The Physics of Field-Aligned Currents

Transcription

1 The Physics of Field-Aligned Currents Andrew N. Wright UNIVERSITY OF ST ANDREWS

2 Magnetospheric Current Circuit There is a rich structure of currents flowing parallel (j ) and perpendicular (j ) to the magnetic field (B). Magnetopause current Ring current Ionospheric currents Region 1 and 2 currents ULF Alfvén waves Magnetopause current Region 1 current Ionospheric Pedersen current Region 2 current Partial ring current [Figure from NASA GSFC.] View from tail First Prev Next Last Go Back Full Screen Close Quit

3 Quasi-Neutrality and Current Continuity The Ampère-Maxwell equation states Taking the divergence yields B/µ 0 = j + ε 0 E t. E 0 = j + ε 0. t Using Gauss s Law, E = ρ /ε 0 (where ρ = net charge density) we find Quasi-neutrality (ρ 0) j + ρ t = 0. j 0: Currents are self-closing. The displacement current (ε 0 E/ t) is neglected. ρ 0 means (n e n i )/n e 1. Debye length is ε 0 kt e /e 2 n e 100 m (magnetosphere), 0.01 m (ionosphere).

4 Some Magnetohydrodynamic Driving Mechanisms Imposed velocity shear [Rönnmark, GRL, 1998] Fundamental standing (ULF) Alfvén wave Axisymmetric oscillation of magnetic shells b φ and u φ components only j and j currents

5 Generation of j (MHD description) Single fluid MHD momentum equation ρ dv dt = j B p + F Solve for j ( j = ρ dv ) dt + p F B B 2 Since j = 0 we find j j s + j = 0, j = along B j ds The field-aligned current (j ) flows to maintain quasi-neutrality (ρ 0)

6 What is j microscopically? Net drift of charged particles parallel to B Consider the parallel component of the equation of motion for a charged particle (uniform B), dv dt = qe m. E can be used to establish a field-aligned current. Since m e /m i 1 the electrons are more mobile, and carry most of the parallel current: j ev e In MHD m e /m i 0: electrons are represented by a massless charge-neutralizing fluid (E 0) To generate j requires E How does E arise? Causal interpretation in ideal MHD difficult since E/ t has been neglected

7 Guiding centre description of particle motion Particles execute a circular trajectory about B whose centre drifts. Valid when Gyroradius background scale length Gyroperiod background timescale Guiding centre drifts parallel to B arise from E and magnetic mirror force m dv dt = qe + µ B The magnetic moment µ = mv 2 /2B is a constant of motion. Guiding centre drifts perpendicular to B (can depend upon q, m and energy) arise from Grad B drift B curvature drift Polarization drift (E(t)) E B drift

8 Generation of j (particle description) In general, given E(r, t) and B(r, t), electrons and ions drift relative to one another current can flow net charge density is likely to develop ρ 0 As ρ becomes non-zero, E and E change to satisfy and influence the particle motion Effect of even a small E : E = ρ /ε 0 electrons are accelerated parallel to B j is established parallel electron motion acts to reduce ρ the plasma remains quasi-neutral (ρ 0) Interestingly, E still satisfies B/µ 0 = j + ε 0 E t, even though the last term is still negligible. First Prev Next Last Go Back Full Screen Close Quit

9 Ring Current and Standing Alfvén Wave j v e v e electrons j E +ve E v i j E ve E j j electrons electrons j j ions j E E v e B 0 B 0 v e electrons j Looking earthward from the tail Warm ion cloud drifts westward Slight charge imbalance generates E, electron motion and j Snapshot of Alfvén wave current circuit E(t) in equatorial region produces polarization drift Ions drift across L-shells leading to charge imbalance and subsequent j

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11 Magnetosphere-Ionosphere Equilibrium Near the Earth A simple equilibrium has a total ion number density comprising: constant magnetospheric contribution (n M 1 cm 3 ) exponentially decreasing ionospheric contribution (n I cm 3, scale height km) If n = n I + n M and B is dipolar, B/n has a peak at a few thousand km altitude below B/n peak: B/n exp(+r/h) above B/n peak: B/n 1/r 3 First Prev Next Last Go Back Full Screen Close Quit

12 Upward and Downward Currents and the Auroral Acceleration Region Upward Current: magnetospheric electrons precepitated visible aurora Downward Current: ionospheric electrons evacuated to magnetosphere Current-Voltage (energy) relations for upward and downward currents? [Marklund et al., Nature, 2001.]

