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Multi-Spacecraft Observations of Collisionless Shocks in the Heliosphere


In this work, we introduce background relevant to and our own analyses of collisionless shock observations in the heliosphere. The observations of interest are in situ measurements collected by spacecraft immersed in the plasma. We introduce basic concepts in the physics of shocks and space plasmas and describe some specific techniques appropriate for the analysis of shock observations. Then we discuss the spacecraft mission that provided the data for our studies: a four-probe constellation known as Magnetospheric Multiscale (MMS). Instruments providing the most necessary measurements to our work (electric fields, magnetic fields, and particle distributions and moments) are discussed individually. The subsequent three chapters, detailing the analyses we performed on this data, represent the work we have published on the subject.

In the first paper, we compare shock normals, planarities, and Normal Incidence Frame (NIF) cross-shock potentials determined from electric field measurements and proxies, for a subcritical (Fast Magnetosonic Mach number M_F=1.1±0.1) interplanetary (IP) shock and a supercritical bow shock (M_F=2.13±0.04). The low-Mach shock’s cross-shock potential was 26±6V. The shock scale was 33km, too short to allow comparison with proxies from ion moments. Proxies from electron moments provided potential estimates of 40±5V. Shock normals from magnetic field minimum variance analysis were nearly identical, indicating a planar front. The high-Mach shock’s cross-shock potential was estimated to be from 290 to 440V from the different spacecraft measurements, with shock scale 120km. Reflected ions contaminated the ion-based proxies upstream, whereas electron-based proxies yielded reasonable estimates of 250±50V. Shock normals from electric field maximum variance analysis differed, indicating a rippled front.

For the second paper, we investigate the dependence of shock parameters (speed v_sh, normal n ̂, and angle θ_Bn) on the choice of upstream and downstream regions for 51 bow shock crossings in MMS Fast Survey data. We summarize guidelines for selecting stream regions based on the magnetic field and particle moments. Preferred upstream and downstream combinations were identified by minimizing RH conservation errors. Comparing parameters from different up/downstream combinations provided a measure of how stream region choices affect the parameters. Shifting from the preferred stream region combination to another would cause <5° change in n ̂ for 90% of shocks, <15km/s change in v_sh of 70% of shocks, and <5° change in θ_Bn for 84% of shocks. All parameters would shift by more than their standard deviations σ. The most robust is n ̂, which would change by <1σ for 22% and <3σ for 86% of shocks, while v_sh is the least robust, changing by <3σ for only 12% of shocks. Summary plots and detailed lists of parameters are provided in a separate Supplement, freely available at

In the third paper, we return to the IP shock that was recorded crossing the MMS constellation on 2018 January 8. Plasma measurements upstream of the shock indicate efficient proton acceleration in the IP shock ramp: 2-7 keV protons are observed upstream for about three minutes (~8000 km) ahead of the IP shock ramp, outrunning the upstream waves. The differential energy flux (DEF) of 2-7 keV protons decays slowly with distance towards the upstream region (dropping by about half within 8 Earth radii from the ramp) and is lessened by a factor of about four downstream from the ramp (within a distance comparable to the gyroradius of ~keV protons). Comparison with test-particle simulations has confirmed that the mechanism accelerating the solar wind protons and injecting them upstream is classical shock drift acceleration. This example of observed proton acceleration by a low-Mach, quasi-perpendicular shock may be applicable to astrophysical contexts, such as supernova remnants or the acceleration of cosmic rays.

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