Cluster investigations on the self-reformation of perpendicular Earth’s bow shock

Cluster investigations on the self-reformation of perpendicular Earth’s bow shock C. Mazelle1, B. Lembège2, A. Morgenthaler3, K. Meziane4, J.-L. Rauch5, J.-G. Trotignon5, E.A. Lucek6, I. Dandouras1 1CESR, UPS - CNRS, 9 Avenue du Colonel Roche, Toulouse, 31400, France (christian.mazelle@cesr.fr), 2 LATMOS / IPSL , CNRS UVSQ, Velizy, France, 3LATT, Observatoire Midi-Pyrénées, Univ. of Toulouse, France 4Physics Department, University of New Brunswick, Fredericton, NB, Canada, 5LPCE, CNRS, 3A, Avenue de la recherche scientifique,France 6Space & Atmospheric Physics Group, Imperial College London, UK. Cluster 17th workshop, Uppsala, Sweden, May 12-15 2009

Outline Aim: Experimental evidence of shock front nonstationarity from determination of characteristic sub-scaleswith multi-satellite observations • previous (pre-Cluster) experimental determinations of scales. • Multi-spacecraft analysis from Cluster. Cases studies. Methodology and cautions. • Statistical analysis of Cluster results. • Comparison with PIC numerical simulations results. • Comparison with previous experimental results. • perspective: Cross-scale mission, Heliospheric shock.

Physical characteristics of supercritical quasi-perpendicular shock Above a critical value of MA, dispersion is not sufficient to balance steepening as well as "resistive" dissipation: other ("viscous") dissipation process by reflected ions mandatory  characteristics substructures: reflected gyrating ion Ramp Foot Overshoot

Non stationarity of supercritical quasi-perpendicular shock PIC Numerical simulations: 1D: Biskamp and Welter, 1972; Lembège and Dawson, 1987; Hada et al., 2004; Schöler and Matsukyo, 2004; …. 2D: Lembège and Savoini, 1992; Lembège et al., 2003 … Terrestrial shock geometry • PIC simul.: Shock non stationary -> Cyclic "shock front self-reformation". • Different proposed mechanisms of non stationarity • signatures : variation of the characteristic structures (foot, ramp, overshoot). Bn= 90° [Lembège et al., 2003] B 2D PIC MA= 5 Time mp/me=400 Earth B Q- (45° - 90°) n Normalized distance

Numerical simulations of supercritical quasi-perpendicular shock PIC Numerical simulations: 1D: Biskamp and Welter, 1972; Lembège and Dawson, 1987; Hada et al., 2004; Schöler and Matsukyo, 2004; …. 2D: Lembège and Savoini, 1992; Lembège et al., 2003 … Terrestrial shock geometry • PIC simul.: Shock non stationary -> Cyclic "shock front self-reformation". • Different proposed mechanisms of non stationarity • signatures : variation of the characteristic structures (foot, ramp, overshoot). Bn= 90° [Lembège et al., 2003] B 2D PIC Overshoot Foot Time Cluster Earth B Q- (45° - 90°) Ramp n c/ωpi Normalized distance

Outline Aim: Experimental evidence of shock front nonstationarity from determination of characteristic sub-scales with multi-satellite observations • previous (pre-Cluster) experimental determinations of scales. • Multi-spacecraft analysis from Cluster. Cases studies. Methodology and cautions. • Statistical analysis of Cluster results. • Comparison with PIC numerical simulations results. • Comparison with previous experimental results. • perspective: Cross-scale missions, Heliospheric shock.

Ramp thickness: some previous ISEE results ISEE: thicknesses of the laminar (low b) shocks : 0.4 – 4.5 c/ωpi [Russell et al., 1982] ion inertial length scale Supercritical shocks: ramp thickness typically of ~ c/ωpi [Russell and Greenstadt, 1979; Scudder, 1986] (a) (b) [Newbury and Russell, GRL, 1996] very thin shock (b) (a)

Previous study from Cluster data (1) first examples of some aspects of shock nonstationarity (or at least variability) were presented by Horbury et al. [2001]: High time resolution is mandatory to reveal the different sub-structures of the shock even for a 'nearly' perpendicular shock Differ. signat. of shock crossing shock front variability: what responsible process?

Outline Aim: Experimental evidence of shock front nonstationarity from determination of characteristic sub-scaleswith multi-satellite observations • previous (pre-Cluster) experimental determinations of scales • Multi-spacecraft analysis from Cluster. Cases studies. Methodology and cautions. • Statistical analysis of Cluster results. • Comparison with PIC numerical simulations results. • Comparison with previous experimental results. • perspective: Cross-scale missions, Heliospheric shock.

