The Kinetic Physics of Magnetotail Dynamics: Reconnection, Ballooning, and Dipolarization Fronts P.L. Pritchett UCLA Collaborators: F.V. Coroniti Y. Nishimura Outline • Introduction to magnetotail and PIC simulations • Effect of Bz in stabilizing spontaneous tearing instability • Observational guidance • Possible role of ballooning/interchange instability • Generates fronts with ion kinetic scale thickness and ~ RE east-west extent • Generates intense off-axis waves ahead of fronts • Leads to structuring of auroral streamers • Properties of jet (dipolarization) fronts associated with localized reconnection • Summary/Questions Essential complication in the magnetotail (as opposed to magnetopause) is the presence of a quasi-permanent Bz component of the magnetic field. Field lines generally are never strictly anti-parallel. Bz ~ 0.1 B0. Characteristic Parameters • Proton Cyclotron Frequency in 20 nT field : Ωi0 = 1.9 s-1 (Ωi0-1 = 0.52 s) • Proton Inertial Length at density of 0.3 cm-3 : di = c/ωpi = 416 km = RE/15 • Proton (5 keV) Gyroradius in 20 nT field: ρi0 = VTi/Ωi0 = 520 km • Stochasticity Parameter (Büchner & Zelenyi): κj = (Bn/B0) (L/ρj0)1/2 ~ 0.5 for protons (L = 2 RE) ~ 5 for electrons (Te = Ti/5) • Curvature Radius Rc = 1/kc, kc = n ⋅ [(b ⋅ ∇)b] = (1/Bn)(dBx/dz) on axis Characteristics of (Most) PIC Simulations PIC simulations follow full dynamics of ions and electrons; must resolve all spatial and temporal scales. Cost of simulation: In 2D ∝ (M /m ) , i e 2 For Harris current sheet equilibrium: In 3D ∝ (M /m ) i e 5/2 c/VTe = (1 + Ti/Te)(1/2) ωpe/Ωce Magnetotail: Ti/Te ~ 7, ωpe/Ωce ~ 8 - 10, c/VTe ~ 25 Typical PIC Simulation: Ti/Te = 4, ωpe/Ωce = 2, c/VTe = 4.5 ∝ (ω Cost in 3D ∝ (ω Cost in 2D pe/Ωce) 3 pe/Ωce) 4 Spatial Scales: given in units of c/ωpi (normally) Velocity: given in units of VA (or sometimes VTi), typically ~ 1000 km/s Reconnection Onset in Presence of Bz Harris Sheet • Usual Reconnection Configuration: Harris Current sheet; not directly applicable to magnetotail due to Bz. 5 z −5 −5 0 B 0 10 x Bz/B0 = 0.05 z 5 0 −5 0 10 20 30 40 x kρen = kL (meTe/MiTi)1/2 (ρi0/L)(B0/Bn) < 1 0.5 0.010 1 - 0.10 Bn/B0 > 0.0005 - 0.005 Bn > 0.01 - 0.1 nT 0 0.2 −10 • Ion Tearing Instability? • Unless half width comparable to di, growth rate too small to overcome ion magnetization. • Electron stabilization effect: Either electron adiabaticity (Lembège & Pellat, 1982) or simply conservation of Py in 2D system (Pellat et al., 1991) ensures that tearing mode EM field produces strong compression of electron density. Energy associated with this compression exceeds free energy in reversed B configuration. • Condition for electron stabilization: kρen < 1. 5 0.4 0 z • Electron Tearing Instability: not viable since cyclotron motion removes electron Landau resonance. B Thus spontaneous tearing instability unlikely to occur in magnetotail 2D PIC Simulations kρen = 3.7 Ti = Te Ti = 4 Te 0 312 625 0.04 kρen = 1.8 0 395 790 B /B 0 0.03 Bz/B0 0.03 0.04 0.01 0 0.02 z 0.02 0.01 0 10 20 −3 10 30 40 x/di 0 50 0 10 −4 6 7 8 −4 10 10 6 7 8 −5 10 30 40 x/di 50 Mode Intensities −5 10 −6 −6 0 200 t i0 400 5 600 10 −0.05 0 0 200 400 600 t i0 0 5 0 z/di z/di 20 −3 Mode Intensities 10 10 −0.05 0 −0.1 −0.1 −5 −0.15 0 20 x/di 40 −5 −0.15 0 20 x/di 40 2D x,z simulations: Bz = 0.02 B0, half-width L = ρi0, mi/me = 64, nb = 0 Since Reconnection Clearly Occurs in Magnetotail, What are the Alternatives? • External Driving: