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Reformation of an oblique shock observed by Cluster∗ Bertrand Lefebvre Space Science Center, University of New Hampshire, Durham, NH 03824, USA † Yoshitaka Seki Institute of Space and Astronomical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan. Steven J. Schwartz Space and Atmospheric Physics, The Blackett Laboratory, 0 Imperial College London, London SW7 2BW, UK 1 0 2 Christian Mazelle CESR / UPS-CNRS, 9 Avenue du Colonel Roche, Toulouse, 31400, France n a J Elizabeth A. Lucek 8 Space and Atmospheric Physics, The Blackett Laboratory, 2 Imperial College London, London SW7 2AZ, UK ] On 16 March 2005, the Cluster spacecraft crossed a shock almost at the transition between the h quasi-perpendicularandquasi-parallelregimes(θ =46◦)precededbyanupstreamlow-frequency Bn p (≈ 0.02 Hz in the spacecraft frame) wavetrain observed for more than 10 mn. The wave semi- - cycle nearest to the shock was found to grow in time, steepen and reflect an increasing fraction e c of the incoming ions. This gives strong indication that this pulsation is becoming a new shock a front, standing ∼ 5λp upstream of the main front and growing to shock-like amplitude on a time- p scale of ∼ 35Ω . Downstream of the main shock transition, remnants of an older front are found p s indicating that the reformation is cyclic. This provides a unique example where the dynamics . s of shock reformation can be sequentially followed. The process shares many characteristics with c simulations of reforming quasi-parallel shocks. i s y h I. INTRODUCTION thought to be part of the quasi-parallel shock transition p region. At the quasi-perpendicular shock, Horbury et al. [ [16] have noticed on some Cluster crossings a significant The question of the stability of the shock structure 1 has regained recent interest with the advent of mul- variability in magnetic field profiles, particularly in the v foot, despite a relatively small spacecraft separation. A tipoint measurements at the Earth’s bow shock. Nu- 9 large variability in magnetic and electric field time se- merical simulations have indicated for a long time that 0 ries was also observed by Lobzin et al. [22] at a high even under steady upstream conditions and for a broad 2 Mach number quasi-perpendicular shock crossing, com- 5 range of parameters collisionless shocks can exhibit plemented with bursty variations in reflected ions occur- . dramatic structural changes and eventually self-reform 1 ing on a time scale comparable to a proton gyroperiod. quasi-periodically [3, 5, 21]. However experimental ev- 0 Another formof non-stationaritywasfound by Moullard 0 idence of this kind of behaviour in space plasmas have et al.[25]whohaveidentifiedcoherentoscillationswitha 1 been limited. For instance, Thomsen et al. [38] and wavelength of a few tens of upstream ion inertial length : Thomsen et al. [39] have observed quasi-periodic varia- v confined to the shock layer and propagating along it. tionsonatime-scaleofapproximatelytwoupstreampro- i X ton gyroperiods in the ion velocity distributions down- The general problem of the shock stationarity is com- r stream of the quasi-parallel Earth’s bow shock which plicatedbytheimportanceoftheshockgeometry. Quasi- a they have attributed to shock reformation. Using multi- parallel and quasi-perpendicular shocks are indeed dis- point Cluster measurements, Lucek et al. [23] have stud- tinguished by significantly different structure, scales and ied the scales and growth of large amplitude pulsations dissipative processes (e.g. [33]). At least for supercrit- (Short Large Amplitude Magnetic Structures, SLAMS) ical shocks resistivity is insufficient to provide the required dissipation, which is then provided in a first step by reflecting upstream part of incoming ions. Assum- ing a specular reflection process and a step-like shock ∗An edited version of this paper was published by AGU. transition one finds out that the limit between quasi- Copyright (2009) American Geophysical Union. Lefebvre, perpendicular and quasi-parallel shocks θ = 45◦ cor- Bn B., Y. Seki, S. J. Schwartz, C. Mazelle (2009), Refor- responds to the angle below which the guiding-centre of mation of an oblique shock observed by Cluster, J. Geo- thereflectedionsisdirectedupstreaminsteadofbeingdi- phys. Res. 114, A11107, doi:10.1029/2009JA014268. http://dx.doi.org/10.1029/2009JA014268 rected back towards the shock [12]. However specularly †URL:http://www.spaceplasma.unh.edu/~bertrand reflected ions at shocks only slightly below θBn = 45◦ 2 may still re-encounter the shock front during the course netospheric mode not optimized for the solar wind, and of their gyromotion unless the shock angle is actually CIS/HIA data were available onspacecraft1 and 3 only. lowerthan ∼40◦ [31]. Only then are these reflected ions Electron data came from the Low Energy Electrostatic able to escape upstream, and by backstreaming against Analyzer (LEEA) of the Plasma Electrons And Current the solar wind flow they excite upstream waves (e.g. Experiment (PEACE) [17]. In this burst mode, a 3d [27]). As these