Kinetic Alfven waves in space plasmas by Yuriy Voitenko

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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)
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Aurora multifractal?
(photo by Jan Curtic)
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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.
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• At small wave lengths cascading AWs meet natural
  length scales reflecting plasma microstructure
• ion gyroradius ?i (reflects gyromotion and ion
  pressure effects)
• ion gyroradius at electron temperature ?s
  (reflects electron pressure effects)
• ion inertial length ?i (reflects effects due to
  ion inertia), and
• electron inertial length ?e (reflects effects
  due to electron inertia).

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MHD Alfven wave
z
Bo
Cross-field ion currents
due to ion polarisation drift
Wave electric field Ex vary with z but not with x
x
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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
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decay of a pump KAW into two co-streaming KAWs
(1998b)
kzVAK(k1?)
?
?P ?1 ?2 kP k1 k2
kzVAK(kP?)
?P
kzVAK(k2?)
?1
?2
k1z
k2z
kPz
kz
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decay of a pump KAW in two counter-streaming KAWs
(1998b)
?P ?1 ?2 kP k1 k2
?
kzVAK(kP?)
kzVAK(k1?)
?P
?1
kzVAK(k2?)
?2
k2z
k1z
kPz
kz
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Electron energization by KAWs effect of parallel
electric field Ez B0
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Electron heating by KAWs Landau damping
Fi
Fe
Vz
VTi
Vph1
Vph2
VA
KAWs are here
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Super-adiabatic cross-field ion acceleration
Resonant plasma heating and particle acceleration
Demagnetization of ion motion
Kinetic wave-particle interaction
Kinetic Alfvén waves
Kinetic instabilities
Parametric decay
Turbulent cascade
Phase mixing
MHD waves
Unstable PVDs
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Wygant et al. (2002) evidence of parallel
electron acceleration by KAWs at 4 Earth radii
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Equation for cross-field ion velocity in the
presence of KAWs
Specify KAW fields as
In the vicinity of demagnetizing KAW phases
the solution can grow exponentially as
where K is the KAW phase velocity (dispersion).
In the two-fluid model
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?n-a/?p
O
H
He
0.5A
1
2
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(mi/qi)/(mp/qp)
A-1
2A-1
1 kx2?p2
B
___
________
A kx?p
K(kx)
B0
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• Some important properties of the super-adiabatic
• ion acceleration by KAWs
• Non-resonant, frequency independent
• Bulk kick-like acceleration across the magnetic
  field
• after single super-critical KAW fluctuation
• Depends on the parallel ion velocity
• Threshold-like in wave amplitude and/or
  cross-field wavelength

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Perpendicular velocity of an ion in a
super-critical KAW wave train
t
Phase portrait of the ions orbit in the region
of super-adiabatic acceleration (transition of
the demagnetizing wave phase 3 pi)
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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.
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KAW turbulence (Voitenko, 1998) (i) dual
perpendicular cascades (ii) power law spectra ?
k?-p , 2ltplt4 (iii) excitation of the
counter-streaming KAWs - imbalanced
turbulence, ? k?-2 (p2)
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Hamrin et al. (2002) estimated spectral slope of
the BBELF turbulence observed by Freja as p-2,5
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Spectra steepened with higher k intermittent
dissipation range
acceleration occurs around spectral break
Approximate condition for non-adiabatic ion
acceleration
Constant Nb depends on the KAW amplitudes at the
spectral break
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Effect of surfing acceleration of ions
along Bo
Condition for non-adiabatic ion acceleration by
power-law spectrum
Let it be satisfied for ions with initial
at some , where they 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) -gt positive feed-back loop
spreading of the acceleration
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k



_

-
1
I o n
-
c y c l o t r o n

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

L
a
a
d
n
i
a
d
b
a
KAW
a
u

M A C R O ( M H D )
t
i
c






-
1

k
r


-
1
R

ç

i


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Conclusions

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