Outline: • Introduction of the shock. • The shock in the space. • The property of the shock. • Why do we want to study shock? • Shock acceleration of the particles. • Bow Shock • CIR shock and Interplanetary traveling shock • Termination shock and Anomalous Cosmic ray
What is a shock? The travelling of a bullet. Its speed is about 1.5 times of the sound speed.
The definition of the shock From Landau & Lifshitz’s Fluid Mechanics
The perturbation in a supersonic stream will not affect the region out of Mach cone (upstream).
The image shows a bow shock around the very young star, LL Ori. It is located in the intense star-forming region known as the Great Nebula in the constellation Orion. A bow shock can be created in space when two streams of gas collide. …
为什么要研究激波? • The energetic particles are often related to the shock; • Shock accelerate the charged particles; • Shock and CME? • Termination shock? • Support Astronomy study in supernova remnants.
Energies range from supra-thermal to 1020 eV • Galactic Cosmic Rays (GCRs) • Anomalous Cosmic Rays (ACRs) • Solar Energetic Particles (SEPs) • Energetic Storm Particles (ESPs) • Corotating Interaction Regions (CIRs) • Planetary Bow shocks
研究高能粒子的意义 • Composition, energy spectra, temporal and spatial evolution, anisotropy • Source material • Where and how acceleration takes place? • How they get transported to observed? • Provides information about • Origin of matter • Physics of particle acceleration and transport • Serve as probes of interstellar space and interplanetary medium
Rankine Hugoniot relations • Continuity equations • Normal-component momentum flux is conserved • Energy flux is continuous
VSW B n Time Upstream Downstream The general properties of shock • The velocity, density, pressure and other parameters have discontinuities at the shock;
reflected IMF transmitted ? Particle trajectory ΘBn n Shock 激波加速机制还没有完全被理解
Particles Acceleration Mechanisms • Electric Field (F=qE) • Quasi-static large-scale electric fields (could be generated during reconnection) • e.g., solar flares, planetary magnetospheres • Stochastic Acceleration (1949-1950’s) • Particles gain or lose energy over short intervals, but gain energy over longer timescales • e.g., solar flares, interplanetary medium, near shocks • Shock Acceleration (1970’s) • Particles gains energy as scattering centers converge • First-order Fermi process • e.g., shocks, compression regions
Shock acceleration Bn >45º
Shock Drift Acceleration (SDA) • Strong gradient in B • Particles drift along the shock front in the direction of the E field • Quasi-perpendicular shocks
Intermediate distribution Diffuse distribution Quasi-Parallel Diffuse ions Ion Foreshock Boundary FAB Specularly reflected ions Earth B Quasi-Perpendicular Field-aligned beams 地球舷激波周围离子加速的情况
The energetic particles flow at the quasi-perpendicular bow shock H. Kucharek et al 2004
Cluster orbit and formation • Four identical satellites • The satellites can be in string-of-pearlsformation for substorm events (related to aurora) or tetrahedron formation for 3D structure of discontinuities http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=24451 • Orbit period 57 hours • Perigee: 4 Re • Apogee: 18-20 Re • Separation of satellites in tetrahedronformation: between 100 and 1000 km 33
Four-satellite timing analysis Average shock front is determined more accurately • s1, s2, s3, s4 and t1, t2, t3, t4 are coordinates and time when shock front crossing satellite (1,2,3,4), respectively. Assumption: Shock front does a constant motion within the tetrahedron . 34
Cluster instruments used in this investigation • Fluxgate Magnetometer (FGM): magnetic field B find signature of shock crossing -- magnetic field jump • Cluster Ions Spectrometry (CIS) consists of the Hot Ions Analyzer (HIA) and the Composition and Distribution Function analyzer (CODIF): HIA -- solar wind bulk velocity VSW CODIF -- FABs bulk velocity Vb 35
Benefits of Multi-satellite measurement • The orientation and motion of a plane discontinuity; • The spatial gradient of a vector . Future mission -- MMS
Upstream Downstream E B Shock B T= t2 T= t1 Proton trajectory Source of field-aligned beams Perpendicular Shock
Bow Shock Crossing Jan 24, 2001 • Vsw = 420 km/s, qBN ≈ 70o, MA = 11, b = 0.36 • Vsw = 420 km/s • qBN ≈ 70o • MA = 11 • b = 0.36 Moebius et al. 2001
Reference frames • Solar wind rest frame (plasma rest frame) The frame travelling with solar wind flux and there is no electric field in this frame. • Shock rest frame and spacecraft rest frame (SC frame) In shock frame, shock is at stationary and there is a motional electric fieldVSW×B; satellite frame is approximately equal to shock frame due to their relatively slow motion comparison withVSW. • de Hoffmann Teller frame (HT frame) A moving frame to eliminateVSW×Belectric field throughVSWalongB. 39
de Hoffmann Teller frame (HT frame) Moving frame in the shock layer
n Ion in S/C Frame Generation mechanism of FABs: direct reflecting model n: shock normal B B: IMF Vi: solar wind velocity Vr V//r V//i Vi VHT Paschmann et al., 1980 Vi (SC frame) V//i = Vi - VHT (HT frame) |V//r| = |V//i| (HT frame) kinetic energy conservation Vr = V//r+ VHT (SC frame) Schwartz et al., 1984 41
Invalidation of the HT frame • When ΘBn approaching 90 degree, the denominator is zero. Then VHT is infinite.
Source of field-aligned beams: • Direct reflection Sunnerup (1969) • Leakage of downstream heated plasma Edmiston et al. (1982) • Leakage along the shock normal Schwartz et al., (1983)
Source of field-aligned beams: Theoretical Consideration Schwartz and Burgess 1984 There seems to be evidence that field- aligned ion beams may be produced by either direct reflection of the incident solar wind ions at the shock or by leakage of a small portion of heated magnetosheath ions into the upstream region. Assumption: Planar shock, HT frame is the proper frame of reference.
Dynamic of the Earth’s Bow Shock • The dynamic of the Earth’s bowshock creates variations of the localΘBn, whichcan lead to particle release in turn.
The complicate shock surface Scholer and Kucharek, 2002
Standing shock wave downstream of Bow Shock near CUSP Color contours of the x component velocity (Vx) in the noon‐meridional plane, the locations of the cusp, and the neutral points are shown; the SSWs exist in the magnetosheath, attaching to the magnetopause and extending to the bow shock: (a) SSW1 and SSW2 in case 1 and (b) SSW3 in case 2.