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Perpendicular relativistic ($\gamma_0=10$) shocks in magnetized pair plasmasare investigated using two dimensional Particle-in-Cell simulations. Asystematic survey, from unmagnetized to strongly magnetized shocks, ispresented accurately capturing the transition from Weibel-mediated tomagnetic-reflection-shaped shocks. This transition is found to occur forupstream flow magnetizations $10^{-3}<\sigma<10^{-2}$ at which a strongperpendicular net current is observed in the precursor, driving the so-calledcurrent-filamentation instability. The global structure of the shock and shockformation time are discussed. The MHD shock jump conditions are found in goodagreement with the numerical results, except for $10^{-4} < \sigma < 10^{-2}$where a deviation up to 10\% is observed. The particle precursor lengthconverges toward the Larmor radius of particles injected in the upstreammagnetic field at intermediate magnetizations. For $\sigma>10^{-2}$, it leavesplace to a purely electromagnetic precursor following from the strong emissionof electromagnetic waves at the shock front. Particle acceleration is found tobe efficient in weakly magnetized perpendicular shocks in agreement withprevious works, and is fully suppressed for $\sigma > 10^{-2}$. Diffusive ShockAcceleration is observed only in weakly magnetized shocks, while a dominantcontribution of Shock Drift Acceleration is evidenced at intermediatemagnetizations. The spatial diffusion coefficients are extracted from thesimulations allowing for a deeper insight into the self-consistent particlekinematics and scale with the square of the particle energy in weaklymagnetized shocks. These results have implications for particle acceleration inthe internal shocks of AGN jets and in the termination shocks of Pulsar WindNebulae.

Perpendicular relativistic shocks in magnetized pair plasma