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

The concept of the de Hoffmann–Teller frame is revisited for a high Mach-number quasi-perpendicular collisionless shock wave. Particle-in-cell simulation shows that the local magnetic field oscillations in the shock layer introduce a residual motional electric field in the de Hoffmann– Teller frame, which is misleading in that one may interpret that electrons were not accelerated but decelerated in the shock layer. We propose the concept of the adaptive de Hoffmann–Teller (AHT) frame in which the residual convective field is canceled by modulating the sliding velocity of the de Hoffmann–Teller frame. The electrostatic potential evaluated by Liouville mapping supports the potential profile obtained by electric field in this adaptive frame, offering a wide variety of applications in shock wave studies.