replace the charge deficiency inside the gap, and finally the gap will be filled up. However, if a vacuum gap extends to the light cylinder, charged particles created in the gaps will escape from the magnetosphere, so the gap will not be quenched. Hence, stable outer gaps (if they exist) are those from the null surface to the light cylinder along the last closed field lines. In each outer gap, the inner boundary of the outer gap lies near the intersection of the null surface where $\rho=0$ and the boundary of the closed field lines of the star on which the magnetosphere current does not flow. The thickness of the outer gap is bounded from above by a layer of electric current which contributes a surface charge density.

According to CHR model, four outer gaps exist in the open zone in the plane of (${\bf{\Omega}}$, ${\bf{\mu}}$) (two of them are topologically connected in three dimensional space), but only two longer outer gaps should give observed fan beams. They argued that these two longer outer gaps may create enough $\gamma$-ray and $e^{\pm}$ pairs to quench the two shorter, less powerful ones. In the CHR model, the $\gamma$-ray emission is approximated to 