Example of analysed shock crossing from Cluster B (nT) 5 Hz data

Methodology use of high time resolution data Downstream asymptotic value ramp • Determination of the limits of the structures in time series for each satel. data • Determine the 'apparent' space width (along each sat. traj.)-> compar. between the 4 s/c. • Determine the normal velocity of the shock in s/c frame (Vshock, Vs/c, angle n - s/c traj.) • Main goal: to determine the real spatial width of the structures (ramp, foot, overshoot) • Careful error determination 1st overshoot B (nT) foot 22 to 64 Hz data upstream value Time (hrs.) along the normal

Methodology use of high time resolution data Downstream asymptotic value ramp • Determination of the limits of the structures in time series for each satel. data • For the ramp: look for the 'steeper' slope (time linear fitting) -> defines the 'reference satellite' • Determine the 'apparent' space width (along each sat. traj.)-> compar. between the 4 s/c. • Determine the normal velocity of the shock in s/c frame (Vshock, Vs/c, angle n - s/c traj.) • Main goal: to determine the real spatial width of the structures (ramp, foot, overshoot) • Careful error determination 1st overshoot B (nT) foot 22 to 64 Hz data upstream value Time (hrs.) along the normal

Methodology use of high time resolution data Downstream asymptotic value ramp • Determination of the limits of the structures in time series for each satel. data • For the ramp: look for the 'steeper' slope (time linear fitting) -> defines the 'reference satellite' • Determine the 'apparent' width (along each sat. traj.)-> compar. between the 4 s/c. • Determine the normal velocity of the shock in s/c frame (Vshock, Vs/c, angle n - s/c traj.) • Main goal: to determine the real spatial width of the structures (ramp, foot, overshoot) • Careful error determination 1st overshoot B (nT) foot 22 to 64 Hz data upstream value Time (hrs.) along the normal

Methodology use of high time resolution data Downstream asymptotic value Timing method: gives shock normal n and velocity V in s/c frame ramp • Determination of the limits of the structures in time series for each satel. data • For the ramp: look for the 'steeper' slope (time linear fitting) : defines the 'reference satellite' • Determine the 'apparent' width (along each sat. traj.)-> compar. between the 4 s/c. • Determine the normal velocity of the shock in s/c frame (Vshock, Vs/c, angle n - s/c traj.) • Main goal: to determine the real spatial width of the structures (ramp, foot, overshoot) • Careful error determination 1st overshoot V n B (nT) foot 22 to 64 Hz data For ech pair of satellites i and j : upstream value Time (hrs.) along the normal

Methodology use of high time resolution data Downstream asymptotic value overshoot ramp ramp • Determination of the limits of the structures in time series for each satel. data • For the ramp: look for the 'steeper' slope (time linear fitting) : defines the 'reference satellite' • Determine the 'apparent' width (along each sat. traj.)-> compar. between the 4 s/c. • Determine the normal velocity of the shock in s/c frame (Vshock, Vs/c, angle n - s/c traj.) • Main goal: to determine the real spatial width of the structures (ramp, foot, overshoot) • Careful error determination 1st overshoot B (nT) B (nT) foot 22 to 64 Hz data foot -1 0 1 upstream value Time (hrs.) c/ωpi along the normal

Validity criteria for the method (1) Key points: • Criterion 1: careful determination of the Bn - determination of the 'mean' normal seen by the 4-spacecraft set (timing correlation analysis). - check the conservation of normal magnetic field component Bn. - check the mean upstream magnetic field vector seen by each satellite: -> estimate of B0 for the tetrahedron and associated error. • Criterion 2: careful conversion of temporal scales (time series of the shock crossings) to real spatial scales - take into account the shock velocity in each s/c frame - relative orientations of the s/c trajectories w.r.t. the shock normal: determination of the width along the normal. A long 'temporal' scale can lead to 'real' narrow ramp width … !

Validity criteria for the method (2) • Criterion 3: careful determination of the upstream parameters solar wind ion density and temperature caution: not reliable when Cluster CIS in magnetospheric mode. Use of ACE data and Cluster/WHISPER (plasma frequency) data. caution: He++/H+ ratio (to avoid ~20 % error in mass density) -> determination of Alfvèn velocity -> MA -> determination of bi

Four spacecraft measurements of the quasi-perpendicular terrestrial bow shock: [Horbury et al., JGR, 2002] clean, sharp shock 5 vectors/s complex, disturbed shock shock with probable acceleration

Characteristics of the sample From 455 shocks: 24 shocks with all validated criteria Number of occurence Bn MA i majority below 0.1 majority above 84°

Typical shock crossing Bn= 89° ± 2° MA=4.1 i=0.05 C4 C4 C3 C3 Lramp= 5 c/pe n X’ (km) Z’ (km) C1 C1 C2 C4 C2 C2 Sequence of crossings order Y’ (km) Y’ (km) S/c positions in (x,n) plane and perpendicular to n |B| C1 at ref. time (ramp middle of ref. sat. 4) . Very thin ramp: some electron inertial lengths . Variablilty of ion foot, ramp and overshoot thicknesses • evidence of shock non-stationarity and self-reformation C3 c/ωpi

Outline Aim: Experimental evidence of shock front nonstationarity from determination of characteristic sub-scaleswith multi-satellite observations • previous (pre-Cluster) experimental determinations of scales. • Multi-spacecraft analysis from Cluster. Cases studies. Methodology and cautions. • Statistical analysis of Cluster results. • Comparison with PIC numerical simulations results. • Comparison with previous experimental results. • perspective: Cross-scale missions, Heliospheric shock.

