Plasma transport via kinetic Alfvén waves運動論的アルヴェン波によるプラズマ輸送

D3 井筒智彦

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Outlines

1. Introduction

2. Mechanism of plasma transport via kinetic Alfvén waves in a high-beta plasma

3. Evidence for plasma transport via kinetic Alfvén waves across the magnetopause: THEMIS event study

4. Contribution of kinetic Alfvén waves to the formation of the low-latitude boundary layer: THEMIS statistical study

5. Generation and roles of kinetic Alfvén waves in the magnetosphere

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Introduction

1

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How does SW plasma penetrate into the MSP?

• Formation of the magnetosphere (boundary layer, plasma sheet, ring current, ...)

• Physics of turbulence, wave particle interaction, ...

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Method: in-situ spacecraft observations

• Available data– 【 particle 】 plasma velocity distribution function: f [T3L-6]

• plasma moments: density, velocity and temperature

– 【 wave 】 magnetic and electric field

MSH MSPMP

penetrated MSH plasma

ex) N [L-3]=∫f dv3

V [L/T]=∫v ・ f dv3

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Candidate mechanisms for plasma entry

Solar wind

LLBL/CDPS

reconnection @poleward-of-cusp

Kelvin-Helmholtz vortex

kinetic Alfven waves

efficient entry for northward IMF

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Kinetic Alfven Waves (KAWs)

• Kinetic/Vlasov waves and instabilities [e.g., Schwartz et al., 1996]

– Fast magnetosonic/whistler waves – Alfven ion cyclotron (AIC) waves (ω<Ωci)

– Slow/ion acoustic waves– Mirror mode

• Kinetic Alfven waves– arise from mode conversion @vA gradient [Hasegawa, 1976]

– identical to AIC waves @quasi-⊥ propagation & k⊥ρi~1

– linearly polarized with low-β & low-frequency limit [Hollweg, 1999]– non-zero field-aligned electric field, δE//

– high phase velocity, ω/k//>vA 　 [Hasegawa, 1976]

dispersion relation in a low-β plasma [adopted from Stasiewicz et al. (2000)]

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Observations of KAWs

• KAWs are observed in the form of turbulence in the solar wind, magnetosheath, and magnetopause

• Magnetic spectra break at k⊥ρi=1 ~ k⊥ρs=1– due to Landau and/or transit-time damping [Leamon et al., 1999]

In the magnetopause adjacent to the MP[Chaston et al., 2008]

Around the dayside magnetopause[Yao et al., 2011]

In the solar wind [Sahraoui et al., 2010]

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Problems on plasma transport via KAWs• Previous studies on the wave-induced transport are mainly

based on wave data.

1. How do KAWs transport plasma in a high-β plasma?2. Does the KAW-induced transport actually contribute to the

LLBL formation?3. How often/where the KAW-induced transport occurs?4. What is the role of KAWs in the magnetosphere?

Calculate diffusion coefficient from observed fluctuations

Few studies have focused on properties of transported particles.“There is no direct confirmation of this hypothesis (diffusion induced by waves) from particle data.” [Paschmann, 1997]Q

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Mechanism of plasma transport viakinetic Alfven waves in a high-beta plasma

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Plasma transport via KAWs in a low-β plasma• In a low-β plasma

– δB=(δBx, 0, 0) & δE=(0, δEy, δEz) for k=(0, ky, kz)

[Lysak and Lotko et al., 1996; Stasiewicz et al., 2000]

– In turbulent KAWs, quasi-linear theory predicts that particles satisfying Landau resonance condition vz=ω/kz are transported.

[Hasegawa and Mima, 1978]

• Breakdown of the frozen-in condition by δE decouples the plasma from magnetic field line. [Lee et al., 1994]

k

Resonant particles are transported in the ±x direction

Diffusion coefficient

[Lee et al., 1994; Chaston et al., 2008]

B0

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Plasma transport via KAWs in a high-β plasma

• In a high-β (β~1) plasma– KAWs become compressive [Gary, 1986; Hollweg, 1999]

δB=(δBx, δBy, δBz) & δE=(δEx, δEy, δEz)

– Transit-time damping induced by δBz has been considered to contribute to the transport [Chaston et al., 2008]

• However, the diffusion coefficient and its physical origin for the high-β case have not been shown.– Moreover, there are some mistakes in previous papers even for the low-β

case.• direction of the transport [Lee et al., 1994]• energy of transported particles [Johnson and Wing, 2009]• the ratio of resonant particles [Lee et al., 1994; Chaston et al., 2008]

• In this study, I will1. provide a simple explanation for the underlying physics of the

transport and the expression of D for the high β case2. suggest a new method to verify whether the KAW-induced transport

occurred

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Physics of the transport via high-β KAWs

ExB drift These drift motions are physical origin of cross-field transport.

• QL theory predicts resonant particles (vz=ω/kz) are transported.

