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Shock structure Shock acceleration Astrophysical shocks CLUSTER role Shocks in space: Perspectives and unsolved problems A theoretician’s point of view Michael Gedalin Ben-Gurion University Beer-Sheva, Israel World Space Environment Forum, 2005 BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Motivation and objectives Half-century of collisionless shock research soon. Great improvement of in situ observations. More information on astrophysical shocks. Great improvement of computational facilities. Time for fully quantitative theory. BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Warnings about the talk Theory oriented Biased (?) Personal views Proper theory Quantitative predictions. Incomplete A few subjects only. Figures For illustrative purposes only. M. Gedalin BEN-GURION UNIVERSITY Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Outline 1 Shock structure Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? 2 Shock acceleration Ion injection Electron acceleration 3 Astrophysical shocks 4 CLUSTER role BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? Shock structure: low-Mach bt 40 Monotonic transition, small noncoplanar component. 30 20 bm bn 10 15 10 5 0 Two-fluid HD: several c cos θ/Mωpi −5 15 10 5 0 −5 Ion reflection insignificant. bl 40 30 Ion heating: downstream gyration. 20 10 06:09:00 UT 06:10:00 UT 06:11:00 UT From Zilbersher et al., 1998 No dissipation included. BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? Shock structure: high-Mach s1347 −150 −100 −50 0 50 100 25 btotal1 20 15 Variety of profiles, fine structure. 10 5 25 Foot: ≈ 0.4Vu /Ωi , supported by single particle equation of motion. btotal2 20 15 10 5 −150 −100 −50 0 50 Overshoot: downstream ion gyroradius, downstream distribution gyration. 100 time −10 −8 −6 −4 −2 0 2 4 6 8 10 duration1 3 2 1 Ramp: down to several c/ωpe , related to electron dynamics, no theory, simulations controversial. duration2 3 2 1 −2 0 2 4 6 8 time 10 12 14 16 18 From Newbury et al., 1998 BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? S1D: What is this ? MHD 1D and stationary at large scales. Present: transition layer Most important processes. In situ observations at bow shock. Timescale to compare with: ion gyroperiod Much larger: time-independent fields for ions, shock structure adiabatically follows slow changes of plasma parameters. Comparable: time-dependent fields, energy non-conservation, no pressure balance. BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? Shock (non)stationarity: observations −40 −20 0 20 40 60 80 100 120 Low-Mach: stationary and one-dimensional, combined method (model+observations+numerical) 140 btotal1 30 High-Mach: non-stationary and/or non-one-dimensional (Gedalin et al., 2001). 20 10 btotal2 30 Reason: insufficient smoothing of the downstream gyrating ion distribution. 20 10 −20 0 20 40 60 time 80 100 120 140 From Newbury et al., 1998 No theory is available at present for either case (what instead of pressure balance ?). BEN-GURION UNIVERSITY M. Gedalin Shocks in space scale in x for the two runs varies by a factor 2 so that in units As can be seen from the bottom panel of Figure 3 the incident Shock structure of the ion scale due to the different mass ratios the profiles solar wind ions interact strongly with the whistler waves, Shock acceleration Quasi-perpendicular shocks: scales, stationarity, one-dimensionality both runs are comparable. Let us first discuss results from which leads to a deceleration in the individual whistler ofshocks Astrophysical structure (upper four Quasi-parallel panels) At t!ci =shocks: 6.7 the magnetic field? trains and to vortices of the incident ions in vix – x CLUSTER phase run 1role . The cross-shock potential increases in the foot over 20l e space. Since the instability results from the interaction between the ion beam mode of the incoming solar wind has the same length scale, i.e., it extends over about 1 ion ions and the electron whistler the reflected ions are not inertial length. As the shock reforms (t!ci = 7.3) a sharp much affected, and these vortices do not result in individual ramp appears which leads to a large electric field spike over "4le (not shown here), but a large part of the potential drop small-scale reformation events. [15] Since the instability discussed above is on the occurs already in the foot region, so that at t!ci = 7.3 only whistler mode branch it should disappear for exact perpen- 60% of the cross-shock potential