Photoionized Plasmas: Connections Between Laboratory and Astrophysical Plasmas
Kinetic Alfvén waves in space plasmas · • where and how (1) transforms into (2) • what are...
Transcript of Kinetic Alfvén waves in space plasmas · • where and how (1) transforms into (2) • what are...
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Kinetic Alfvén waves in space plasmas
Yuriy Voitenko
Belgian Institute for Space Aeronomy, Brussels, Belgium
Solar-Terrestrial Center of Excellence, Space Pole, Belgium
Recent results obtained in collaboration with V. Pierrard, J. De Keyser, P. Shukla
CHARM kick-of meeting (8-9 October 2012, Leuven, Belgium)
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Solar-terrestrial example: solar atmosphere à solar wind à magnetosphere à space weather
ALFVEN WAVES AND TURBULENCE !
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MHD AWs
KAWs
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
Unstable PVDs
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Existence of electromagnetic–hydrodynamic waves (H. Alfvén, Nature 150, 405–406, 1942)
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MHD VS. KINETIC ALFVÉN WAVE
Kinetic Alfvén wave (KAW) - extension of Alfvén mode in the range of small perpendicular wavelength (Hasegawa and Chen, 1974-1980)
[ ] ( ) 0;;)( 22222 =⋅∂⋅∂−∂ ⊥⊥⊥ trzBKV zAt
)( ⊥⋅= kKVk AzωKAW dispersion:
Padé approximation for the KAW dispersion function:
( );/11)( 22pep TTkkK ++= ⊥⊥ ρ
pρ - proton gyroradius.
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EXAMPLE 1: KAW turbulence in the solar wind
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• where and how (1) transforms into (2) • what are transition scales and spectra
• dissipative effects and velocity distributions of particles
• turbulence in kinetic vs. inertial regime
RECENT PROGRESS IN TURBULENCE
(1) MHD Alfvénic turbulence evolves anisotropically towards large wavenumbers perpendicular to the mean magnetic field: e.g. J. Shebalin, P. Goldreich, S. Sridhar, G. Howes, A. Schekochihin… (2) Alfvén waves with finite (kinetic Alfvén waves - KAWs) differ drastically from MHD Alfvén waves: e.g. A. Hasegawa, L. Chen, J. Hollweg, D.-J. Wu, Y. Voitenko, ……
WE STILL DO NOT KNOW:
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KAW
k
ρ ⊥
||
k i - 1
δ i - 1
R ç
- 1
_
| |
N o n l i n e a r C h e r e n k o v
I o n – c y c l o t r o n
N o
n –
a d
I a
b a
t I c
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He et al. (2011,2012); Podesta & Gary (2011):
AT THE PROTON KINETIC SCALES THERE ARE TWO COMPONENTS: ION-CYCLOTRON (20 %) AND (DOMINANT) KINETIC ALFVEN (80%)
He et al. (2011,2012)
RECENT OBSERVATIONAL EVIDENCES FOR KAWs
Follows MHD 2D component?
Follows MHD “slab” component?
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Theoretical predictions for whistlers are not supported by observations:
RECENT OBSERVATIONAL EVIDENCES FOR KAWs Exploiting B II Bo component to discriminate KAWs vs. whistlers:
Salem et al. (2012) : IDENTIFICATION OF KINETIC ALFVEN WAVE TURBULENCE IN THE SOLAR WIND
He et al. (2012) : DO KINETIC ALFVEN / ION-CYCLOTRON OR FAST-MODE/WHISTLER WAVES DOMINATE THE DISSIPATION OF SOLAR WIND TURBULENCE NEAR THE PROTON INERTIAL LENGTH?
He et al. (2012)
Salem et al. (2012)
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SOLAR WIND TURBULENCE
Sahraoui et al. (2010): high-resolution magnetic spectrum
MHD AW RANGE KINETIC RANGE ?
exhibits 4 different slopes (!) in different ranges.
