Electromagnetic Fields Inside the Magnetoshpere. Outline

Transcription

1 Electromagnetic Fields Inside the Magnetoshpere P. K. Toivanen Finnish Meteorological Institute, Space Research Outline Introduction to large-scale electromagnetic fields Magnetic field geometry Modelling methods B = µ o J Magnetospheric convection E B = 0 Magnetospheric current systems Magnetospheric dynamics Motivation Magnetic field models Historical models Present-day models Electric field models Deformation method Motivation Euler potentials Theory Example & Model construction 3D electric fields Modelling example Equatorial models SSC, April 06, 2000 Ionospheric models Dayside compression

2 Intro to Large-Scale Electromagnetic Fields Magnetic Field Geometry Internal magnetic field Dipole tilt Solar wind pressure Open field lines Closed field lines Cusp

3 Intro to Large-Scale Electromagnetic Fields (cont.) Convection Ionosphere: Global convection maps to the ionospheric convection Typically two-shell pattern (IMF B Z < 0) High-latitude convection from noon to midnight Return convection at lower latitudes via dawn and dusk Can be measured by radars

4 Intro to Large-Scale Electromagnetic Fields (cont.) Convection (cont.) Equatorial plane: Earthward convection in the midtail Plasma flow around the co-rotating plasmasphere to the dayside Return convection along the flanks Electric field associated with the convection 0.5mV/m Cannot be globally measured

5 Intro to Large-Scale Electromagnetic Fields (cont.) Convection (cont.) Tail cross-section: Convection across the tail lobes towards the plasma sheet Turns to earthward convection at the plasma sheet

6 Intro to Large-Scale Electromagnetic Fields (cont.) Current Systems Cross-tail current Ring current Magnetopause current Field-aligned currents

7 Intro to Large-Scale Electromagnetic Fields (cont.) Magnetospheric Dynamics Magnetic storms Magnetopause compression Ring current enhancement Substorms Tail stretching Dipolarization

8 Why Analytical Field Models? Physical Reasons Link between the interplanetary medium and the ionosphere Guide and Energize charged particles Confines radiation belts and controls the auroral phenomena Store a huge amount of energy Practical Reasons Satellite conjunctions (along magnetic field lines) Ground-based stations and spacecraft conjunctions Test particle simulations (Dr. Ganushkina) Mapping of ionospheric convection to the magnetosphere Subtract the backround field from observation

9 Magnetic Field Models For historical models: See Stern, JGR, IGRF (International Geomagnetic Reference Field) Geopack (coordinate transformations, tilt...) T89 (Tsyganenko, JGR, 1989) Computationally fast Extremely widely used Parametrized by Kp T96 More realistic current systems Larger set of input parameters All available at T89 (dash-dotted) Toivanen (solid)

10 Electric Field Models Equatorial model: Volland, JGR, ϕ = Ar γ sin φ, where A is a constant, and γ = 2, typically. Ionospheric model: Heppner and Maynard, JGR, mV/m Xgsm[Re] deg deg 60deg Ygsm[Re]

11 Modelling Methods and Shortcomings Magnetic Field Represent mathematically the field from each major current systems Represent the expected response of the field to physical factors thatcan be determined Calibrate the model against a database of average magnetic field observations, tagged by values of the solar wind parameters Force balance is not automatically built into the models Unreliable in highly time-variable situations such as substorms event-oriented models (Deformation method below + Dr. Ganushkina)

12 Modelling Methods and Shortcomings (cont.) 3D Electric Field Equipotential mapping (static) A E dl = 0 a) E is E is X X GSM Y GSM e Y is E is Y Z GSM ex is B Generalized mapping A E dl = A t B da Induction included b) X GSM Y GSM Z GSM X is X E ms Y dl X, da X e ms Y dl X A X e X ms E ms AX E ms X Computationally tedious Toivanen, P. K., et al., JGR, c) X GSM Y GSM Z GSM Y X is dl Y ms X X da Y dl Y, A Y AY Y X ms

13 Motivation Deformation Method Solving Faraday s law is complicated ( E = t B) No explicit vector potential in magnetic field models Electrostatic component difficult to include t A may have a component parallel to B Euler potentials Physical electromagnetic fields Field (A, φ) (α, β, φ) B A α β E vacuum t A φ t (α β) φ E plasma - t α β + t β α φ

14 Deformation Method (cont.) For a given α(x, y) As to Homer, this can be done to a magnetic field: B = α β B = T B Take a magnetic field given in some coordinates. Replace these coordinates by some transformed coordinates. α(x, y) = α( x, ŷ) Multiply the resulted magnetic field by the matrix T (given on the next slide). The given field is then given in terms of the original coordinates References Stern, D. P., JGR, Tsyganenko, N. A., JGR, 1998.

