AACIMP 2009 Summer School lecture by Yuriy Voitenko.

1. Alfvén waves and space weather
Yuriy Voitenko
Space Physics Dept, Belgian Institute for Space
Aeronomy, (Brussels, Belgium)
15 August 2009 4th Kyiv Summer School

2. outline
 Motivation 1. Fundamental plasma physics: Alfvén waves
 Motivation 2. Space weather: energy conversion in space
plasmas
 Retrospect: Alfvén wave and its modifications: ion-cyclotron wave,
kinetic Alfvén wave, and ion-cyclotron kinetic Alfvén wave
 Theory vs. observations
 Open issues

3. • Most matter is in the plasma state (ionized gas)
• Examples: stars, interstellar and interplanetary
medium, planetary magnetospheres.The Sun: plasma
ball. Earth’s magnetosphere: magnetic plasma bottle
• Magnetic fields (MFs) penetrate plasmas and reduce
the ability of plasma to move across the magnetic field
• Most important things introduced by MFs: magnetic
plasma structuring, energy accumulation/release, and
magnetic plasma waves

5. Solar actrivity -> space weather

7. Сонячна
активність =
магнітна
активність

9. Alfvén waves
definitions:
• B 0 - background magnetic field
• z - axis along B 0

• r⊥ - 2D plane ⊥ B 0
• V A = B0 / 4π n0mi - Alfven velocity
• n0 - number density (number of electrons =
number of ions)
• mi - ion mass

10. Why plasma follows local magnetic field lines?
Lorentz force traps plasma particle bending their trajectories
around particular magnetic field lines by cyclotron gyration:

B0 d V⊥ e 
F = m
⊥ i= eE + V × B
⊥ ⊥ 0
dt c
d 2V⊥
= − Ω i2V⊥
dt 2
F
Cyclotron frequency:
F Ωi=
eB0
V mi c
V Ion gyro-radius: ρ = V / Ω i

11. Hannes Alfvén
1970 Nobel Laureate in Physics
for fundamental work and discoveries in magneto-
hydrodynamics with fruitful applications in different
parts of plasma physics

( ∂ − V ∂ ) ⋅ B⊥ ( z; r⊥ ; t ) = 0
2
t
2 2
A z
 
Harmonic solution: B⊥ ( z; r⊥ ; t ) = Bk ( r⊥ ) sin ( ω t − k z z )
-> dispersion relation: ω = k z VA
-> relation between temporal
and spatial wave scales: τ = λ z / VA
MHD plasma model make AW highly degenerated in the
plane ⊥ B0. Short ⊥ wavelengths -> ultraviolet singularity

13. Alfvén waves – transversal ‘magneto-inertial’ waves

14. BUT:
at small wave length we meet natural length scales
reflecting plasma microstructure. The most important
of them are:
 thermal ion gyroradius ρi (reflects gyromotion and
ion pressure effects);
 thermal ion gyroradius at electron temperature ρs
(reflects electron pressure effects);
 ion inertial length δi (reflects effects due to ion
inertia), and
 electron inertial length δe (reflects effects due to
electron inertia).

15. Wave electric field
Thermal ion gyro-radius:
E (x ) ρi = VTi/Ωi
ρi
x
Effective (gyro-averaged) electric field is smaller
than the field in the centre of the particle orbit:
Ei ( x ) = Λ 0 ( k ρ ) × E ( x )
2
⊥ i
2
Λ 0 ( k ⊥ ρ i ) = I 0 ( k ⊥ ρ i ) exp( − k ⊥ ρ i )
2 2 2 2 2 2

16. z MHD Alfven wave:
Bo
Cross-field ion currents due to
ion polarisation drift
Wave electric field Ex vary with z but not with x
x

17. kinetic Alfven wave: effect of short cross-field wavelength
Bo
Cross-field
ion currents
build up
ion charges
Field-aligned
electron currents
compensate
ion charges

18. Kinetic Alfvén wave: retrospect
The micro length scales restrict applicability of ideal MHD.
First attempts to extend the Alfvén wave mode in the
domain of short perpendicular wavelengths:
Fejer and Kan (1969); Stefant (1970).
Later on, a kinetic theory accounting for some linear and
nonlinear properties of Alfvén waves due to finite- ρi effects
has been developed by A. Hasegawa and co-authors:
Hasegawa and Chen (1976); Hasegawa and Mima (1979);
Hasegawa and Uberoi (1982); Chen and Hasegawa (1994)

19. Akira Hasegawa
2000 Maxwell Prize for
… Alfvén wave propagation
in laboratory and space plasmas…
Kinetic Alfvén wave (KAW) -
extension of Alfven mode in the range of small
perpendicular wavelength

[ t A z
2 2
⊥ ]
∂ − V ∂ ⋅ K (∂ ) ⋅ B⊥ ( z; r⊥ ; t ) = 0
2 2 2
KAW dispersion
ω = k z VA ⋅ K ( k ⊥ )

23. The last 10 years have seen a rapid accumulation of
evidence:
Alfvén waves in their kinetic form – KAWs – are
responsible for plasma energization in various ‘active’
regions of space plasmas.