Enhanced convection Ey field arising from southward IMF can force thinning of current sheet and force local reversal of Bz profile [Pritchett and Coroniti, 1995, 1997; Hesse and Schindler, 2001]. • Direct day-night coupling [Nishimura et al., 2014]: dayside flow channel and PMAF followed by polar cap airglow patch that crosses the polar cap followed by nightside PBIs and plasma sheet flow bursts. • Turbulence in the Tail: local reversals of Bz might arise randomly from tail variability. • Sitnov & Schindler (2010): May be able to circumvent electron stabilization for equilibria with more than 2 characteristic spatial scales (“hump” configuration). • Non-Reconnection processes: Role of bubbles in the magnetotail [Pontius and Wolf, 1990; Chen and Wolf, 1993]. Once produced, bubbles should propagate earthward due to buoyancy effect, perhaps explaining formation of fronts in near-Earth plasma sheet. Plasma Sheet • Curved magnetic geometry (finite B normal) can have significant effects on particle dynamics for both electrons and ions: bounce and drift resonant interactions. • Must use (at least) 2D equilibrium to describe tail current sheet. • Mid-tail minima in Bz are observed during periods of extended magnetospheric convection (Sergeev et al., 1994) and expected from MHD models (Hau et al., 1989). • Bz minimum also observed by Saito et al. [2010] (THEMIS) at ~ 10 RE: persists for 20 minutes. Sergeev et al., 1994 Plasma Sheet Onset Conditions Saito et al. [2010]: THEMIS observations on April 8 & 12, 2009. • Infer Bz minimum at 10 RE, persists for Figure 20 2. Magnetic field B and B (averaged for 3 min) as a function of location for 8 April 2009 event. The three umns represent features of (left)-1 1 hr, 3 min prior to dipolarization. hr(middle) 20 min and (right) -20 m -3 mThe latitudinal profile o min prior to breakup are categorized into two types: (bottom left) flat profile and (bottom middle and right) increasing function of ∣Z ∣ 3.1. Model Assumptions which is applicable for thin current sheet geometry and • Equatorial Bz as small as 1 nT Bz being closely located in r‐! plane. [ ] In local Cartesian coordinates with x and y all or two spacecraft z r GSM 11 corresponding to r and !, respectively, t (min) magnetic field measured at a point (r, !, z) is B(t, r, !, z). Simultaneous two‐point observation gives: !Bz ¼ -6 @Bz @Bz @Bz !r þ !! þ !z; @r @! @z ð1Þ Machida et al. [2009]: Statistical study of temporal where D means difference between two points. From the above analyses we may assume: and spatial development of near-Earth magnetotail @B @B around substorm onset using Geotail data. j%j j ð2Þ j @z @r z z that r and z are distances from the Earth and the mag equator (Br = 0), respectively. In this model mag field lines are confined in a plane (local two‐dimensi or 2D geometry) and a direction of r is defined fro direction of Br. 3.2. Gradient Analysis for 2D Magnetic Field Struc [12] For 2D geometry B(r, z) = (Br(r, z), Bz(r, z)) in local Cartesian coordinates, r · B = 0 is @Br ðr; zÞ @Bz ðr; zÞ þ ¼ 0: @r @z and Observe enhanced Bz around -20RE with a minimum earthward at ~-18RE; tailward of max Bz decreases, suggesting a possible hump structure. @Bz ’ 0; @! ð3Þ [13] In the northern hemisphere, Bz > 0 and Br < 0. T signs may hold for the magnetotail configuration o macroscale for most of the time. In order to obtain r 3 of 5 0 4 |z| x Simulation Model (a) 0.4 • 3D Particle-in-Cell 1 2 3 1A