low-frequencywavesgrowto large ampli- distribution with reduced polar resolution (3DX1) was tudes they interact with the incoming solar wind, giving transmitted to the ground every spin, and consists of quasi-parallel shocks a more extended and visibly more 26 energy levels in the range 0.007-1.7 keV, 6 polar and complexanddynamicstructurethanquasi-perpendicular 32 azimuthal angular bins. This data was then reduced ones. Clearlythere is more to collisionless shockdissipa- on the ground to pitch-angle distributions using high- tionthansimplespecularreflection. Inthecaseofcurved resolution FGM data, and corrected for the spacecraft shocks such as the Earth’s bow shock this picture is fur- potential effect using spin-resolution EFW data. Mag- ther complicated by ions streaming from other parts of neticfieldandparticlefromtheMAGandSWEPAMin- the shock which also contribute to instabilities near the struments onboard the Advanced Composition Explorer quasi-parallel shock. Burgess et al. [7] provide a recent (ACE)spacecraft[36]wereusedtocomputetheupstream review of observations of quasi-parallel shock structure solar wind parameters. The time delay taken by the so- and processes (see also [6]). larwindtotravelfromtheLagrangepointtotheEarth’s Observationshavethereforeshownthatthebowshock bowshockwastakenintoaccountassumingitmoveswith can significantly deviate from the textbook picture of a a constant velocity parallel to the GSE x-axis. locally planar and stationary structure and that it may eventually reform. However the scales and complexity of shock reformation combined with the limited number III. SHOCK OBSERVATIONS of measurement points have not provided so far direct evidence by following sequentially the reformation of a A. Global shock properties and Cluster shock front. configuration This paper presents a case study of a crossing by the Cluster fleet [10] of a shock with θ ≈45◦. The region Bn The solar wind as monitored by ACE, time-shifted by upstream of the shock exhibits a low-frequency quasi- thesolarwindtraveltimefromtheLagrangepointtothe monochromatic wave as more commonly observed up- shock, remains steady and quiet during the whole time stream of quasi-parallel shocks. The wave cycle nearest interval and for nearly half an hour before, in particu- to the shock ramp is found to steepen and grow into a lar with a velocity around 400 km/s and no important pulse-like structure which we argue corresponds to the change in magnetic field direction. Because of the pres- formation of a new shock-ramp. The four Cluster space- ence of large amplitude fluctuations extending far up- craftwereabletosequentiallyobservethisprocesswhich stream of the shock (and of the CIS instrument mode), we interpret to be shock reformation. the asymptotic upstream field and particle parameters are estimated from the ACE measurements (taking into account the solar wind travel time to the shock). II. DATA The crossing occurs at (12.7,0,4.6)Re (GSE), from downstream to upstream (outbound crossing). The This study concentrates on a shock crossing on 16 shock timing analysis (which assume a planar surface March 2005 around 1530 UT by Cluster occurring dur- moving at constant speed) [32] yields a normal nˆ = ing a data burst mode interval. The quartet was in a (0.93,−0.12,0.35)(GSE), a shock angle between the up- tetrahedron configuration with inter-spacecraft separa- stream magnetic field and the normal θ = 45◦ and Bn tions of the order of 1300 km. The magnetic field data a velocity along normal of -13 km/s in the spacecraft from the Flux-Gate Magnetometer (FGM) [2] used in frame. The Abraham-Shauner method [32] which makes this study wasaveragedat a resolutionof one vectorper useoftheMHDjump(Rankine-Hugoniot)conditionsfor spin-period(4s)or10vectorspersecond,averagedfrom the magnetic and velocity fields (and assumes as well a a 67 vectors/second sampling frequency in burst mode. planarsurfaceandshockstationarity)yieldsasimilarre- The electric field data from the Electric Field and Wave sult, nˆ =(0.93,−0.10,0.35)and θ =46.5◦. The shock Bn (EFW) [13] instrument used here has a temporal resolu- isthereforewithinexperimentalerrorsattheformallimit tionofapproximately2ms. Iondatawasprovidedbythe of quasi-perpendicular and quasi-parallelshocks, and we HotIonAnalyzer(HIA) ofthe ClusterIonSpectrometer shall generically call it an oblique shock. (CIS) [28] which measures fluxes of positive ions irre- Theprojectedspacecraftlocationsontothecoplanarity spective of species in the energy range 0.005-26 keV/e plane show that Cluster-1 (C1), 3 and 4 are approxi- and takes a spin period to build a full 3d distribution mately aligned along the shock normal while C1 and 2 (transmitted to the ground every spin in burst mode) are perpendicular to it and cross the ramp nearly simul- and has an angular resolution of 22.5◦ × 22.5◦. How- taneously (fig. 1). The shock is crossed first by C4, then ever during this interval the instrument was in a mag- by C1 and 2 together and finally by C3. 