exists across the main dicular shocks. In Figure 5 the results from high mass ratio ramp. The scale of the foot is determined by the gyroradius two mi/me = 1840 runs with !Bn = 87! and !Bn = 90! are so that the whole potential drop occurs over a scale given by compared. Instead comparing run 2 with the equivalent !Bn the gyroradius. The magnetic field and potential profiles of = 90! run, we have performed two additional realistic mass the mi/me = 1840 run are similar. At t!ci = 6.4 the magnetic ratio runs with higher Alfvén Mach number and lower field strength in the foot has increased to twice the upstream values of the ion and electron b: run 3 with !Bn = 87!, value, and small wavelength waves are superimposed on the MA = 6.2, be = 0.1, bi = 0.05, and run 4 with !Bn = 90! and the same values for MA and the ion and electron b, respectively. Figure 5 compares the magnetic field Bz profile and the profile of the electric field Ex component between these two runs at the same time. As can be seen from Figure 5 the short wavelength waves in the foot region indeed disappear in the !Bn = 90! run. Furthermore, no other electrostatic wave component is observed in the foot in the Shock (non)stationarity: simulations of the ncident s ratios he foot ting of r wind h-order ectrons agnetic in the etween and the rmined ee-fluid magnefor the n run 2 For the allel to respec! to the eglects Early (e.g. Quest et al., 1985): M = 22, reforming shock, 1D full- particle. Figure 1. (a) Stacked profiles of the magnetic field Bz component for a shock simulation (run 1) with upstream parameters #Bn = 87!, bi = 0.1, be = 0.2. Mass ratio is assumed to be mi/me = 400, (wpe/!ce)2 = 10. (b) Stacked profiles of the magnetic field Bz component for a shock simulation (run 2) with upstream parameters #Bn = 87!, bi = 0.1, be = 0.2. Mass ratio is assumed to be mi/me = 1840, (wpe/!ce)2 = 4. stacked magnetic field profiles (Bz component) in the same format as in Figure 1a for the time period 5.6– 7.3 !!1 ci . It can be seen that the magnetic magnitude in the foot From Scholer et al.,field 2003 increases with time, and a new shock ramp emerges out of the foot. Thus, reformation is not an artifact of the use of an unrealistic low ion to electron mass ratio. However, in the realistic mass ratio case (run 2), the pronounced dip between the newly emerging shock ramp and the former ramp disappears. This has consequences for the identification ofM. Gedalin Recent: M = 4.2, β = 0.1 reforming shocks. Steepening of the ramp down to several electron inertial lengths BEN-GURION UNIVERSITY Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? Shock (non)stationarity: theory 1200 Phys. Plasmas, Vol. 9, No. 4, April 2002 Krasnoselskikh et al. 1D theoretical model, two-fluid HD. Upstream whistler generation. Shock front non-stationarity when whistler no longer takes away the energy and prevent steepening. FIG. 5. The stackplot for the component B z of the magnetic field in the shock wave with # Bn !57° and M A !5.5. No ion reflection included. Illustrative simulations supportive, not definitive. range mentioned above can be considered as nonsignifithat a self-sustained shock is formed after a transitory period From Krasnoselskikh etthe use al.,the 2002 cant in this case. lasting about several ion gyroperiods calculated with of downstream magnetic field. In the present simulations the total run time covers about 4 ion gyroperiods calculated with the use of upstream magnetic field. As it was noted above, there exists a close relationship between the properties of linear waves and the structure of the shock waves in plasmas.1,2 In particular, the dispersion relation influences the shape of the subcritical shock waves. In numerical modeling, a special care should be taken to avoid the distortion of the dispersion relation due to the Two series of runs were performed, where the angle # Bn between the shock normal and the magnetic field upstream of the shock is equal to 57° and 80°, respectively, and Mach number varies in the wide range from about 1.6 to 8.6 in the both series. Using the simulation results, we describe the evolution of the shock wave structure as the Mach number increases. We begin the analysis from the # Bn !57° shock waves. In this case the first critical Mach number is M cr$2.54, the M. Gedalin Shocks in space BEN-GURION UNIVERSITY Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? One-dimensionality: rippling in high-Mach Rippling Observations: strong variations of normal magnetic field