(Plasma Instabilities and) Magnetic Reconnection

Transcription

1 (Plasma Instabilities and) Magnetic Reconnection Prof. Christopher J. Owen UCL/Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, United Kingdom 8 th September 2016

2 Outline Very brief introduction to instabilities Ohms laws in a plasma, magnetic topology; What is reconnection?; Characteristics of reconnection models; Reconnection in different applications; Observational tests of reconnection processes; The way forward MMS; Conclusions. 8 th September 2016

3 Basic Concept of an Instability Unstable Equilibrium Stable Equilibrium If the stable equilibrium is perturbed, the ball returns to starting position, or oscillates about it if the damping is weak; If the unstable equilibrium is perturbed, the ball runs away. If W(x) is the potential energy, then the particle feeds a force: FX = - W/ x Equilibria occur when W/ x = 0 To lowest order in the Taylor expansion about an equilibrium point, the change in potential energy is: The equilibria are stable when The equilibria are unstable when ଶ ଶ ଶ 8 th September 2016

4 List of plasma instabilities Bennett pinch instability (also called the z-pinch instability ) Beam acoustic instability Bump-in-tail instability Buneman instability Cherenkov instability Chute instability Coalescence instability Collapse instability Counter-streaming instability Cyclotron instabilities, including: Alfven cyclotron instability Electron cyclotron instability Electrostatic ion cyclotron Instability Ion cyclotron instability Magnetoacoustic cyclotron instability Proton cyclotron instability Nonresonant Beam-Type cyclotron instability Relativistic ion cyclotron instability Whistler cyclotron instability Diocotron instability (similar to the Kelvin-Helmholtz fluid instability) Disruptive instability in tokamaks) Double emission instability Drift wave instability Edge-localized modes Electrothermal instability Farley-Buneman instability Fan instability Filamentation instability Firehose instability (also called Hose instability) Flute instability Free electron maser instability Gyrotron instability Helical instability (helix instability) Helical kink instability Hose instability (also called Firehose instability) Interchange instability lon beam instability Kink instability Kelvin-Helmholtz fluid instability Lower hybrid (drift) instability (in the Critical ionization velocity mechanic Magnetic drift instability Magneto-rotational instability (in accretion disks) Magneto-thermal instability (Laser-plasmas) Modulation instability Non-Abelian instability (see also Chromo-Weibel instability) Chromo-Weibel instability Non-linear coalescence instability Oscillating two stream instability, see two stream instability Pair instability Parker instability (magnetic buoyancy instability) Peratt instability (stacked toroids) Pinch instability Sausage instability Slow Drift Instability Tearing mode instability Two-stream instability Weak beam instability Weibel instability z-pinch instability, also called Bennett pinch instability 8 th September 2016

5 Some notes on instabilities So plasmas can host numerous instabilities! Note that any equilibrium will not exist for long if it is unstable; Plasma instabilities are a source of turbulence and related phenomena which can in turn drive transport of energy, momentum and/or plasmas; Instabilities often play an important role in energy conversion between electromagnetic fields and the plasma; Thus plasma instabilities are responsible for a number of energetic phenomena (magnetospheric substorms, stellar flares, coronal mass ejections, etc.) 8 th September 2016

6 Some Examples Rayleigh-Taylor Instability Dense fluid sitting on top of sparse fluid Kelvin-Helmholtz Instabilty Flow shear across a boundary N.B. fluid B-field Vortex formation in nonlinear stage 8 th September 2016

7 Some Examples B Resistive Instabilities: Tearing Instability: A B Current Filamentation CS Kink Instability: Deformation leads to high magnetic pressure at A, low at B; Thus tendency to amplify the perturbation. N.B. Magnetic tension due to any B-field along tube will have a stabilising effect. 1-D (Harris-type) current sheet equilibrium becomes unstable to long-wavelength resisitive modes Current filamentation and reconfiguration of the B-field; Magnetic energy release B 8 th September 2016

8 Ideal MHD Ohms Law Many (most) solar, solar wind, terrestrial and planetary plasmas are sufficiently tenuous that collisions between particles are rare, there are very long mean free paths and classical resistivity is very low: E + v B = 0 This corresponds to frozen-in flow which is a good approximation for large-scale space plasma systems. 8 th September 2016