3 TABLE I: Main shock parameters at the asymptotic upstream and downstream locations. Upstream parameters were taken fromACEdata. Frame-dependentquantitiesaregivenintheNormalIncidenceframe(theshockrestframewheretheupstream solar wind velocity is directed along theshock normal). Parameters units upstream downstream B nT 9 27 n cm−3 5.6 19.6 p Proton ram energy eV 946 78 T eV 4 198 p β – 0.1 2.2 p T eV 17 54 e β – 0.5 0.6 e Proton gyrofrequency,f Hz 0.14 0.41 gp Proton inertial length, λ km 96 51 p Thermal proton gyroradius, ρ km 22 54 p Convected proton gyroradius, vp1/Ωgp km 493 167 Specularly-reflected proton gyroradius km 4536 – Phase-standing whistler wavelength, λ km 75 – w θ deg 47 77 Bn Alfvén velocity, c km/s 77 122 A Alfvén Mach number,M – 5.5 1.00 A Magnetosonic Mach number,M – 4.6 0.8 ms The shock is super-critical with an Alfvén Mach num- periods downstream of the ramp with a shorter period ber M =5.5. The protonthermalto magnetic pressure ∼36 s, although it is not entirely clear whether they A ratio for this shock is low, β = 0.1. Other shock and correspond to a transmitted wave or to the overshoot- p plasma parameters are summarized in Table I. undershoot cycle. Minimum Variance Analysis (MVA, see e.g. [35]) ap- plied suggests that the wavevector is roughly aligned B. The upstream low-frequency wave with the magnetic field (the deviation, θkB ≈ 24◦, is mainly in the out of coplanarity plane direction), k/k = ±(0.63,0.38,0.67) (NML). The wave has a high degree An upstream ultra-low frequency wave (ULF) with a period ∼42 s (f = 24 mHz) in the spacecraft frame of polarization (0.92), is left-hand polarized (with respect to the magnetic field) in the spacecraft frame with is observed for over 10 minutes from the ramp (fig. ellipticity ε = −0.81 and has a low compression ratio 2). The time-series appear quasi-monochromatic at 4 s- C =(δn/n )2(B2/δB2)=0.12 (tab. II). resolution,but considerable broadbandhigher-frequency e 0 0 fluctuations are seen in the higher-resolution data. The More properties can be derived from the time delays ULF oscillations can be seen in the magnetic field inten- between spacecraft assuming a planar wavefront. Al- sityaswellasallthreecomponentsandstronglyincrease though in general for a monochromatic wave the time in amplitude in the vicinity of the ramp. For instance, delays can only be determined modulo the wave period, at the shock ramp the magnetic field fluctuations along we find that the smallest delays determined from the the shock normalreachδB /B ≈1.7, andthe fluctua- time-series provide a direction close to that of the MVA, N N tionsinthenon-coplanarcomponentofthemagneticfield namely k/k = (0.66,0.37,0.65) in NML coordinates (2◦ δB arenearlyaslargeasthe overalldifferencebetween away from the MVA result). The corresponding phase M upstream and downstream magnetic field component in velocityin the spacecraftframe is 142km/swhichyields the maximum variance direction B . The general shock a wavelength of 5930 km. From the wavevector and L profile, ULF wave characteristics and its relative loca- the meanupstreamplasmavelocity,the frequencyinthe tion with respect to the shock seem remarkably similar plasmaframeisfoundtobe0.01Hzandtheplasmaframe onallfourspacecraftdespitethelargespacecraftsepara- phase velocity is 56 km/s, lower than but comparable to tion and temporal spread of the crossings (the first and the upstreamAlfvénspeed(76 km/s). Inthis frame,the last shock crossings are approximately 80 s apart). This wave propagates against the solar wind flow and there- gives to the wave an unexpected appearance of phase- fore is right-hand polarized. The properties summarized stationarity with respect to the shock (to be discussed in table II such as wavelength ∼ R , upstream prop- E in the final section). Oscillations extend over one or two agation direction and right-hand polarization are fairly 4 10 10 C1 (cid:0)t=0s RE RE ]T30 C2 (cid:0)t=4s /E 0 /E 0 [n20 CC43 (cid:0)(cid:0)tt==4(cid:1)14s9s S S B G G y z 10 10 10 (cid:0) (cid:0) ] 20 0 10 20 0 10 20 T n xGSE/RE xGSE/RE [ 10 N 10 B 0 (d) (u) 20 ] T n 5 [ 0 M B 20 (cid:2) k /(cid:2)p 0 ]nT 20 rL v(dNI) v(uNI) [BL 0 (cid:0)5 -20 0 20 40 15:26:36 15:28:59 15:31:22 15:33:45 x [(cid:3)] and UT [h:m:s] p 10 (cid:0) 10 5 0 5 10 (cid:0)(cid:0) r /(cid:1) FIG.2: 4s-resolutionmagneticfieldintensity(toppanel)and N p components in shock normal coordinates on all four spacecraft. Dataaretime-shiftedtoallowcomparisonsoftheshock FIG. 1: Shock crossing configuration. Top panels show the structure and upstream wavetrain measured by the space- upstreammagneticfieldlinesandthelocation ofthecrossing craft. Time information is translated into distance assum- (black square) in the GSE xy and xz planes. The main pan- ingthewholestructuretravelsattheconstantshockvelocity els show the asymptotic magnetic fields, solar wind velocity estimated from thetimings. inthenormalincidenceshockframe, andprojection ontothe coplanarity (NL) plane of spacecraft locations and direction of the upstream wavector. The grey area corresponds to the high degree of polarization, an effect of the alignment of main shock ramp, and distances are normalized to the up- the wavevector with the shock normal should be to