• The forces such particles feel are

– the force induced by δEz cause ExB drift for ions and electrons

– the force induced by δBz cause gradient-B drift for ions

grad-Bdrift

B0

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Diffusion coefficient• D in a low-β plasma

can be regarded as D~ΣVD12 ・ τ ・ R where

– drift velocity VD1=kyδEz/(kzB0)

– timescale τ~1/kzvth

– the fraction of resonant particles R=exp(-(ω/kz)2/vth2)

• D in a high-β plasma can be written as

• D ~ Σ VD2 ・ τ ・ R

strength of the transport for each k (V//). Diffusion equationrate of total density change (integrated over energy)

Maxwellian dist.

focus on the energy dependence of the transported particles

[Hasegawa and Mima, 1978]

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New verification method using particle data• In turbulent KAWs with a breakpoint at k⊥ρs=1

– Two drift velocities maximize at the breakpoint of the spectrum.– Transport occurs for particles with v//>vA.

• If the plasma transport via KAWs occurs and its history is held, we can find, by comparing particle distribution functions, that1. Particles with v//>vA are selectively transported

2. Maximum transport occurs at the breakpoint

Calculations are done for β=0.5, Te/Ti=0.2 and θ=89.95° using equations in Hollweg (1999).

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Notes

• Diffusion coefficient– over estimated @Lee1994 & Chaston2008

• β dependence– In the MSH (β~1), the transport induced by δBz is more

effective– The amount of the transport increases with increasing β

• mainly because lower energy particles become to resonate In the MSP (β<<1), KAWs cannot transport cold plasma.

• Landau damping (LD) & transit-time damping (TD)– VD1/VD2=qδEz/(μkzδBz)=(electric force)/(mirror force)=LD/TD

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Problems to be solved

• Transport of NON-resonant particles– compose a large part of LLBL particles

• Effect of differences between ions and electrons– The number of transported particles: electrons >> ions– Drift velocity: ion > electrons in a high-β plasma may lead charge separation What effects?

• Generation of KAWs @MP– KAWs generated from mode conversion cannot form the LLBL.

Bz By Ex

X

MSH

MSP

X X

Lin et al., 2010

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Summary

• Mechanism of plasma transport via KAWs in a high-β plasma has not been understood.

• In this study,1. I showed that the physical origin of the cross-field transport is

δE//-induced ExB drift with VD1=k⊥δE///(k//B0) and δB//-induced grad-B drift with VD1=(μk ⊥δB//)/(q B0).

2. Diffusion coefficient related to δB// was derived to be

3. I suggested a new method for the verification of the KAW-induced transport which focuses on the selectivity of the transport:(1) Particles with v//>vA are transported.

(2) Maximum transport occurs at the breakpoint of the spectrum (@k⊥ρi~1).

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Evidence for plasma transport across the magnetopause via kinetic Alfven waves:

THEMIS event study

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THEMIS observations on 2007-06-03

SRC

BG

MIX

MSH parameters β~0.5 Te/Ti~0.2

MLT=16.2

fbreak=0.8~1.0 Hz k⊥ρi=0.9~1.3

0245-0254UT

breakpoint

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Transport efficiency in velocity space

Ratio<1 high ratio @V//> VA

highest ratio @V//=350~500km/s

k⊥ρi=1.2~1.7

(Solutions of linear Vlasov-Maxwell eq. for β=0.5, Te/Ti=0.2, θ=89.95°.)

TR/SRC

Ratio<1 high ratio @V//> VA

highest ratio @k⊥ρi=0.9~1.3

Predictions

Observations are fairly consistent withthe picture of plasma transport via KAWs!

SRC TR=MIX-BG

Results

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Discussion: Other entry mechanisms• Poleward-of-cusp reconnection

– Model: MSH plasma is captured at the rate of C1 independently of V and then parallelly heated by a factor of C2

– Observations on 2008-07-11 [Hasegawa et al., 2009]

• Plasma mixing or reconnection within well developed Kelvin-Helmholtz (KH) vortices– There is no signature of such rolled-up KH vortices– If they exist, the observed selective transport cannot be explained because

mixing is not selective and reconnection is accompanied by heating.

Model for C1=0.5, C2=1.2Reconnection event on 2008/07/11

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Contribution of kinetic Alfven waves to the formation of the low-latitude boundary

layer: THEMIS statistical study

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Statistical study

• THEMIS observations on 2007.6 ～ 2007.9• Full distribution function is available @THEMIS-C• Detection of LLBL or cold-dense plasma (CDP) of

magnetosheath origin inside the magnetosphere →85 CDP(LLBL) events

• KAW-induced transport event (“KAW event”)

Criteria・ Parallel anisotropic transport・ Efficiency < 1・ VA @MSH < V//,peak < ω/k// @k⊥ρs=2

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Spatial distribution of “KAW event”

24 events are selected as “KAW event”.

