Alfvén waves and space weather

Yuriy Voitenko

Space Physics Dept, Belgian Institute for Space Aeronomy, (Brussels, Belgium)

15 August 2009 4th Kyiv Summer School

Motivation 1. Fundamental plasma physics: Alfvén waves Motivation 2. Space weather: energy conversion in space

plasmas Retrospect: Alfvén wave and its modifications: ion-cyclotron wave,

kinetic Alfvén wave, and ion-cyclotron kinetic Alfvén wave Theory vs. observations Open issues

outline

• Most matter is in the plasma state (ionized gas)• Examples: stars, interstellar and interplanetary

medium, planetary magnetospheres.The Sun: plasma ball. Earth’s magnetosphere: magnetic plasma bottle

• Magnetic fields (MFs) penetrate plasmas and reduce the ability of plasma to move across the magnetic field

• Most important things introduced by MFs: magnetic plasma structuring, energy accumulation/release, and magnetic plasma waves

Solar actrivity -> space weather

Сонячна активність =

магнітна активність

Alfvén waves

• - background magnetic field• z - axis along• - 2D plane • - Alfven velocity• - number density (number of electrons =

number of ions)• - ion mass

⊥r

0B

0B0B

⊥iA mnBV 00 4/ π=

im

0n

definitions:

Why plasma follows local magnetic field lines?Why plasma follows local magnetic field lines?

0BVceEe

dtVdmF i

×+== ⊥⊥

⊥⊥

Ion gyro-radius:Ion gyro-radius:

V

V

F

F⊥

⊥ Ω−= Vdt

Vdi2

2

2

cmeB

ii

0=Ω

Cyclotron frequency:

0B

iV Ω= /ρ

Lorentz force traps plasma particle bending their trajectories around particular magnetic field lines by cyclotron gyration:

Hannes Alfvén

Az V/λτ =

( ) ( ) ( )zktrBtrzB zk −= ⊥⊥⊥ ωsin;;

Az Vk=ω

MHD plasma model make AW highly degenerated in the plane ⊥ B0. Short ⊥ wavelengths -> ultraviolet singularity

1970 Nobel Laureate in Physics for fundamental work and discoveries in magneto-hydrodynamics with fruitful applications in different parts of plasma physics

Harmonic solution:

-> dispersion relation:-> relation between temporal and spatial wave scales:

( ) ( ) 0;;222 =⋅∂−∂ ⊥⊥ trzBV zAt

Alfvén waves – transversal ‘magneto-inertial’ waves

BUT:

at small wave length we meet natural length scales reflecting plasma microstructure. The most important of them are:

thermal ion gyroradius ion gyroradius ρρii (reflects gyromotion and (reflects gyromotion and ion pressure effects); ion pressure effects); thermal ion gyroradius at electron temperature thermal ion gyroradius at electron temperature ρρss (reflects electron pressure effects); (reflects electron pressure effects); ion inertial length ion inertial length δδii (reflects effects due to ion (reflects effects due to ion inertia), and inertia), and electron inertial length electron inertial length δδee (reflects effects due to (reflects effects due to electron inertia).electron inertia).

Thermal ion gyro-radius:Thermal ion gyro-radius: ρρii = V = VTiTi//ΩΩii

ρρii

Wave electric fieldWave electric field

)()()( 220 xEkxE ii ×Λ= ⊥ ρ

)exp()()( 22220

220 iii kkIk ρρρ ⊥⊥⊥ −=Λ

x

)(xE

Effective (gyro-averaged) electric field is smaller Effective (gyro-averaged) electric field is smaller than the field in the centre of the particle orbit:than the field in the centre of the particle orbit:

z

x

Bo

ion polarisation drift

Cross-field ion currents due to

Wave electric field Ex vary with z but not with x

MHD Alfven wave:

Field-aligned electron currents

compensate ion charges

kinetic Alfven wave: effect of short cross-field wavelength

Bo

Cross-field ion currents

build up ion charges

Kinetic Alfvén wave: retrospect

The micro length scales restrict applicability of ideal MHD.

First attempts to extend the Alfvén wave mode in the domain of short perpendicular wavelengths: Fejer and Kan (1969); Stefant (1970).

