Electron dynamics and cross-shock potential at the quasi-perpendicular Earth's bow shock

International audience[1] The evolution of the electron distribution function through quasi-perpendicular collisionless shocks is believed to be dominated by the electron dynamics in the large-scale coherent and quasi-stationary magnetic and electric fields. We investigate the electron distributions measured on board Cluster by the Plasma Electron and Current Experiment (PEACE) instrument during three quasi-perpendicular bow shock crossings. Observed distributions are compared with those predicted by electron dynamics resulting from conservation of the first adiabatic invariant and energy in the de Hoffmann-Teller frame, for all pitch angles and all types of trajectories (passing and, for the first time, reflected or trapped). The predicted downstream velocity distributions are mapped from upstream measurements using an improved Liouville mapping technique taking into account the overshoots. Furthermore, for one of these crossings we could take advantage of the configuration of the Cluster quartet to compare mapped upstream velocity distributions with those simultaneously measured at a relatively well magnetically connected downstream location. Consequences of energy and adiabatic invariant conservation are found to be compatible with the observed electron distributions, confirming the validity of electron ''heating'' theories based on DC fields as zeroth-order approximations, but some systematic deviations are found between the dynamics of low-and high-adiabatic invariant electrons. Our approach also provides a way to estimate the cross-shock electric potential profile making full use of the electron measurements, and the results are compared to other estimates relying on the steady state dissipationless electron fluid equations. At the temporal resolution of the instruments, the scales associated to the change of the potential generally appear to be comparable to those of the magnetic field, but some differences between the methods appear within the shock transition. It is argued that potentials evaluated from Liouville mapping rely on less restrictive hypotheses and are therefore more reliable. Finally, we show how, in contrast to methods using electron velocity moments, the technique can be used to produce high-time-resolution electric potentials and discuss the electric potential profiles through the shock. Citation: Lefebvre, B., S. J. Schwartz, A. F. Fazakerley, and P. Décréau (2007), Electron dynamics and cross-shock potential at the quasi-perpendicular Earth's bow shock