Collisionless Magnetic Reconnection

1
Collisionless Magnetic Reconnection

• J. F. Drake
• University of Maryland
• Magnetic Reconnection Theory 2004
• Newton Institute

2
Collisionless reconnection is ubiquitous

• Inductive electric fields typically exceed the
  Dreicer runaway field
• classical collisions and resistivity not
  important
• Earths magnetosphere
• magnetopause
• magnetotail
• Solar corona
• solar flares
• Laboratory plasma
• sawteeth
• astrophysical systems?

3
Resistive MHD Description

• Formation of macroscopic Sweet-Parker layer

V (? /L) CA (?A/?r)1/2 CA ltlt CA

• Slow reconnection
• sensitive to resistivity
• macroscopic nozzle

• Petschek-like open outflow configuration does
  not appear in resistive MHD
• models with constant resistivity (Biskamp
  86)
• Why Sweet-Parker?

4
Singular magnetic island equilibria

• Allow reconnection to produce a finite magnetic
  island ( )
• Shut off reconnection (? 0) and evolve to
  relaxed state
• Formation of singular current sheet
• Equilibria which form as a consequence of
  reconnection are singular (Jemella, et al, 2003)
• Sweet-Parker current layers reflect this
  underlying singularity
• Consequence of flux conservation and requirement
  that magnetic energy is reduced (Waelbroeck, 1989)

5
Overview

• MHD Reconnection rates too slow to explain
  observations
• solar flares
• sawtooth crash
• magnetospheric substorms
• Some form of anomalous resistivity is often
  invoked to explain discrepancies
• strong electron-ion streaming near x-line drives
  turbulence and associated enhanced electron-ion
  drag
• observational evidence in magnetosphere
• Non-MHD physics at small spatial scales produces
  fast reconnection
• coupling to dispersive waves critical
• Results seem to scale to large systems
• Disagreements in the published literature
• Mechanism for strong particle heating during
  reconnection?

6
Kinetic Reconnection

• Coupling to dispersive waves in dissipation
  region at small scales produces fast magnetic
  reconnection
• rate of reconnection independent of the mechanism
  which breaks the frozen-in condition
• fast reconnection even for very large systems
• no macroscopic nozzle
• no dependence on inertial scales

7
Generalized Ohms Law

• Electron equation of motion

?s
c/?pi
c/?pe
scales
kinetic Alfven waves
Electron inertia
whistler waves

• MHD valid at large scales
• Below c/?pi or ?s electron and ion motion
  decouple
• electrons frozen-in
• whistler and kinetic Alfven waves control
  dynamics
• Electron frozen-in condition broken below c/?pe
• Non-gyrotropic pressure tensor dominates

8
Kinetic Reconnection no guide field

• Ion motion decouples from that of the electrons
  at a distance from the x-line
• coupling to whistler and kinetic Alfven waves
• Electron velocity from x-line limited by peak
  phase speed of whistler
• exceeds Alfven speed

c/?pi
9
GEM Reconnection Challenge

• National collaboration to explore reconnection
  with a variety of codes
• MHD, two-fluid, hybrid, full-particle
• nonlinear tearing mode in a 1-D Harris current
  sheet
• Bx B0 tanh(x/w)
• w 0.5 c/?pi
• Birn, et al., JGR, 2001, and companion papers

10
GEM tearing mode evolution

• Full particle simulation (Hesse,GSFC)

11
Rates of Magnetic Reconnection
Birn, et al., 2001

• Rate of reconnection is the slope of the ? versus
  t curve
• All models which include the Hall term in Ohms
  law yield essentially identical rates of
  reconnection
• Reconnection insensitive to mechanism that breaks
  frozen-in condition
• MHD reconnection is too slow by orders of
  magnitude

12
Reconnection Drive

• Reconnection outflow in the MHD model is driven
  by the expansion of the Alfven wave
• Alfvenic outflow follows simply from this picture
• Coupling to other waves in kinetic and two-fluid
  models
• Whistler and kinetic Alfven waves
• Dispersive waves

13
Why is wave dispersion important?

• Quadratic dispersion character
• ?? k2
• 
  Vp k
• smaller scales have higher velocities
• weaker dissipation leads to higher outflow speeds
• flux from x-line vw
• insensitive to dissipation

