of the dispersed data indicates that the spectral indices evolve as a function of pulse phase (Weisskopf, 2002). The Chandra result is in semi-quantitative agreement with previous measurements (e.g. Pravdo et al. 1997; Massaro et al. 2000) at various energies. However, the Chandra results extend the phase coverage through pulse minimum. In summary, observations strongly suggest that these phase-dependent properties come from different parts of the pulsar magnetosphere. The question is how to explain theoretically the phase dependent properties of the observed high-energy radiation from the Crab pulsar as well as from other gamma-ray pulsars. We suggest that the above examples indicate the necessity of using three dimensional outer magnetospheric gap (hereafter outer gap) models to explain the observed data.

THREE DIMENSIONAL OUTER GAP MODELS
==================================

The outer gaps, powerful acceleration regions, can form in the vicinity of “null charge surface" (${\bf{\Omega}}\cdot{\bf{B}}=0$) (Holloway, 1973; Cheng et al. 1976) because the charged carriers on each side of the null charge surface have opposite charges. In fact, the charge density of the magnetosphere in the corotating frame of a neutron star is (Goldreich and Julian, 1969) $\rho_0\sim
-({\bf{\Omega}}\cdot{\bf{B}}/ 2\pi c)$, where ${\bf{B}}$ and ${\bf{\Omega}}$ are the magnetic field and angular velocity of 