Pulsar magnetosphere

A pulsar magnetosphere is the plasma and electromagnetic field surrounding a pulsar. Close to the star, charges tend to screen electric fields parallel to the magnetic field and approximately corotate; near the light cylinder, relativistic motion and field distortion become essential.

In an idealized corotating pulsar magnetosphere, plasma moves with $\mathbf{u}=\mathbf{\Omega }\times \mathbf{r}$. In Gaussian units, ideal magnetohydrodynamics then gives $\mathbf{E}=-\mathbf{u}\times \mathbf{B}/c$.

The Goldreich-Julian density is the charge density needed to support corotation in an idealized pulsar magnetosphere. Where exterior currents vanish,in Gaussian units.

The light cylinder is the notional cylindrical surface on which rigid corotation with angular speed $\Omega$ would reach the speed of light.

The light cylinder radius is $R_{\mathrm{LC}}=c/\Omega$. A nonrelativistic corotation model must fail as cylindrical radius approaches this scale.

A pulsar polar cap is the region on the stellar surface threaded by magnetic field lines that reach the outer magnetosphere rather than closing close to the star.

For an aligned dipole whose last relevant field line reaches equatorial radius $R_e$, the polar-cap opening angle obeys ${\sin }^2{\theta }_{\ast }=R_{\ast }/R_e$. It is approximately $\sqrt{R_{\ast }/R_e}$ for a small cap.