component. Numerical rippling: surface waves (?). R. E. Lowe andMcKean D. Burgess: Rippling inet quasi-perpendicular shocks From al., 1995 673 simulations, ripples are ion scale features at the shock front, which move along the shock surface. The waves associated with the rippling can be seen in the Bx component with a wavelength of 4 to 8 ion inertial lengths and an amplitude of around 2B0 . These peaks also appear to be connected to the structure behind the shock, but not in any simple manner. The ripples are most clearly visible in the shock normal component of the magnetic field, although there is also structure due to rippling in the other field components. Hodograms of Bx –By and Bx –Bz at the overshoot do not show any straightforward relationship between the components, in agreement with the results of Winske and Quest (1988). We also ran an equivalent simulation in which the upstream magnetic field, B 0 , pointed out of the simulation plane. In this geometry the dimensionality of the simulation suppresses parallel propagating waves and structures, such as AIC waves and the shock ripples, so that the shock structure closely resembled that of a one-dimensional simulation, with little variation in the shock normal component Bx . The average profiles of the magnetic field and density were broadly similar in both simulations. This suggests that rippling does not significantly affect other properties of the shock, such as the shock width and the presence of the foot, ramp and overshoot. Rippling: related to ion gyration, improves pressure balance, does not eliminate nonstationarity. Fig. 2. A map of |Bx | taken from a simulation with θBn = 88◦ and Vin = 4vA , giving MA ≈ 5.7. The maximum value of Bx is approximately 2B0 and the profile of |B| is superimposed. BEN-GURION UNIVERSITY From Lowe and Burgess, 2003 V0 . Simulation units are normalised in terms of the upstream values of the magnetic field, B0 , the ion cyclotron frequency, 4 Fourier analysis M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? Structure or no structure: Patchwork Is there any fine structure ? Observational difficulties, no theory. Patchwork: steepening short magnetic structures form the quasi-parallel shock front. No clear transition. From Schwartz and Burgess, 1991 Simulated waves upstream of the quasiparallel shock: steepen when approaching the ”front”. From Scholer and Kucharek, 1999 BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Quasi-perpendicular shocks: scales, stationarity, one-dimensionality Quasi-parallel shocks: structure ? Patchwork: observations E. A. Lucek et al.: Cluster observations of structures at quasi-parallel bow sho A. Lucek et al.: Cluster magnetic field observations at a quasi-parallel bow shock 1703 E. A. Lucek et al.: Cluster magnetic field observations at a quasi-parallel bowE.shock 1701 90 18:00 20:00 22:00 2 Feb. 2001, hour min (UT) 24:00 Fig. 1. Magnetic field data recorded by Cluster 4 through the quasiparallel shock on 2 February 2001. Data are displayed in the GSE coordinate system. Panels show magnetic field elevation (θ) and longitude (φ) angles in degrees, three magnetic field components (Bx , By , Bz ) and the magnetic field magnitude |B| in nT. 45 0 30 −20 90 Pred θBn 20 16:00 90 20 |B| −50 Pred θBn 0 10 0 20:00 0 20:30 21:00 21:30 22:00 22:30 20:54:30 20:54:45 20:55:00 20:55:15 2 Feb. 2001, hour min (UT) 2 Feb. 2001, hour min sec (UT) Fig. 2. The angular variations of the spin-averaged magnetic field Fig. 5. and Magnetic field fourPanels spacecraft Cluster 1 (black) upstream at data ACEfrom (lightthe blue). showat 22 vectors/s From Lucek et al., 2002, atmagnetic 2004 showing magnetic magnitude enhancements field elevation (θ) andfield longitude (φ) angles in GSE within co- a pulsation region. field The format of the figure is asand in the Fig.angle 4. beordinates, magnetic magnitude (|B|) in nT tween the model bow shock normal and the magnetic field (Pred θB n). ACE data are lagged to give good correspondence between the magnetic field angles seen at ACE and at Cluster. When the them is a structure less well correlated between the spacedata sets do not have clear features in common, ACE data are not craft (atbetween 20:55:00 UT).and On21:10 these plotted, for example, ∼20:50 UT.time scales, although the θ° φ° BY (nT) 30 60 20 0 30 0 |B| 60 0 0 −30 −60 10 40 30 15 0 20 45 0 20:55:30 |B| (nT) |B| 10 50 40 Bz −50 0 30 0 −60 20 20 0 0 14:00 −180 |B| (nT) 30 Bz −180 600 400 55:08 55:12 55:16 55:20 55:24 55:28 200 2 Feb. 2001, hour 20 min