14
Wave dispersion and the structure of nozzle

• Controlled by the variation of the wave phase
  speed with distance from the x-line
• increasing phase speed

• Closing of nozzle
• MHD case since Bn and CA increase with distance
  from the x-line

- decreasing phase speed

• Opening of the nozzle
• Whistler or kinetic Alfven waves v B/w

15
Dispersive waves

• Geometry
• whistler
• kinetic Alfven

16
Whistler Driven Reconnection weak guide field

• At spatial scales below c/?pi whistler waves
  rather than Alfven waves drive reconnection. How?

• Side view

• Whistler signature is out-of-plane magnetic field

17
Whistler signature

• Magnetic field from particle simulation
  (Pritchett, UCLA)

• Self generated out-of-plane field is whistler
  signature

18
Coupling to the kinetic Alfven wave with a guide
field

• Signature of kinetic Alfven wave is odd parity
  density perturbation

Kleva et al, 1995
19
Structure of plasma density
Bz00

• Even parity with no guide field
• Odd parity with guide field
• Kinetic Alfven structure

Bz01.0
Tanaka, 1996 Pritchett, 2004
20
Parameter space for dispersive waves

• Parameters

• For sufficiently
• large guide field
• have slow
• reconnection

Rogers, et al, 2001
21
Fast versus slow reconnection

• Structure of the dissipation region
• Out of plane current

With dispersive waves
No dispersive waves

• Equivalent results in Cafaro, et al. 98,
  Ottaviani, et al., 1993

22
Positron-Electron Reconnection

• Have no dispersive whistler waves
• Displays Sweet-Parker structure yet reconnection
  remains fast

Hesse et al. 2004
23
Fast Reconnection in Large Systems

• Large scale hybrid simulation

• Kinetic models yield Petschek-like open outflow
  configuration
• Consequence of coupling to dispersive waves
• Rate of reconnection insensitive to system size
  vi 0.1 CA
• Does this scale to very large systems?
• Disagreements in the literature on this point

24
Dissipation mechanism

• What balances Ep during guide field reconnection?
• In 2-D models non-gyrotropic pressure can balance
  Ep even with a strong guide field (Hesse, et al,
  2002).

Bz0
Bz1.0
y
y
25
3-D Magnetic Reconnection

• Turbulence and anomalous resistivity
• self-generated gradients in pressure and current
  near x-line and slow shocks may drive turbulence
• In a system with anti-parallel magnetic fields
  secondary instabilities play only a minor role
• current layer near x-line is completely stable
• Agreement on this point?
• Strong secondary instabilities in systems with a
  guide field
• strong electron streaming near x-line leads to
  Buneman instability and evolves into nonlinear
  state with strong localized parallel electric
  fields produced by electron-holes and lower
  hybrid waves
• resulting electron scattering produces strong
  anomalous resistivity that may compete with
  non-gyrotropic pressure

26
Observational evidence for turbulence

• There is strong observational support that the
  dissipation region becomes strongly turbulent
  during reconnection
• Earths magnetopause
• broad spectrum of E and B fluctuations
• fluctuations linked to current in layer
• Sawtooth crash in laboratory tokamaks
• strong fluctuations peaked at the x-line
• Magnetic fluctuations in Magnetic Reconnection
  eXperiment (MRX)

27
3-D Magnetic Reconnection with guide field

• Particle simulation with 670 million particles
• Bz5.0 Bx, mi/me100
• Development of strong current layer
• Buneman instability evolves into electron holes

y
x
28
Buneman Instability

• Electron-Ion two stream instability
• Electrostatic instability
• g w (me/mi)1/3 wpe
• k lde 1
• Vd 1.8Vte

Ez
z
Initial Conditions Vd 4.0 cA Vte 2.0 cA
x
29
Formation of Electron holes

• Intense electron beam generates Buneman
  instability
• nonlinear evolution into electron holes
• localized regions of intense positive potential
  and associated bipolar parallel electric field

Ez
z
x
30
Electron Energization
Electron Distribution Functions
Scattered electrons
Accelerated electrons
31
Anomalous drag on electrons

