Transcript Magnetic Reconnection Project - University of California

A Fermi mechanism for electron
acceleration during magnetic reconnection
J. F. Drake
University of Maryland and SSL
•M. Swisdak
•H. Che
•M.A. Shay
University of Maryland
University of Maryland
University of Delaware
Magnetic Energy Dissipation in the Universe
• The conversion of magnetic energy to heat and high speed flows underlies
many important phenomena in nature
–
–
–
–
solar and stellar flares
Energy releases from magnetars
magnetospheric substorms
disruptions in laboratory fusion experiments
• More generally understanding how magnetic energy is dissipated is
essential to model the generation and dissipation of magnetic field energy
in astrophysical systems
– accretion disks
– stellar dynamos
– supernova shocks
• Known systems are characterized by a slow buildup of magnetic energy
and fast release
– mechanism for fast release?
– Why does reconnection occur as an explosion?
• Why does so much energy go into electrons?
Magnetic Free Energy
• A reversed magnetic field is a source of free energy
B
xxxxxxxxxxxxxxxxxxxxxxxxx x
J
•Can imagine B simply self-annihilating
•What happens in a plasma?
Energy Release from Squashed Bubble
2
B
1
F  ( p  ) 
B  B
8
4
magnetic tension
• Magnetic field lines want to become round
Energy Release (cont.)
w
L
• Evaluate initial and final magnetic energies
– use conservation law for ideal motion
• magnetic flux conserved
• area for nearly incompressible motion
Wf ~ (w/L) Wi << Wi
•Most of the magnetic energy is released
R
Flow Generation
• Released magnetic energy is converted into plasma flow
1 2 B2
v 
2
8
2
B 1/ 2
v  vA  (
)
4
A  L / v A
•Alfven time A is much shorter than observed energy release time
Magnetic Reconnection
• Key features of this picture have been in space and
laboratory observations
• Dissipation required to break field lines
• Key issue is how newly reconnected field lines at very small
scales expand and release their tension
• d
Intense currents
Kivelson et al., 1995
Fast Flows at
the
Magnetopause
Scurry et al. ‘94
Reconnection in Solar Flares
• X-class flare:  ~ 100 sec.
• Alfven time:
• A ~L/cA ~ 10 sec.
=> Alfvenic Energy Release
F. Shu, 1992
RHESSI observations
• Exploring timing of production of energetic electrons and
ions during flares
Jan 20, 2005 X7 flare
Krucker/Hurford
Flares in high magnetic field
neutron stars
• Magnetars: Isolated neutron stars with:
– B ~ 1015 Gauss
– Strongest B-fields in universe.
• Giant Flare (SGR 1806-20)
–
–
–
–
Dec. 27, 2004, in our galaxy!
Peak Luminosity: 1047 ergs/sec.
Largest supernova: 4 x 1043 ergs/sec.
Cause: Global crust failure and magnetic
reconnection.
– Could be a source of short duration
gamma ray bursts.
Rhessi data: Hurley et al., 2005
Resistive MHD Description
• Formation of macroscopic Sweet-Parker layer
V ~ ( /L) CA ~ (A/r)1/2 CA << CA
•Slow reconnection  not consistent with observations
•sensitive to resistivity
•macroscopic nozzle
• Petschek-like open outflow configuration does not appear in resistive MHD
models with constant resistivity (Biskamp ‘86)
Hall Reconnection
• MHD model breaks down in the dissipation region at small
spatial scales where electron and ion motion decouple
• Key is to understand how newly reconnected field lines
expand at very small spatial scales where MHD no longer
valid
– The outflow from the x-line is driven by whistler and kinetic
Alfven waves  dispersive waves
– fast reconnection even for very large systems
• No ad hoc assumptions
• Key signatures of Hall reconnection have been measured
by magnetospheric satellites and laboratory experiments
Hall versus MHD reconnection
Hall
MHD
–
–
MHD model produces rates of energy release too slow to
explain observations -- macroscopic nozzle a la SweetParker
Hall model produces fast reconnection as suggested by
Petschek
Magnetic Reconnection Simulation
QuickTime™ and a
BMP decompressor
are needed to see this picture.
Energetic electron production
• 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)
• Why is the electron energy linked to the energy release?
– 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
Wind spacecraft trajectory through the Earth’s
magnetosphere
• d
Wind
Intense currents
Kivelson et al., 1995
Wind magnetotail
observations
• 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
Electron acceleration by the reconnection electric field
• What is the structure of parallel electric
fields during reconnection?
• Guide field reconnection produces deep
density cavities that map the magnetic
separatrix
E||
– Pritchett and Coroniti, 2004
• The parallel electric field is localized
within these cavities
– Cavities are microscopic in length
• Parallel electric fields are too spatially
localized to be a significant source of
large numbers of energetic electrons
n
