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We report on the first self-consistent multidimensional particle-in-cell numerical simulations of nonhomogeneous pair discharges in polar caps of rotation-powered pulsars. By introducing strong inhomogeneities in the initial plasma distribution in our simulations, we analyze the degree of self-consistently emerging coherence of discharges across magnetic field lines. In 2D, we study discharge evolution for a wide range of physical parameters and boundary conditions corresponding to both the absent and free escape of charged particles from the surface of a neutron star. We also present the results of the first 3D simulations of discharges in a polar cap with a distribution of the global magnetospheric current appropriate for a pulsar with 60° inclination angle. For all parameters, we find the coherence scale of pair discharges across magnetic field lines to be of the order of the gap height. We also demonstrate that the popular “spark” model of pair discharges is incompatible with the universally adopted force-free magnetosphere model: intermittent discharges fill the entire zone of the polar cap that allows pair cascades, leaving no space for discharge-free regions. Our findings disprove the key assumption of the spark model about the existence of isolated distinct discharge columns.

We present the results of 3D particle-in-cell simulations that explore relativistic magnetic reconnection in pair plasma with strong synchrotron cooling and a small mass fraction of nonradiating ions. Our results demonstrate that the structure of the current sheet is highly sensitive to the dynamic efficiency of radiative cooling. Specifically, stronger cooling leads to more significant compression of the plasma and magnetic field within the plasmoids. We demonstrate that ions can be efficiently accelerated to energies exceeding the plasma magnetization parameter, ≫ σ , and form a hard power-law energy distribution, f _i ∝ γ ^−1 . This conclusion implies a highly efficient proton acceleration in the magnetospheres of young pulsars. Conversely, the energies of pairs are limited to either σ in the strong cooling regime or the radiation burnoff limit, γ _syn , when cooling is weak. We find that the high-energy radiation from pairs above the synchrotron burnoff limit, ε _c ≈ 16 MeV, is only efficiently produced in the strong cooling regime, γ _syn < σ . In this regime, we find that the spectral cutoff scales as ε _cut ≈ ε _c ( σ / γ _syn ) and the highest energy photons are beamed along the direction of the upstream magnetic field, consistent with the phenomenological models of gamma-ray emission from young pulsars. Furthermore, our results place constraints on the reconnection-driven models of gamma-ray flares in the Crab Nebula.