Later on, a kinetic theory accounting for some linear and nonlinear properties of Alfvén waves due to finite- ρρii effects has been developed by A. Hasegawa and co-authors:

Hasegawa and Chen (1976); Hasegawa and Mima (1979); Hasegawa and Uberoi (1982); Chen and Hasegawa (1994)

2000 Maxwell Prize for … Alfvén wave propagation in laboratory and space plasmas…

Akira Hasegawa

Kinetic Alfvén wave (KAW) - extension of Alfven mode in the range of small perpendicular wavelength

[ ] ( ) 0;;)( 22222 =⋅∂⋅∂−∂ ⊥⊥⊥ trzBKV zAt

)( ⊥⋅= kKVk AzωKAW dispersion

The last 10 years have seen a rapid accumulation of evidence:

Alfvén waves in their kinetic form – KAWs – are responsible for plasma energization in various ‘active’ regions of space plasmas.

Aurora from ground (photo by Jan Curtic)

W ygant et al. 2002

Conic ion distribution in aurora observed by FAST (L ynch et al. 2002)

– FAST observations: ion conics are associated with broad-band low-frequency (BBELF) and ion-cyclotron (EMIC) waves (Lund et al., 2000)

– Identification of BBELF waves as KAWs (Stasiewicz et al., 2000)

– Freja observations: KAWs activity accompanied by the field-aligned electron acceleration and cross-field ion heating (Andersson et al., 2002)

– Polar observations: KAWs and plasma energization at ~ 4 RE (Wygant et al., 2002)

Auroral example

Alfven W ave P oynting F lux: P owering the Aurora

(K eiling et al. 2002,2003; W ygant et al. 2002)

Cross-field ion energization by KAWs

(Voitenko and Goossens: ApJ, 605, L149–L152, 2004)

Equation for cross-field ion velocity in the presence of KAWs:

In the vicinity of demagnetizing KAW phases

the solution is

Specify KAW fields as:

Perpendicular velocity of an ion in a KAW wave train with a super-critical cross-field wave vector

Phase portrait of the ion’s orbit in the region of super-adiabatic acceleration (transition of the demagnetizing wave phase 3 pi)

t

At 1.5-4 solar radii there is an additional deposition of energy that:

(i) accelerates the high-speed solar wind; (ii) increases the proton & electron temperatures measured in interplanetary space; (iii) produces the strong

preferential heating of heavy ions seen there with UV spectroscopy.

HERECORONAL

EXAMPLES

(Esser et al., 1999)

Cross-field temperature of ion species in the solar corona (SOHO observations)

SOLAR ATMOSPHERE:

PROPAGATION AND DISSIPATION OF ALFVÉN WAVES

Cranmer (2004)

Photospheric/chromospheric motions can drive the observed AW flux

Strong flux of MHD Alfvén waves propagates from the Sun along open field lines in the region of increasing Alfvén velocity.

At 1.5 – 4 solar radii MHD Alfvén waves partially dissipate transforming into kinetic Alfvén waves – KAWs, which energize plasma:

accelerate ions across the magnetic field by Ex

accelerate electrons along the magnetic field by Ez

k

ρ ⊥

||

k i -1

δ i -1

R

-1

_

| |

I o n - c y c l o t r o n

L a n d a u

M A C R O ( M H D )

m i c r o ( k i n e t i c )

(Voitenko and Goossens: Phys. Rev. Let., 94, 135003, 2005)Nonlinear excitation of KAWs by MHD Alfven waves

kz V

A K(k2⊥ )

k zV AK(k 1⊥

)k zV A

k1z kz

ω

ωP

ωP = ω1 + ω2

kP = k1 + k2

k2z kPz

ω1

ω2

K(k⊥) < 1 if βm = βme/mp < 1

k

ρ ⊥

||

k i -1

δ i -1

R

-1

_

| |

I o n - c y c l o t r o n

L a n d a u

M A C R O ( M H D )

m i c r o ( k i n e t i c )

Resonant excitation and damping

The transient brightenings, observed in the low corona by Yohkoh and SOHO (blinkers, nano- and microflares), attracts a growing interest (Shimizu et al., 1992; Innes et al., 1997; Berger et al., 1999; Roussev et al., 2001; Berghmans et al., 2001). Magnetic reconnection in current sheets may produce reconnection outflows and consequent plasma heating, line broadening, etc. On the other hand, a considerable fraction of the energy can be released by the dynamical evolution of the current sheets themselves. So, Fushiki and Sakai (1994) have shown that the fast waves can be emitted in the solar atmosphere by a pinching current sheet.

Decay of fast waves and coronal heating events

k

ρ ⊥

||

k i -1

δ i -1

R

-1

_

| |

I o n - c y c l o t r o n

L a n d a u

M A C R O ( M H D )

m i c r o ( k i n e t i c ) S t o c h a s t i c

ICAWICKA

W

KAW

Hinode XRT 2006 Nov 13 04:53:14

Numerous observations (Yohkoh, SOHO, Hinode) suggest that the solar transients (flares, microflares, blinkers, etc.) are produced by magnetic reconnection. Magnetic reconnection occurs via current dissipation in magnetic interfaces (current sheets) between interacting magnetic fluxes.

