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Shock accelerated electrons are found in many astrophysical environments, andthe mechanisms by which they are accelerated to high energies are still notcompletely clear. For relatively high Mach numbers, the shock is supercritical,and its front exhibit broadband fluctuations, or ripples. Shock surfacefluctuations have been object of many observational and theoretical studies,and are known to be important for electron acceleration. We employ acombination of hybrid Particle-In-Cell and test-particle methods to study howshock surface fluctuations influence the acceleration of suprathermal electronsin fully three dimensional simulations, and we give a complete comparison forthe 2D and 3D cases. A range of different quasi-perpendicular shocks in 2D and3D is examined, over a range of parameters compatible with the ones observed inthe solar wind. Initial electron velocity distributions are taken as kappafunctions, consistent with solar wind \emph{in-situ} measurements. Electronacceleration is found to be enhanced in the supercritical regime compared tosubcritical. When the fully three-dimensional structure of the shock front isresolved, slightly larger energisation for the electrons is observed, and wesuggest that this is due to the possibility for the electrons to interact withmore than one surface fluctuation per interaction. In the supecritical regime,efficient electron energisation is found also at shock geometries departingfrom $\theta_{Bn}$ very close to 90$^\circ$. Two dimensional simulations showindications of unrealistic electron trapping, leading to slightly higherenergisation in the subcritical cases.

Electron acceleration at quasi-perpendicular shocks in sub- and supercritical regimes: 2D and 3D simulations