Polar lights indicate energetic electrons accelerated at higher altitudes. These electrons excite atoms that emits lights of different colours.
Alfvén Waves and Space Weather
Alfvén waves and space weather Yuriy Voitenko Space Physics Dept, Belgian Institute for Space Aeronomy, (Brussels, Belgium) 15 August 2009 4 th Kyiv Summer School
<ul><li>Motivation 1. Fundamental plasma physics: Alfvén waves </li></ul><ul><li>Motivation 2. Space weather: energy conversion in space plasmas </li></ul><ul><li>Retrospect: Alfvén wave and its modifications: ion-cyclotron wave, kinetic Alfvén wave, and ion-cyclotron kinetic Alfvén wave </li></ul><ul><li>Theory vs. observations </li></ul><ul><li>Open issues </li></ul>outline
<ul><li>Most matter is in the plasma state (ionized gas) </li></ul><ul><li>Examples: stars, interstellar and interplanetary medium, planetary magnetospheres.The Sun: plasma ball. Earth’s magnetosphere: magnetic plasma bottle </li></ul><ul><li>Magnetic fields (MFs) penetrate plasmas and reduce the ability of plasma to move across the magnetic field </li></ul><ul><li>Most important things introduced by MFs: magnetic plasma structuring, energy accumulation/release, and magnetic plasma waves </li></ul>
Alfvén waves <ul><li>- background magnetic field </li></ul><ul><li>z - axis along </li></ul><ul><li>- 2D plane </li></ul><ul><li>- Alfven velocity </li></ul><ul><li>- number density (number of electrons = number of ions) </li></ul><ul><li>- ion mass </li></ul>definitions:
Why plasma follows local magnetic field lines? Ion gyro-radius: Cyclotron frequency: Lorentz force traps plasma particle bending their trajectories around particular magnetic field lines by cyclotron gyration:
Hannes Alfvén MHD plasma model make AW highly degenerated in the plane B 0 . Short wavelengths -> ultraviolet singularity 1970 Nobel Laureate in Physics for fundamental work and discoveries in magneto-hydrodynamics with fruitful applications in different parts of plasma physics Harmonic solution: -> dispersion relation: -> relation between temporal and spatial wave scales:
<ul><li>BUT: </li></ul><ul><li>at small wave length we meet natural length scales reflecting plasma microstructure. The most important of them are: </li></ul><ul><li>thermal ion gyroradius i (reflects gyromotion and ion pressure effects); </li></ul><ul><li>thermal ion gyroradius at electron temperature s (reflects electron pressure effects); </li></ul><ul><li>ion inertial length i (reflects effects due to ion inertia), and </li></ul><ul><li>electron inertial length e (reflects effects due to electron inertia). </li></ul>
Thermal ion gyro-radius: i = V Ti / i i Wave electric field Effective (gyro-averaged) electric field is smaller than the field in the centre of the particle orbit:
z x Bo ion polarisation drift Cross-field ion currents due to Wave electric field Ex vary with z but not with x MHD Alfven wave:
Field-aligned electron currents compensate ion charges kinetic Alfven wave: effect of short cross-field wavelength Bo Cross-field ion currents build up ion charges
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- i effects has been developed by A. Hasegawa and co-authors: Hasegawa and Chen (1976); Hasegawa and Mima (1979); Hasegawa and Uberoi (1982); C hen and Hasegawa ( 1994 )
2000 Maxwell Prize for … Alfvén wave propagation in laboratory and space plasmas… Akira Hasegawa Kinetic Alfvén wave (KAW) - extension of Alfven mode in the range of small perpendicular wavelength KAW dispersion
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.