15 Generalized Deformation Method Consider a transformation q i = f i (q 1, q 2, q 3 ) Let A = α β A = MÂ; M hl = ĥl h h h f l Let [ φ] = φ [ φ] = M[ φ] Let B = α β B = T B; T ij = 1 2 ε ihkm hl M kq ε lqj Let E = t α β + t β α φ E = M(Ê + t q B) For deformed fields: A B = 0 B = 0 B 0, even if B = 0 [ φ] B = 0, if φ B = 0 E B = 0 [ φ] = 0 E = t B

16 In spherical coordinates (r, θ, ϕ): Initial Dipole Fields Euler potentials: α r 1 sin 2 θ and β ϕ B = µ om 2πr 3 cos θe r + µ om 4πr 3 sin θe θ A = µ om 4πr 2 sin θe ϕ Assume equipotential dipole field lines: φ B = 0 φ(r, θ, ϕ) = φ is (r is, θ is (r, θ), ϕ is (ϕ)) Dipole magnetic field lines (r is, sin θ is, ϕ is ) = (constant, [ ] 1 r is 2 r sin θ, ϕ) Assume an ionospheric electric field E is = (E is θ, E is ϕ ) E = φ = φ is = ( ) 3 r is 2 r ( 1 2 sin θ cos θ is E is θ e r + cos θ cos θ is E is θ e θ + E is ϕ e ϕ )

17 An Example: Dipole Expansion Dipole field (dash-dotted) α = µ om o 4πr m m(r) sin2 θ r = rh(r) 1 H(r) = a ( 1 tanh ( r r o r a = (1 c) ( 1 tanh ( r is r o r m = m o, if r = r is m = cm o, if r Expanded dipole (solid) Ring current )) + c )) 1

18 Noon-midnight meridian Consecutive deformations: Dipole expansion (a) Field topology (b) Near-Earth plasma sheet (c) Dayside compression (d) Magnetopause and lobes (e) Tilt effect (f) Model Construction

19 Model Construction (cont.) Equatorial plane Last closed field lines: Dipole expansion (a) Field topology (b) Near-Earth plasma sheet (c) Dayside compression (d) Magnetopause and lobes (e)

20 SSC, April 06, 2000 Solar wind pressure pulse Negative excursion of IMF B Z Dayside compression at 1640 UT Subsolar magnetopause position (R E ) Shue et al., [1998] GUMICS-4 OC boundary GUMICS-4 j y currents time (hrs) (a) Bz [nt] (b) By [nt] (c) Epsilon [10 12 W] (d) P [npa] (e) SYM H [nt] (f) IU [nt] IL [nt] April 6-7, 2000 WIND (8 min delay) WIND (8 min delay) WIND (8 min delay) WIND (8 min delay) UT [hours of April 6]

21 Magnetic Field GOES 8 located at noon close to the magnetic equator (see next slide) Measured field at GOES 8 (black) Modelled field (red) Magnetic field compression (B GSM Z ) B GSM X B GSM Y B GSM Z

22 Magnetic Field (cont.) Polar located at noon close to the northern cusp (see next slide) Measured field at Polar (black) MHD model from GU- MICS (blue) Magnetic field compression (B GSM X ) B GSM X B GSM Y B GSM Z Large deflection of B GSM Y

23 Magnetic Field Configurations 1630 UT Polar( ), GOES8 ( ) 1650 UT

24 Electric Field Configurations Static electric field at 1630 UT Corresponds to the mapped ionospheric convection Determined by deformation to the initial dipole potential field = Polar, = GOES 8

25 Electric Field Configurations (cont.) Static electric field at 1650 UT = Polar, = GOES 8 Field close to the Earth is due corotation (plasmashpere)

26 Electric Field Configurations (cont.) Induced electric field at 1640 UT Corresponds to the field lines motion Due to time-evolution of B GSM Y

27 Electric Field at Polar Convection electic field, Polar (black), modelled (red), GUMICS (blue) E GSE X E GSE Z

28 Electric Field at Polar (cont.) Induced electic field, Polar (black), modelled (red), GUMICS (blue) E GSE X E GSE Z

29 Electric Field at Polar (cont.) Total electric field, Polar (black), modelled (red), GUMICS (blue) E GSE X E GSE Z