24ev/85ev~28%

LLBL/CDP thickness deduced from multipoint observations

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Generation and roles of kinetic Alfven waves in the

magnetosphere

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AIC/EMIC wave excited by T⊥/T//>1

Alfven-ion-cyclotron (AIC) wave/Electromagnetic ion cyclotron (EMIC) wave

V//

V⊥

ion

e-

B

δBx

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Oblique propagation @density gradient

• Wave polarization @f=0.24~0.29 Hz

δEx

δE

y

Right

Left

linear

circula

r

Gary, 1986

β=1

1: linearly polarized2: linearly & right-handed3: linearly & left-handed4 ・ 5: circularly left-handed

large θ

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• New(?) mechanism for the generation of KAWs1. T⊥/T//>1

2. Parallel propagating AIC/EMIC wave3. Quasi-⊥ propagating AIC wave @density gradient4. Narrowband, strong KAW

• Roles in the magnetosphere1. Plasma transport

• Not contribute to transport of cold-plasma

2. Anomalous resistivity• Reconnection trigger in the compressed current sheet??

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Abbreviation & Notation• MSP ： MagnetoSPhere 磁気圏• MSH ： MagnetoSHeath マグネトシース• MP ： MagnetoPause 磁気圏境界面• LLBL ： Low-Latitude Boundary Layer 低緯度境界層• CDPS: cold dense plasma sheet 低温高密プラズマシート• QL theory: quasi-linear theory 準線形理論• β: plasma beta プラズマベータ• k ： wavenumber 波数• λ ： wavelength 波長• ω: angular frequency 角周波数• ρi ： ion gyro-radius イオンジャイロ半径• ρs ： ion acoustic gyro-radius イオン音波ジャイロ半径• Ωci : ion gyro-frequency イオンジャイロ周波数• vA : Alfven velocity アルヴェン速度• Vth: thermal velocity 熱速度• D ： Diffusion coefficient 拡散係数　 [L2T-1]• //: parallel to the ambient magnetic field 磁場平行方向• ⊥: perpendicular to the ambient magnetic field 磁場垂直方向

k=2π/λ

ρs =(Te/Ti)1/2 ρi

β=Pgas/Pmag=nκT/(B2/2μ0)

Vth =(κT/m)1/2

VA =B/(μ0mn)1/2

ρi =Vth,i/Ωci

Ωci=qB/mi

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References• Chaston, C., et al. (2008), Turbulent heating and cross-field transport near the magnetopause from THEMIS,

Geophys. Res. Lett., 35, 17-+, doi:10.1029/2008GL033601.• Gary, S. P. (1986), Low-frequency waves in a high-beta collisionless plasma Polarization, compressibility and

helicity, Journal of Plasma Physics, 35, 431-447, doi:10.1017/S0022377800011442.• Hasegawa, A. (1976), Particle acceleration by MHD surface wave and formation of aurora, J. Geophys. Res., 81,

5083-5090, doi:10.1029/JA081i028p05083.• Hasegawa, A., and K. Mima (1978), Anomalous transport produced by kinetic Alfven wave turbulence, J.

Geophys. Res., 83, 1117-1123, doi:10.1029/JA083iA03p01117.• Hasegawa, H., et al. (2009), Boundary layer plasma flows from high-latitude reconnection in the summer

hemisphere for northward IMF: THEMIS multi-point observations, Geophys. Res. Lett., 36, 15,107-+, doi:10.1029/2009GL039410.

• Hollweg, J. V. (1999), Kinetic Alfven wave revisited, J. Geophys. Res., 104, 14,811-14,820, doi:10.1029/1998JA900132.

• Johnson, J. R., and S. Wing (2009), Northward interplanetary magnetic field plasma sheet entropies, Journal of Geophysical Research (Space Physics), 114, 0-+, doi:10.1029/2008JA014017.

• Lee, L. C., J. R. Johnson, and Z. W. Ma (1994), Kinetic Alfven waves as a source of plasma transport at the dayside magnetopause, J. Geophys. Res., 99, 17,405-+, doi:10.1029/94JA01095.

• Lin, Y., J. R. Johnson, and X. Y. Wang (2010), Hybrid simulation of mode conversion at the magnetopause, Journal of Geophysical Research (Space Physics), 115, 4208-+, doi:10.1029/2009JA014524.

• Leamon, R., J., et al. (1999), Dissipation range dynamics: Kinetic Alfven waves and the importance of βe, J. Geophys. Res., 104, 22331-22344, doi:10.1029/1999JA900158

• Paschmann, G., (1997), Observational Evidence for Transfer of Plasma Across the Magnetopause, , Space Science Reviews, 80, 217-234, doi: 10.1023/A:1004926004806

• Lysak, R. L., and W. Lotko (1996), On the kinetic dispersion relation for shear Alfven waves, J. Geophys. Res., 101, 5085-5094, doi:10.1029/95JA03712.

• Stasiewicz, K., et al. (2000), Small Scale Alfvenic Structure in the Aurora, Space Science Reviews, 92, 423-533.• Yao, Y., C. C. Chaston, K.-H. Glassmeier, and V. Angelopoulos (2011), Electromagnetic waves on ion gyro-radii

scales across the magnetopause, Geophys. Res. Lett., 38, L09,102, doi:10.1029/2011GL047328.

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QL theory for low-β KAWs