= Drift-kinetic equation
{title2=$\partial_tf+\dot{\mathbf R}\cdot\nabla f+\dot v_\parallel\partial_{v_\parallel}f=0$}
The collisionless equation in the title transports a gyrophase-independent <phase-space distribution function> at fixed <first adiabatic invariant>. Its leading <guiding center> position has $\dot{\mathbf R}=\mathbf u_\perp+v_\parallel\mathbf b$. The parallel acceleration includes $(q/m)E_\parallel-\mu\mathbf b\cdot\nabla B$ and, when required, terms from motion of the local frame. Both $v_\parallel$ and the parallel derivative refer to the exact perturbed <magnetic field>.
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