Two-dimensional simulations of a curved shock: Self-consistent formation of the electron foreshock

A collisionless curved shock is analyzed in a supercritical regime with the help of a two-dimensional electromagnetic full particle code. Curvature ef fects are included self-consistently and allow one to follow continuously t he transition from a narrow and step-like strictly perpendicular shock to a wider and more turbulent oblique shock within the quasi-perpendicular rang e 65 degrees < theta (Bn) < 90 degrees. Present results reproduce the forma tion of the electron foreshock without any simplifying assumptions. In agre ement with experimental data, local bump-on-tail parallel distribution func tions are well recovered in the foreshock region and correspond to electron s backstreaming along the magnetic field lines. Present detailed analysis s hows that local back-streaming distributions have two components: (i) a hig h parallel energy component corresponding to back-streaming electrons chara cterized by a field-aligned bump-in-tail or beam signature, and (ii) a low- energy parallel component characterized by a loss cone signature (mirrored electron). Two types of bump-in-tail patterns, broad and narrow, are identi fied at short and large distances from the curved shock, respectively, and are due to different contributions of these two components according to the local impact of the time-of-flight effects. Present results allow one to i dentify more clearly the nature of the bump-in-tail pattern evidenced exper imentally (narrow type). These also confirm that mirroring electrons make t he dominant contribution to the bump-in-tail pattern in the total distribut ion in agreement with previous studies. Results suggest that low and high p arallel energy populations are intimately related and may contribute togeth er to the upstream wave turbulence.