Failure of the single x-line model: sun
• Solar observations up to 50%
of the energy can go into
electrons
– Parallel electric fields are
highly localized around the
x-line
• Magnetic energy is not
released at the x-line but
downstream as the
reconnected fields relax
their stress
• X-line has negligible
volume on the physical
scale of the region where
energy is released in the
corona
• Can’t come close to
explaining the large number
of electrons gaining energy
Tsuneda 1997
Failure of the single x-line model:
magnetosphere
•
Energetic electrons should be accelerated by the electric field toward the dawn side of the
magnetotail and energy would be limited to the potential drop across the tail (around 150
keV).
–
–
Observations indicate are more equally spread
Energies in the meV range are sometimes observed
Energetic electrons in
a cross section of the
magnetotail
•
•
IMP 7 & 8 data (Meng et al
1981)
Electrons with energy 220kev2.5MeV
– Exceeds potential drop across
the tail
•
Dawn-dusk asymmetry stronger
during quiet times than active
times
– Not consistent with traditional
cross tail acceleration.
•
During active times must have a
diffusive process for energy gain
in the tail
– Must be able to gain energy
while moving in either direction
across the tail
Erec
Failure of the single x-line model:
magnetosphere
•
Energetic electrons produced by
parallel electric fields should be
highly localized around the xline and adjacent separatrices
– Electrons are broadly
distributed in observational data
•
Electron velocities are
dominantly moving parallel to B
– Nearly isotropic at high energy
in the data
A multi-island acceleration model
• A single open x-line does not produce the energetic electrons
observed in the data
• The development of multiple magnetic islands is expected from
theory and simulations of reconnection
• Observations of secondary magnetic islands with
magnetospheric satellites and solar observations of localized
downflows also call into question a single x-line model
Generation of multiple magnetic islands
• Narrow current
layers spawn
multiple
magnetic islands
in guide field
reconnection
• In 3-D magnetic
islands will be
volume filling
Cluster magnetotail reconnection event
Eastwood et al, 2007
• Fields are noisy with identifiable discrete magnetic islands
TRACE observations of downflow blobs
• Data from the April
21, 2002, X flare
• Interpreted as patchy
reconnection from
overlying reconnection
site
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
A Fermi electron acceleration mechanism
inside contracting islands
CAx
• Energy is released from newly reconnected field lines through contraction
of the magnetic island
• Reflection of electrons from inflowing ends of islands yields an efficient
acceleration mechanism for electrons even when the parallel electric field
is zero
• When an ambient guide field is present, electrons can gain energy while
moving either into or out of the page  crucial for explaining the tail
observations.
Electron Dynamics in simulation fields
•
Electrons follow field lines and drift outwards due to EXB drift
– Eventually exit the magnetic island
•
Gain energy during each reflection from contracting island
– Increase in the parallel velocity
•
Electrons become demagnetized as they approach the x-line
– Weak in-plane field and sharp directional change
– Scattering from parallel to perpendicular velocity
• Sudden increase in Larmor radius
• Isotropic distribution consistent with observations? Probably
Energy Gain
x
CAx
• Calculate energy gain through multiple reflections from the contracting
island
d
CAx
 2 G
dt
x
G  G(Bx , Bz )
– Note that rate of increase of energy is independent of the mass
• Should the energy gain of ions and electrons be comparable?
– The bulk ions don’t have time to bounce
– Only super Alfvenic ions gain energy with multiple bounces
– Particle simulations of reconnection miss this mechanism because the electron
velocities because of artificial mass ratios are only marginally above the Alfven
speed
PIC Simulations of island contraction
• Separating electron heating due to the Fermi mechanism from heating due to
E|| during reconnection is challenging
– Study the contraction of an isolated, flattened flux bundle (mi/me=1836)
– E|| =0
T||
• Strong increase in T|| inside the bundle during contraction
 T|| ~ 3T
• 60% of released energy goes into electrons
Multi-island reconnection
uup
y
CAx
x
• Large energy gains require interaction with multiple magnetic
islands  energy gain linked to geometrical change of island
aspect ratio
• Consider a reconnection region with multiple islands in 3-D
with a stochastic magnetic field
– Electrons can wander from island to island
• Stochastic region assumed to be macroscopic
Kinetic equation for energetic particles
• Ensemble average over multiple islands
d 2 dcAx

