Alfvénic turbulence at ion kinetic scales

Yuriy Voitenko

Solar-Terrestrial Centre of Excellence, BIRA-IASB, Brussels, Belgium

Recent results obtained in collaboration with J. De Keyser, V. Pierrard, J. S. Zhao, D. J. Wu

STORM annual meeting (25-26 November 2013, Graz, Austria)

1. MHD Alfvénic turbulence evolves anisotropically toward large wavenumbers (perpendicular to the mean magnetic field) [Goldreich and Sridhar,1996]

2. Alfvén waves at ion (proton) kinetic scales (KAWs with finite differ drastically from MHD Alfvén waves [Hasegawa and Chen, 1974]

3. Alfvén turbulence at ion kinetic scales is much less known [see however Voitenko, 1998; Voitenko and De Keyser, 2011]

OUTLINE

KAW

k

||

k i -1

i-1

R

-1

_

| |

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

C h e r e n k o vM A C R O ( M H D )

I o n – c y c l o t r o n

N o

n –

a d

I a

b a

t I c

ICW

KINETIC ALFVEN WAVES - KAWs

Kinetic Alfvén wave (KAW) - extension of Alfvén mode in the range of high perpendicular wavenumbers.

Padé approximation for the KAW dispersion:

p - proton gyroradius.

=1

-5/3

-7/3

MHD RANGE

KAW RANGE

THEORY (Howes; Schekochihin et al., 2008-2013) P

ower

Spe

ctra

l Den

sity

SOLAR WIND TURBULENCE

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

MHD RANGE KAW RANGE?

exhibits 4 different slopes (!)

( f ~ k_perp )

Counter-propagating KAWs interact (Voitenko, 1998):

MHD VS KINETIC ALFVÉN TURBULENCE

AT MHD SCALES (MHD AWs):

Only counter-propagating MHD AWs interact (Goldreich and Sridhar, 1995)

AT KINETIC SCALES (KAWs):

Co-propagating KAWs interact (Voitenko, 1998):

ALFVÉNIC TURBULENCE SPECTRA (THEORY)

weak turbulence;

strong turbulence;

Strongly dispersive range (SDR kinetic):

weak turbulence;

strong turbulence;

Non-dispersive range (MHD):

weak turbulence;

strong turbulence;

Weakly dispersive range (WDR kinetic):

STEEPEST!

DOUBLE-KINK SPECTRAL PATTERN (Voitenko and De Keyser, 2011)

Three possible interpretations: (1) dissipative (left), or (2) dispersive (right), or (3) =(1)+(3)

ALFVÉNIC TURBULENCE IN SOLAR WIND

KAW range = WDR KAW range + SDR KAW range

MHD RANGE SDR KINETIC

WDRkinetic

( f ~ k_perp )

PUZZLE 1:

KAWs VERSUS OTHER WAVE MODES AT ION SCALES

RECENT OBSERVATIONS OF WAVE MODES

Wave-vector inclination (top) and frequency (bottom) versus wavenumber [Narita et al., 2011].

The dispersion analysis suggests whistlers/magnetosonic waves rather than kinetic Alfven waves.

FW/whistlers are not supported by these observations:

RECENT OBSERVATIONS OF WAVE MODES

Exploiting B II Bo component to discriminate KAWs vs. FW/whistlers:

Salem et al. (2012) : IDENTIFICATION OF KINETIC ALFVEN TURBULENCE IN THE SOLAR WIND

He et al. (2012) : DO KINETIC ALFVEN / ION-CYCLOTRON OR FAST-MODE/WHISTLER WAVES DOMINATE?

He et al. (2012)

Salem et al. (2012)

PUZZLE 2:

PARALLEL AGAINST PERPENDICULAR ION HEATING

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

Kinetic-scale Alfvénic turbulence covers the tails’ velocity ranges

• 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, 2013)NUMERICAL SIMULATIONS Pierrard and Voitenko, 2013)

VELOCITY-SPACE DIFFUSION OF SW PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2013)

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, 2013)

Generation of proton tails by turbulence

VzVTp Vph2

Fp

proton diffusion occurs here

VA

DIFFUSION

MHD RANGE

( f ~ k_perp ~ Vz)

SDR kineticWDRkinetic

PUZZLE 3:

REDUCED INTERMITTENCY AT ION SCALES

Alexandrova et al. (2008)

FLATNESS DECREASES AT ION SCALES, WHICH IS COUNTER-INTUITIVE

AW turbulent spectrum (solid line) and ”threshold” spectrum for non-adiabatic ion acceleration (dashed line).Cross-field non-adiabatic ion acceleration is associated with the first spectral kink, where the turbulent spectral power raises above the threshold spectrum.

acceleration

SPECTRALLY LOCALIZED SELECTIVE DISSIPATION

1. Nonlinear kinetics becomes important at scales that are still larger than the ion gyroradius

2. Alfvenic turbulence is formed by weakly/mildly dispersive KAWs3. Main dissipation mechanisms: nonlinear Landau damping and

non-adiabatic ion acceleration

This explains many phenomena revealed by the field and particle observations:

• Steepest spectra at ion scales and double-kink spectral pattern• Suprathermal ion tails and beams along MF• Proton heating across MF• spectrally localized selective dissipation removing highest

amplitudes in the vicinity of the spectral break Reduced intermittency observed by Alexandrova et al. (2008) • switch to weak turbulence and steepest spectra (were

observed by Smith et al. 2006 and Sahraoui et al. 2010)

SUMMARY