• Parallel electric field scatter electrons
  producing effective drag
• Average over fluctuations along z direction to
  produce a mean field electron momentum equation
• correlation between density and electric field
  fluctuations yields drag
• Normalized electron drag

32
Electron drag due to scattering by parallel
electric fields
y

• Drag Dz has complex spatial and temporal
  structure with positive and negative values
• Results not consistent with the quasilinear model

x
33
Energetic electron production in nature

• The production of energetic electrons during
  magnetic reconnection has been widely inferred
  during solar flares and in the Earths
  magnetotail.
• In solar flares up to 50 of the released
  magnetic energy appears in the form of energetic
  electrons (Lin and Hudson, 1971)
• Energetic electrons in the Earths magnetotail
  have been attributed to magnetic reconnection
  (Terasawa and Nishida, 1976 Baker and Stone,
  1976).
• The mechanism for the production of energetic
  electrons has remained a mystery
• Plasma flows are typically limited to Alfven
  speed
• More efficient for ion rather than electron
  heating

34
Observational evidence

• Electron holes and double layers have long been
  observed in the auroral region of the ionosphere
• Temerin, et al. 1982, Mozer, et al. 1997
• Auroral dynamics are not linked to magnetic
  reconnection
• Recent observations suggest that such structures
  form in essentially all of the boundary layers
  present in the Earths magnetosphere
• magnetotail, bow shock, magnetopause
• Electric field measurements from the Polar
  spacecraft indicate that electron-holes are
  always present at the magnetopause (Cattell, et
  al. 2002)

35
Electron acceleration during reconnection
Bz01.0

• Strongest bulk acceleration in low density
  cavities where Ep is non-zero
• Not at x-line!!
• Pritchett 2004
• Length of density cavity increases with system
  size
• Maximum vparallel increases with system size
• Longer acceleration region

36
Structuring of the parallel electric field along
separatrix 2-D

• The parallel electric field remains non-zero in
  the low density cavities that parallel the
  magnetic separatrix
• Drive strong parallel electron beams
• Strong electron beams break up Ep into localized
  structures
• Electron holes and double layers
• Most intense in density cavities

By1.0
37
Electron-holes and double layers

• Structure of Ep along field line
• Electron holes and double layers
• Structures predominate in low density cavity
  remote from the x-line

38
Electron distribution functions
cavity

• Cold energetic beam in cavity
• Hot streaming plasma ejected along high density
  separatrix

Outflow separatrix
39
Electron heating

• Electron cooling in cavity accelerators
• Well known from accelerator theory
• Cooling along direction of acceleration
• Strong heating along high density side of
  separatrix
• Beams are injected into x-line from cavity
  accelerator
• Scattered into outflow along high density
  separatrix
• Strong acceleration within secondary island
• Multiple passes through acceleration region

40
Electron energization with a guide field

• Bz1.0
• High energy tail from multiple interactions with
  x-line in secondary island

41
Electron acceleration in a secondary island

• Test particle acceleration in the secondary
  island is consistent with the large electron
  heating seen in the full simulation in this region

42
Conclusions

• Fast reconnection requires either the coupling to
  dispersive waves at small scales or a mechanism
  for anomalous resistivity
• Coupling to dispersive waves
• rate independent of the mechanism which breaks
  the frozen-in condition
• Can have fast reconnection with a guide field
• Turbulence and anomalous resistivity
• strong electron beams near the x-line drive
  Buneman instability
• nonlinear evolution into electron holes and
  lower hybrid waves
• seen in the ionospheric and magnetospheric
  satellite measurements
• Electron Energization
• Large scale density cavities that develop during
  reconnection with a guide field become large
  scale electron accelerators
• Secondary islands facilitate multiple
  interactions of electrons with this acceleration
  cavity and the production of very energetic
  electrons

43

• d

• Intense currents

Kivelson et al., 1995
44
Satellite observations of electron holes

• Magnetopause observations from the Polar
  spacecraft (Cattell, et al., 2002)

45
Wind magnetotail observations

• Recent Wind spacecraft observations revealed that
  energetic electrons peak in the diffusion region
  (Oieroset, et al., 2002)
• Energies measured up to 300kev
• Power law distributions of energetic electrons