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10 Magnetic Topology Conserved Strict frozen-in implies no mixing of plasma populations and thus distinct and identifiable (through the plasma on them) tubes of magnetic flux; However, this very nature can lead to a violation of the conditions which created it! 8 th September 2016

11 Generalised Ohms Law for a Plasma Potential difference between 2 points can in principle be altered by flow of current and/or other properties of the plasma: The RHS terms are: j 1 ne e E v B j j B.Pe 2 1 ne j B 1.P e ne m e 2 ne j t 1 ne resistive term (like the ordinary Ohms law); Hall term due to Lorentz force; ne j t term due to a possible anisotropic electron pressure; 8 th September 2016 term due to contribution of electron inertia to current; m

12 Induction Equation Many of you will be familiar with the Induction equation for a plasma which can be derived from an Ohms law with just the resistive term on the RHS: B t v B 1 A dimensional analysis on the scales of the terms of the RHS leads to the magnetic Reynolds number for the Convection Term Diffusion Term plasma, R M = VL/η and timescale for diffusion Τ D = L 2 /η; Most solar system plasmas have large L, very low η, so large R M, Τ D ; However, if variations over small scale lengths develop, then the diffusion effects can become significant. 8 th September B ; o

13 Topology Changer Treumann and Baumjohann, 2014 If sharp gradients (small L) are allowed to form then diffusion processes can become important. This diffusion allows the field to evolve on the small scale, but this can lead to changes in the more global topology of the field. 8 th September 2016

14 SLOW INFLOW FAST OUTFLOW JET? Magnetic Reconnection Key Points Application of strict frozen-in flow implied that magnetic field and plasma from different sources could not mix; However, the frozen-in flow approximation is not always valid where gradients are sharp; Reconnection allows: 1. Magnetic field regions that were previously independent to interact; 2. The plasma populating the magnetic fields to intermix; 3. Plasma is accelerated into jets as magnetic energy is released. 8 th September 2016

15 What is outflow speed? Simple case can be derived in back-of-theenvelope consideration of energy conversion: Consider elemental volume of inflow plasma, number density n, in field of strength B, which E x B drifts into a 1-d current sheet; Consider further that, for simplicity all the associated inflow magnetic energy flux is converted to outflow ion kinetic energy flux during the interaction with the current sheet, ignoring inflow KE: What will be the outflow speed of the particles? 8 th September 2016

16 Answer Upstream magnetic energy density is: 2 So magnetic energy flux into area A of current sheet: ExB Particle flux into same area: ExB If each particle (ion) gains K.E. equal to its share of the available magnetic energy then: ExB 2 2 o ExB i out 2 o o ; 8 th September 2016

17 Timescales Note that the timescale for propagation of the outflow across the system (T out = L/V out ) is much larger than the diffusion timescale (Τ D = L 2 /η); Indeed the ratio of these timescales defines the Lundqvist number: S = T D /T out = LV out /η S is very large in many astrophysical situations: E.g. S ~ in solar corona hence resistive diffusion can be considered very slow and ineffective. This was a problem for early models of reconnection, despite more sophisticated analysis 8 th September 2016

18 Early Steady-State Models a) Sweet-Parker: Broad inflow, Narrow outflow channel; Reconnection rate: ௩ ௩ ೠ ଵ b) Petschek reconnection: standing slow mode MHD shockwaves in the inflow region Reconnection rate: ௩ గ ௩ ೠ ଵ ୪୬ Generally these rates are too small to account for observations (e.g. of flares, magnetopause reconnection, M ~ 0.1) 8 th September 2016

19 But does η 0 arise? True Ohmic resistivity (due to collisions of the charge carriers retarding flow) in the plasma remains low; Anomalous resistivity can, in principle, arise through a number of ways of scattering particles and retarding the flow of current, e.g.: Wave-particle interactions in the diffusion region; Turbulent/stochastic motions in the diffusion region; Effects of various possible instabilities in the diffusion region; Identification of specific mechanisms (which may anyway be different in different contexts) has been hampered by lack of sufficiently detailed observations and simulations; (Indeed in early simulations reconnection often occurred due to numerical resistivity inherent within the codes!) 8 th September 2016