24. Aurora from ground (photo by Jan Curtic)

25. W ygant et al. 2002

26. Conic ion distribution in aurora observed by F A S T (L ynch et al. 2002

27. Auroral example
– FAST observations: ion conics are associated with
broad-band low-frequency (BBELF) and ion-cyclotron
(EMIC) waves (Lund et al., 2000)
– Identification of BBELF waves as KAWs (Stasiewicz et
al., 2000)
– Freja observations: KAWs activity accompanied by the
field-aligned electron acceleration and cross-field ion
heating (Andersson et al., 2002)
– Polar observations: KAWs and plasma energization at
~ 4 RE (Wygant et al., 2002)

28. A lfven W ave P oynting F lux: P owering the
A urora
(K eiling et al. 2002,2003; W ygant et al. 2002)

29. Cross-field ion energization by KAWs
(Voitenko and Goossens: ApJ, 605, L149–L152, 2004)
Equation for cross-field ion velocity in the presence of KAWs:
Specify KAW fields as:
In the vicinity of demagnetizing KAW phases
the solution is

30. Perpendicular velocity of an ion in a KAW wave train
with a super-critical cross-field wave vector
t
Phase portrait of the ion’s orbit in the region of super-adiabatic
acceleration (transition of the demagnetizing wave phase 3 pi)

31. HERE
CORONAL
EXAMPLES
At 1.5-4 solar radii there is an additional deposition of energy that:
(i) accelerates the high-speed solar wind; (ii) increases the proton & electron
temperatures measured in interplanetary space; (iii) produces the strong
preferential heating of heavy ions seen there with UV spectroscopy.

32. Cross-field temperature of ion species in the solar corona
(SOHO observations)
(Esser et al., 1999)

33. SOLAR ATMOSPHERE:
PROPAGATION AND DISSIPATION OF ALFVÉN WAVES
Cranmer (2004)

34. Photospheric/chromospheric motions can drive the observed AW flux

36.  Strong flux of MHD Alfvén waves propagates from
the Sun along open field lines in the region of
increasing Alfvén velocity.
 At 1.5 – 4 solar radii MHD Alfvén waves partially
dissipate transforming into kinetic Alfvén waves –
KAWs, which energize plasma:
 accelerate ions across the magnetic field by Ex
 accelerate electrons along the magnetic field by
Ez

37. k ||
-1_ m
ic
δi Ion-cyclotron ro
(k
in
et
ic
)
L
a
n
M d
AC
R a
O u
(M
H
D
)
| | k⊥
R-1
 ρ -1
i

38. Nonlinear excitation of KAWs by MHD Alfven waves
(Voitenko and Goossens: Phys. Rev. Let., 94, 135003, 2005)
ωP = ω1 + ω2
k P = k1 + k2
ω VA )
k z
k 1⊥
K(
ωP k zV
A
ω1
kV
z
A K(
k
2⊥ )
ω2
k2z kPz k1z kz
K(k⊥) < 1 if βm = βme/mp < 1

39. k ||
-1_ m
ic
δi Ion-cyclotron ro
(k
in
et
ic
)
L
a
n
M d
AC
R a
O u
(M
H
D
)
|
-1
| k⊥
R ρ -1
i

40. Resonant excitation and damping

41. Decay of fast waves and coronal heating events
The transient brightenings, observed in the low corona by
Yohkoh and SOHO (blinkers, nano- and microflares),
attracts a growing interest (Shimizu et al., 1992; Innes et
al., 1997; Berger et al., 1999; Roussev et al., 2001;
Berghmans et al., 2001). Magnetic reconnection in
current sheets may produce reconnection outflows and
consequent plasma heating, line broadening, etc.
On the other hand, a considerable fraction of the energy
can be released by the dynamical evolution of the current
sheets themselves. So, Fushiki and Sakai (1994) have
shown that the fast waves can be emitted in the solar
atmosphere by a pinching current sheet.

44. k ||
-1_ I on- cy cl otr om
n
δi ic
ICAW ro ICKA
(k W
in
S et
ic
t )
o L
c a
h KA
n
M a W d
AC
R s a
O t u
(M
H i
D
) c
| | k⊥
R-1
 ρ -1
i

45. ENERGY RELEASE IN THE SOLAR CORONA
Hinode XRT
2006 Nov 13 04:53:14
Numerous observations (Yohkoh, SOHO, Hinode) suggest that the solar
transients (flares, microflares, blinkers, etc.) are produced by magnetic
reconnection. Magnetic reconnection occurs via current dissipation in magnetic
interfaces (current sheets) between interacting magnetic fluxes.