13 Gyrotropic Electron Vlasov Equation: f(s, v, v, t) Retains information of ionospheric and magnetospheric electron populations f t + v f s ( ee m e + v2 2B B s ) f v + v v 2B B s f v = 0 s = field-aligned coordinate. For a steady current E = φ E = φ/ s. Constants of motion are total energy: W = 1 2 m ev 2 eφ magnetic moment: µ = m e v 2 /2B Solve for f(s, v, v ) with v (W, µ), v (W, µ) Liouville s Theorem (f is constant along an electron trajectory) n e = n i φ(s) and j = e v fd 3 v Solution relates current flow to potential drop along the field line

14 Upward Current (downgoing electrons) Assuming a potential drop φ m : map magnetospheric electrons down to the ionosphere using W and µ to identify the loss cone. Calculate j at the ionosphere in terms of φ m : ( kt j n 0 e 1 eφ ) m 2πm e kt The Knight relation [Planet. Space Sci., 1973]. Useful for interpreting data (electron energies) Good for incorporating in global modelels Knight s solution says little about quasi-neutrality or φ(s) variation E needed to overcome mirror force v Where does acceleration occur? E e v e acceleration region

15 Upward Current Quasi-Neutral Solution Quasi-neutral solution for previous B/n variation gives [Cran-McGreehin, 2006] Plots of normalized potential and E along B. (Ionosphere at s = 0) Below B/n peak, ambipolar E traps ionospheric electrons Above B/n peak, E helps precitating electrons overcome the mirror force adjust mirroring magnetospheric electrons to maintain quasi-neutrality

16 Downward Current (upgoing electrons) Some ionospheric electrons are accelerated upward into the magnetosphere Ionosphere Magnetosphere Velocity parallel to B Beam l m lc l e l p l 0 [Cran-McGreehin and Wright, JGR, 2005a,b] Field-aligned coordinate is l. Important locations are l p : location of the B/n peak l c : ionospheric electron trapping point/beam emergence height

17 Downward Current Quasi-Neutral Solution Quasi-neutral solution for previous B/n variation gives [Cran-McGreehin and Wright, JGR, 2005a,b] Plots of normalized potential and E along B. (Ionosphere at s = 0) Electron acceleration is centred around the B/n peak Ionospheric j of µam 2 correspond to potential drops along B of kev

18 Analytical Current-Voltage Relation (Downward Current) The potential drop (φ m ) depends upon j and n at the B/n peak, as well as the magnetospheric electron temperature (T ) [Cran-McGreehin and Wright, JGR, 2005b] If j 2 p m e/2kt n 2 pe 2 < 1.7 then φ m 3 2 ( j 2 p m1/2 e n p e 5/2 kt ) ( ) 1 j 4 p m2 3 ekt n 4 pe 7 + j2 p m e 6n 2 pe 3 If j 2 p m e/2kt n 2 pe 2 > 1.7 then φ m kt e ln ( j 2 p m e n 2 pe 2 kt Approximations accurate to at least 5% May only need one or two terms ) + j2 p m e 2n 2 pe 3 + kt e

19 A conclusion is what you come to when you re tired of thinking. First Prev Next Last Go Back Full Screen Close Quit

20 Conclusion and Summary Field aligned currents are an integral part of the magnetosphere arise from both large scale driving and internal particle drifts carried mainly by electrons (accelerated by E ) Downgoing electrons excite the aurora Details of φ(s) and E (s) are different for upward and downward currents (but B/n peak location is important) Analytical Current-Voltage relations available

21 Future Work Allow ions to move and modify background density Address time-dependence Combine large and small scale physics of acceleration region (FAST) Other acceleration mechanisms (wave-particle interactions?) Interpret with governing equations

22 Optical auroral emissions: CANOPUS First Prev Next Last Go Back Full Screen Close Quit LATITUDE (EDFL) MPA (Altitude at 110 km) UT/ nm 9.4 kr 0.2 kr TIME (MINUTE) Auroral emissions are modulated with the Alfvén wave period [Xu, Liu, Samson] Emissions excited by kev energy electron precipitation Electron acceleration is an integral part of the Alfven wave Electron energization not described in single fluid MHD Latitudinal scale 200 km

23 FAST: Field-Aligned Electron Motion and j Downward j : upward moving ionospheric electron beam Upward j : downward moving magnetospheric electron beam