2004 I 3
From QED
The collision operator is:
The steady state Vlasov equation is:
If we linearize this:
Using f0e = fM, this becomes:
If we guess :
So that:
Then:
Plugging in (and using p = cosθ)
Plugging in the maxwellian and doing the first integral:
Transforming to x = v / vTe:
Then the resistivity is:
The parallel resistivity is changed in the banana regime by conductivity reduction, which occurs because trapped particles cannot carry current. The new resistivity will thus be:
Where ε = r / R0, and ε1 / 2 is the fraction of trapped particles. The regime is valid as long as the collision frequency is less than the bounce frequency. The bounce frequency is given by:
The collision frequency is also increased by 1 / ε for the trapped particles, so:
This page was recovered in October 2009 from the Plasmagicians page on Generals_2004_I_3 dated 22:21, 9 May 2007.