di- stream protoninertiallengthλ . Spacecraft inthisplaneare p minishtheperturbationsduetothewavetotheplanarity approximatelyalignedalongtheshocknormalforC1(black), of the shock surface. In addition the oscillationsseem to 3(green)and4(blue),whileC2(red)crossestheshocknearly remain in-phase with the shock as if the ramp was part simultaneouslytoC1butapproximately10λ awayalongthe p shock front. The spacecraft travel from downstream to up- ofonecycleandothercycleswerephase-standingnextto stream. it. Indeed, the timings of the pulse nearest to the shock rampconfirmthe wavevectoralignmentwith the normal (consequently θ ≈40◦) and a velocity nearly identical kB typical of ULF waves studied using ISEE [15] or Cluster to that of the shock, about -13 km/s in the spacecraft [1, 8] datasets, and are thought to result from an elec- frame. This yields a wavelength an order of magnitude tromagnetic ion/ion right-hand resonant instability due lower than further upstream, λ≈500km≈5λ . p toionsbackstreamingfromthe shock. Finally,the phase Besides changes in wavevector and velocity, the wave velocity along the shock normal in any shock rest frame experiences a strong amplification near the shock. The is estimated to be v(shock)·nˆ ≈ −80 km/s showing that cyclestandingnearesttothe rampindeednearlyreaches ϕ asexpectedthewaveisnotphase-standingbutconvected shock-like amplitudes and displays an interesting be- towards the shock by the solar wind. haviour detailed in the next section. Applying MVA to shorter time intervals (2 wave periods) however reveals that these properties change closer to the shock front. As shown in fig. 3 the wavevector C. The growing and steepening pulse upstream of approximately aligns itself with the shock normal, the the shock ramp polarization becomes less circular and the compression ratio increases. These changes appear during intervals As noted in the previous paragraph, upstream mag- which do not yet include the shock ramp, corresponding netic field fluctuations reach their largest amplitude at to specific properties of the cycle nearest to the ramp thewavecyclenearesttotheshockfront. Thislargeam- which may be affected by the shock foot and reflected plitude pulse-like structure is crossed by the spacecraft ions. Since the wave is assumed to be planar and has a in the same order as the shock ramp (C4 first, followed 5 TABLE II:Properties of theupstream ultra-low frequency wave in spacecraft and plasma frames. Spacecraft Plasma Frequency/f 0.14 0.07 gp Wavelength /λ 62 62 p Phase velocity /c 1.8 0.74 A Polarization degree 0.92 0.92 Polarization Left-hand Right-hand Ellipticity -0.81 + 0.81 Compression ratio 0.12 0.12 [nT]B2300 C1 slope: 0.0042 s(cid:0)1 ~ 0.03 fcpu CCCC1234 10 ] g 50 ] [de(cid:2)0 [BnT ,(cid:1)(cid:0)50 (cid:3)(cid:4) 1 (cid:0)0.6 10 (cid:5) (cid:0)0.8 (cid:0)1.0 15:29 15:30 15:31 0.4 16Mar05 Universal Time [h:m] Ce 0.2 FIG.4: Mainshockrampandupstreampulse,shownwith4s 15:28 15:30 15:32 15:34 16Mar05 Universal Time [h:m] resolutionFGMdata. Thepulsegrowthrateisapproximately 0.03f . cpu FIG. 3: Wave properties in spacecraft frame derived from MVA on 84s intervals of 4s resolution data. The top panel proton gyroperiods for the pulse to grow to shock-like showsthemagneticfieldintensity. Nextpanelshowsthepolar angleθ betweenkandnˆ,andφwhichistheazimuthalangle amplitudes. in the LM plane with respect to the L axis. The dotted lign High-resolution magnetic field data show that besides indicates θ . Lower panels show theellipticity and electron Bn growing in amplitude the structure is found to steepen compression ratio. (fig. 5). The steepening is most visible in B and occurs L on the upstream edge of the pulse (apart perhaps from C2 on which the ”downstream” side of the pulse seems nearlysimultaneouslybyC1andC2andthenC3),show- atleastassteepasitsupstreamside). Asthe steepening ing that it is not a partial recrossing of the shock front proceeds quasi-periodic whistler-like fluctuations (at ≈ but a distinct upstream structure. The time delay be- 0.15Hz,bestseenonB )areemittedupstreamandthe M tween the crossings of the shock ramp and the feature is measuredelectricfieldmagnitude (E2+E2)1/2 increases x y nearly the same for all four spacecraft (about 20s), sug- too and reachesonC3 values comparableto those in the gesting that this structure extends parallel to the shock ramp. Furthermore, high-resolutiondata reveal that the ramp and remains at a constant distance from it. pulse is seen slightly earlier on C2, consistent with its position slightly upstream of C1 as sketched in Fig 1. As shown in fig. 4 the magnetic field intensity of the However, that data also shows the pulse’s growth and structure is the lowest at the crossing by C4, larger at steepening to be more advanced at C2. This shows that C1 and C2 (and slightly more so at C2 than C1) and at this separationscale the pulse’s structure and growth largest at C3 where its amplitude is comparable to that is not perfectly homogeneous along the shock plane. ofshockitself. ThesameobservationappliestoB . The L structure is therefore growing in time. An exponential Finally one notes on C1 and C2 in between the pulse fit to the peak amplitudes yields a growth rate of γ ≈ and the shock ramp localized dips in B reaching nega- L 4·10−3Hz≈0.03f . Theamplitudesareequallywellfit tive values, similar to that observed during the reforma- gpu by a linear curve with slope 0.011B s−1 ≈ 0.08B f . tion cycle in 1d [5, 40] and 2d [30] quasi-parallel shock u u gpu Both models estimate that it takes up to ∼35 upstream hybrid simulations. 