20 Hall Reconnection Of course, each of the other terms in the generalised Ohms law potentially provides a means to support the occurrence of magnetic reconnection; Over the last ~10 years consideration of reconnection in the background of Hall MHD has received significant attention; Hall term arises due to differences in the behaviour of ions and electrons i.e. this is a two-fluid effect: Key issue electrons remain frozen to field for longer than the ions; Thus diffusion region develops two-scale structure the ion diffusion region is larger than the electron diffusion region; Quadrupolar out-of-plane magnetic fields develop; Net effect inclusion of Hall term increases reconnection rate. 8 th September 2016

21 OUTFLOW Hall Reconnection Geometry +ΔB Y -ΔB Y HALL CURRENT SYSTEMS INFLOW -ΔB Y +ΔB Y Fast ion flows associated with field reconfiguration Ion and electron decoupling in ion DR Hall electric current Quadrupole out-of-plane magnetic field components Electron diffusion in e - DR topology change 3D Multi-scale process! electron demagnetized, (electron diffusion region ~25 km, T ~ 0.1s) ion demagnetized (ion diffusion region ~1000 km T ~ 1s) Outflow jets (Global scale ~10s R E, T ~ secs mins) 8 th September 2016

22 OUTFLOW Hall Reconnection Geometry +ΔB Y -ΔB Y HALL CURRENT SYSTEMS INFLOW E Y E Y -ΔB Y +ΔB Y A cross-tail electric field E Y drives reconnection (it can be shown to be equivalent to the reconnection rate). How/where is this electric field supported? Consider the generalised Ohms Law: E v i B j j B en e m e e dv dt e.p en e e 8 th September 2016

23 Ohm s Law Reconnection Electric Field E Y e.g. Hall-MHD simulations by Yin et al., Phys. Plasmas, 2003: A) Ideal MHD contribution is significant on the large scale; B) Ion decoupling scale (Hall) contribution appears around central sheet; C) The contribution from the electron pressure tensor term is very localised. This originates from the derivatives of the off-diagonal terms. Z Z Z Z Z Z v i B j B en e P en e e A B C E Y X Sun 8 th September 2016

24 Magnetic Reconnection in Action 8 th September 2016

25 Magnetic Reconnection in the Universe (i) Example: SGR Magnetar produced an intense gamma-ray flare on December 27, 2004: Loss of equilibrium through magnetic diffusion and/or reconnection drives small cracks in the neutron star crust frequent short γ-ray bursts; Global rearrangements of the magnetic field in the interior and magnetosphere (reconnection?) of the star (Movie from NASA Web) giant flares. 8 th September 2016

26 A Model of Solar Flares Solar flares are dramatic events releasing up to J of stored magnetic energy over a period of hours strong brightening in soft x- rays; Flares generate plasma heating and fast particle beams - signatures across the EM spectrum from gamma rays to radio; Primary energy release process believe to be magnetic reconnection. Tsuneta th September 2016

27 Evidence for Reconnection in Flares Yokoyama et al, th September 2016

28 Evidence for Reconnection in Flares Yokoyama et al, 2000 Plasmoid ejection X-Point Inflow Heated plasma on reconnected loop CME ejection and coronal loop formation interpreted as a result of magnetic reconnection the breaking and reconfiguring of the solar magnetic field. These are interpretations of remotely sensed data but can we directly examine the physics of this process?

29 The In situ Advantage? How can we get to the real physics underpinning reconnection processes and test otherwise poorly constrained hypotheses? The only hope to realistically probe reconnection physics within a reasonable timescale is through relevant in-situ measurements in regions in which it occurs in and around our own magnetosphere;

30 The Magnetospheric Plasma Laboratory The in situ Advantage The terrestrial magnetosphere and its surroundings are readily accessible laboratories Reconnection occurs in a number of contexts: Although the parameter regimes may differ significantly, unique in situ measurements of processes in and around the terrestrial magnetosphere have potential value to the broader understanding of reconnection? BOW SHOCK Magnetopause SOLAR WIND

31 Reconnection in the Solar Wind Reconnection may occur coherently over very large spatial distances and persist for many hours Phan et al., 2006

32 Reconnection in the Solar Wind On the other hand, evidence also exists for reconnection happening in more localised patches in space and/or time:. (this example form Foster et al. 2016) Foster et al., 2015

33 Some tests of reconnection in or around the terrestrial magnetosphere.

34 [Phan et al., 2001] De Hoffman-Teller and Walen Tests On reconnected field lines, MHD and cold plasma theory suggests that as the plasma crosses the current layer, it should be accelerated by speeds ~VA, the external Alfvèn speed (± the external flow speed). Strong correlations from these analyses can provide an operational test of whether an observed plasma flow may be a result of reconnection.

