Confirmation of quasi‐perpendicular shock reformation in two‐dimensional hybrid simulations

Abstract

Shock reformation involves regions of a shock undergoing periodic collapse and redevelopment on a time scale close to the ion cyclotron period. Reformation is often observed in one‐dimensional (1‐D) hybrid and particle in cell (PIC) simulations of quasi‐perpendicular collisionless shocks provided the Alfvén Mach number MA and ion plasma beta βi are sufficiently high and low, respectively. Initial 2‐D PIC simulations showed some evidence for shock reformation, with ion reflection providing the main energy dissipation mechanism, while recent spacecraft observations showed a reforming shock with large amplitude whistler waves in the foot region. While recent spacecraft observations showed an case with reforming shock crossing with whistler waves dominated in the foot region. However, recent 2‐D hybrid and PIC simulations suggest that reformation does not occur in exactly perpendicular 2‐D shocks. This paper re‐examines shock reformation in quasi‐perpendicular shocks using 1‐D and 2‐D hybrid simulations. We find that 2‐D quasi‐perpendicular shocks (θbn = 85°) indeed undergo cyclic reformation providing MA and βi are high and low enough, respectively. For low MA ≤ 4, 2‐D quasi‐perpendicular shocks are found to be quasi‐stationary, despite 1‐D simulations predicting reformation, confirming and extending recent work for perpendicular 2‐D shocks. The dynamics of reformation are quite different in 2‐D than in 1‐D: in 2‐D large amplitude whistler waves grow in the shock foot, have amplitudes of order the downstream magnetic field, and affect the reformation. The whistlers have almost zero phase speeds in the shock frame and oblique wave vectors with respect to the upstream magnetic field. The predicted reformation period increases in 2‐D compared with 1‐D and increases nonlinearly as MA decreases towards the reformation threshold.