Bz/B0 0.3 0.2 Bz 0.1 • 2D Current sheet equilibrium in x,z with minimum in equatorial Bz field 0 0 100 200 • mi/me = 64, L/ρi0 = 1.6, ρi0 = 16 Δ, 512 X 1024 X 256 grid Density • Boundary conditions: x: closed, δEy = 0, particles reflected into opposite half z plane y: periodic z: conducting (b) 0 n/n 1 2 3 1A −2 10 0 100 200 300 400 500 x 6 B0 ≈12 nT; (c) 1 2 3 1A Bx lobe 0 4 x∞ equatorial β ~ 600 500 0 10 B /B • Lobe field = 2.4B0 at x = 192 400 x 2 10 • Electrons are adiabatic in right half of tailward gradient Bz region 300 2 0 0 100 200 300 x 400 500 Entropy Bubbles and the Entropy Profile The behavior of bubbles has been shown to be closely connected to the variation of the entropy as a function of distance down the tail (Birn et al., 2004). 1 1A 6 300 Constant B S It has long been speculated that small, isolated density depletions (“bubbles”) could form in the mid- or distant tail and propagate earthward due to buoyancy (Pontius and Wolf, 1990; Chen and Wolf, 1993). 400 z 200 Tailward Grad 100 Tailward Grad 0 200 300 400 500 x MHD Interchange Instability: • Hurricane et al. (1996) showed that the Lembege-Pellat (constant Bz) profile is unstable. • Maltsev & Mingalev (2000) showed criterion is satisfied for an increasing Bz if dV/dr < 0, where V = ∫dl/B is the flux tube volume. • More generally, tail-like equilibria are stable (unstable) when the entropy S increases (decreases) with distance down the tail (Schindler & Birn, 2004). The present equilibria have a decreasing entropy profile in the region of the tailward gradient in Bz and thus are likely to be unstable. 2D Reconnection Bz (a) (c) 1 Bz/B0 Bz/B0 2 1.5 1 0.5 0 −50 −40 −30 −20 −10 0 10 0 Density (b) (d) 1 2.5 10 2 1.5 1 0.5 0 −50 n/n0 2D simulation of a Harris sheet driven by a finite duration Ey driving field peaked at x = 0 produces an X line with fronts propagating both earthward and tailward. 180 200 220 0.5 n/n0 Alternative interpretation: The tailward gradient region in Bz could also represent the leading edge of a reconnection front viewed in the rest frame of the front. 2.5 0 10 180 200 220 −1 −40 −30 −20 x/di −10 0 10 10 (a) Bz Potential 500 0.15 400 0.1 512. 512. 256. 256. 0. 0. 0.05 y 300 0 200 −0.05 100 −0.1 0 0 (b) 100 200 x Ey 500 0.1 0. 128. 256. 0. 128. 256. 400 0.05 y 300 0 200 −0.05 100 −0.1 0 0 100 200 x Mode structures develop in right half of tailward gradient region where electrons are adiabatic. Equatorial plane structure has character of an interchange mode. Ue|| Ey (a) y = 464 (a) 0.12 100 y = 450 0.6 100 0.4 0.1 50 0.08 0.06 0 z z 50 0.2 0 0 0.04 0 0 100 200 x (b) y = 496 0 100 z 50 0 0 100 200 x Mode structures also extend along field lines earthward toward ionosphere. Unlike MHD interchange modes, there is large perturbation resulting from the finite E|| field. 0 100 200 x (b) y = 474 0.5 100 50 z 0.02 0 0 0 100 200 x Mode Intensities −2 10 Initial case: kyρin ~ 6 3.9 4.7 5.5 6.3 7.1 7.8 8.6 9.4 −4 10 −6 10 ky in −8 10 0 10 20 t i0 40 50 60 Mode Intensities −2 10 Second case: kyρin ~ 1 30 0.5 1.0 1.6 2.1 2.6 3.1 3.7 4.2 −4 10 −6 10 ky in −8 10 0 20 40 60 t i0 80 100 120 Mode Identification • Consider linear kinetic analysis where we model δφ and δB|| along equilibrium field lines and compute the local ion and electron density perturbations at the midplane. • Ions: Motion is stochastic (destroys gyromotion) and mode localized in x,z to ρin scale straight line orbits, respond only to electrostatic