A study of the dispersion of the electron distribution in the presence of E and B gradients: Application to electron heating at quasi‐perpendicular shocks

Abstract

Abstract. The dynamics of electrons in the presence of E and B field gradients is considered. The results are applied to electron heating in quasi-perpendicular shocks. The main focus is on the transitions between adiabatic and overadiabatic heating and from perpendicular to oblique geometry. Contrary to previous results, it is shown that the divergence of initially close electron trajectories always takes place in the quasiperpendicular collisionless shock front. In the case of negligible electric field gradients at the shock front, the divergence rate depends only upon the magnetic field gradient and results in adiabatic heating. If the electric field gradient is not negligible, divergence rate depends on increasing electric field gradients. In this case, the divergence rate in the first part of the ramp will exceed the "adiabatic" divergence rate. This enhancement is significant for scales of the electric field of about 4-6 c/wv•. Under the conditions of the Earth's bow shock the magnetic field and particularly its gradients affect the electron trajectory divergence rate and thus the process of thermalization of electrons.

Electric field scales at quasi-perpendicular shocks

“…This existence of large gradients in the electric field has repercussions for processes involved in the heating of electrons. In the presence of electric field gradients the electron gyration frequency can deviate from its classically calculated value, leading to an increase in its Larmor radius and the possibility of a breakdown in adiabaticity (Balikhin et al, 1998).…”

Spatial scales of the magnetic ramp at the Venusian bow shock

“…Studies have also established that the electron dynamics at the shock front (e.g. demagnetisation and thermalisation) are influenced by the shock spatial scales within the transition (Balikhin and Gedalin, 1994;Gedalin et al, 1995a,b;Balikhin et al, 1998). Typically the magnetic transition across the collision-less shock is the most commonly studied due to the reliability and availability of magnetic field measurements.…”

Non-adiabatic electron behaviour due to short-scale electric field structures at collisionless shock waves

“…While Balikhin et al (1993) draw a strong connection between the scale length of the shock and subsequent heating, they do not alter the scales of the electric and magnetic fields independently of each other, nor do they study the effect of displacing one with respect to the other. This work was subsequently extended into the oblique regime by Balikhin et al (1998). In this paper the authors also included terms that account for the changing magnetic field, which were previously neglected, and found that the divergence in phase space always occurs and that the rate of divergence is dependent on the gradients of both the magnetic and electric fields.…”

“…The new scale length associated with the electric field spikes is relevant to the discussion of shock scale lengths and heating at oblique shocks by Balikhin et al (1998). Other shock features of interest which could influence the electron dynamics include foot and overshoot regions, as well as the time dependence of the field profiles and higher-frequency fluctuations (Lembege and Savoini, 2002;Sundkvist et al, 2012).…”

“…Indeed, the relative field scales of shocks is a topic which we study within this paper. In their paper, Balikhin et al (1998) outlined possible relationships between the fields, though it is a matter of contention which of them occurs in reality, since various observations and simulations support differing views.…”