= Pulsar dispersion delay
{title2=$\Delta t\propto f^{-2}$}
A <radio wave> traversing a dilute cold <plasma> has a <group velocity> that depends on its <frequency>. In the ideal unmagnetized limit, the <dispersion relation> is $\omega^2=c^2k^2+\omega_p^2$, where $\omega_p$ is the angular <plasma frequency>. For $\omega\gg\omega_p$, differentiate to obtain $v_g=c\sqrt{1-\omega_p^2/\omega^2}$, then expand $1/v_g$ to first order. The excess travel time over a vacuum path is
$$
t(f)-t(\infty)\simeq\frac{e^2}{8\pi^2\epsilon_0m_ec}\frac{1}{f^2}\int n_e\,dl.
$$
Here $f=\omega/(2\pi)$ is ordinary <frequency>, $e$ is the magnitude of the <elementary charge>, $m_e$ is the <electron mass>, $\epsilon_0$ is the <vacuum permittivity>, $n_e$ is <Electron> number density, and $c$ is the <speed of light>. This approximation neglects magnetic corrections, collisions and multipath scattering; its positive sign means lower <frequencies> arrive later.
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