perturbation δni/nL = [Z′(s)/2] eδφ/T = -[1 + sZ(s)] eδφ/T, s = (ω - kyvdi)/kyvTi δni/nL = -[0.532 + 0.577i] eδφ/T WRONG PHASE RELATION Electron orbits average interaction with wave fields over flux tube volume; flux-tube averaged perturbed ion density becomes <δni/nL> = -[0.75 +sZ(s)/2] = -[0.515 + 0.289i]eδφ0/T AGREES WITH SIMULATION • Electrons: Electron orbits are adiabatic (κe >> 1) but wave and drift frequencies are not small compared with the bounce frequency. Thus full kinetic response including bounce and drift resonance interactions must be retained. Find that perturbed electron and ion flux tube averaged densities are in agreement. • Perturbed densities yield dispersion relation consistent with the simulations. The dominant polarizations δφ and δB|| are similar to polarization of lower hybrid drift instability in straight magnetic field geometry; the present ballooning/interchange mode appears to be related to the low frequency limit of the LHDI. Effect of Background Density on BICI (a) t = 56 i0 nb/n0 = 0 1000 (b) t = 69 i0 1000 0.45 0.4 800 (c) t = 103 i0 n /n = 0.08 b 0 1000 1.2 800 1 t = 122 i0 1000 0.8 0.3 800 0.7 800 0.25 0.35 600 (d) 0.8 600 0.3 600 0.6 600 0.5 y 0.2 0.25 400 0.2 400 0.6 0.4 0.15200 200 0.4 400 200 400 0.15 0.3 200 0.2 0.1 0.2 0.1 0.1 0 300 400 x 500 0 200 300 400 500 x 0 200 300 400 500 x 0 0 200 400 x • Initial case (nb = 0): linear BICI spectrum peaks at kyρin ~ 6 (wavelength ~ ρin); during earthward propagation, heads narrow and peak Bz increases, leaving several dominant heads with width ~ 600 - 900 km. • Second case (nb/n0 = 0.08): peak wavenumber is much smaller (kyρin ~ 1.0 - 1.5). Nonlinear evolution produces single dominant head with width ~ 5000 - 6000 km. This is now compatible with observed scale of DFs. Equatorial Plane DF Structure Profile at y = 630 1 (a) Bz Bz/B0 • Transition thickness of Bz (from 0.25 to 0.80) occurs over distance of 11 Δ = 1.1 di. 0.5 • Density drops by factor of 3 across the front. 0 100 8 • Ey strength increases with Bz to a peak of ~ 11 mV/m 150 200 250 (b) Density n/n0 6 4 as opposed to leaving amplification of front. 0 100 0.2 0 −0.2 −0.4 −0.6 −0.8 100 0 150 200 250 (c) cEy/vTiB0 • Electron bulk flow exceeds the ion behind the front but is smaller ahead of front. Magnetic flux frozen in to electron flow net increase in flux entering front 2 E y 150 200 250 (d) −0.5 Ux/vTi • Ion bulk flow speed increases only slowly across front and reaches max. behind the front [“growing” DF Fu et al., 2011] −1 −1.5 100 U ix Uex 150 200 x 250 Ωi0t = 127 Breakup of DF Head and FACs Bz, Jx,y B z 700 800 750 1 690 700 1.2 y • As DF propagates earthward, Bz increases; breakup occurs when local ρin < DF thickness. 0.5 650 680 600 • Multiple sub-heads comparable to local gyroradius. 550 50 800 • Pair of Region 1 sense FACs associated with each subhead. • FAC structuring of the DF is manifested in auroral streamer. A number of such structured streamers have been observed by THEMIS. J|| 10 750 0.8 660 5 y 700 650 0 600 −5 550 50 670 100 150 200 250 y • Cross-tail current Jy diverted around each of the heads. 1 0 100 150 200 250 x 650 0.6 640 0.4 630 620 0.2 610 0 600 100 110 120 x 130 THEMIS ASI OBSERVATION Structured Auroral Streamer 70° 100 km Streamer 65° FSIM Streamer breaking into substructures FSMI Size at 110 km: Map to plasma sheet: Simulation: substructure ~ 30 km ~ 1000 km width subhead ~ 800 km poleward portion ~ 100 km ~ 3000 km upward FAC region ~ 4000 km x = 100, y = 620, z = 20 • Away from the center of the plasma sheet, the DF is strongly modulated in time in association with intense wave activity. 