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4. Shock

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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

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What is a shock?

The travelling of a bullet. Its speed is about 1.5 times of the sound speed.

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炮弹出膛速度大于声速，产生激波。

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飞机突破音障

“Termination Shock” in Your Sink

Fundy Tidal Bore

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http://en.wikipedia.org/wiki/Bay_of_Fundy

Fundy Tidal Bore

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c

c

vvM

vv

/

/sin

From Landau & Lifshitz’s Fluid Mechanics

The definition of the shock

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The perturbation in a supersonic stream will not affect the region out of Mach cone (upstream).

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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. …

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Remnant of Tycho's Nova, SN 1572.

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The Earth’s Bow Shock

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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.

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• Galactic Cosmic Rays (GCRs)

Anomalous Cosmic Rays (ACRs)

Solar Energetic Particles (SEPs)

Energetic Storm Particles (ESPs)

Corotating Interaction Regions (CIRs)

Planetary Bow shocks

Energies range from supra-thermal to 1020 eV

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Particle Population

Temporal scales

Spatial scales

Energy range Acceleration mechanisms

GCRs continuous global GeV --->TeV Diffusive shock

ACRs continuous Global 10-100 MeV Diffusive shock, shock drift, or other?

SEPs keV ---> GeV Reconnection, stochastic, selective heating, shock

ESPs days extended keV ---> 100 MeV Diffusive shock, shock drift, stochastic

CIRs 27 days Large-scale

keV ---> 10 MeV

Diffusive shock, shock drift, stochastic

Planetary bow shocks

continuous local keV ---> MeV

Diffusive shock, shock drift

Energetic particles properties

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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

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Continuity equations

Normal-component momentum flux is conserved

Energy flux is continuous

)()( 2222

1221

212

111

2222

2111

2211

wvvwvv

vpvp

vv

nnnn

nn

nn

Rankine Hugoniot relations

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The velocity, density, pressure and other parameters have discontinuities at the shock;

Time

VSW

B

n

Upstream Downstream

The general properties of shock

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Shock structure

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?

transmitted

reflected

Particle trajectory

Shock

IMF

n

ΘBn

激波加速机制还没有完全被理解

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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

Particles Acceleration Mechanisms

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Shock acceleration

ˆ n

Rc

Rc

Bn >45º

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Strong gradient in B

Particles drift along the shock front in the direction of the E field

Quasi-perpendicular shocks

E u1 B1 u2 B2 (5.36)

Conservation of magnetic moment :

Particles reflected if their velocity

v u1 tanBn B1 /B2 (5.37)

ˆ n

Rc

Rc

Energy gain E ~pu1

Bn (5.38)

Average gain 1 - 5 x original energy

require multiple encounters

Shock Drift Acceleration (SDA)

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Quasi-Perpendicular

Quasi-Parallel

Diffuse ions

FAB

Ion

Fore

shoc

k Bou

ndar

yB Earth

Field-aligned beams

Specularly reflected ions

Intermediate distribution Diffuse

distribution

地球舷激波周围离子加速的情况

29H. Kucharek et al 2004

The energetic particles flow at the quasi-perpendicular bow shock

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Cluster orbit and formation

http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=24451

• Four identical satellites

• The satellites can be in string-of-pearls formation for substorm events (related to aurora) or tetrahedron formation for 3D structure of discontinuities

• Orbit period 57 hours

• Perigee: 4 Re

• Apogee: 18-20 Re

• Separation of satellites in tetrahedron formation: between 100 and 1000 km

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Four-satellite timing analysis

Assumption: Shock front does a constant motion within the tetrahedron .

• s1, s2, s3, s4 and t1, t2, t3, t4 are coordinates and time when shock front crossing satellite (1,2,3,4), respectively.

nsntVshock ˆˆ

Average shock front is determined more accurately

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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

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Benefits of Multi-satellite measurement

The orientation and motion of a plane discontinuity;

The spatial gradient of a vector .

