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The concept of the de Hoffmann–Teller frame is revisited for a highMach-number quasi-perpendicular collisionless shock wave. Particle-in-cellsimulation shows that the local magnetic field oscillations in the shocklayer introduce a residual motional electric field in the de Hoffmann–Tellerframe, which is misleading in that one may interpret that electrons were notaccelerated but decelerated in the shock layer. We propose the concept of theadaptive de Hoffmann–Teller (AHT) frame in which the residual convectivefield is canceled by modulating the sliding velocity of the deHoffmann–Teller frame. The electrostatic potential evaluated by Liouville mapping supports the potential profile obtained by electric fieldin this adaptive frame, offering a wide variety of applications in shockwave studies

Adaptation of the de Hoffmann–Teller frame for quasi-perpendicular collisionless shocks