511th WE-Heraeus-Seminar

From the Heliosphere into the Sun– Sailing against the Wind –

Collection of presentationsEdited by Hardi Peter (peter@mps.mpg.de)

Physikzentrum Bad Honnef, GermanyJanuary 31 – February 3, 2012

http://www.mps.mpg.de/meetings/heliocorona/

Linking turbulence and velocity distributions in the solar wind

Yuriy Voitenko, Viviane Pierrard, and Johan De Keyser

Belgian Institute for Space Aeronomy, Brussels, Belgium

511th WE-Heraeus-Seminar (1-3 February 2012, Bad Honnef, Germany)

transition from MHD to kinetic range:

S� what scales?

S� spectral effects?

S� dissipative effects?

{growing k_perp} MHD Alfvén waves kinetic Alfvén waves

OUTLINE

{perp. cascade} MHD Alfvén turbulence kinetic Alfvén turbulence

0.1 1 Role of weakly dispersive range was not addressed S� � does it exist?

At small wave lengths cascading AWs meet natural length scales reflecting plasma microstructure: �� ion gyroradius �i

�� ion gyroradius at electron temperature �s

�� ion inertial length �i

�� electron inertial length �e

EVIDENCE OF KAWs AT PROTON KINETIC SCALES Exploiting B II Bo component:

Salem et al. (2012) : IDENTIFICATION OF KINETIC ALFV´EN WAVE TURBULENCE IN THE SOLAR WIND

He, Tu, Marsch, and Yao (2012) : DO OBLIQUE ALFV´EN/ION-CYCLOTRON OR FAST-MODE/WHISTLER WAVES DOMINATE THE DISSIPATION OF SOLAR WIND TURBULENCE NEAR THE PROTON INERTIAL LENGTH?

He, Tu, Marsch, and Yao (2012)

Salem et al. (2012)

He et al. (2011,2012); Podesta & Gary (2011):

ÂT THE PROTON KINETIC SCALES OBLIQUE ALFVEN (70%) AND ION-CYCLOTRON (30%) WAVES ARE DOMINANT

NONLINEAR KAW INTERACTION: KINETIC THEORY

k1z kz

��

��P

k2z kPz

��1

��2

��P = ��1 + ��2; kP = k1 + k2

Nonlinear interaction rate:

Interaction among counter-propagating KAWs (Voitenko, 1998)

Interaction among co-propagating KAWs (Voitenko, 1998)

k1z kz

��

��P

��P = ��1 + ��2; kP = k1 + k2

k2z kPz

��1 ��2

Nonlinear interaction rate:

MHD / KINETIC TRANSITION SCALE

comparing MHD AW nonlinear rates (Goldreich and Sridhar, 1995; Boldyrev 2005, Gogoberidze 2007) with two KAW nonlinear rates (Voitenko, 1998a,b), we arrive to the transition wavenumbers:

To counter-propagating KAWs:

To co-propagating KAWs:

N.B.:

ALFVEN TURBULENCE SPECTRA

� weak turbulence;

� strong turbulence;

Strongly dispersive range (kinetic):

� weak turbulence;

� strong turbulence;

Non-dispersive range (MHD):

� weak turbulence;

� strong turbulence;

Weakly dispersive range (kinetic):

DOUBLE-KINK SPECTRAL PATTERN

Example double-kink spectrum (Chen et al., 2010):

non-dissipative interpretation

1��

DOUBLE-KINK SPECTRAL PATTERN

Two interpretations: dispersive (left) and dissipative (right)

Sahraoui et al. (2010) suggested proton Landau damping around 1 Hz. Then the problem: dissipation with that slope consumes almost all flux.

Double-kink spectral pattern (Sahraoui et al., 2010):

Vz Vk1 Vk2

Fs

KAW velocities are here�

LANDAU DAMPING IS NOT MAXWELLIAN !

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

KAW velocities are here�

S� We use the kinetic Fokker-Planck equation with diffusion terms due to Coulomb collisions and KAWs

S� Put boundary at 14 Rs (above the Alfven point) S� Use a model Alfvenic spectrum as observed at

>0.3 AU and project it back to 14 Rs following ~ 1/r^2 radial profile for the turbulence amplitude

S� Plug the obtained spectrum in the diffusion term for wave-particle Cherenkov interactions

S� Solve numerically using spectral method S� Observe tails in the obtained proton VDFs

PARALLEL PROTON VELOCITY-SPACE DIFFUSION: KINETIC SIMULATIONS

KAW velocities are in this range

PARALLEL PROTON VELOCITY-SPACE DIFFUSION: KINETIC SIMULATIONS

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 kinetic Alfven waves

Proton velocity distributions with tails are reproduced not far from the boundary

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

KAW velocities are here�

PARALLEL PROTON ACCELERATION BY KAWS: NON-LINEAR CHERENKOV RESONANCE

MOTIVATION:

PARALLEL PROTON ACCELERATION BY KAWS: NON-LINEAR CHERENKOV RESONANCE

proton trajectories in z-Vz plane

KAW pulse�

PARALLEL PROTON ACCELERATION BY KAWS: NON-LINEAR CHERENKOV RESONANCE

Reflected protons set up a beam

KAW pulse�

Free protons

Number density of reflected protons as function of the relative KAW amplitude B/B�. The proton beta �_{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.

�_{p��} = 0.49

0.36

0.25

0.16

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

AW spectrum and localization of nonlinear Landau damping. Coincides with reduced intermittency?

Nonl. L.D.

SPECTRAL LOCALIZATION OF DISSIPATION

Alexandrova et al. (2008)

weakly dispersive KAW range: S� transition MHD -> KAW turbulence at <<1 S� steepest kinetic spectra S� universal double-kink spectral form; S� non-adiabatic perpendicular ion heating, and S� parallel proton acceleration at nonlinear Cherenkov res: S� � selective dissipation removing highest amplitudes; S� � spectrally localized (near first kink); S� � � local reduction of turbulence strengt and

intermittency (as observed by Alexandrova et al. 2008); S� � � � switch to weak turbulence and steepest

spectra (as observed by Smith et al. 2006).

SUMMARY

KAW

k

�� ��

||

k i - 1

�� i - 1

R ç

- 1

_

| |

a

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

Where to go from? S� From MHD turbulence: S� � Go to small scales (parallel and/or perpendicular) and look

there at kinetic dissipation versus nonlinear dissipation versus dispersive transition,

S� � � how MHD-to-KAW transition works? S� � � how MHD-to-ICAW transition works? S� � � or MHD-to-ICKAW transition - ion-cyclotron kinetic

Alfven waves? S� � Look at particles velocity distributions and spatial

distributions, S� � � associate with particular fluctuations. S� Inside MHD turbulence: Nature of 2D and slab components?

Are there respective cascades? Are they connected? Sunward versus anti-sunward

S� � � spectral break – scale dependent, amplitude dependent? – see observations by Markovskii et al. (2008)