= Quasilinear diffusion
{title2=$\partial_tf_0=\partial_v(D\partial_vf_0)$}
The diffusive evolution of an averaged <phase-space distribution function> caused by weak fluctuating fields in the <quasilinear approximation>. In a stationary homogeneous one-dimensional electrostatic problem, if the potential's temporal <power spectral density> is $S_{\varphi,k}(\omega)$ with covariance $\int S_{\varphi,k}(\omega)e^{-i\omega\tau}d\omega/(2\pi)$, then
$$
D(v)=\frac{e^2}{2m_e^2}\sum_k k^2S_{\varphi,k}(kv).
$$
This follows from the real part of the one-sided time correlation along an unperturbed particle trajectory. Both signs of the spatial <wavenumber> are included. The action-space counterpart for regular <stellar orbits> is <quasilinear diffusion in action space>.
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