Rippled quasi‐perpendicular collisionless shocks: Local and global normals

Abstract

[1] Proper determination of the shock normal is necessary for reliable determination of observed heliospheric shock parameters and comparison of observations with theory. The existing methods work sufficiently well for low and moderate Mach numbers one-dimensional stationary shocks. Higher-Mach-number shocks are no longer planar at the scales of the ion convective gyroradius or smaller. In rippled shock fronts, the local shock normal may differ substantially from the global normal. The former is determined by the local direction of the fastest variation of the magnetic field, while the latter is determined by the far upstream and far downstream plasma conditions. Here we use 2-D hybrid modeling of quasi-perpendicular collisionless shocks with moderate and high Mach numbers to quantify the difference between the directions of the two normals. We find that the angle between the local normal and the global normal may be as large as 40 ı within the front of a rippled heliospheric shock. The coplanarity method of the shock normal determination is sensitive to the choice of the region for the magnetic field averaging. We also find that the usage of the sliding averaging region in the close vicinity of the shock transition provides satisfactory estimates of the global normal.Citation: Ofman, L., and M. Gedalin (2013), Rippled quasi-perpendicular collisionless shocks: Local and global normals,

Cross‐Shock Potential in Rippled Versus Planar Quasi‐Perpendicular Shocks Observed by MMS

“…This is presumably a typical feature of high Mach number shocks, in agreement with several past modeling studies of shocks (Burgess, ; Burgess & Scholer, ; Lowe & Burgess, ; Ofman & Gedalin, , ; Winske & Quest, ) as well as observations reported by (Johlander et al, ). In particular, Ofman and Gedalin (, ) discussed the deviation of the shock normal due to rippling, based on their 2‐D hybrid simulation study. The geometry of our observations is sketched in Figure , which shows the bow shock surface, with the electric field MVA normal in red at each spacecraft.…”

“…Individual normals deviated from the timing analysis normal by up to 30°. This is presumably a typical feature of high Mach number shocks, in agreement with several past modeling studies of shocks (Burgess, 2006;Burgess & Scholer, 2007;Lowe & Burgess, 2003;Ofman & Gedalin, 2013a, 2013bWinske & Quest, 1988) as well as observations reported by (Johlander et al, 2016). In particular, Gedalin (2013a, 2013b) discussed the deviation of the shock normal due to rippling, based on their 2-D hybrid simulation study.…”

“…To conclude, we present the results of a comparative study of two quasi‐perpendicular collisionless shocks in the solar wind, with low (IP shock) and high (bow shock) Mach number: The cross‐shock NIF potential from electric field measurements is 24–28 V for the IP shock (with 41–42 V from the electron proxies), and 290–440 V for the bow shock (with 240–260 V from the electron proxies). The ion proxies cannot be used for high Mach number shocks because the ion moments are spoiled by reflected ions before and during the ramp. The low Mach number IP shock surface was almost planar on the scale of the MMS spacecraft configuration as well as on the scale of the MMS and ARTEMIS separation distance (~20 R E ). The high Mach number bow shock surface was rippled on the scale of the MMS spacecraft configuration, in agreement with the results of Burgess (), Burgess and Scholer (), Lowe and Burgess (), Ofman and Gedalin (, ), and Winske and Quest () and the observations of Johlander et al (). …”

Interplanetary shocks and foreshocks observed by STEREO during 2007–2010

“…They found that smaller and slower magnetic clouds can drive more corrugated shocks. In addition, several works using hybrid simulations [ Winske and Quest , ; Lowe and Burgess , ; Ofman and Gedalin , ] have shown that shock rippling occurs due to instability and/or surface waves inherent to the shock when the Alfvénic Mach number M A is >4.7. The scale of this rippling is of the order of the ion inertial length.…”

Ion distributions in the Earth's foreshock: Hybrid‐Vlasov simulation and THEMIS observations

“…Early simulations were one dimensional in space and used hybrid particle‐in‐cell (hybrid‐PIC) algorithms [e.g., Leroy et al , ]. They soon moved to full particle simulations [e.g., Lembège and Dawson , ] and increased in dimensionality to 2‐D hybrid‐ and full‐PIC simulations [e.g., Lembège and Savoini , ; Savoini et al , ], gaining in complexity and detail of the physical description at large scales [e.g., Lin , ; Omidi et al , ; Blanco‐Cano et al , ] as well as for local kinetic processes [e.g., Ofman and Gedalin , ] and even reaching three spatial dimensions for hybrid‐PIC simulations of the magnetosphere [e.g., Lin and Wang , ]. PIC‐based methods suffer from the statistical noise inherent to the random sampling of the particle distribution injected in the simulation and the low number of particles that can feasibly be simulated.…”