Global MHD Eigenmodes of the Outer Magnetosphere

Transcription

1 Global MHD Eigenmodes of the Outer Magnetosphere Andrew Wright UNIVERSITY OF ST ANDREWS

2 Magnetospheric Structure: Cavities and Waveguides The Earth s magnetosphere is structured by magnetic fields and plasmas. It is highly nonuniform. Closed dipolar field lines Open field lines Solar wind field lines Magnetic tail Nonuniformities Trap waves Couple waves [Figure from NASA GSFC.]

3 Slow Flow Moderate Flow Reflecting Boundary Cavity and Waveguide Mode Excitation Fast Flow Trapped Leaky Modes Trapped Over Reflected Modes Dawn Flank Dusk Flank Over Reflected Modes Magnetosheath Plasma Flow Fast Mode Ray Trajectory Magnetopause Over Reflecting Boundary Impulsive excitation KH surface mode always unstable Behaviour determined by U sheath flow speed c s sheath sound speed V A magnetospheric Alfvén speed U < V A c s : leaky modes. V A c s < U < V A + c s : modes become trapped U > V A + c s : modes become KH unstable (over-reflection) (equatorial plane view)

4 Fast Alfvén Wave Coupling in a Flank Waveguide 1 V 2 A 2 ξ x t 2 + k2 zξ x = 1 B b z x ; 1 2 ξ y VA 2 t 2 + k2 zξ y = 1 B ( b z y ; b ξx z = B x + ξ ) y y Contours of energy density. (a) t = 20, (b) t = 40 V A (x) traps fast energy near the x = 1 (outer) boundary Alfvén resonances grow where ω A (x) matches a fast frequency Mode coupling persists in a dipolar field geometry and for arbitrary driving

5 Theory of Waves in the Magnetotail I z lobe PSBL Z Tail Lobe z=0 plasma sheet low V A To Earth PSBL x=0 PSBL lobe x 0 Plasma Sheet V A PSBL Reconnection releases energy as tail reconfigures Tail reverberates with fast waveguide modes Fast modes couple to Alfvén waves on open field lines Similar to waves in a solar flux tube Tail Lobe

6 Theory of Waves in the Magnetotail II z=1 ray 1 ray 2 ray 3 z r z t z=0 Fast modes channelled along plasma sheet : ω 2 /V 2 A(z t ) = k 2 + k2 y V A z r initial source V g z t A specific fast k wavepacket travels with speed V g (k ) Just beyond the ray turning point (z t ) the fast mode couples to the Alfven mode, z r : ω 2 /VA(z 2 r ) = k 2 The Alfven wave propagates with speed V A (z r )

7 Phasemixing in the Magnetotail x f (z) x A (z) z=0 x=0 Continuum of k produces Alfvén waves in the Lobe and PSBL ω A (z) and k (z) are predictable from theory The Alfvén waves phasemix as they propagate Large currents develop in the PSBL where phasemixing is strongest

8 Magnetotail Simulations Fast mode (top panel) and Alfvén (bottom panel) energy densities Fast mode guided along plasma sheet Alfvén waves are excited

9 Field-Aligned Currents and Phase-Mixing Alfvén wave amplitude depends upon azimuthal wavenumber Alfvén waves largest in the Boundary Layer Phase-mixing leads to large currents: b y exp i[k A (z)x ω A (z)t] j ( b y / z)/µ o, and requires electron acceleration, giving auroral emissions

10 Optical auroral emissions: CANOPUS LATITUDE (EDFL) MPA (Altitude at 110 km) UT/ nm 9.4 kr 0.2 kr TIME (MINUTE) Strongest emissions from PSBL field lines Modulated by wave period Slope = V ph of Alfven waves Electron acceleration is an integral part of the Alfven wave Electron energization not described in single fluid MHD

11 Electron Energization and Wave Damping Nonlinear two-fluid energy conservation: ( 1 t 2 nm ev 2 e + 1 ) ( 2 nm iv 2 i + b µ o 2 nm ev 2 e v e + E b ) µ o Finite m e kinetic energy flux into ionosphere Chaston (GRL, 2002) and Vaivads (GRL, 2003): Poynting and electron energy flux similar Electron energization can be a significant drain on Alfven wave energy = 0

12 Magnetotail Processes 7 6 v e j Lobe PSBL 1 (1) Reconnection causes tail to reverberate and reconfigure (2) Fast modes excite Alfvén waves (3) Alfven waves phase-mix (4) Strong j develops in PSBL (5) Electrons (v e ) carry j (6) Converging field geometry intensifies current requiring electron energization from wave energy (7) Where phase-mixing (and j ) are weak, reflected and incident Alfvén waves have similar amplitude

13 Energy sources: Summary Flank modes: impulses and KH instability Tail modes: substorm energy release Fast-Alfvén wave coupling on closed (flank) and open (tail) field lines Phasemixing effects: Large j Electrons are energized kev Alfvén wave is damped Auroral emissions modulated with the Alfvén wave period Theory and data give a unified view of flank and magnetotail dynamics References given in Wright and Mann, AGU Mon., 2006 Wright and Allan J. Geophys. Res., These are available on andy/

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15 The Auroral Acceleration Region v e E acceleration region v e Acceleration region at altitudes of 1 2 R E j B (current focussed by converging B) v e j /(ne) and n const v e B electrons need to speed up Observations: j µa/m 2 Energy kev v e /V A 1 E mv/m

16 Physics of Field-Aligned Current Generation "! % '& )(+*-,/. $# (6587 :9;& )( :9"& 4("7 <>=@?BADCFEF G=@H JI 3 I 3 )(;7 & KML 3ON 2 3 P( & $# RQ (;7 :9SQ (TVUXW EY G= H +I 3 4( &

17 electrons Current Circuit j j electrons j ions j electrons j j electrons j