User:Peak/Test/jsMath

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

${\displaystyle {\frac {\langle \Delta {\vec {v}}_{\alpha }\rangle }{\Delta t}}={\frac {4\pi e_{\alpha }^{2}e_{\beta }^{2}\log \Lambda _{\alpha \beta }}{m_{\alpha }^{2}}}{\frac {\partial H}{\partial {\vec {v}}}}}$

When colliding with a species that is Maxwellian, this can be simplified to the form ${\displaystyle \langle \Delta {\vec {v}}_{\alpha }\rangle /\Delta t=-\nu _{s}^{\alpha /\beta }{\vec {v}}\,}$, where ${\displaystyle \nu _{s}^{\alpha /\beta }}$ 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 ${\displaystyle \nu _{s}^{\alpha /\beta }}$ given in the NRL formulary.