ENERGY RELEASE IN THE SOLAR CORONA

Earth size

ENERGY RELEASE IN THE SOLAR CORONA

Classical resistivity require unphysically thin current sheets and cannot explain the observed rates of energy release.

Q1: what is the nature of the currents’ dissipation?Q2: what is the role of the currents’ inhomogeneity?Q3: at what length scales they dissipate?

the shear-current driven instability of kinetic Alfven waves is the most likely mechanism for triggering anomalous resistivity and hence initializing solar transients. The scaling relations for reconnection rates and widths of magnetic interfaces are derived.

The linear Vlasov response

is used to calculate current and charge perturbations in

The KAW phase velocity and the growth/damping rate in a kinetic regime:

where

• Instability range in Vk-ky plane

• Instability range in (kz-ky) plane

Excitation of KAWs by non-uniform currents

VzVAVTi Vph1 Vph2

Fi

Fe

KAWs are excited here and here

CONCLUSIONS-I (shear-current-driven KAWs)

In the presence of shear currents, the phase velocity of KAWs decreases drastically (well below Alfven velocity)

The shear-current-driven instability of KAWs can be driven by VERY weak currents

The KAW instability produces an anomalous resistivity strong enough to release energy for quasi-steady coronal heating and for impulsive coronal events

magnetic reconnection and solar flares

Plasma Inflow

KAW Flux and Plasma Heating

Kinetic Alfven model of solar flares

(Voitenko, 1998):

(1) Sunward reconnection outflow creates neutralized beams of 0.1-1 MeV

protons. (2) Partial conversion of

beam energy into flux of kinetic Alfvén waves. (3) Plasma heating and

particles acceleration by KAWs. (4) Loop top HXR source.

1

2

3

4 3

13 January 1992 (Masuda) flare

• Model input:Model input:loop half-length L = 2×109 cm; number density in loop legs n0 = 2.5×109 cm-3;

loop top n0 = 1010 cm-3; proton beam nb = 109 cm-3; magnetic field B0 = 57 G; initial temperature Te = 6×106 K;• Model output: Model output: KAW instability growth time τ = γ -1 = 3×10-5 s; relaxation distance < 105 cm;final temperature Te = 7×107 K; spreading velocity >= 4×108 cm/s; flux of escaping (> 20 KeV) electrons 1017 el. cm-2 s-1

b

Tsuneta (1997):

Tsuneta, 1997

Geomagnetic substorm model (ANGELOPOULOS ET AL., 2002):

(1) Earthward energy flux couples to localized fluctuations.(2) Partial dissipation via kinetic Alfvén wave interaction with electrons.(3) Further dissipation via inertial Alfvén wave interaction with electrons.(4) Ion heating by electrons, and eventual upflow.

Solar wind

PROTON VELOCITY DISTRIBUTIONS

IN THE SOLAR WIND AT r ~ 0.3 AU, HELIOS MEASUREMENTS

(after Marsch et al., 1982)

proton beamsanisotropic core protons

Main features:

Tu et al. (2002, 2003) suggested that the proton beams could be shaped by quasi-linear diffusion caused by cyclotron waves.

The last 10 years have seen a rapid accumulation of evidence suggesting that kinetic Alfvén waves – KAWs – are very important for plasma energization observed in various space plasmas (solar wind, planetary magnetospheres and ionospheres). In view of KAW activity observed in solar wind (e.g. Leamon et al., 1999; Bale et al., 2005; Podesta, 2009) we propose the following scenario for the proton beam formation:

(1) kinetic Alfvén wave flux is generated in the solar wind linearly (by kinematical conversion of MHD Alfvén waves), or nonlinearly (by MHD turbulent cascade);

(2) due to increasing wave dispersion, the KAWs’ propagation velocity increases;

(3) the protons trapped by the parallel electric potential of KAWs are being accelerated anti-sunward by the accelerated KAW propagation, forming supra-thermal proton beams at ~ 1.5VA

COLLISIONLESS TRAPPING CONDITION:

Creation of proton beams by KAWs

VzVTp Vph1 Vph2

Fp

KAWs trap protons here and release/maintain here

ACCELERATION

MHDwaves

Kinetic Alfvénwaves

Super-adiabatic cross-field ion acceleration

Resonant plasma heating and particle acceleration

Demagnetization of ion motion Kinetic wave-particle interaction

Phase mixing

Turbulent cascade

Kinetic instabilities

Parametric decay

UnstablePVDs

Thank you!

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