Plasma Interactions with Electromagnetic Fields

Transcription

1 Plasma Interactions with Electromagnetic Fields Roger H. Varney SRI International June 21, 2015 R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

2 1 Introduction 2 Particle Motion in Fields 3 Generation of Electric Fields in Plasmas Ambipolar Electric Fields Dynamo Theory Electrodynamical Magnetosphere-Ionosphere Coupling R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

3 Introduction The Ionosphere and Thermosphere R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

4 Introduction Magnetic Structure of the Ionosphere and Magnetosphere R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

5 Particle Motion in Fields Particle Motion in a Uniform B field y m dv dt = qv B Separate by components z x Electrons m dv x dt = m dv y dt = qv yb z qv xb z B = B z ẑ Solution to coupled system with v 0 = v 0ˆx v x = v y = Gyrofrequency: Ω = qb m v 0 cos(ωt) sgn(q)v 0 sin(ωt) Ions R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

6 Particle Motion in Fields The E B Drift E B V D v D = E B B 2 R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

7 Particle Motion in Fields Electric Fields in Different Frames of Reference Lorentz Force: F = q[e+v B] In a different frame of reference moving with velocity u F = q [ E +(v u) B ] The force must be the same in all reference frames: F = F E = E+u B The frame moving at the E B drift velocity is special: E = E+ E B B 2 B = E E B 2 B 2 = 0 Assuming: E = 0 R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

8 Ambipolar Electric Fields Ambipolar Electric Fields and Ambipolar Diffusion Steady state parallel electron momentum equation: [ m e t (n eu e )+ (n e ue 2 ) ] = p e n e ee E = 1 en p e e Substitute into parallel ion momentum equation: + m i [ t (n iu i )+ (n i u 2 i ) ] = p i n i n p e m i n i g e m i n i ν ij (u i u j ) E R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23 j

9 Dynamo Theory Fundamentals of Ionospheric Electrodynamics Electrostatic Limit of Maxwell s Equations: 1 E B = µ 0 J+ 0 c 2 t 0 B E = t Ohm s Law for the ionosphere: J = 0 E = Φ J = σ E+J 0 Putting everything together yields a boundary value problem: σ Φ = J 0 R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

10 Dynamo Theory Ohm s Law for the Ionosphere Steady-state momentum equation for each species (zero neutral wind case): 0 = n α q α (E+u α B) ν αn m α n α u α Resulting Ohm s Law: J = σ P σ H 0 n α q α u α J = σ H σ P 0 E α 0 0 σ 0 R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

11 Dynamo Theory Conductivity Profiles R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

12 Dynamo Theory Other Kinds of Current Substitute F for q α E in steady state momentum equation. Wind drag: F = ν αn m α u n J = σ (u n B) Gravity: F = m α g J = Γ g Pressure Gradients (Diamagnetic Currents): F = 1 n α p α J = D α p α Complete Dynamo Equation: ( σ Φ = σ (u n B)+Γ g+d α p α ) R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

13 Dynamo Theory Slab Model of the F-region Dynamo J = σ P (E+u n B) Two ways to achieve J = 0 1 Parallel currents which close elsewhere 2 J = 0 J = 0 E = u n B V D = E B B 2 = u n B B B 2 = u n R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

14 Dynamo Theory Slab Model of the E-region Dynamo Suppose E x is the eastward component of u n B in the E-region. A vertical electric field forms to oppose the vertical Hall current. σ H E x = σ P E z = E z = σ H σ P E x The Hall current from this new E z adds to the existing Pedersen current from E x J x = σ H E z +σ P E x = [ (σ H /σ P ) 2 +1 ] σ P E x σ C E x R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

15 Dynamo Theory Equatorial Fountain Effect 1000 Ne (cm 3 ) 7 6 Altitude Vertical Drift (m/s) Latitude Local Time 3 R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

16 Dynamo Theory Influences of Atmospheric Tides (Immel et al. 2006) R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

17 Electrodynamical Magnetosphere-Ionosphere Coupling Current Systems in the Ionosphere and Magnetosphere R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

18 Electrodynamical Magnetosphere-Ionosphere Coupling Closure of Field Aligned Currents in a Slab Ionosphere 3D potential equation with magnetospheric currents: σ Φ = J mag Integrate over altitude, assume equipotential field lines: Σ Φ = J mag dz Expand the divergence: J mag = J + J z J goes to 0 above ionosphere, thus: J mag dz = J 2D slab ionosphere potential equation: Σ Φ = J R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

19 Electrodynamical Magnetosphere-Ionosphere Coupling High Latitude Convection Patterns R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

20 Electrodynamical Magnetosphere-Ionosphere Coupling Energy Transport: Poynting s Theorem Poynting s Theorem: t [ ǫ 0 E 2 ] [ ] + B 2 E B + 2µ 0 µ 0 }{{} Energy Flux 2 } {{ } Energy Density = J E }{{} Joule Heating Ionospheric Joule Heating: Use E field in the neutral wind frame J E = ( σ E ) E = σ P E+u n B 2 = n i m i ν in u i u n 2 See Appendix A of Thayer and Semeter, 2004, JASTP. R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

21 Electrodynamical Magnetosphere-Ionosphere Coupling Joule Heating Weimer, R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

22 Electrodynamical Magnetosphere-Ionosphere Coupling Conductivity Effects on Magnetosphere (Lotko et al., 2014) R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23

23 Electrodynamical Magnetosphere-Ionosphere Coupling Summary of Ionospheric Electrodynamics ( σ Φ = σ (u n B)+Γ g+d ) p α +J mag α The ionospheric potential, and thus the E B drifts, depend on: Neutral winds (driving from below) Magnetospheric currents (driving from above) Ionospheric conductivities (chemistry) Ionospheric pressure gradients (energetics) R. H. Varney (SRI) Plasmas and EM Fields June 21, / 23