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)

Solar-terrestrial example: solar atmosphere à solar wind à magnetosphere à space weather

ALFVEN WAVES AND TURBULENCE !

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

Existence of electromagnetic–hydrodynamic waves (H. Alfvén, Nature 150, 405–406, 1942)

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.

EXAMPLE 1: KAW turbulence in the solar wind

•  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:

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

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?

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)

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 )

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)

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):

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!

ALFVÉNIC TURBULENCE IN SOLAR WIND

Sahraoui et al. (2010): high-resolution magnetic spectrum

MHD RANGE SDR KINETIC WDR

kinetic

( f ~ k_perp )

EXAMPLE 2: proton energization in the solar wind

by KAW turbulence

•  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)

VELOCITY-SPACE DIFFUSION OF SW PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2012)

•  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)

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)

PROTON VELOCITY DISTRIBUTIONS WITH TAILS IN THE SOLAR WIND (after E. Marsch, 2006)

Kinetic-scale Alfvénic turbulence covers the tails’ velocity ranges

Vz Vph1 Vph2

Fs

KAW velocities

NON-MAXWELLIAN LANDAU DAMPING

PARALLEL PROTON ACCELERATION BY KAWs: NON-LINEAR CHERENKOV RESONANCE

MOTIVATION:

COLLISIONLESS TRAPPING CONDITION:

Generation of proton beams by KAWs Stage 1: proton trapping by KAWs

Vz VTp Vph1

Fp

proton trapping occurs here

Generation of proton beams by KAWs Stage 2: “acceleration” due to increasing

Vz VTp Vph

Fp

ACCELERATION

Vph

Generation of proton beams by KAWs

Vz VTp Vph1 Vph2

Fp

KAWs trap protons here and release/maintain here

ACCELERATION

PARALLEL PROTON ACCELERATION BY KAWs: NON-LINEAR CHERENKOV RESONANCE

Reflected protons set up a beam

KAW pulse

Passing by (free) protons

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

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

PROTON VELOCITY DISTRIBUTIONS WITH BEAMS (after E. Marsch, 2006)

KAW velocities are here

•  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

•  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

EXAMPLE 3: inertial Alfvén turbulence

in the auroral zones

Aurora – multiscale Alfvén wave flux (photo by Jan Curtic)

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

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

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.

NONLINEAR IKAW INTERACTION AND TURBULENCE (Voitenko, Shukla, De Keyser, 2012)

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:

•  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;

(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.

(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