6 20 C1 30 []nTN10 []BnT20 B 0 10 5.5 10 104 s)i5.0 []BnTM-100 E []eV111000123 log(count44323.....05055 -20 30 C3 30 ]T ]nT20 [Bn20 [BL10 10 5.5 []mV/m46000 E []eV111000234 og(counts)i44353.....05005 2+Ey20 10115:26 15:28 15:30 15:32 l2.5 2Ex 0 16Mar05 Universal Time [h:m] 15:28:30 15:29:00 15:29:30 15:30:00 15:30:30 16Mar05 Universal Time [h:m:s] FIG.6: EnergyspectrogramsofionsfromCIS/HIA,summed overallangles. Upstream,bothsolarwindandenergeticions are strongly affected by the wave. At the shock, a distinct FIG. 5: High-resolution (10 vectors per-second) magnetic population of reflected ions around 3 keV is observed at the field measurements of the growing structure in shock NML shockramponC1butnotonC3,whereitisobservedonthe coordinates. The structure is not only found to grow in upstream steepened structureinstead. amplitude but also to steepen while emitting whistlers, and measured electricfield intensitiescorrespondingly increase to reach ramp-likevalues. getic population of energetic gyrating ions observed at the ”old” shock ramp. These are only seen at the upstream steepened structure, as if it became a new shock D. Particles and cross-shock potential front where most of the ion reflection occurs. One notes however that there is little appreciable ion heating be- If the growingfeature is indeed becoming a new shock tween this structure and the old ramp, suggesting that front, then it should affect the heating and reflection of some solar wind plasma is not processed by a full ramp incoming solar wind particles and correspondingly de- structure but caught in between. velop an electric potential jump. fig. 6 shows magnetic Specular ion reflection being associated to the cross- intensity profile and ion energy spectra (from CIS/HIA, shock potential at least part of the potential jump must all species and summed over all view angles) on C1 and occur at the new front. One of the most reliable ways C3. Two distinct ion populations are clearly observedin to estimate the electric potential acrossa shock is to use the solar wind. The lowest energy one (≈ 1 keV) is the electrondatacombinedwithLiouvillemapping([20]and incomingsolarwindbeamwhichundulates underthe ef- references therein). Based on assumptions of conserva- fectofthewave,yieldinglargeoscillationsofthevelocity tion of electron energy in the de Hoffmann-Teller frame moment. It seems howeverthat the wave results in little and first adiabatic invariant, this technique relates the ornoionheating(whichis neverthelessdifficult tocheck changesinelectronvelocitydistributionsbetweentwolo- quantitatively in the absence of reliable temperature es- cationstotheunknownpotentialdifference. Avariantof timates due to the particular CIS instrument mode). this technique is used which takes into account the field Thereisalsoahigherenergy(≈3keV),lessdensebut maxima in between the two locations [20]. hotter population which is strongly modulated by the The estimated cross-shock potentials on all four- wave suggesting that some of these energetic ions could spacecraft in the de Hoffmann-Teller frame are shown be trapped by the large-amplitude wave. The highest in fig. 7, where time-series have been shifted in order to count rate of energetic ions on C1 appears during the make the main magnetic ramps coincide. Their down- shock ramp crossing around 15:28:40 UT. This distinct stream values are remarkably similar on all four space- ion population has an energy around 3 keV and should craft despite the shock non-stationarity. However the consist of gyrating specularly-reflected protons. A simi- location of the main potential jump with respect to the lar but lower count-rate group of ions is observed on the main magnetic ramp seems to differ from spacecraft to next peak of magnetic intensity. The situation on C3 spacecraft. During the C4 crossing, when the new ramp is slightly different however. There is no distinct ener- was just starting to form, the potential jump occurs at 7 these authors have slightly different parameters and in particular higher Mach number. 