Theory Helps Observations: Determination of the Shock Mach Number and Scales From Magnetic Measurements

Abstract

The Mach number is one of the key parameters of collisionless shocks. Understanding shock physics requires knowledge of the spatial scales in the shock transition layer. The standard methods of determining the Mach number and the spatial scales require simultaneous measurements of the magnetic field and the particle density, velocity, and temperature. While magnetic field measurements are usually of high quality and resolution, particle measurements are often either unavailable or not properly adjusted to the plasma conditions. We show that theoretical arguments can be used to overcome the limitations of observations and determine the Mach number and spatial scales of the low-Mach number shock when only magnetic field data are available.

Non-locality of ion reflection at the shock front: dependence on the shock angle

“…The magnetic compression is given by The relation of the non-coplanar component approximately follows the theoretical analysis (Gedalin 1998) and was successfully applied to observational analysis (Gedalin et al. 2022). The electric field is normalized on .…”

“…Modelling of the shock profile is a necessary part of any theoretical investigation and allows us also to extract information from observations (Gedalin et al. 2022). Although test particle analysis is sometimes considered inferior compared with sophisticated self-particle simulations, it has the advantage of controlling each parameter separately, which allows us to determine multi-parameter dependencies.…”

Implications of weak rippling of the shock ramp on the pattern of the electromagnetic field and ion distributions

“…Most shock observations have been and are being performed at the Earth bow shock. As a result of these observations and theory development, it seems that at present the structure of low-Mach-number shocks is thoroughly studied observationally and understood rather well (Greenstadt et al 1980;Russell et al 1982;Mellott & Greenstadt 1984;Jones & Ellison 1987;Gosling, Winske & Thomsen 1988;Farris, Russell & Thomsen 1993;Gedalin 1996b;Balikhin et al 2008;Gedalin, Friedman & Balikhin 2015;Gedalin et al 2022) (see, however, Wilson et al (2017)). With the increase of Mach number the shock front undergoes structural changes, developing rippling and time dependence (Bale et al 2005;Moullard et al 2006;Lobzin et al 2008;Krasnoselskikh et al 2013;Burgess et al 2016;Hao et al 2016).…”

MESSENGER Observations of Standing Whistler Waves Upstream of Mercury's Bow Shock

“…The “1 Hz” whistler waves have been commonly observed upstream of the bow shock of Mercury (Fairfield & Behannon, 1976; Le et al., 2013), where they propagate along the magnetic field and farther upstream (∼30,000 km). Although phase standing whistler waves have been observed at Mercury, they have not yet been analyzed (Gedalin et al., 2022).…”