* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Alaska-SubstormChap
Survey
Document related concepts
Partial differential equation wikipedia , lookup
Noether's theorem wikipedia , lookup
Euler equations (fluid dynamics) wikipedia , lookup
Electromagnetism wikipedia , lookup
History of fluid mechanics wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Derivation of the Navier–Stokes equations wikipedia , lookup
Maxwell's equations wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Navier–Stokes equations wikipedia , lookup
Transcript
Substorms: Ionospheric Manifestation of Magnetospheric Disturbances P. Song, V. M. Vasyliūnas, and J. Tu University of Massachusetts Lowell • Substorms: • Defined by ground observations: AE index • Originated in the magnetosphere • There is an ionosphere between the magnetosphere and ground • Conventional (global) ionospheric models • Electrostatic: B=constant • Ionosphere does not “generate” waves • Oscillations in the ionosphere are controlled by the magnetospheric driver • Processes at the interface between magnetosphere and ionosphere • Magnetospheric wave reflection • Wave mode conversion: transmitted waves in the ionosphere are fast modes • New M-IT models: • Inductive: B changes with time • Dynamic: in particular ionospheric motion perpendicular to B • Multi fluid: allowing upflows and outflows of different species • Wave propagation/reflection: overshoots • Summary M-I Coupling via Waves (Perturbations) • The interface between magnetosphere and ionosphere is idealized as a contact discontinuity with possible small deformation as the wave oscillates • Magnetospheric (Alfvenic) perturbation incident onto the ionospheric interface • For a field-aligned Alfvenic incidence (for example on cusp ionosphere) B k, B0 : B in a plane normal to k (2 possible components) • Polarizations (reflected and transmitted) (noon-midnight meridian) • Alfven mode (toroidal mode) B,u k-B0 plane Magnetosphere • Fast/slow modes Ionosphere (poloidal mode) B,u in k-B0 plane • Antisunward ionospheric motion =>fast/slow modes (poloidal) => NOT Alfven mode (toroidal) Global Consequence of A Poleward Motion • Antisunward motion of open field line in the open-closed boundary creates – a high pressure region in the open field region (compressional wave), and – a low pressure region in the closed field region (rarefaction wave) • • • Continuity requirement produces convection cells through fast mode waves in the ionosphere and motion in closed field regions. Poleward motion of the feet of the flux tube propagates to equator and produces upward motion in the equator. Ionospheric convection will drive/modify magnetospheric convection Ionosphere Reaction to Magnetospheric Motion • Slow down wave propagation (neutral inertia loading) • Partial reflection • Drive ionosphere convection – Large distance at the magnetopause corresponds to small distance in the ionosphere – In the ionosphere, horizontal perturbations propagate in fast mode speed – Ionospheric convection modifies magnetospheric convection (true 2-way coupling) • Amplification of Magnetic Perturbation at the Ionosphere At the magnetosphereionosphere boundary, the boundary conditions are maintained by the incident, reflected and transmitted perturbations. u nu • The reflected perturbations have a phase reversal between dB and dV from the incident. The inertia of the ionospheric plasma minimizes the velocity change across the boundary |interface u ' nucontact |interface i , f ,a , s f ,a , s B | interface i , f ,a , s p| interface p ' |interface i, f ,s u f ,s B ' | f ,a , s interface • contact f ,s ˆ B B B f ,s C A2 C A2 ˆ 0 f ,s ˆ ˆ 2 V f ,sk f ,s k f , s B0 , V f , s Cs2 B0 V f ,s B0 ua CA Ba B0 . V Vinc Vref , B Binc B ref 2 Binc • The magnetic perturbation nearly doubles across the boundary => forming a strong current Basic Equations • Continuity equations ns (ns v s ) Pss ' ns L s t s' • Momentum equations (ns v s ) nk T ne (ns v s v s s B s I) s s (Es v s B) t ms ms s = e, i or n, and es = -e, e or 0 Field-aligned flow allowed ns (G r 2Ωr v s Ωr (Ωr r )) ns st ( vt v s ) v s Pss ' ns vs L s t s' • Temperature equations Ts m 2 2 1 2 mt v s Ts Ts ( v s ) q s st [2(Tt Ts ) ( vt v s )2 ] t 3 3 ns k B 3 kB t ms mt Q s CL s • Faraday’s Law and Ampere's Law B E t 1 0 B 0 E J ni ev i ne ev e t i Simplifying Assumptions (dt > 1sec) • Charge quasi-neutrality – Replace electron continuity with • Neglecting the electron inertial term in the electron momentum equation – Electric field, E, can be eliminated in