30 ] T n [B20 C1 (cid:0)t=0s IV. SUMMARY AND DISCUSSION C2 (cid:0)t=4.15s C3 (cid:0)t= 49.8s 10 C4 (cid:0)t=4(cid:1)1.5s The shock analysed in this paper is oblique (θ ≈ Bn 45◦), moderate Mach number (M ≈ 5.5) and low-β A (β ≈0.1). i 100 ] Upstream of the shock a long-wavelength (λ ≈ V T [ 62λp), low-frequency (f ≈ 0.07fp in the plasma frame) H(cid:3)50 and right-hand polarized in the plasma frame quasi- monochromatic wave propagates against the solar wind 0 flow approximately parallel to the upstream magnetic -20 -10 0 10 20 field (θkB ≈ 24◦). Its properties are consistent with a 15:26:36 15:27:48 15:28:59 15:30:11 15:31:22 magnetosonic-like wave excited by a weak (n ≪n) and x [(cid:2)] and UT [h:m:s] b p cool (v < v ) ion beam backstreaming from the shock Tb b through an electromagnetic ion/ion right-hand resonant FIG. 7: Magnetic field intensity (top) and estimated electric instability [11]. Such an instability has its maximum potential(bottom)time-shiftedinordertomakethemagnetic growth rate for field-aligned wavevectors and obeys the rampscoincide. Thedownstreamcross-shockpotentialvalues linear dispersion relation in the cold plasma approxima- are very similar on all four spacecraft. However the location tion ω = k v − Ω (real part). In the low frequency of main potential jump seems to move upstream of the main k b p limit ω ≪ Ω one therefore has k ≈ Ω /v . Assum- magnetic ramp. p k p b ing that the energetic ion population seen in fig. 6 (∼3 keV in the spacecraft frame) corresponds to the backstreaming ions yields an estimate for the phase velocity themagneticramp. Itisthenobservedfurtherupstream ω/k ≈ (ω/Ω )v ≈ 80 km/s in good agreement with onC1andC2crossings,andnearthenewlyformedramp k p b the timing results, but the wavelength is found to be on C3. λ ≈ 8300 km which is larger than the observed wavelength of 5900 km. It is therefore likely that the 3 keV population (which actually spreads from 2 to 10 keV) is E. Large-amplitude downstream perturbations and modulated by the wave but not its source. Instead the indications of a reformation cycle wave may have been generated further upstream by a beam of ions coming from anotherpart of the shock. In- Large perturbations are also found downstreamof the deedthe wavepropertiesdescribedinthis paragraphare main shock ramp as shown in fig. 8, localised at ap- also similar to those of ULF waves in the ion foreshock proximately the same distance from the main ramp as [8, 15], waves which are generally not observed simul- the upstream pulse. On all four spacecraft a depression taneously to the field-aligned beams but in association in the mean magnetic field intensity is observed. Large to diffuse-ions or gyrating beams in cyclotron resonance magnetic field and electric field fluctuations are present with the wave [24]. The observed high energy ion popu- within this depression. The amplitudes of the electric lation modulated by the wave is therefore more likely to fieldfluctuationsarecomparabletoorevenlargerthanat be either a gyrating beam of reflected ions which man- the main ramp. The depth of the depression and ampli- aged to escape from the shock or gyrating ions trapped tudeofthefluctuationsarealsodecreasingintime,being by the wave. thelowestonC3whichisthelasttocrosstheshock. The Due to its small phase velocity the waveis swept back decreaseoccurson time scales comparableto the growth bythesolarwind,andclosertotheshockthewaveprop- oftheupstreampulse. Theseperturbationscanbeinter- erties change significantly. The wavevector aligns itself preted as remnantsof anolder shock rampwhich decays withtheshocknormal,whichcouldbeduetoanincrease intime, showingthatthe previouslydescribedformation of refraction index in the foot region. A similar align- ofanewrampisnotanisolatedeventbutpartofaquasi- ment was found in the 2D hybrid simulations of Scholer periodic reformation cycle. Based on the growth rate of et al. [30], which they attributed to an increase in den- the upstream pulse and the decay of downstream per- sity of the diffuse ions near the shock. This alignment turbations, the reformation period can be estimated as makes the perturbations of the shock due to the wave several tens of upstream proton gyroperiods, and could more homogeneous along the shock surface. It is this be a few periods of the upstream low-frequency wave. greaterdeviationfromparallelpropagationwhich allows This is significantly longer than the period of variations the wave to become more compressionaland steepen, an of the downstream ion populations (∼ 2f−1) observed effectwhichwasconjecturedbyHadaetal.[14]tohappen pu by Thomsen et al. [38], although the shocks studied by as ULF waves are convected into areas of the foreshock 8 Old Main New 40 C4 ] T n [20 B 0 m] 100 / V m 50 [ y x | E 0 | 40 C2 ] T n [20 B 0 m] 100 / V m 50 [ y x | E 0 | 40 C1 ] T n [20 B 0 m] 100 / V m 50 [ y x | E 0 | 40 C3 ] T n [20 B 0 m] 100 / V m 50 [ y x | E 0 | -5 0 5 15:28:28 15:28:59 15:29:30 x [(cid:0)] and UT [hh:mm:ss] p FIG. 8: Time-shifted high-resolution magnetic field intensity and electric field (|E |=(E2+E2)1/2). Spacecraft are ordered xy x y in the order by which they cross the shock. Besides the growth of the upstream pulse which becomes a new ramp, data show strong perturbationsapproximately onewavelength downstream of themain ramp. Thiscan beinterpreted asremnantsof an old shock front from a previous reformation cycle. 