0 115 120 125 130 120 125 130 125 130 125 130 2.8 2.6 (b) |B | x 2.4 2.2 115 (c) Density n/n0 2 1 0 cEy/vTiB0 • cEy/VTiB0 = 2 - 3 or 30 - 50 mV/m. • EM waves with δE/δB ~ 4 VA. Bz 0.2 • This activity is a precursor to the actual arrival of the DF. • The modulation is most apparent in Ey, Bx, and density, with less pronounced variation in Bz. (a) B/B0 0.4 B/B0 Off-Axis Properties of DF at the edge of the density gradient 0.6 2 115 (d) 120 E y 0 −2 • Similar intense waves much closer to the axis have been reported by M. Zhou et al. (2014), Bz >> Bx. Front position: 115 x= 208 120 t i0 138 70 Observation of large-amplitude magnetosonic waves at dipolarization fronts M. Zhou et al. 2014 Journal of Geophysical Research: Space Physics 2014JA019796, 2 JUN 2014 DOI: 10.1002/2014JA019796 http://onlinelibrary.wiley.com/doi/10.1002/2014JA019796/full#jgra51055-fig-0003 Intense EM Waves 2 20 1 t 125 i0 −20 0 −2 120 −40 500 (b) E 600 y y −1 700 −2 y = 628 115 2 −3 z 20 500 0 0 (c) Ey 50 100 x 150 200 3 y = 636 2 125 20 −0.5 z 4 130 0 0 1 0 120 −1 −1 −2 −20 −1.5 −40 700 Ey y = 622, z = 20 t 40 650 i0 −40 600 y (b) • Frequency = 0.24 ωlh = 0.96 Ωi,loc 550 1 0 −20 • Standing wave structure along field lines 2 0 0 40 • Wavelength = 0.7 x (local di) = 700 km 3 130 1 −1 • Waves propagate duskward at 0.51 VTi Ey x = 100, z = 20 (a) Ey x = 112 40 z • Wave activity concentrated in region of DF and extends somewhat duskward. (a) 0 50 100 x 150 200 115 −3 0 100 200 x y = 618 Particle Distributions in regions of intense waves x = 110, z = -22 Large net parallel drift for electrons that reverses sign depending on wave phase; net ion - electron parallel drift ~ 3.5 VTi. Likely to drive electromagnetic ion cyclotron instability [Perraut et al., 2000]. 4. 4. 0. 0. -4. Also strong ∂fe/∂v⊥ > 0 slope electron cyclotron harmonic waves. 4. 16. 16. 0. 0. -16. Zhou et al. (2014) attribute waves to ∂fi/∂v⊥ > 0 and identify it as ion Bernstein. y = 626 16. -4. 4. -16. 16. E J y = 620 Dissipation E J y = 620 40 40 20 20 2 0 2 −20 −2 −2 0 50 100 150 E J y = 628 −40 200 40 2 −2 −20 −4 0 50 100 150 150 200 E J y = 644 2 0 0 −40 200 −2 0 50 100 150 E J y = 644 200 40 20 10 0 5 −20 0 0 50 100 x 150 200 6 20 z z 100 E J y = 628 −20 40 −40 50 20 z 0 0 −40 0 40 20 • Strong dissipation is localized (on slightly sub-di scale) at the sub heads of the DF, E′ . J ~ 2 nW/m3. 0 0 0 −20 −40 z z 4 z • In wave region alternating regions of generator (E . J < 0) and load (E . J > 0); very little dissipation (E′. J > 0), where E′ = E + U x B. 4 6 4 0 2 −20 0 −40 −2 0 50 100 x 150 200 Poynting Vector Components Sx y = 628 Sy y = 628 40 Sz y = 628 40 40 0.4 0.2 20 20 0 −0.4 0 0 50 100 150 200 −0.8 0 0 −2 −2 −20 −20 −0.6 −40 2 z z z −0.2 −20 4 20 0 0 6 2 −4 −4 −40 0 50 Sx y = 636 100 150 −6 −40 200 0 50 Sy y = 636 40 150 200 Sz y = 636 40 40 4 0.5 20 100 5 20 2 20 0 0 0 −0.5 −20 −40 −1 0 50 100 x 150 200 z 0 z z 0 −20 −2 −20 −40 −4 −40 0 50 100 150 200 0 −5 0 x Intense Poynting Vector Fluxes: • Circulating cell patterns (north-dawn-south-dusk) ~ 1 mW/m2 • Alternating components to and from ionosphere ~ 0.1 mW/m2 50 100 x 150 200 Properties of Reconnection Fronts • Multi-point studies suggest that full width of high-speed flow channels in plasma sheet are of order 1 - 3 RE (Sergeev et