Future mission -- MMS

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Upstream

E

B

Downstream

Proton trajectory

T= t1T= t2

B

Sho

ck

Perpendicular Shock

Source of field-aligned beams

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• Vsw = 420 km/s

• BN ≈ 70o

• MA = 11

• = 0.36

Bow Shock Crossing Jan 24, 2001• Vsw = 420 km/s, BN ≈ 70o, MA = 11, = 0.36

Moebius et al. 2001

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Reference frames

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• 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 field VSW×B; satellite frame is approximately equal to shock frame due to their relatively slow motion comparison with VSW .

• de Hoffmann Teller frame (HT frame) A moving frame to eliminate VSW×B electric field through VSW along B.

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de Hoffmann Teller frame (HT frame)

Moving frame in the shock layer

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Generation mechanism of FABs: direct reflecting model

Paschmann et al., 1980Vi (SC frame) V//i = Vi - VHT (HT frame)

|V//r| = |V//i| (HT frame) kinetic energy conservation

Vr = V//r + VHT (SC frame)

nIon in S/C FrameB

V//r

n: shock normalB: IMF Vi: solar wind velocity

VHT

Vi V//iV//i

Vr

n̂B

)BV(n̂=V i

HT

Schwartz et al., 1984

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Drift shock acceleration

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Invalidation of the HT frame

When ΘBn approaching 90 degree, the denominator is zero. Then VHT is infinite.

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B

The variation of bulk velocity of FABs

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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)

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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 properframe of reference.

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Dynamic of the Earth’s Bow Shock

• The dynamic of the Earth’s bowshock creates variations of the localΘBn, which can lead to particle release in turn.

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The complicate shock surface

Scholer and Kucharek, 2002

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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.

Standing shock wave downstream of Bow Shock near CUSP

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CIR shock

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Superposed-epoch analysis of the plasma parameters for CIRs [Gosling et al., 1996]. Note the well defined pressure pulse and compression region in the modified portion of the slow stream.

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MHD simulation of (1) high speed streams which cause the development of CIR structure and (2) the propagation of transient shocks which also modify the CIR structure (bottom two panels particularly) [Akasofu and Hakamada,

1983].

INTERPLANETARY TRAVELLING SHOCK

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Example of a CME and associated forward/reverse shock pair observed by Ulysses near 5 AU [Gosling, 1996].

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Schematic of a coronal mass ejection in the form of a magnetic cloud [Cravens, 1997] with a shock.

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Example of a CME and associated forward/reverse shock pair observed by Ulysses near 5 AU [Gosling, 1996].

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Cane, H.V et al., "The role of interplanetary shocks in the longitude

distribution of solar energetic particles," JGR 93, 9555 (1988)

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Interplanetary travelling shock

It is recognized that all interplanetary travelling shocks are associated with CMEs.

They may all encountered multiple shock processes.

Diffuse and shock drift processes.

59蓝底 PPT 来自 Joe Giacalone ACE/RHESSI/WIND meeting, 2003

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Quiz 5

1.简单描述一下激波。

2.地球舷激波（ Earth’s Bow Shock）准垂直区域可呢个的加速机制有哪些？选择一个简单描述一下

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Cosmic ray

Ray ？ Particles!

89% proton, 10% He2+, and others

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The great power law in the sky

http://en.wikipedia.org/wiki/Cosmic_ray

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Pickup ions and Anomalous Cosmic Rays (ACR)

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Correlation between GCR and ACR at 1AU (ACE news # 136)

http://www.srl.caltech.edu/ACE/ACENews/ACENews136.html

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ACR in Cosmic ray spectrum

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Pick-up ions accelerated at the CIR shock

有助于理解 termination shock 对 pick-up ions 的加速；

1AU 附近，有利于观测。

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Summary

Shock 的基本概念 Shock 与高能粒子 Earth’s quasi-perpendicular bow shock

acceleration Diffusive shock acceleration and cosmic

ray