35 Particle Distributions in the Dayside Boundary Layer - Theory VF Log f (m-6 s3) (I) (IR) (MT) He+ (R) O+ (RR) VL (km s-1) Magnetospheric populations of ionospheric (I) and ring current (R) origin are partially reflected and accelerated at the MP (IR, RR). The external magnetosheath population (MT) is accelerated and transmitted through the MP. Only those magnetosheath particles with speeds greater than VF (=VDHT) can move into the boundary layer. The resulting distribution of sheath particles has a D -shape [Cowley, 1982].

36 Particle Distributions in the Dayside Boundary Layer - Observation Magnetosheath Boundary Layer Smith and Rodgers [1992]

37 Gosling et al., [1990] Effects of IMF BY

38 Asymmetric Plasma Entry to Magnetotail

39 Cowley [1982] Magnetotail Twisting i) Southward BZ Owen et al. [1995]

40 Magnetotail Twisting ii) N BZ

41 Hall Reconnection Geometry OUTFLOW INFLOW +ΔBY -ΔBY HALL CURRENT SYSTEMS -ΔBY Fast ion flows associated with field reconfiguration Ion and electron decoupling Hall electric current +ΔBY Quadrupole out-of-plane magnetic field components Electron diffusion 3D Multi-scale process! electron demagnetized, (electron diffusion region ~25 km, T ~ 0.1s) ion demagnetized (ion diffusion region ~1000 km T ~ 1s) Outflow jets (Global scale ~10s RE, T ~ secs mins)

42 J (na m-2) Current Sheet Lobe Some Observational Evidence for Hall Reconnection Runov et al., [2003] demonstrated the existence of quadrupolar BY structure during multiple Cluster crossings of the current sheet; B Y (nt) Earthward Flow Region, North Lobe Quadrant Alexeev et al., [2005] determined parallel currents carried by electrons and showed average electron J e reverses at B X ~ nt, with a corresponding enhanced +ve B Y. B X (nt)

43 .and many more Manifestations of time dependent reconnection modulated by the interplanetary magnetic field. Flux Transfer Events; Magnetospheric substorms; Twisting of the magnetosphere by magnetic torques applied by reconnected field lines; Asymmetric plasma entry into magnetosphere; Reconnection in Kelvin-Helmholtz vortices; Velocity-dispersed plasma entry into the boundary layers and magnetic cusps; Etc.

44 The Way Forward Although Cluster (and other multi-point missions) have provided some real constraints for hypothesis testing, it is unable, for example, to resolve the controlling microphysics of the electron diffusion region: Particle instruments generally restricted to timescales associated with spacecraft spin rates for full 3D measurements This is insufficient to determine, for example: the roles played by electron pressure gradient and inertial effects (c.f. generalised Ohms law; the role of turbulent dissipation in driving magnetic reconnection in the electron diffusion region; the rate of magnetic reconnection and the parameters that control it. the role played by ion inertial effects in the physics of magnetic reconnection.

45 Important Scale Sizes 100,000 km 500 km 100 km Unstable, thin current sheets have thickness < 1000 km Electron diffusion region thickness is of order 10 km Current sheet motion is typically 10 to 100 km/s Required time resolution for electron diffusion region is ~30 ms 45

46 Magnetospheric Multiscale Mission The MMS Mission science addresses magnetic reconnection using the Earth s magnetosphere as a laboratory; Small spacecraft separations, very fast plasma measurements used to target the time and space scales of the electron diffusion region; Launch occurred on March 12,

47 Fast Plasma Instrument (FPI) First Video Plasma Analyzer Objective: Image full sky at 32 energies: electrons in 30 ms, ions in 150 ms DIS DES DIS DES Design Concept: Four ion and four electron dual DES deflecting-aperture top hat DIS sensors for field of view and aperture DIS DES Dual Electron Sensor: DES DES Cutaway Dual Ion Sensor: DIS 47