al., 1996; R. Nakamura et al., 2004). • Can such finite cross-tail flows be produced directly by reconnection? • Hall MHD studies indicate that expansion of a finite reconnection region proceeds at a rate given by the relative electron - ion flow speed (Huba and Rudakov, 2002; Shay et al., 2003; TKM Nakamura et al., 2012). netohydrodynamic effects for three-dimensional magnetic reconnection with finite Hall magnetohydrodynamic effects for three-dimensional magnetic reconnection wit width along the direction of the current width along the direction of the current Ions carry initial current sical Research: Space Physics 3, A03220, 16 MAR 2012 DOI: 10.1029/2011JA017006 ley.com/doi/10.1029/2011JA017006/full#jgra21592-fig-0001 Electrons carry initial current Journal of Geophysical Research: Space Physics Volume 117, Issue A3, A03220, 16 MAR 2012 DOI: 10.1029/2011JA017006 http://onlinelibrary.wiley.com/doi/10.1029/2011JA017006/full#jgra21592-fig-0002 • Use 3D PIC simulation in which localized region is initiated by periodically blocking the Jy current density in the center of the current sheet (Pritchett & Coroniti, 2002). This represents the upper limit to the effects that can be produced by the onset of an anomalous resistance within a growth phase thin near-Earth current sheet. The blocking leads to an enhancement of the Ey and to the formation of a localized reconnection region. • Initial blocking region: 0 < x < 3di, 30di < y < 34di • System size: -64di < x < 64di, 0 < y < 64di J J iy 36 0 y 36 0.1 34 34 y/di −0.2 32 0 32 0 2 x/di 4 6 8 28 −4 −2 36 0 34 −0.2 −0.1 32 −0.4 −0.4 30 30 28 −4 −2 E/ t ey −0.2 30 0 2 x/di 4 6 8 −0.3 28 −4 −2 −0.6 0 2 x/di 4 6 8 Bz Add 0.02 normal field and vary width of blocking region. 50 0.5 y/di 40 30 0 20 −0.5 −50 Bz 0 t = 75 i0 50 0.5 30 0 20 −0.5 −50 0 0 50 t = 75 i0 x/di 1 30 0 20 −1 −50 Bz w = 8di 0 50 x/di Density w = 8di 1.5 1 y/di 20 0.5 0 10 4 30 3 20 2 10 1 −0.5 0 • Appears likely to have a minimum width of front. Uix 40 10 50 30 • Breakup less pronounced on tailward propagating front. −50 50 40 10 0.5 20 10 50 1 30 y/di 10 1.5 40 y/di 50 t = 75 i0 y/di • Extended front appears to break up on scales of a few di. Density y/di • Max Bz follows electrons slightly dawnward, but the jet front is blown duskward by the ion flow; elongated front on scale of tens of di >> initial perturbation. t = 47 i0 −20 0 x/di 20 0 −20 0 x/di 20 Summary/Questions • Key feature of plasma sheet is presence of a finite Bz component. This necessitates a kinetic treatment of plasma sheet dynamics. • Spontaneous tearing instability appears to be unlikely due to magnetization of the electrons. How can reconnection be initiated? • Jet (dipolarization) fronts are common feature of the tail; possess kinetic scale thickness. What determines the cross-tail extent of ~ 1 - 3 RE? • Ballooning/interchange mode reproduces the key features of the fronts and predicts the structuring of auroral steamers and the presence of intense off-axis EM waves near Ωci. Recent THEMIS observations offer confirmatory examples of these features. • But how common are the conditions of decreasing entropy with radial distance down the tail that appear to be necessary for excitation of the modes? • Can localized perturbations (perhaps from the dayside) produce reconnection jets that mimic the properties of the BICI mode? • What happens when these fronts impact a growth-phase thinned near-Earth plasma sheet system?