Evidence of the Nonstationarity of the Terrestrial Bow Shock from Multi-Spacecraft Observations: Methodology, Results and Quantitative Comparison with PIC Simulations
Authors: Mazelle Christian , Lembege Bertrand 
Published: September 2020

Abstract. The nonstationarity of the terrestrial bow shock is analyzed in detail from in situ magnetic field measurements issued from the FGM experiment on board of Cluster mission. Attention is focused on statistical analysis of quasiperpendicular 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/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 deep details. Main results are: (i) most statistics clearly evidence 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); (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/theoretical works. A comparison 2D PIC simulation for a perpendicular supercritical shock (used as reference), has been performed and it shows that: (a) the ramp thickness varies only slightly in time over a large fraction of the reformation cycle and reaches a lower bound value of the order of a few electron inertial length, (ii) 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 (iii) 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 much elements of analysis were missing in previous reported works 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. This absence of these precise elements of analysis makes the comparison with present work difficult, worse, it makes some final results and conclusive statements quite questionable at present time. A 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/upper bound values) within which the spatial scales of the fine structures can extend.