Kinetic Alfvén turbulence driven byMHD turbulent cascade

Yuriy Voitenko & Space Physics teamBelgian Institute for Space Aeronomy, Brussels, Belgium

Multifractal and turbulence workshop - 2010 (8-11 June 2009, Space Pole, Belgium)

Aurora – multifractal? (photo by Jan Curtic)

Outline

Kinetic Alfvén waves (KAWs) are the extensions of their MHD counterparts in the range of short (kinetic) cross-field wavelengths comparable to ion gyroradius or electron inertial length (Hasegawa and Chen, 1975 ).

Contrary to MHD Alfvén waves, KAWs are efficient in the field-aligned acceleration of electrons and ions and cross-field acceleration of ions.

What to see:

the alfvenicity determines the transition between MHD and kinetic domains where different cascade mechanisms dominate.

KAWs interact nonlinearly among themselves and form power-law turbulent spectra (Voitenko, 1998a,b).

KAWs interact with plasma and deposit energy in plasma species.

Spectral distributions of the KAW energy provides the possibility of a spectrally localised ion heating acceleration.

At small wave lengths cascading AWs meet natural length scales reflecting plasma microstructure:

ion gyroradius ion gyroradius ii (reflects gyromotion and ion (reflects gyromotion and ion

pressure effects); pressure effects); ion gyroradius at electron temperature ion gyroradius at electron temperature ss (reflects (reflects

electron pressure effects); electron pressure effects); ion inertial length ion inertial length ii (reflects effects due to ion (reflects effects due to ion

inertia), and inertia), and electron inertial length electron inertial length ee (reflects effects due to (reflects effects due to

electron inertia).electron inertia).

z

x

Bo

due to ion polarisation drift

Cross-field ion currents

Wave electric field Ex vary with z but not with x

MHD Alfven wave:

kinetic Alfven wave: short cross-field wavelength

Bo

Cross-field ion currents build up

ion space charges and holes

Field-aligned electron currents try to compensate ion charges

but fail (electron inertia and/or

electron pressure effects) Parallel electric field arise

decay of a pump KAW into two co-streaming KAWs (1998b)

k zV AK(k 2

)

k zV AK(

k 1)

k zV AK(k P

)

k1z kz

P

P = 1 + 2; kP = k1 + k2

k2z kPz

1

2

Час розпаду [(VA/р)(kPρi)3(Bk/B0)]

-1.

decay of a pump KAW in two counter-streaming KAWs (1998b)

kz V

AK(k2 )

k zVAK(k 1

)k zV AK(k P

)

k1z kz

P

k2z kPz

1

2

Час розпаду [(VA/р)(kPρi)2(Bk/B0)]

-1.

P = 1 + 2; kP = k1 + k2

Electron energization by KAWs:effect of parallel electric field

Ez || B0

Electron heating by KAWs: Landau damping

Vz

VA

VTi Vph1 Vph2

Fi

Fe

KAWs are here

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

Wygant et al. (2002) – evidence of parallel electron acceleration by KAWs at 4 Earth radii

Equation for cross-field ion velocity in the presence of KAWs:

In the vicinity of demagnetizing KAW phases

the solution can grow exponentially as

Specify KAW fields as:

where K is the KAW phase velocity (dispersion). In the two-fluid model

0.5A

n-a/p

(mi/qi)/(mp/qp) A-1 2A-1

A = kxp K(kx)1 + kx

2p2

________B0

B___

O+H+ He+

1 2 16

Some important properties of the super-adiabatic ion acceleration by KAWs:

•Non-resonant, frequency independent•Bulk kick-like acceleration across the magnetic fieldafter single super-critical KAW fluctuation•Depends on the parallel ion velocity•Threshold-like in wave amplitude and/or cross-field wavelength

Perpendicular velocity of an ion in a super-critical KAW wave train

Phase portrait of the ion’s orbit in the region of super-adiabatic acceleration (transition of the demagnetizing wave phase 3 pi)

t

PROTON VELOCITY DISTRIBUTIONS IN THE SOLAR WIND

(HELIOS MEASUREMENTS)

The origin of velocity space relates to

the maximum of the distribution.

Isodensity contours correspond to

fractions of 0.8, 0.6, 0.4, 0.2 and of

0.1, 0.03, 0.01, 0.003, 0.001 (dashed

contours). The vector of solar wind

flow is along VY axis, the vector of

magnetic field is along dash line.

KAW turbulence (Voitenko, 1998): (i) dual perpendicular cascades;(ii) power law spectra k

-p , 2<p<4; (iii) excitation of the counter-streaming KAWs - imbalanced turbulence, k

-2 (p=2);

Hamrin et al. (2002) estimated spectral slope of the BBELF turbulence observed by Freja as p=-2,5

Spectra steepened with higher k: intermittent dissipation range

Approximate condition for non-adiabatic ion acceleration

acceleration occurs around spectral break

Constant Nb depends on the KAW amplitudes at the spectral break

Condition for non-adiabatic ion acceleration by power-law spectrum:

Let it be satisfied for ions with initial at some , wherethey undergo initial cross-field acceleration.Then magnetic mirror force come into play and accelerate these ions upward along Bo, increasing upward (negative) . Increased , in turn makes more turbulent energy accessible for ions (the condition is satisfied at lower and higher perturbation amplitudes) -> positive feed-back loop

Effect of : surfing acceleration of ions along Bo

spreading of the acceleration

KAW

k

||

k i -1

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 )

N o n a d i a b a t

c i

• transition MHD->KAW at low k_perp ;• parallel electron/ion heating;• importance of KAW turbulent spectra;• cross-field ion heating by KAW turbulence;

Conclusions