dated 22:27, 9 May 2007.