47. ENERGY RELEASE IN THE SOLAR CORONA
Earth size

48. Classical resistivity require unphysically thin current sheets and cannot explain
the observed rates of energy release.
Q1: what is the nature of the currents’ dissipation?
Q2: what is the role of the currents’ inhomogeneity?
Q3: at what length scales they dissipate?
the shear-current driven instability of kinetic Alfven waves is the most likely
mechanism for triggering anomalous resistivity and hence initializing solar
transients. The scaling relations for reconnection rates and widths of magnetic
interfaces are derived.

50. The linear Vlasov response
is used to calculate current and charge perturbations in

52. The KAW phase velocity and the growth/damping rate in a kinetic regime:
where

53. • Instability range in Vk-ky plane

54. • Instability range in (kz-ky) plane

55. Excitation of KAWs by non-uniform currents
Fi
Fe
VTi Vph1 Vph2 VA Vz
KAWs are excited here and here

58. CONCLUSIONS-I (shear-current-driven KAWs)
 In the presence of shear currents, the phase
velocity of KAWs decreases drastically (well
below Alfven velocity)
 The shear-current-driven instability of KAWs can
be driven by VERY weak currents
 The KAW instability produces an anomalous
resistivity strong enough to release energy for
quasi-steady coronal heating and for impulsive
coronal events

59. magnetic reconnection and solar flares

60. Kinetic Alfven model Plasma Inflow
of solar flares
(Voitenko, 1998):
1
(1) Sunward reconnection 2
outflow creates neutralized
beams of 0.1-1 MeV 4
KAW Flux 3
protons. and Plasma
(2) Partial conversion of Heating 3
beam
energy into flux of kinetic
Alfvén waves.
(3) Plasma heating and
particles
acceleration by KAWs.
(4) Loop top HXR source.

61. 13 January 1992 (Masuda)
flare
• Model input:
loop half-length L = 2×109 cm;
number density in loop legs n0 = 2.5×109 cm-3;
loop top n0 = 1010 cm-3; proton beam nb = 109 cm-3;
magnetic field B0 = 57 G;
initial temperature Te = 6×106 K;
• Model output:
KAW instability growth time τ = γ -1 = 3×10-5 s;
relaxation distance < 105 cm;
final temperature Te = 7×107 K;
spreading velocity >= 4×108 cm/s;
17 -2 -1

62. Tsuneta (1997):

63. Tsuneta, 1997

64. Geomagnetic substorm
model (ANGELOPOULOS
ET AL., 2002):
(1) Earthward energy flux
couples to localized
fluctuations.
(2) Partial dissipation via
kinetic Alfvén wave
interaction with electrons.
(3) Further dissipation via
inertial Alfvén wave
interaction with electrons.
(4) Ion heating by electrons,
and eventual upflow.

65. Solar wind

66. PROTON VELOCITY
DISTRIBUTIONS
IN THE SOLAR WIND AT r ~ 0.3 AU,
HELIOS MEASUREMENTS
(after Marsch et al., 1982)
Main features:
anisotropic core protons proton beams
Tu et al. (2002, 2003) suggested that the
proton beams could be shaped by quasi-
linear diffusion caused by cyclotron waves.

67. The last 10 years have seen a rapid accumulation of evidence suggesting
that kinetic Alfvén waves – KAWs – are very important for plasma
energization observed in various space plasmas (solar wind, planetary
magnetospheres and ionospheres).
In view of KAW activity observed in solar wind (e.g. Leamon et al., 1999;
Bale et al., 2005; Podesta, 2009) we propose the following scenario for the
proton beam formation:
(1) kinetic Alfvén wave flux is generated in the solar wind linearly (by
kinematical conversion of MHD Alfvén waves), or nonlinearly (by MHD
turbulent cascade);
(2) due to increasing wave dispersion, the KAWs’ propagation velocity
increases;
(3) the protons trapped by the parallel electric potential of KAWs are being
accelerated anti-sunward by the accelerated KAW propagation, forming
supra-thermal proton beams at ~ 1.5VA

68. COLLISIONLESS
TRAPPING CONDITION:

69. Creation of proton beams by KAWs
Fp
ACCELERATION
VTp Vph1 Vph2 Vz
KAWs trap protons here and release/maintain here

70. Super-adiabatic cross-field Resonant plasma heating and
ion acceleration particle acceleration
Demagnetization of ion motion Kinetic wave-particle interaction
c
i
t
e
n
K
n
é
v
f
l
A
s
e
v
a
w
Phase Turbulent Kinetic Parametric
mixing cascade instabilities decay
H
M
D Unstable
a
w
e
v
s PVDs

71. Thank you!

72. references

73. references (continuation)

74. references (continuation)

75. references (continuation)

76. references (continuation)