sec (UT) 17 06 45 17 07 00 17 07 15 17 07 30 2002 Feb 20 (051) hour min sec (UT) 0 500 |V| (kms−1) −20 −50 180 0 −60 BZ (nT) φ° 60 0 B (nT) Y φ° By 0 |V| (kms−1) 0 0 360 −90 60 −90 0 Bx φ° 50 50 By 0 180 −90 20 −180 |B| 0 BX (nT) x B θ° −20 180 0 180 0 NP (cm−3) φ° −90 0 θ° 360 0 180 20 θ° 0 90 90 90 250 17 07 45 Fig. 6. The variation of the θBn angle predicted using the bow 1. Anacross example a well developed SLAM structure. Panels shock modelFig. normal theofmagnetic field enhancement at magnetic field elevation andelevation longitude(θ)angles, θ and φ (de20:55:15 UT.show Panels show the magnetic field and longrees),in BGSE co-ordinates, field magniX , Bcoordinates, Y , BZ in GSE gitude (φ) angles the magnetic fieldmagnetic magnitude −3 ), and plasma flow tude |B| (nT), proton number density N (cm P (|B|) and θBn . speed |V | (km/s). The different colours show data from the four spacecraft: 1 (black), 2 (red), 3 (green) and 4 (magenta). 0 04 39 Fig. 2. Part o waves and SLA CLUSTER: quasiparallel shocks and shocklets ahead. No correlation at 600 km separation, correlation at 100 km. Magnetic field gradient at ion inertial length. Support but not decisive in the absence of theory. from the timing of the shock crossings at the four spacecraft. Using the simplifications outlined by Horbury et al. (2002), the model shock normal is likely to be accurate to within 10◦ , which is sufficient to demonstrate the trends in the magnetic field direction across the shock on 2 February 2001. Figure 2 shows the magnetic field data from Cluster 1 (in black) and ACE (in light blue) during the shock transition, together with the angle between the local magnetic field direction and the model bow shock normal (Pred θBn ) estimated using the simplified Peredo model. Detailed comparison of the Cluster and ACE measurements shows that throughout the interval of interest, the delay time between ACE and Cluster is not constant, and that there are several intervals where the correspondence is poor. In Fig. 2 the time delay is altered such that the data sets show a good correspondence at three clear discontinuities (at ∼20:45, ∼21:40 and ∼21:50 UT). When the two data sets are dissimilar, such as between 20:50 and signatures at the four spacecraft are related, there are significant differences, suggesting that spatial changes occur on order of the which at this time was the magneticthe field tended to spacecraft rotate fromseparation, an orientation nearly between fewshock hundred and atothousand kilometres. Comparparallel to the modelabow normal, a direction more ison ordering of(e.g. the spacecraft that although the perpendicular to of thethe shock normal Schwartz etshows al., 1992; signatures appear to be convected towards the Earth (for exMann et al., 1994). ample, the signature at Cluster 2 (red) or 3 (green) typically Figure 3 shows the Cluster orbit and spacecraft tetrahedron leads at Cluster 4 (magenta)), theaordering configuration on 2that February 2001. A cut though nominalof the spacebothon between the leading model bow craft shockvaries is shown each panel. At theand endtrailing of the edges of the structures, between the two structures, even though they day, when the shock isand encountered, Cluster 2 is separated are three only separated s. 1000 km in the X– from the other spacecraftby by30 about YGSE plane, mainly thecase YGSECluster direction, lying closer the smaller enIn theinfirst 1 (black) sees atomuch nose of thehancement, magnetosphere. The other 2three are despite Cluster and spacecraft Cluster 4 observing signaquite closelytures aligned the orbit in the X–Y plane, al-the enhanceGSEand of awith similar magnitude before after though separated in Z , with spacecraft separations of the GSE 1. This suggests that the difference between ment at Cluster order of 400–800 km. Cluster 1 lies at the highest Z , and M. Gedalin Shocks in space Between ∼ fied. The dur scale of the tetrahedron. The timing differences between sucfor which th cessive magnetic field enhancements might arise from differmaximum |B lower level of correlation, suggesting that significant variaent trajectories the structures, theofstructures derestimated tionsthough in the plasma occurredoronfrom scales 100 km in this rehaving different orientations. analysis bein gion. underlying Such small-scale processes might be related to plasma The second magnetic field enhancement, at 20:55:15 UT, which can oc thermalisation. SLAMS. The is more similar between the four spacecraft. Figure 6 shows by integratin