A Three-Fluid Approach to Model Coupling of Solar Wind-Magnetosphere-Ionosphere- Thermosphere

Transcription

1 A Three-Fluid Approach to Model Coupling of Solar Wind-Magnetosphere-Ionosphere- Thermosphere P. Song Center for Atmospheric Research University of Massachusetts Lowell V. M. Vasyliūnas Max-Planck-Institut für Sonnensystemforschung Katlenburg-Lindau, Germany Three-fluid equations 1-D propagation: propagation speed, damping 1-D solutions: steady state, time dependent. Joule heating? Summary

2 Motivation Magnetospheric Approach: Height-integrated ionosphere Ohm s law in the neutral frame Neutral wind velocity is function height and time Ionospheric Approach Structured ionosphere Time dependent ionosphere Magnetosphere is a prescribed boundary Not self-consistent: ion velocity is function of height and different from electric drift velocity

3 Basic Description of Multi-fluid System For each of three species (eles, ions, neutrals): including interspecies collisions Continuity equations Momentum equations Energy equations Maxwell equations Electric current j = ez N u en u i i i e e

4 Equations for M-I-T Coupling (neglecting photo-ionization, horizontally uniform) Faraday s law Ampere s law B E = t 1 B = µ j+ c 0 2 E t Generalized Ohm s law m j m m m = j B Ne( E+ U B ) Nm( ν ν )( U u ) + ( ν + ν + ν ) j+ F F e t e m m e e e e 0 e 0 e e en in n in en ei e i i i Plasma momentum equation NeU me mi = j B 0 Ne( miνin + meνen)( U u n) + ( νen νin) j + F t e Neutral momentum equation Nnun me m = N ( mν + mν )( U u ) ( ν ν ) j+ F t e n e i in e en n en in n Energy equations 3 d P U 1 P w w 2 dt ρ c [log ] = J* [ E+ B] + ν [( ) ( )] 5/3 pnρ un U + ξ n 3 d P 1 P w w 2 2 n n [log ] = ν [( ) ( )] 5/3 pnρ un U ξ n dt ρn ξ = ( u U) /[ c ( w + w ) + c w w]~1 n n 1 n 2 n w, w: thermal speeds.

5 Simplified Equations for M-I-T Coupling Faraday s law Ampere s law Generalized Ohm s law (1-D, no parallel flow, δb << B 0 ) B E = t Plasma momentum equation Neutral momentum equation B = µ j+ 1 c 0 2 E t me j = j B0 Ne e ( E+ U B0) Nm e e( νen νin)( U un) e t + me me ( in en ei ) e m ν + ν + ν j i NeU me mi = j B 0 Ne( miνin + meνen)( U u n) + ( νen νin) j t e N u m d du mn = Ne( miνin + meνen)( U un) ( νen νin) j η t e dz dz n n e n

6 Ionospheric Parameters at Winter North Pole

7 Wave Propagation Model Locally uniform media 1-D field-aligned propagation Turn-on reconnection at the magnetopause at t=0: a step function Fourier decompose perturbations of all frequencies Propagation at group velocity- a function of frequency Perturbations in all physical quantities are considered

8 Parallel Propagation Dispersion Relation (incompressible) 2 2 ω ω ν inν e ωνe νin ν ω in pe 1 νin m i ± α = 1 i 2 ΩΩ e i Ωi ΩΩ e i ΩΩ e i Ωi ω ΩΩ i e ( n 1) ω Assuming: ν e /Ω e << ν in /Ω i, ν in << ν e, η = 0 α = m i N e /m n N n = 10-3~-10 <<1 Where n = kc/ω =n R + in I, k= k R + ik I V phase = c/n R = ω/k R, V group = dω /dk R. Three parameter regimes: Low collision: ν in << ν e << Ω i << Ω e, Z > 250 km mid collision: Ω i << ν in << ν e << Ω e, High collision: Ω i << Ω e << ν in << ν e, 90 < Z < 250 km Z < 80 km.

