We compute the patterns of γ-ray emission due to curvature radiation in dissipative pulsar magnetospheres. Our ultimate goal is to construct macrophysical models that are able to reproduce the observed γ-ray light-curve phenomenology recently published in the Second Fermi Pulsar Catalog. We apply specific forms of Ohm's law on the open field lines using a broad range for the macroscopic conductivity values that result in solutions ranging, from near-vacuum to near Force-Free. Using these solutions, we generate model γ-ray light curves by calculating realistic trajectories and Lorentz factors of radiating particles, under the influence of both the accelerating electric fields and curvature radiation-reaction. We further constrain our models using the observed dependence of the phaselags between the radio and γ-ray emission on the γ-ray peak-separation. We perform a statistical comparison of our model radio-lag vs peak-separation diagram and the one obtained for the Fermi standard pulsars. We find that for models of uniform conductivity over the entire open magnetic field line region, agreement with observations favors higher values of this parameter. We find, however, significant improvement in fitting the data with models that employ a hybrid form of conductivity; specifically, infinite conductivity interior to the light-cylinder and high but finite conductivity on the outside. In these models the γ-ray emission is produced in regions near the equatorial current sheet but modulated by the local physical properties. These models have radio-lags near the observed values and statistically best reproduce the observed light-curve phenomenology. Additionally, these models produce GeV photon cut-off energies.

We present the magnetic and electric field structures as well as the currents and charge densities of pulsar magnetospheres which do not obey the ideal condition, E · B = 0. Since the acceleration of particles and the production of radiation requires the presence of an electric field component parallel to the magnetic field, E , the structure of non-Ideal pulsar magnetospheres is intimately related to the production of pulsar radiation. Therefore, knowledge of the structure of non-Ideal pulsar magnetospheres is important because their comparison (including models for the production of radiation) with observations will delineate the physics and the parameters underlying the pulsar radiation problem. We implement a variety of prescriptions that support nonzero values for E and explore their effects on the structure of the resulting magnetospheres. We produce families of solutions that span the entire range between the vacuum and the (ideal) Force-Free Electrodynamic solutions. We also compute the amount of dissipation as a fraction of the Poynting flux for pulsars of different angles between the rotation and magnetic axes and conclude that this is at most 20-40% (depending on the non-ideal prescription) in the aligned rotator and 10% in the perpendicular one. We present also the limiting solutions with the property J = ρc and discuss their possible implication on the determination of the "on/off" states of the intermittent pulsars. Finally, we find that solutions with values of J greater than those needed to null E locally produce oscillations, potentially observable in the data.