Transcript Magnetic Reconnection Project

Collisionless Magnetic
Reconnection
J. F. Drake
University of Maryland
Magnetic Reconnection Theory 2004
Newton Institute
Collisionless reconnection is ubiquitous
• Inductive electric fields typically exceed the Dreicer
runaway field
– classical collisions and resistivity not important
• Earth’s magnetosphere
– magnetopause
– magnetotail
• Solar corona
– solar flares
• Laboratory plasma
– sawteeth
• astrophysical systems?
Resistive MHD Description
• Formation of macroscopic Sweet-Parker layer
V ~ ( /L) CA ~ (A/r)1/2 CA << 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?
Singular magnetic island equilibria
• Allow reconnection to produce a finite magnetic island (   0 )
• 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)
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?
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
Generalized Ohm’s Law
• Electron equation of motion
4 dJ
1
1
1
 E  vi  B 
J  B    pe  J
2
 pe dt
c
nec
ne
c/pe
Electron
inertia
c/pi
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
s
kinetic
Alfven
waves
scales
Kinetic Reconnection: no guide field
• Ion motion decouples from that of the electrons at a
distance c/pi 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
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
GEM tearing mode
evolution
• Full particle simulation
(Hesse,GSFC)
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 Ohm’s 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
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
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
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
Dispersive waves
• Geometry
• whistler
c
k CA
pi
=
  ky
=
• kinetic Alfven
k 
=
c
  ky
k Cs
pi
By0
B0
ky
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
Whistler signature
• Magnetic field from particle simulation (Pritchett, UCLA)
•Self generated out-of-plane field is whistler signature
Coupling to the kinetic Alfven wave: with a
guide field
• Signature of kinetic
Alfven wave is odd
parity density
perturbation
Kleva et al, 1995
Structure of plasma
density
Bz0=0
• Even parity with no
guide field
• Odd parity with
guide field
– Kinetic Alfven
structure
Bz0=1.0
Tanaka, 1996
Pritchett, 2004
Parameter space for dispersive waves
• Parameters
•For sufficiently
large guide field
have slow
reconnection
Rogers, et al, 2001
 y  4nT / B
2
0y
B02 m e
  (1  ) 2
B0 y m i

none
kinetic Alfven
1
whistler
kinetic Alfven
whistler
1
y
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
Positron-Electron Reconnection
• Have no dispersive whistler waves
– Displays Sweet-Parker structure yet reconnection remains fast
Hesse et al. 2004
Fast Reconnection in Large Systems
•Large scale hybrid simulation
T= 160 -1
T= 220 -1
•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
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).
4 dJz
1
1
 E z  (v e  B) z  (  pe ) z
2
 pe dt
c
ne
Bz=0
Bz=1.0

y
y
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
Observational evidence for turbulence
• There is strong observational support that the dissipation
region becomes strongly turbulent during reconnection
– Earth’s 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)
3-D Magnetic Reconnection: with guide field
• Particle simulation with 670 million particles
• Bz=5.0 Bx, mi/me=100
• Development of strong current layer
– Buneman instability evolves into electron holes
y
x
Buneman Instability
• Electron-Ion two stream instability
• Electrostatic instability
– g~~(me/mi)1/3 pe
– k lde ~ 1
– Vd ~ 1.8Vte
Ez
z
Initial Conditions:
Vd = 4.0 cA
Vte = 2.0 cA
x
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
B
x
Electron Energization
Electron Distribution Functions
vz
B
Scattered electrons
Accelerated electrons
vx
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
p ez
 en 0 E z  en˜E˜ z 
t
– correlation between density and electric field fluctuations yields
drag
• Normalized electron drag
cn˜E˜ z 
Dz 
n0 v A B0
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
Energetic electron production in nature
• The production of energetic electrons during magnetic
reconnection has been widely inferred during solar flares and
in the Earth’s 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 Earth’s 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
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 Earth’s 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)
Electron
acceleration
during
reconnection
•
•
vparallel
Strongest bulk
acceleration in low
density cavities where
Ep is non-zero
– Not at x-line!!
– Pritchett 2004
•
Bz0=1.0
Length of density
cavity increases with
system size
Maximum vparallel
increases with system
size
– Longer acceleration
region
ne
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
By=1.0
– Electron holes and double layers
– Most intense in density cavities
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 xline
Electron
distribution
functions
• Cold energetic beam
in cavity
• Hot streaming
plasma ejected
along high density
separatrix
cavity
Outflow
separatrix
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
Electron energization with a guide field
• Bz=1.0
• High energy tail
from multiple
interactions with xline in secondary
island
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
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
• d
Intense currents
Kivelson et al., 1995
Satellite
observations
of electron
holes
• Magnetopause
observations
from the Polar
spacecraft
(Cattell, et al.,
2002)
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