alfvén waves and space weather
DESCRIPTION
AACIMP 2009 Summer School lecture by Yuriy Voitenko.TRANSCRIPT
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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