9 Dispersion Relation Left-hand mode Right-hand mode

10 Phase Velocity

11 Neutral collision and neutral motion effect

12 Attenuation Depth

13 Low Frequency Regime (T = 1 sec ~ 3 hours) Propagation velocity: decreases from V A to α 1/2 V A = B/(µ 0 m n N n ) 1/2 Neutral inertia-loading process Attenuation (penetration) depth D = 1/k I : shorter for higher frequencies longer for lower frequencies low frequencies (PC frequencies) can survive from damping Wavelength λ = V phase /ω: high frequencies (> 1 Hz): λ << L (gradient scale ~10 1~3 km) low frequencies (~1.3 mhz): λ ~ 1700 km

14 Temporal-variations Observed in the Ionosphere Signal observed in the ionosphere is the summation of signals of all frequencies i( ωt kz ) ω Isphere Isphere QtZ (, ) Q ( Z ) e d Isphere = ω Amplitudes for different quantities are related by the perturbation relations.

15 1-D Propagation Inhomogeneous parallel incompressible 2 [, 2 Ψ ω Ω ie, ( z), vi, j( z), α( z)] Q = 0 z Amplitudes as functions of height and frequency can be derived

16 Three-Fluid Steady State 1-D Solution Steady state 1-D (vertical) Generalized me j B= Ne e ( E+ U B) + Nm e eν en( U un) ν ej, Ohm s law e Plasma Momentum Neutral momentum Viscosity η = 5 π 16 mkt Boundary conditions Upper boundary: 1000 km, j = 0 Lower boundary: 80 km, u n = U = 0 E =E 0 ŷ n 2 πσ me j B= Nm e iν in( U un) ν enj, e d dun j B= η. dz dz n

17 Steady State M-I Coupling Solution

18 Effects of Neutral Coupling

19 Ionospheric response to an IMF reversal (1-D stratified) Generalized Ohm s law me j me me Ne( ) ( )( ) + ( in en ei ) e m ν + ν + ν j e + Nm e e νen νin n e t = j B E U B U u Plasma momentum equation NeU me mi = j B Ne( miνin + meνen)( U u n) + ( νen νin) j t e Neutral momentum equation N u m d du mn = Ne( miνin + meνen)( U un) ( νen νin) j η t e dz dz n n e n Upper boundary: z=1000 km, j = 0 Lower boundary: z=80 km, u n = U = 0 E =E (t)ŷ, at upper boundary step function, 0 => -0.5 E 0 => +E 0. i

20 Time Dependent M-I Coupling

21 Time Dependent M-I Coupling

22 Time Dependent M-I Coupling

23 Magnetospheric energy input: J E Joule Heating Joule heating: J E * frame dependent t t Conventional interpretation: J = σ( E+ u B) = σe ' E' = E+ u B Comments: J E= J E' + un ( J B) Heating Mechanical work Ohm s law is derived assuming cold gases, no energy equation is used. Ohm s law is frame dependent In multi-fluid, there are multiple frames: plasma and neutral wind. The behavior at lowest frequencies indicates a drag process, not Joule heating Energy equations show: Joule heating (electromagnetic dissipation) is near zero. Heating is through ion-neutral collisions: fractional Thermal energy is nearly equally distributed between ions and neutrals n n

24 Summary A 3-fluid theory is proposed to study solar wind-magnetosphereionosphere/thermosphere coupling Uniform cold plasma parallel-propagation problem is solved 1-D propagation: in progress Frequency integration: in progress 1-D steady state problem is solved 1-D time dependent: solved Challenge: parameters vary in many orders

25 Summary Q: What does the ionosphere see after an IMF change/change A: in magnetopause reconnection? A sequence of several fronts propagate down, each with major perturbations in a particular quantity. Neutral collisions slow down the low frequency perturbations. attenuate the high frequency waves. Enhancement in the F-layer Pedersen current Followed by decrease in the F-layer Pedersen current and Increase in E-layer Hall current. Effect of neutrals is better described as a neutral drag than an Ohmic dissipation process.