Role of overshoots in the formation of the downstream distribution of adiabatic electrons

Abstract

Abstract. We analyze the influence of the magnetic overshoot on the downstream electron distributions formed as a result of the collisionless adiabatic motion of the electrons in the quasi-stationary electric field in shock front. We show that a substantial overshoot can result in a significant distortion of the downstream distribution due to cutting out the electrons with high perpendicular velocities. We calculate numerically the electron distribution in the v -vñ plane, as well as expected cuts through the distribution depending on the angle with respect to the magnetic field direction, also taking into account the averaging procedure of the ISEE type apparatus. These distorted distributions and cuts should be clearly observed in the downstream region just behind the shock transition layer. Absence of such observations would indicate that the above picture of adiabatic electron dynamics in the static field is significantly incomplete, and estimates based on these assumptions should be considered with caution.

Quasi-perpendicular Shock Structure and Processes

“…Since this structure is only observed at supercriti- cal shocks, it was suggested (Morse, 1976) and confirmed by computer simulation (Leroy et al, 1982) that the overshoot structure is associated with a reflected and heated ion population. It is also known that overshoot phenomena play a role in ion acceleration (Giacalone et al, 1991) and electron heating (Gedalin and Griv, 1999). ISEE-1 and -2 measured magnetic overshoot thicknesses using two-point timing to obtain shock speed (Livesey et al, 1982) and found that the observed thickness was ordered by the downstream ion gyroradius.…”

Numerical simulation of electron distributions upstream and downstream of high Mach number quasi‐perpendicular collisionless shocks

“…Similarly, Gedalin et al [1995] studied the effects of electron nonadiabatic motion only in the ramp region. However, Hull et al [1998, 2001] and Gedalin and Griv [1999] investigated electron distribution functions using Liouville's theorem in the adiabatic approximation, mapping model upstream and downstream boundary electron velocity distribution functions to regions inside model shocks. Recently, Yuan et al [2007a] examined only the importance of overshoots in the magnetic field and cross‐shock potential on the upstream and downstream electron distributions.…”

Collisionless electrons in a thin high Mach number shock: dependence on angle and <font face="Symbol" ><b><i>b</i></b></font>

“…There is the place to make several comments about the model and the analysis. First, the collisionless electron dynamics, whether adiabatic or nonadiabatic, is not able to describe properly the formation of the inner (low energy) part of the downstream electron distribution where a gap forms (Feldman, 1985;Veltri et al, 1990Veltri et al, , 1992Veltri and Zimbardo, 1993a, b;Hull et al, 1998;Gedalin and Griv, 1999). Therefore, it is impossible to make conclusions about the downstream electron temperature unless we know the mechanism for the gap ®lling and the details of electron dynamics aect directly only the high energy tail.…”

“…For a number of shocks the relation v 2 c af = const is inconsistent with the width of the downstream distribution and cYd a cYu by far exceeds f d af u (where u and d refer to upstream and downstream, respectively), which is not satisfactorily explained by the adiabatic mechanism (Schwartz et al, 1988). While the adiabatic regime is studied comprehensively (Hull et al, 1998;Gedalin and Griv, 1999) and the dependence on the shock Mach number w u av e , angle between the shock normal and upstream magnetic ®eld h, and upstream electron b e 8pn e e af 2 u is determined easily, the corresponding dependencies for the nonadiabatic case are not analyzed so far. Previous studies dealt with the dependence on the cross-shock potential and electron temperature for perpendicular geometry (Balikhin and Gedalin, 1994;Gedalin et al, 1995), local criteria of demagnetization , and mapping of upstream distribution to the downstream distribution Gedalin et al, 1998a).…”