the change2.2 in theSignatures orientation the magnetic field direction, of of SLAMS scale size tal flux betw relative to the model bow shock normal across this strucAnother quasi-parallel occurred on 3 February 2002 the maximum ture. The angle between the two shock directions is denoted θBn . was located near noon, ∼8.3 RE below the were then plo This figure while showsCluster that although there are differences between BEN-GURION UNIVERSITY ecliptic The region upstream the spaceshock was popcraft pair per the magnetic field plane. magnitude signatures at theoffour ulated by exceptionally wellfield developed ULF waves, visitransverse to craft, the behaviour of the magnetic direction at the ble most clearly in the magnetic a spatial grad four spacecraft is quite similar. Moving fromfield rightelevation (upstreamand longitude anglesto(Fig. and bythe SLAMS, visible asupincreases in terest is whet of the enhancement) left 2), (through enhancement): |B|. When the tetrahedron scale was ∼100 km, the time debetween the stream of the leading edge, the magnetic field direction is ◦ lay between the different spacecraft observing an enhancethis effect m within 45 of the model bow shock normal; across the leadment in magnetic field magnitude was significantly shorter Shock structure Shock acceleration Astrophysical shocks CLUSTER role Ion injection Electron acceleration Injection problem Diffusive acceleration theory Well developed, spectra known, but: a) phenomenological (in many cases no connection with mechanism of scattering), and b) requires pre-acceleration (injection). Pick-up ions Efficiently injected: already superthermal in the shock frame. Thermal to superthermal Simulations show this occur but physics of the phenomenon is still unclear. BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Ion injection Electron acceleration Surfing acceleration Ions trapped by electric and magnetic forces. ! " er / Planetary and Space Science 51 (2003) 665 – 680 V.D. Shapiro, D. Uc u y + x B Ey Acceleration by motional electric field along the front. 667 (1984) using both analytical calculations and numerics generalized the mechanism for quasiperpendicular periodic wave with Bx !Bz and showed that acceleration in y-direction can be signi!cantly larger than that in strictly perpendicular case. This is possible by allowing ion acceleration in two directions. Using simulations, Lembege et al. (1983) pointed out that the sur!ng acceleration is an e#ective dissipation mechanism for magnetosonic wave. Sagdeev et al. (1984) have been the !rst who considered shock sur!ng acceleration at a strictly perpendicular magnetosonic solitary pulse and derived the resulting dissipation which transforms the pulse into a perpendicular shock wave. Ohsawa (1985, 1986) and Ohsawa and Sakai (1985) used simulations to investigate the formation of self-consistent shock structure from sur!ng acceleration. The idea of shock sur!ng acceleration has been applied to the acceleration of solar energetic particles by fast magnetosonic shocks in the corona (Ohsawa and Sakai, 1987), He3 ions in impulsive "ares (Ohsawa and Sakai, 1988a), energetic storm particles and ion enhancement at interplanetary shocks (Ohsawa and Sakai, 1988b), and cometary water-group pick-up ions at comets (Srivastava et al., 1993). Hoshino and Shimada (Shimada and Hoshino, 2000; Hoshino and Shimada, 2002) studied electron acceleration by perpendicular magnetosonic wave. They found that the interaction between ions re"ected by the shock and incoming electron "ow produces Buneman instability resulting in excitation of electron solitary structures. Electrons are re"ected by these structures and accelerate under the action of the motional electric !eld as in the sur!ng acceleration. They also conclude that if the shock wave is su$ciently strong electrons undergo unlimited acceleration, since electrostatic repulsive force dominates the Lorentz force and electrons can be trapped theoretically for in!nitely long time. Webb et al. (1994) pointed out that shock sur!ng acceleration may be important for interstellar Crucial: time spent in the shock front. Requires low initial velocities: pick-up only (?). Fig. 2. Schematic diagram for shock sur!ng acceleration at a perpendicular shock. From Shapiro and Ucer, 2003 hancements at the interplanetary traveling shocks (Sarris and Van Allen, 1974; Pesses et al., 1979, 1982; Decker, 1981). In the shock drift acceleration mechanism, ion energy gain is due to ion curvature and gradient drifts in