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A two‐dimensional electrodynamic model is used to study particle acceleration and non‐thermal emission mechanisms in the pulsar magnetosphere. We solve the distribution of the accelerating electric field with the emission process and the pair‐creation process in the meridional plane, which includes the rotational and magnetic axes. By solving the evolutions of the Lorentz factor, and of the pitch angle, we calculate the spectrum in optical through γ‐ray bands with the curvature radiation, synchrotron radiation and inverse‐Compton process, not only for outgoing particles but also for ingoing particles, which have been ignored in previous studies.  We apply this theory to the Vela pulsar. We find that the curvature radiation from the outgoing particles is the major emission process above 10 MeV bands. In soft γ‐ray to hard X‐ray bands, the synchrotron radiation from the incoming primary particles in the gap dominates in the spectrum. Below hard X‐ray bands, the synchrotron emissions from both outgoing and ingoing particles contribute to the calculated spectrum. The calculated spectrum is consistent with the observed phase‐averaged spectrum of the Vela pulsar.  Taking into account the predicted dependence of the emission process and the emitting particles on the energy bands, we compute the expected pulse profile in X‐ray and γ‐ray bands with a three‐dimensional geometrical model. We show that the observed five‐peak pulse profile in the X‐ray bands of the Vela pulsar is reproduced by the inward and outward emissions, and the observed double‐peak pulse profile in γ‐ray bands is explained by the outward emissions.  We also apply the theory to PSR B1706−44 and PSR B1951+32, for which X‐ray emission properties have not been constrained observationally very well, to predict the spectral features with the present outer‐gap model.

Particle acceleration and non‐thermal emission in the pulsar outer magnetospheric gap