Evidence of the nonstationarity of the terrestrial bow shock from multi-spacecraft observations: methodology, results, and quantitative comparison with particle-in-cell (PIC) simulations
Authors: Mazelle Christian , Lembège Bertrand 
Published: July 2021

Abstract. The nonstationarity of the terrestrial bow shock is analyzed in
detail from in situ magnetic field measurements issued from the fluxgate magnetometer (FGM)
experiment of the Cluster mission. Attention is focused on statistical
analysis of quasi-perpendicular supercritical shock crossings. The present
analysis stresses for the first time the importance of a careful and
accurate methodology in the data processing, which can be a source of
confusion and misunderstanding if not treated properly. The analysis performed
using 96 shock front crossings shows evidence of a strong variability of the
microstructures of the shock front (foot and ramp), which are analyzed in
great detail. The main results are that (i) most statistics clearly show that the
ramp thickness is very narrow and can be as low as a few c/ωpe
(electron inertia length); (ii) the width is narrower when the angle
θBn (between the shock normal and the upstream magnetic field)
approaches 90∘; (iii) the foot thickness strongly varies, but its
variation has an upper limit provided by theoretical estimates given in
previous studies (e.g., Schwartz et al., 1983; Gosling and Thomsen, 1985;
Gosling and Robson, 1985); and (iv) the presence of foot and overshoot, as shown
in all front profiles, confirms the importance of dissipative effects.
Present results indicate that these features can be signatures of the shock
front self-reformation among a few mechanisms of nonstationarity identified
from numerical simulation and theoretical studies. A comparison with 2D particle-in-cell (PIC) simulation for a perpendicular supercritical shock
(used as reference) has been performed and shows the following: (a) the ramp
thickness varies only slightly in time over a large fraction of the
reformation cycle and reaches a lower-bound value on the order of a few
electron inertial length; (b) in contrast, the foot width strongly varies
during a self-reformation cycle but always stays lower than an upper-bound value in agreement with the value given by Woods (1971); and (c) as a
consequence, the time variability of the whole shock front is depending on
both ramp and foot variations. Moreover, a detailed comparative analysis shows that many elements of
analysis were missing in previous reported studies concerning both (i) the
important criteria used in the data selection and (ii) the different and
careful steps of the methodology used in the data processing itself. The
absence of these precise elements of analysis makes the comparison with
the present work difficult; worse, it makes some final results and conclusive
statements quite questionable at the present time. At least, looking for a
precise estimate of the shock transition thickness presents nowadays a
restricted interest, since recent results show that the terrestrial shock is
rather nonstationary, and one unique typical spatial scaling of the
microstructures of the front (ramp, foot) must be replaced by some
“variation ranges” (with lower-bound and upper-bound values) within which the
spatial scales of the fine structures can extend.