Transcript Magnetic Reconnection Project

The Structure of the Parallel Electric Field and
Particle Acceleration During Magnetic
Reconnection
• J. F. Drake
• M.Swisdak
• M. Shay
University of Maryland
• M. Hesse
GSFC
• C. Cattell
University of Minnesota
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
Overview
• MHD model yields reconnection rates to low to explain
observations in nature
– solar flares
– sawtooth crash
– magnetospheric substorms
• Non-MHD physics at small spatial scales produces fast
reconnection
– Focus on reconnection with a guide field and the coupling to dispersive
kinetic Alfven waves
– Structure of the parallel electric field
• 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
– Parallel electric field develops structure in the form of electron holes and
double layers
– Observational evidence in from recent Cluster data
Generalized Ohm’s Law
• Electron equation of motion
4 dJ

2
pe
dt
c/pe
Electron
inertia
E
1
c
vi  B 
1
J B
nec
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
1
ne
  pe  J
s
kinetic
Alfven
waves
scales
Coupling of reconnection to the kinetic Alfven
wave
• 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
Conditions for Dispersive waves
• Geometry
• whistler
c
 pi
k CA
=
  ky
k 
=
• kinetic Alfven
 pi
k Cs
=
  ky
c
B y0
B0
ky
Parameter space for dispersive waves
• Parameters
 y  4 nT / B
2
0y
2
  (1   )
B0 m e
2
B0y m i
•For sufficiently
large guide field
have slow
reconnection
Rogers, et al, 2001

none
kinetic Alfven
1
whistler
kinetic Alfven
whistler
1
y
Fast versus slow reconnection
• Can calculate parameters for which whistler versus
kinetic Alfven waves dominate dynamics or have no
dispersive waves
With dispersive waves
No dispersive waves
Rogers et al, 2001
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
Dissipation with a guide field
Ep
• The breaking of the
frozen-in condition and
electron energization
occurs in locations
where the parallel
electric field Ep is nonzero
– Largest near x-line and
along low density side of
separatrix
Transverse structure of Ep
• Transverse width scales
with electron Larmor
radius e
– Much smaller than had
been believed
– Earlier theory was the ion
scale s
– Why?
mi/me=100
mi/me=400
Structure of Ep
• The structure of Ep is controlled by the development of an
electrostatic field that shorts out the parallel inductive
electric field
Ep  
1 Az
c t
 b  
• Earlier theories predicted the transverse scale s
– incorrect because presumed ions magnetized
– For small transverse scales ions are unmagnetized

– Transverse scale is es
(    1)b     
2
e0
2
T0 AÝz

Te c

2
e0
 
2
e
T0
1
Te
T0

1
Te

T0
n 0e
1
Ti

d v b   g e (v )
3
Dissipation mechanism
• What balances Ep during guide field reconnection?
• Scaling with electron Larmor scale suggests the nongyrotropic pressure can balance Ep (Hesse, et al, 2002).
4 dJ z

2
pe
dt
 Ez 
1
c
(v e  B) z 
1
ne
Bz=1.0

y
(  pe ) z
Electron
acceleration
vparallel
Bz0=1.0
• 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
ne
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
Electron
distribution
functions
• Cold energetic beam
in cavity
• Hot streaming
plasma ejected
along high density
separatrix
cavity
Outflow
separatrix
Structuring of the Parallel Electric Field
during 3-D Magnetic Reconnection with guide
field
• Bz=5.0 Bx, mi/me=100
• Development of strong current layer
– Buneman instability evolves into electron holes
y
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
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
t
  en 0 E z  e  n˜ E˜ z 
– correlation between density and electric field fluctuations yields
drag
• Normalized electron drag
Dz 
c  n˜ E˜ z 
n0 v A B0
Electron drag due to scattering by parallel
electric fields
• Drag Dz has
complex spatial y
and temporal
structure with
positive and
negative values
• Results not
consistent with the
quasilinear model
• How far along
separatrix does
turbulence spread?
x
Structuring of the parallel electric field
along separatrix: 2-D
• Strong electron beams break up Ep into localized
structures
– Electron holes and double layers
– Most intense in density cavities
– In 2-D not near x-line because beams in out-of-plane direction
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
Fine structure of holes and double layers
• Electron-holes correspond to depletions of the electron density
– Modest enhancements of the local ion density
– Hole velocities much slower than electron beam velocity
• Consistent with smaller scale 3-D simulations
• Consistent with Buneman source
• Double layers correspond to bipolar charged layers
Ep
ne
Cluster
observations
• Consistent with
those on geotail
and polar
– Electron holes
– Double layers
• First direct
measurement of
consistency with
electron beams
Cattell, et al, 2004
Cluster: electron
velocity distributions
• Electron holes seen
only with distinct,
relatively cold beam
feature
– Only in top two
panels
– No electron holes
seen in the four
bottom panels
Modeling of Cluster data
• A small guide field (By~0.2Bx) is required to reproduce the beams and
double layers in Cluster data -- holes?
Structure of parallel electric fields in Nature
• 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
• Observations and theory now suggest that such structures
form in essentially all of the boundary layers present in the
Earth’s magnetosphere where reconnection takes place
– Magnetotail, magnetopause
• More generally, evidence is now strong that uniform, largescale parallel electric fields do not exist in Nature
– Dissipation always take place in localized non-linear structures
– Consequences for understanding particle heating?
Conclusions
• Fast reconnection requires either the coupling to
dispersive waves at small scales or a mechanism for
anomalous resistivity
• The kinetic Alfven wave dominates in cases with a
large guide field
• The transverse scale length of the region where the
parallel electric field is non-zero is much smaller
than thought previously
– Scales with an effective electron Larmor radius
Conclusions (cont.)
• Non-gyrotropic pressure continues to balance the
parallel electric field near the x-line (Hesse, et al,
2002)
– Consequence of the small spatial scales
• Electron acceleration and heating is controlled by a
spatially non-local region of depleted electron density
(Tanaka, 1997; Pritchett and Coroniti, 2004)
– Low density cavity is a region of extended non-zero
parallel electric field
– An efficient plasma accelerator
– Electron heating results from the injection of energetic
electrons from this cavity into the x-line
Conclusions (cont.)
• Strong electron beams in the low density cavity
produce electron-holes and double layers even in a
2-D simulation
• Electron beams are seen in the magnetotail by
Cluster when and only when electron holes and
double layers are observed (Cattell, et al, 2004).
– Consistent with theory
– Consistent with earlier auroral observations
– Large-scale parallel electric fields are unlikely to exist in
Nature.