9 plitude comparable to that of the shock itself. This 1 pulsation grows in time, steepens and in the process it emits whistlers, reflects more and more ions and con- tributes more significantly to the cross-shock potential 2 jump. Reasonsforthisgrowthandsteepeningcanbethe changeinrefractiveindex,alocalizedinstabilitynearthe shock front such as the interface instability or nonlinear dynamicsofthe pulse andits interactionwiththe shock. B u Furthermoretheamplificationmechanismmaynotoper- atesteadilyintime. ThenegativedipsinB seenonlyon L C1 and C2 during the intermediate growth stage of the pulse may indeed be the signature of a transient dense ion beam reflected from the shock at this stage of the shock reformation (e.g. as in the simulations of Thomas FIG. 9: Illustration of the wave refraction near the shock. et al. [37]). At least this indicates an unusual and tran- The wavefronts (dashed lines) become nearly parallel to the sient processing of ions in between the main ramp and shock surface (thick grey line), which requires a lower phase the pulse during the pulse growth. velocityintheshockframeatlocation1(neartheshock)than at 2 (furtherupstream). Whatevermechanismoperateshere,theseobservations give strong evidence that the wave cycle standing nearest to the shock is forming a new shock front on a time with higher densities of diffuse ions (see also [4, 9]). Be- scale∼35fg−p1uorless,comparabletothatobservedinhy- sides, the wave has all the appearance of phase-standing bridsimulationsofquasi-parallelshocks(e.g. [5,30,37]). with respect to the shock. From a velocity identical to The reformation scale (distance between the shock front thatoftheshockinthisregion,thewavelengthisfoundto and pulsation) is ∼ 5λp, also in good agreement with be 10 times shorter than further upstream. This slowing simulation results. Assuming that the real shock front downofthewaveintheshockframeisentirelyconsistent thus jumps forward such a distance in a time of 35fg−p1u, with its wavevectoralignmentwith the shock normal,as its velocity is found to be only a few km/s larger than illustrated by fig. 9. thatofthe ”former”shock frontinthe solarwind frame, In addition to refractive effects an instability could be which does not induces a significant change in effective operatingnearthe shockfront, partlyaccountingfor the Machnumber. Atapproximatelythesamedistancefrom changes in wave properties and its strong amplification. the main shock ramp but on the downstream side there This could involve, as dicussed by Winske et al. [40], are magnetic and electric field fluctuations with ampli- a relatively dense and cold beam of specularly reflected tudes comparable to those at the main ramp. These can ions observed near the shock front during the reforma- be naturally interpreted as remnants of an older ramp tionprocessinthesimulations,oraninstabilitylocalized which decays on a time scale of at least a few wave pe- atthe shockfrontresultingfromthe interactionbetween riods, which is comparable to the one of the new front upstreamandsomeofdownstreamheatedions. This”information. These remnants show that the observed ref- terface instability” generateswaveson the magnetosonic ormation is not an isolated event but part of a quasi- branch with wavelength intermediate between whistlers periodic reformation cycle. and ULF waves. For M =5 the maximum growth rate The reformation process appears quite coherent along A corresponds to kλ ≈ 0.5 or λ≈ 4πλ . This wavelength the shock surface at the spacecraft separation scale, ∼ p p (λ≈5λ )estimatedneartheshockissmaller,butstillin 10λ ,thankstothewavevectoralignmentwiththeshock p p the rangewhere the growthrate is close to its maximum normal. Some differences in the pulse shape between C1 value. The instability is weakly dependant on θ and and C2 measurements are nevertheless observed. The Bn tends to have its wavector aligned with the shock nor- causeofthisinhomogeneitycouldbethefinitetransverse mal. However the exact mechanism(s) operating on the correlation length of the upstream ULF wave, which is wave near the shock front is (are) certainly more com- typicallyoftheorderof1R accordingtoLe and Russell E plicated since we are dealing with very large-amplitude [19] or between 8 and 18 R according to Archer et al. E (nonlinear)wavesandahighlyinhomogeneoussituation. [1]. This is however a bit large to account for the inho- One can however note that because the wavelengthnear mogeneity, even when projected on the shock front. It the shock is about 6 times the theoretical wavelength is neverthelesspossible that the ULF wavesare unstable of the phase-standing whistler the mechanism leading to to transverseperturbationsabovesome threshold,which reformation is distinct from the whistler-mediated ref- would reduce their perpendicular correlation length as ormation discussed for oblique and quasi-perpendicular their amplitude grows. Another reasoncould be fluctua- shocks by Biskamp and Welter [3], Krasnoselskikh et al. tionsorripplesoftheshocksurfaceandtheinhomogene- [18], Scholer and Burgess [29]. ity of the ion reflection/wave amplification process. The Due to the strong amplification of the wave near the scaleisindeedmoreconsistentwiththeripplewavelength shock, its last cycle before the shock acquires an am- (afewtensofλ )estimatedbyMoullard et al.