differ, so the outer gap is divided into small subzones in the plane containing the rotation and dipole axes. The photon densities and beaming directions for different zone are also different, in which case the particle transport needs to be considered. Under their refinements, they found that the spectral variation of the $\gamma$-radiation over the pulsar period is the result of the different emission processes which play a role throughout the outer magnetosphere, however, they were not able to obtain a self-consistent spectrum which resembled the observed high-energy spectra, and they attributed this shortcoming to the inability to model appropriately the extremely complex emission processes and their interactions. Subsequently, Romani and his co-workers (Romani and Yadigaroglu, 1995; Yadigaroglu and Romani, 1995; Romani, 1996) have improved their three dimensional models and successfully explain the high-energy emission features of pulsars including the phase-resolved spectra of the Vela pulsar. However, in their model they have assumed that there is only one single outer gap and only outgoing current. These two assumptions do not have real physical justification.

CRZ MODEL
=========

Cheng et al. (2000 hereafter CRZ) re-consider the three dimensional magnetospheric outer gap model, following the important ground-breaking work of Romani and co-workers. 