User:Peak/Test/jsMath

The Fokker-Planck drag term can be written in terms of one of the Rosenbluth potentials as


 * $$ \frac{\langle \Delta \vec{v}_\alpha \rangle}{\Delta t} =

\frac{4 \pi e_\alpha^2 e_\beta^2 \log \Lambda_{\alpha \beta}}{m_\alpha^2} \frac{\partial H}{\partial \vec{v}} $$

When colliding with a species that is Maxwellian, this can be simplified to the form $$ \langle \Delta \vec{v}_\alpha \rangle / \Delta t = - \nu_s^{\alpha/\beta} \vec v \,$$, where $$\nu_s^{\alpha/\beta}$$ is the directed momentum loss rate. Starting from the above Rosenbluth potential form, show the steps needed to derive this result, including a derivation of the expression for $$\nu_s^{\alpha/\beta}$$ given in the NRL formulary.