[25]atthe p 10 quasi-perpendicularbowshock. Inanycasethisinhomo- sharessomecharacteristicswithSLAMS[34]. Indeedev- geneityalongtheshockfrontissmallsincethedifferences idence suggests that SLAMS grow very rapidly, picking between C1 and C2 observations are much smaller than up energy from shock-produced energetic ions, and very differences with the other two spacecraft. To a first ap- possibly only in close proximityto the shock [23]. In ad- proximationthereformationthusoccurscoherentlyalong dition,theyarewell-definedentitiesthatpropagatefrom the shock front on scales of at least 10λ . upstreamintothenominalshockandgiverisetothe ref- p ormation of the local shock transition. As such, they are manifestations of the dynamic, structured nature of V. CONCLUSION collisionless shocks under oblique geometries. However their growth mechanism differs from that of the pulse The global picture is thus in general agreement with described in this paper, in that they are found in more thescenarioofquasi-parallelshockreformationproposed turbulentULFwavefieldsandgrowoffofgradientsindif- by Burgess [5]: as some of the specularly reflected ions fuseionpopulationsratherthanthequitemono-energetic escape far upstream they generate waves on the magne- ions observed here. tosonic branch which are then convected back into the Second, there is the low βi. A consequence of this is shock and destabilize it. The major difference between thatspecularlyreflectedionsformarelativelycoldbeam the 1d simulations which inspired this scenario and the well distinct from the backgroundions, helping to shape observationsliesinthe changesinthe wavepropertiesas unstable iondistributions. But the low β also makes the it nears the shock, where wave refraction, an additional specularreflectionitselfmoredelicatebymakingitmore localized instability mechanism such as the interface in- difficult for the shock to adjust the electric potential in stability and probably nonlinear phenomena participate order to reflect the right amount of ions required for the in deflecting, slowing down and amplifying the wave cy- dissipation of the incoming solar wind kinetic energy. In cle which ultimately forms a new shock front. The wave the zero temperature limit specular reflection even re- refraction results in a more coherent reformation along sults in a ”allor nothing” situationwhich clearly cannot the shock surface. On a longer time-scale, this reforma- be steadily sustained, similarly to the 100% ion reflec- tionprocesshasnoreasontostopunlessthereisamajor tion or transmission occuring in the high Mach number change in the upstream conditions and may be repeated perpendicular shock simulations of [26]. The excess of quasi-periodically. In this picture the elementary refor- reflectedions near the shock frontis againa likely possi- mation cycle consists of a shock front and wave locally bility to explain the wave changes in this region, leading recedingatthesamespeedwhilethepulsenearesttothe to the formation of a new shock front. ”old” shock grows to actually become the ”new” shock These two factors show that the shock is in a situ- front upstream of the previous one, the ramp effectively ation where small changes in θBn or electric potential making a jump forward. The old shock slowly vanishes havemajorconsequences,makingtheshockunstableand and a new pulse growsupstream of the new one, repeat- poorly adaptable to changesin the incoming plasma. As ing the reformation cycle. itisperturbedmajorvariationsinreflectedionsstrongly Finally one may list two key elements which conspire modify the energy flow and structure of the shock. The to create this particular shock structure and dynamics dynamicalmodificationsoftheshockscalesandstructure lending themselves unusually well to analysis. maythenbeviewedasafirstorderattemptbytheshock First, there is the shock angle θ ≈ 45◦. It means to correct an inappropriate reflection of ions while try- Bn that relatively small changes in this angle have impor- ing to maintain on average the asymptotic downstream tant consequence on the kinematics of the reflected ions, state. which either cross the shock after half a gyration and thermalise downstream as in quasi-perpendicular shocks or escape upstream and feed ULF waves as in quasi- Acknowledgments parallelshocks. Sinceonaverageveryfewofthereflected ions are expected to escape upstream, this angle may be The authors thank M. Fujimoto, S. P. Gary, T. Hor- the reason why there is such a large gradient in the re- bury and I. Shinohara for fruitful discussions. Parts of flectediondensityneartheshockfrontandthereforewhy this work were supported by a grant to Imperial College the wave undergoes such large changes in this region. In from the UK Science and Technology Facilities Council. somesensethisleadstoasimplerandcompactedversion BL also acknowledges partial support from DOE grant of lower-angle shocks. For instance the growing pulse DE-FG02-07ER54941. [1] Archer, M., T. S. Horbury, E. A. Lucek, C. Mazelle, 110, A05,208, doi:10.1029/2004JA010791. A. Balogh, and I. Dandouras (2005), Size and shape of [2] Balogh,A.,etal.(2001),TheClusterMagneticFieldIn- ULFwavesintheterrestrialforeshock,J.Geophys. Res., vestigation: overviewof in-flightperformance andinitial