Conic ion distribution in aurora observed by FAST (Lynch et al. 2002)
<ul><ul><li>FAST observations : ion conics are associated with broad-band low-frequency (BBELF) and ion-cyclotron (EMIC) waves ( Lund et al., 2000 ) </li></ul></ul><ul><ul><li>Identification of BBELF waves as KAWs ( Stasiewicz et al., 2000 ) </li></ul></ul><ul><ul><li>Freja observations : KAWs activity accompanied by the field-aligned electron acceleration and cross-field ion heating ( Andersson et al., 2002 ) </li></ul></ul><ul><ul><li>Polar observations : KAWs and plasma energization at ~ 4 R E ( Wygant et al., 2002 ) </li></ul></ul>Auroral example
Alfven Wave Poynting Flux: Powering the Aurora (Keiling et al. 2002,2003; Wygant et al. 2002)
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: In the vicinity of demagnetizing KAW phases the solution is Specify KAW fields as:
Perpendicular velocity of an ion in a KAW wave train with a super-critical cross-field wave vector Phase portrait of the ion’s orbit in the region of super-adiabatic acceleration (transition of the demagnetizing wave phase 3 pi) t
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. HERE CORONAL EXAMPLES
(Esser et al., 1999) Cross-field temperature of ion species in the solar corona ( SOHO observations )
SOLAR ATMOSPHERE: PROPAGATION AND DISSIPATION OF ALFVÉN WAVES Cranmer (2004)
Photospheric/chromospheric motions can drive the observed AW flux
<ul><li>Strong flux of MHD Alfv én waves propagates from the Sun along open field lines in the region of increasing Alfv én velocity. </li></ul><ul><li>At 1.5 – 4 solar radii MHD Alfv én waves partially dissipate transforming into kinetic Alfv én waves – KAWs, which energize plasma: </li></ul><ul><li>accelerate ions a cross the magnetic field by Ex </li></ul><ul><li>accelerate electrons along the magnetic field by Ez </li></ul>
(Voitenko and Goossens: Phys. Rev. Let., 94, 135003, 2005) Nonlinear excitation of KAWs by MHD Alfven waves k z V A K (k 2 ) k z V A K (k 1 ) k z V A k 1z k z P P = 1 + 2 k P = k 1 + k 2 k 2z k Pz 1 2 K (k ) < 1 if m = m e /m p < 1
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. Decay of fast waves and coronal heating events
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. ENERGY RELEASE IN THE SOLAR CORONA
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.
The linear Vlasov response is used to calculate current and charge perturbations in
The KAW phase velocity and the growth/damping rate in a kinetic regime: where
<ul><li>Instability range in V k -k y plane </li></ul>
<ul><li>Instability range in (kz-ky) plane </li></ul>
Excitation of KAWs by non-uniform currents V z V A V Ti V ph1 V ph2 F i F e KAWs are excited here and here
<ul><li>CONCLUSIONS-I (shear-current-driven KAWs) </li></ul><ul><li>In the presence of shear currents, the phase velocity of KAWs decreases drastically (well below Alfven velocity) </li></ul><ul><li>The shear-current-driven instability of KAWs can be driven by VERY weak currents </li></ul><ul><li>The KAW instability produces an anomalous resistivity strong enough to release energy for quasi-steady coronal heating and for impulsive coronal events </li></ul>
Kinetic Alfven model of solar flares (Voitenko, 1998): (1) Sun ward reconnection outflow creates neutralized beams of 0.1-1 MeV protons. (2) Partial conversion of beam energy into flux of kinetic Alfvén waves. (3) Plasma heating and particles acceleration by KAWs. (4) Loop top HXR source. 1 2 3 4 3
13 January 1992 (Masuda) flare <ul><li>Model input: </li></ul><ul><li>loop half-length L = 2×10 9 cm; </li></ul><ul><li>n umber density in l oop legs n 0 = 2.5×10 9 cm -3 ; </li></ul><ul><li>loop top n 0 = 10 10 cm -3 ; proton beam n b = 10 9 cm -3 ; </li></ul><ul><li>magnetic field B 0 = 57 G; </li></ul><ul><li>initial temperature T e = 6×10 6 K; </li></ul><ul><li>Model output: </li></ul><ul><li>KAW instability growth time = -1 = 3 ×10 -5 s; </li></ul><ul><li>relaxation distance < 10 5 cm; </li></ul><ul><li>final temperature T e = 7×10 7 K; </li></ul><ul><li>spreading velocity >= 4 ×10 8 cm/s; </li></ul><ul><li>flux of escaping (> 20 KeV) electrons 10 17 el. cm -2 s -1 b </li></ul>
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.
PROTON VELOCITY DISTRIBUTIONS IN THE SOLAR WIND AT r ~ 0.3 AU, HELIOS MEASUREMENTS (after Marsch et al. , 1982 ) proton beams anisotropic core protons Main features: Tu et al. (2002, 2003) suggested that the proton beams could be shaped by quasi-linear diffusion caused by cyclotron waves.
<ul><li> 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). </li></ul><ul><li>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: </li></ul><ul><li>kinetic Alfvén wave flux is generated in the solar wind linearly (by kinematical conversion of MHD Alfvén waves), or nonlinearly (by MHD turbulent cascade); </li></ul><ul><li>due to increasing wave dispersion, the KAWs’ propagation velocity increases; </li></ul><ul><li>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 </li></ul>