the inhomogeneous magnetic !eld at the shock front. Although the shock sur!ng acceleration relies on a strong shock potential and shock drift acceleration does not, the most important distinction between these two mechanisms is the fact that the shock drift acceleration energy gain is proportional to the initial ion energy, while the !nal energy in the shock sur!ng is greater for ions which have lower incident velocities initially (|vx0 |!u where u is the shock speed). This happens because the particles with smaller initial |vx | are trapped longer at the shock front, while they are accelerated by the convective electric !eld. By this reason, shock surf- Requires narrow transition (fine structure helps). Requires (?) stationarity and one-dimensionality. M. Gedalin Shocks in space BEN-GURION UNIVERSITY Shock structure Shock acceleration Astrophysical shocks CLUSTER role Ion injection Electron acceleration Surfing generalizations Invoke additional forces for longer stay in shock Hybrid waves against shock. Electrostatic solitary structures ahead of the ramp. Electrostatic potential with electromagnetic wave. Work for electrons too ? Require S1D or coherency - what about fluctuations/irregularities ? BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Supernova remnant shocks High-Mach number shocks, M ∼ 102 − 103 . Expanding into interstellar medium with weak magnetic field. Radio: synchrotron from accelerated electrons. High efficiency of electron heating/acceleration required. From Chandra, NRAO BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Gamma-Ray-Burst shocks Piston/blast unknown. Highly relativistic shock. Downstream ion gyroradius may exceed the system size. Accelerated electron energies comparable with ion energies. BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role CLUSTER: capabilities vs expectations Ability: multi-spacecraft measurements at variety of scales. Expected: three-dimensional structure resolved. Expected: spatial/temporal variations separated. BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Normals and (non)stationarity 2000 Dec 25 - bowshock normals GSE positions 25 25 Dec 2000, hour 1, min sec (UT) 0 By (nT) 20 E Y (R ) 15 x 10 x20 B (nT) 20 20 10 0 0 5 10 X (RE) 20 60 15 20 25 |B| (nT) 0 −5 −5 40 Model normals Timing normals Coplanarity: Cluster 1 Cluster 2 Cluster 3 Cluster 4 Bz (nT) 60 5 0 40 20 5 0 30 50 31 00 E Z (R ) 30 40 0 Better shock normals. −5 −5 0 5 10 X (RE ) 15 20 25 Nonstationarity timescale estimate. From Horbury et al., 2001 BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration igure 4. The Ex component (in the despun satellite frame), three components and the magnitude of the Astrophysical shocks magnetic field during the 1828 UT shock crossing by spacecraft 1. The X axis shows time in seconds after CLUSTER role 828 UT. Electrostatic subshock he asymptotic plasma bulk velocity is parallel to etic field both in the upstream and downstream he velocity of the HTF with respect to the NIF has NIF NIF tan (qBn)| where Vup is the de of |V HTF| = |Vup velocity in NIF. If qBn is close to right angle, a ertainty in qBn results in huge errors in VHTF ore in the cross-shock potential !HTF. Therefore we will focus on estimating the cross-shock potential in the NIF (!NIF). In order to estimate !NIF from experimental data we need to take into account two terms. The first is a projection of the electric field component along the shock normal, spatially integrated through the shock transition layer. The second term is the result of the satellite velocity with respect to the NIF, i.e., Vsat-NIF = Vup! (Vup " n ) " n Quasistationary cross-shock electric field spikes. igure 5. The Ex component (red) and the magnitude of the magnitude magnetic field (blue) during the rossing of shock at 1828 UT with an expanded time scale as observed by spacecrafts (top) 1 and bottom) 3. From Balikhin et al., 2002 BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Summary: status Pieces of the puzzle Put the pieces together Theory with predictive abilities BEN-GURION UNIVERSITY M. Gedalin Shocks in space Shock structure Shock acceleration Astrophysical shocks CLUSTER role Summary To complete Quasi-perpendicular shock structure (if possible at all). Unified description of particles at shock. To develop Quasi-parallel shock theory. Nonstationary shock model/theory. Hopefully Bridge to astrophysical shocks (or are they completely different ?). Breakthrough from CLUSTER. M. Gedalin Shocks in space BEN-GURION UNIVERSITY