other equations; – electron velocity will be calculated from current definitions. Momentum equations without electric field E (ns v s ) ns k BTs ns k BTene ne(k BTe ) (ns v s v s I) t ms ne ms ns es ( v e B v s B) ns (G r 2Ω r v s Ω r (Ω r r )) ms m , n ,e m,n t s t ns st ( vt v s ) ns me et ( v t v e ) v s ' Pss ' ns v s L s ms s' 1-D Stratified Ionosphere/thermosphere • Equation set is solved in 1-D (vertical), assume B<<B0. • Neutral wind velocity is a function of height and time • The system is driven by a change in the motion at the top boundary • No local field-aligned current; horizontal currents are derived • No imposed E-field; E-field is derived. • test 1: solve momentum equations and Maxwell’s equations using explicit method • test 2: use implicit method (increasing time step by 105 times) • test 3: include continuity and energy equations with 2000 km field-aligned flow 500 km Dynamics in 2-Alfvén Travel Time x: antisunward; y: dawnward, z: upward, B0: downward On-set time: 1 sec Several runs were made: the processes are characterized in Alfvén time Building up of the Pedersen current Song et al., 2009 30 Alfvén Travel Time • The quasi-steady state is reached in ~ 20 Alfvén time. • During the transition, antisunward flow in the Flayer can be large • During the transition, Elayer and F-layer have opposite dawn-dusk flows • There is a current enhancement for ~10 A-time, more in “Pedersen” current Song et al., 2009 Neutral wind velocity •The neutral wind driven by M-I coupling is strongest in F-layer •Antisunward wind continues to increase Song et al., 2009 After 1 hour, a flow reversal at top boundary •Antisunward flow reverses and enhances before settled •Dawn-dusk velocity enhances before reversing (flow rotates) •The reversal transition takes slightly longer than initial transition •Larger field fluctuations Song et al., 2009 After 1 hour, a flow reversal at top boundary “Pedersen” current more than doubled just after the reversal Song et al., 2009 Electric field variations Not Constant! Electric field in the neutral wind frame E’ = E + unxB Not Constant! Song et al., 2009 Heating rate q as function of Alfvén travel time and height. The heating rate at each height becomes a constant after about 30 Alfvén travel times. The Alfvén time is the time normalized by tA, which is ztop defined as tA dz / VA zbottom If the driver is at the magnetopause, the Alfvén time is about 1 min. Height variations of frictional heating rate and true Joule heating rate at a selected time. The Joule heating rate is negligibly small. The heating is essentially frictional in nature. Tu et al., 2011 Heating rate divided by total mass density (neutral mass density plus plasma mass density) as function of Alfvén travel time and height. The heating rate per unit mass is peaked in the F layer of the ionosphere, around about 300 km in this case. Time variation of height integrated heating rate. After about 30 Alfvén travel times, the heating rate reaches a constant. This steady-state heating rate is equivalent to the steady-state heating rate calculated using conventional Joule heating rate J∙(E+unxB) defined in the frame moving with the neutral wind. In the transition period, the heating rate can be two times larger than the steady-state heating rate. Tu et al., 2011 Summary • When the ionosphere is treated self-consistently and dynamically, it – reflects magnetospheric perturbations – oscillates at magnetospheric eigen-mode frequencies (not simply responds to magnetospheric disturbances) – forms an envelop over the eigen-mode oscillations due to constructive or destructive interference until steady state is reached. – has a transient time of 10-20 Alfven times, or 20-40 min – sets convection pattern with the fast mode speed • The above distinct processes predict/explain – Substorm time geomagnetic measurements have intrinsic oscillations, the frequency of which is less correlated with the oscillations in the solar wind – Substorm time geomagnetic perturbations are less correlated with specific time scales of reconnection – Substorm time is about 30 min – The whole ionosphere responds to the magnetospheric changes in 1 min – During substorms, more energy is dissipated within the polar cap proper where frictional heating is the strongest, not in the auroral oval or field-aligned current sheets where convection velocity is the smallest. – The requirement for a substorm is a substantial change in the magnetospheric convection which has to be maintained, with its variations, for at least 30 min.