48 Special MMS First Results issue, August N.B 3 Seconds!

49 Some things not discussed..include: A plethora of simulation results testing / predicting the action of various physical processes in driving magnetic reconnection; Reconnection in more complex 3D magnetic field geometries (mostly relevant to the solar photosphere/corona application); Reconnection at nulls, spines, fans, separators, quasi-separatrix layers, etc. and more. Priest & Forbes, 2000

50 Conclusion: Some Key Questions on Magnetic Reconnection How is reconnection initiated? What triggers reconnection within a current sheet and determines how fast it proceeds? How do the plasmas and magnetic fields disconnect/reconnect in the diffusion regions? How are thin current sheets formed? What is the role of external driving in reconnection onset? What parameters control the spatial/temporal characteristics of a reconnection site? How is a reconnection neutral line (or diffusion region or multiple X-line) structured? Why (when?) is reconnection bursty/steady/intermittent? How significant are the effects of a guide field, velocity shear and density gradients? What are the effects of different particle populations on the reconnection process? What are the consequences of reconnection? How are ions and electrons energized as a consequence of reconnection? How are Alfvén waves and other plasma waves generated near the reconnection site?; how these waves interact with ambient plasma? How does the reconnection jet interact with Earth dipole field?

51 END Thank you for listening.

52 Support/Deleted/No-time-for Slides

53 MHD Equations (Recap) n n v 0 t 2 1 B B. B F v v.p q E t v P 0* t q B E = t.e = 1 E B = o j + 2 c t.b = 0 o A set of magneto-fluid equations that are adequate to describe a plasma: On long time-scales; On long spatial scales. * Or terms representing sources of energy

54 Magnetic Reconnection? On small scale-lengths (i.e. at sharp gradients), a diffusion region (physics unknown) can form where the magnetic field can diffuse through the plasma (i.e. a breakdown of the frozen-in principle).

55 Mixing of Plasma Populations

56 Velocity Filter Effects B VEXB 2VP VEXB VF VP NL Gosling et al. [1990]

57 Cusp Velocity Dispersion for Southward IMF

58 The Cluster Contribution CLUSTER is an ESA mission consisting of 4 spacecraft orbiting in formation with separations varying between a few hundred and ~10000 km Multi-point measurements allow some assessment of the action of gradients, motion of waves and boundaries, and variations across different regions; In situ measurements by Cluster reveal that large-scale dynamics are controlled by processes such as magnetic reconnection; We have been able to directly test some aspects of theoretical models.

59 Empirical Evaluation of Terms in Generalised Ohms Law Note both j B B o B and P e are derived from gradient terms, and thus both need multi-point (i.e. Cluster) measurements; Henderson et al. (2006) attempted to measure and compare these two terms; Looked at small Cluster separations in the magnetotail current sheet: ~ 200 km in Calculated for the first time the spatial derivatives of the full tensor of the plasma distribution; required non-trivial inter-spacecraft calibration efforts

60 Ohm s Law Other components of E also appear: EZ Hall Term Contributions to EZ from Hall and electron pressure tensor are spatially more extended; Z - The field from the Hall term points towards the sheet. EZ -.P Term - The field from the.p term points away from the sheet. X

61 2. Analysis techniques Henderson et al., (2006) Observations taken close to an active X-line on 17th Aug 2003; No encounter with the diffusion region, but observed an anti-correlation in.pe and Hall terms in the component normal to the neutral sheet.

62 JxB/ne (-.P/ne) JxB/ne (-.P/ne) x -5.3

63 Result consistent with the simulations shown earlier, but what are the wider implications? the result is repeatable in other events, although the ratio of the two terms varies; Is this a function of plasma conditions/reconnection rates at the X-point itself (electron scale)? Here the electrons play a crucial role, but the relevant variations occur on time and spatial scales (0.1sec, 10 km) that can not be fully resolved by Cluster. E.g. Electron scale current layers shown here (~20km, 510 le,re) seen for only a fraction of a spin (4 secs, minimum time needed to resolve full particle distribution) Alternately this may be a function of the large (MHD) scale boundary conditions (lobe field strength, plasma sheet density/ temperature)? Andre et al., secs

64 Energetic Particle Acceleration Electron acceleration within the reconnection region: Cold electrons are accelerated to kev energies by very small timescale (millisecond) interactions with electric field solitary waves [Cattell et al., 2005]. Further acceleration to 100 s kev involves nonadiabatic processes in the outflow region [Imada et al., 2007].