( f ~ k_perp )
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Co-propagating KAWs interact (Voitenko, 1998):
Counter-propagating KAWs interact (Voitenko, 1998):
AT KINETIC SCALES (KAWs):
MHD VS KINETIC ALFVÉN TURBULENCE
AT MHD SCALES (MHD AWs): Only counter-propagating MHD AWs interact: (Goldreich and Sridhar, 1995; Boldyrev, 2005; Gogoberidze, 2007)
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ALFVÉNIC TURBULENCE SPECTRA (THEORY)
à weak turbulence;
à strong turbulence;
Strongly dispersive range (kinetic):
à weak turbulence;
à strong turbulence;
Non-dispersive range (MHD):
à weak turbulence;
à strong turbulence;
Weakly dispersive range (kinetic):
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DOUBLE-KINK SPECTRAL PATTERN (Voitenko and De Keyser, 2011)
Two interpretations: dissipative (left) and dispersive (right) Left cannot exist without right! But right can exist without left!
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ALFVÉNIC TURBULENCE IN SOLAR WIND
Sahraoui et al. (2010): high-resolution magnetic spectrum
MHD RANGE SDR KINETIC WDR
kinetic
( f ~ k_perp )
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EXAMPLE 2: proton energization in the solar wind
by KAW turbulence
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• Use kinetic Fokker-Planck equation for protons with diffusion terms due to KAWs
• Calculate proton diffusion (plateo formation) time
• Use observed turbulence levels and spectra
• Estimate generated tails in the proton VDFs and compare with observed ones
VELOCITY-SPACE DIFFUSION OF PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2012)
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VELOCITY-SPACE DIFFUSION OF SW PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2012)
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• We use the kinetic Fokker-Planck equation with diffusion terms due to Coulomb collisions and KAW turbulence
• Set boundary at 14 Rs (above the Alfvén point) • Use a model Alfvénic spectrum as observed at
>0.3 AU and project it back to 14 Rs following ~ 1/r^2 radial profile for the turbulence amplitude
• Plug the obtained spectrum in the diffusion term for wave-particle Cherenkov interactions
• Solve numerically using spectral method • Observe tails in the obtained proton VDFs
VELOCITY-SPACE DIFFUSION OF PROTONS: KINETIC SIMULATIONS (Pierrard and Voitenko, 2012)
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KAW velocities cover this range
Proton VDF obtained at 17 Rs assuming a displaced Maxwellian as boundary condition at 14 Rs by the Fokker-Planck evolution equation including Coulomb collisions and KAW turbulence
Proton velocity distributions with tails are reproduced not far from the boundary
VELOCITY-SPACE DIFFUSION OF PROTONS: KINETIC SIMULATIONS (Pierrard and Voitenko, 2012)
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PROTON VELOCITY DISTRIBUTIONS WITH TAILS IN THE SOLAR WIND (after E. Marsch, 2006)
Kinetic-scale Alfvénic turbulence covers the tails’ velocity ranges
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Vz Vph1 Vph2
Fs
KAW velocities
NON-MAXWELLIAN LANDAU DAMPING
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PARALLEL PROTON ACCELERATION BY KAWs: NON-LINEAR CHERENKOV RESONANCE
MOTIVATION:
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COLLISIONLESS TRAPPING CONDITION:
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Generation of proton beams by KAWs Stage 1: proton trapping by KAWs
Vz VTp Vph1
Fp
proton trapping occurs here
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Generation of proton beams by KAWs Stage 2: “acceleration” due to increasing
Vz VTp Vph
Fp
ACCELERATION
Vph
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Generation of proton beams by KAWs
Vz VTp Vph1 Vph2
Fp
KAWs trap protons here and release/maintain here
ACCELERATION
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PARALLEL PROTON ACCELERATION BY KAWs: NON-LINEAR CHERENKOV RESONANCE
Reflected protons set up a beam
KAW pulse
Passing by (free) protons
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Normalised velocity of reflected protons as function of thermal/Alfven velocity ratio. The relative KAW amplitude =0.03, 0.06, 0.09, 0.12, and 0.2 (from bottom to top). Linkage to local Alfven velocity + good coverage of typical values.
0.09
0.06
0.03
0.12
B/Bo = 0.2
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Number density of reflected protons as function of the relative KAW amplitude B/B₀. The proton beta β_{p‖}=0.16, 0.25, 0.36, and 0.49 (from bottom to top). Trend: large relative beam density with larger plasma beta compatible with observations.