Statistical results (24 shocks = 96 crossings): ramps (1) Thinnest ramp for each shock Lramp in

Statistical results (24 shocks = 96 crossings): ramps (1) Thinnest ramp for each shock • Ramps of the order of a few c/ωpe, for a large range of Bn  electron scale rather than ion electron dynamics important Lramp in

Statistical results (24 shocks = 96 crossings): ramps (1) Thinnest ramp for each shock • Ramps of the order of a few c/ωpe, for a large range of Bn  electron scale rather than ion electron dynamics important • Change of regime around 85-87°  dispersive effects? Tend to broaden the ramp? ? ? Lramp in critical angle between ‘oblique’ and ‘ perpendicular’ shock for lowand Mf ~1cr= 87°(e.g. Balikhin et al., 1995)

Statistical results (24 shocks = 96 crossings): ramps (2) all ramps ion inertial length Larger probability to cross a thin ramp (<< c/ωpi) !

Statistical results (24 shocks = 96 crossings): ramps (3) all ramps Lramp in Lramp in no simple trend trend: thickest ramps decrease with MA only thin ramps close to 90° really perpendicular shocks?

Comparison with 2D PIC simulations mp/me=400

Comparison with 2D PIC simulations: ramps mp/me=400

Statistical Results: ion foots (1) • Foot thickness < Larmor radius as expected • Mainly low values Number of occurence Lfoot in  Ci,upstream

Ion foots: comparison with 2D PIC simulations mp/me=400 Acceleration of the growth of the ion foot both in amplitude and thickness during one self-reformation cycle higher probability to cross an ion foot with a small thickness? seems qualitatively consistent with observations needs more quantitative investigation

Statistical Results: ion foots (2) Comparison of largest observed value with 'stationary' theoretical value [Schwartz et al., 1983] : d = 0.648 Ci,upstream for Bn = 90° and Vn =0°  another signature of shock cyclic self-reformation Red : stationary theoretical values Blue : largest observed values Lfoot in  Ci,upstream Shock number where reflected ion turn-around distance [Woods, 1969]

Statistical results (24 shocks = 96 crossings): overshoot Number of occurence 3 Lovershoot in c/ωpiupstream Majority between 1 and 3 c/ωpi as e.g. in Mellott and Livesey [1987] but also large variability due to self-reformation of the shock

Previous study from Cluster data (2) [Bale et al., PRL, 2003] macroscopic density transition scale Shock scale: convective downstream gyroradius 5 Hz data ion inertial length Fit of the density profile by an analytical shape (hyberbolic tangent) No separation between ramp and foot Typical shock size: ion scales "This technique captures only the largest transition scale at the shock"[Bale et al., 2003] Here, different approach sub-structures taken into account

Statistical results (24 shocks = 96 crossings) Is the shock front thickness simply dependent on Mach Number? Comparaison with results from Bale et al. (2003)

Statistical results (24 shocks = 96 crossings) Is the shock front thickness simply dependent on Mach Number? Comparaison with results from Bale et al. (2003) • result seems to depend on the sample used. • no simple dependence Lramp+footin c /ωpi Signature of non stationarity Magnetosonic Mach number

Previous study from Cluster data (3) [Lobzin et al., GRL, 2007] one case study: highly supercritical Q-perp shock Variability of the shock front with embeded nonlinear whistler wave trains and "bursty" quasi-periodic production of reflected ions proposed as experimental evidence of non stationarity and self-reformation as described in Krasnoselskikh et al. [2002] Bn= 81° MA=10 i=0.6 Here, different approach accumulation of case studies (statistics)

Other shock sub-structures: Electric field spikes (1) [Walker et al., 2004]

Other shock sub-structures: Electric field spikes (2) Histogram of the scale sizes for the spike-like enhancements [Walker et al., 2004] E-field spikes c/ωpi

Other shock sub-structures: Electric field spikes (2) Histogram of the scale sizes for the spike-like enhancements [Walker et al., 2004] E-field spikes magnetic ramps c/ωpi c/ωpi Similar distribution to that for magnetic ramps with smaller values

Other shock sub-structures: Electric field spike (3) Dependence of scale size on Bn [Walker et al., 2004] E-field spikes

Other shock sub-structures: Electric field spike (3) Dependence of scale size on Bn magnetic ramps [Walker et al., 2004] E-field spikes Lramp in Similar trend for only low values close to 90°

Other shock sub-structures: Electric field spike (4) Dependence of scale size on upstream Mach number [Walker et al., 2004] E-field spikes

Other shock sub-structures: Electric field spike (4) Dependence of scale size on upstream Mach number [Walker et al., 2004] magnetic ramps E-field spikes Similar trend: upper limit tend to decrease with increasing Mach Number

Ramp sub-structure Magnetic ramps often reveal sub-structure : nature? 22 Hz data Time (hrs.)

Ramp sub-structure Magnetic ramps often reveal sub-structure : nature? signature due to electric field short scale structure? 22 Hz data Time (hrs.) Need further investigation but electric field data not always available

Cluster investigations on the self-reformation of perpendicular Earth’s bow shock