β_{p‖} = 0.49
0.36
0.25
0.16
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PROTON VELOCITY DISTRIBUTIONS WITH BEAMS (after E. Marsch, 2006)
KAW velocities are here
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• MHD-kinetic turbulence transition occurs in the weakly dispersive
range (WDR): <1 • Steepest spectra occur in WDR up to • Hence: universal double-kink spectral pattern • Hence: quasi-linear proton diffusion • à producing suprathermal proton tails locally in the solar wind • Hence: nonlinear Cherenkov resonance with protons: • à producing proton beams locally in the solar wind • spectrally localized selective dissipation removing highest
amplitudes in the vicinity of the spectral break • à intermittency reduction (observed by Alexandrova et al. 2008) • à switch to weak turbulence and steepest spectra (was
observed by Smith et al. 2006)
SUMMARY
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• à Nature of quasi-perpendicular versus quasi-parallel components of turbulence at MHD and kinetic scales
• à à Are they related? • à à Their respective cascades? • à Role of anisotropy in the MHD-kinetic transition • à Dissipation versus dispersion shaping of kinetic
spectra • à Correlations between nonthermal features in particles’
VDFs and turbulence characteristics • à KAW turbulence driven by non-local interactions • à …
FURTHER DIRECTIONS
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EXAMPLE 3: inertial Alfvén turbulence
in the auroral zones
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Aurora – multiscale Alfvén wave flux (photo by Jan Curtic)
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Simultaneous observations of Alfvén waves at altitudes 7 RE (Polar) and 1.5 RE (FAST) in the main phase of a major geomagnetic storm on 22 October 1999 (Dombeck et al., 2005): • wave energy flux decreased from 45 to 10 erg/cm2/s between Polar and FAST • electron energy flux increased to 20 erg/cm2/s • most wave flux is carried by large MHD-scale Alfvén waves
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PROBLEMS
• Not enough energy in kinetic-scale waves • Depletion at kinetic scales is not observed • How the most energetic MHD part of spectrum is dissipated?
~ k W
k
-p
MHD kinetic
~ k W
k
-p
MHD kinetic
Injected wave spectrum
Depleted spectrum
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Possible solution - turbulent cascade to kinetic scales: Ø ion gyroradius ρi (reflects gyromotion and ion pressure effects); Ø ion gyroradius at electron temperature ρs (reflects electron pressure effects); Ø ion inertial length δi (reflects effects due to ion inertia); Ø electron inertial length δe (reflects effects due to electron inertia). If δe larger than other microscales --> --> inertial regime; Ø parallel wave electric field develop at such length scales --> particle acceleration.
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NONLINEAR IKAW INTERACTION AND TURBULENCE (Voitenko, Shukla, De Keyser, 2012)
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MHD / INERTIAL KAW TRANSITION
MHD nonlinear rate (Boldyrev 2005; Gogoberidze 2007):
MHD/kinetic transition occurs when MHD/kinetic rate = 1: < 0.1 for counter-propagating KAWs = 0.3 for co-propagating KAWs
Compare with nonlinear interaction rates of IKAWs:
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• counter-propagating interaction is stronger and spectra dominate
TURBULENCE SPECTRA IN KINETIC RANGE
• strong turbulence: nonlinear time scales of perturbations are comparable to the linear ones • critical balance condition in spectral representation: equivalent frequency = nonlinear interaction rate • resulting spectra:
à for counter-propagating IKAWs;
à for co-propagating IKAWs;
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(a) UV auroral image from Polar UVI instrument and FAST spacecraft trajectory.
(b) FAST Ex (red) and By
(black) fields. (c),(d) FAST electron and
ion spectrograms. From: Chaston et al. (2008): Phys.Rev.Lett 100, 175003.
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(a) Average B2 (fsp=kx)
spectra. (b) Average E2
(fsp=kx) spectra. From: Chaston et al. (2008): Phys.Rev.Lett 100, 175003,
FAST measurements from August 6 to September 9, 1998 at 1.6 ER
MHD k i n e t i c