A
dt
3
dy
 yi
A  Gi

 xi
• Steady state transport equation for electrons
r
r
1 dcAx 
r
  uf     (v)f  A
vf
3 dy v
– Similar to Parker’s equation for particle heating in a 1-D shock
– Contains no velocity scale  powerlaw solutions
– Missing feedback on energetic particles on the island contraction
Linking energy gain to magnetic energy released
w
L
•
Basic conservation laws
– Magnetic flux  BW = const.
– Area  WL = const.
– Electron action  VL = const.
•
Magnetic energy change with L
B2 L
WB 
0
4 L
– Island contraction is how energy is released during reconnection
•
Particle energy change with L
L
   
0
L
B2
:
 P : 1
4
•
Island contraction stops when
•
Energetic electron energy rises until it is comparable to the released magnetic
energy
Suppression of island contraction by energetic
particle pressure
•
•
•
Explore the impact of the initial  on the contraction of an initially elongated island
With low initial  island becomes round at late time
Increase in p|| during contraction acts to inhibit island contraction when the initial  is
high  contraction stops at firehose marginal stability
  0.3
  1.2
Kinetic equation with back-pressure
•
Include the feedback of energetic particles on island contraction

8 W 
v  cAx  1 
3B 2 

1/2
– Energetic particles can stop island contraction through their large parallel pressure
•
Steady state kinetic equation for electrons
1/2
r
r
1 
8W  dcAx 
r
  uf     (v)f  A  1 
vf
2 
3 
3B 
dy v
•
Can solve this equation numerically in reconnection geometry
– Saturation of energetic particle production
– Two key parameters:
• Initial plasma beta: 0=8p0/B2
• Energy drive: A
Energetic electron spectra
Simulation geometry
•
•
Powerlaw spectra at high energy
The initial plasma beta, 0, controls
the spectral index of energetic
electrons
– For Wind magnetotail parameters
where 0 ~ 0.16, v2f ~ E- 3.6
– For the solar corona where 0 is
small, v2f ~ E-1.5
• Universal spectrum for low 0
•
Results are insensitive to the drive A
for strong drive
– Back pressure always reduces the net
drive so that energy transfer to
electrons is comparable to the
released magnetic energy
The multi-island electron acceleration model
explains many of the observations
• Magnetotail
–
–
–
–
Energy can exceed the cross-tail potential
Weak East-West asymmetry across the tail
Velocity distributions isotropic above a critical energy
Powerlaw energy distributions which match the Wind observations
• Soft spectra a consequence of the relatively large initial plasma pressure
• Solar corona
– Large numbers of energetic electrons
• If island region is macroscopic
– Electron energy gain linked to the released magnetic energy
– Powerlaw energy distributions consistent with the observations
• Harder limiting spectra of E-1.5 a result of the low initial plasma pressure
Critical issues in explaining the solar
observations
• The electron numbers
problem
– The contracting island
region must be macroscopic
Island region
• energetic electrons gain a
large fraction of the
magnetic energy released
Can a similar Fermi process produce energetic
ions?
• The Fermi mechanism if efficient only for ions with
velocities above the Alfven speed
• Need a mechanism producing a seed distribution of
energetic ions
• Observational evidence in the heliosphere of E-1.5 spectra
of protons
Proton spectra of the form j = jo E -1.5 or equivalently f = fov -5 are often observed
103
6
101
3
Phase Space Density (s /km )
Core pickup protons
10-1
H+
SWICS
quiet time
tails
4.23 AU
94 AU
10-3
f(w) = fow -5
-5
10
(in solar w ind f rame)
10-7
Solar wind protons
1 AU
10-9
ULEIS
10-11
1
10
W
100
Ion Speed/Solar Wind Speed
<R> = 4.86 AU
Common in the quiet solar wind (Gloeckler et al, 2006)
tail retailis
2:40:15
PM 1/22/06
Similarity to spectra from the Fermi mechanism
striking
*FWtail
*tail+SW
SW distribution
1FW
FW
<FW>mean
FWnet
FWbkg
sum core+tail quiet
FWPI up
FW -26day to TS LECP
FW -20day to TS LECP
FW -26day to TS LECP
FW -20day to TS LECP
FW(Vr broadened)
Tail w ith cutoff
Conclusions
• Acceleration of high energy electrons is controlled by a Fermi
process within contracting magnetic islands
• Reconnection in systems with a guide field involves the
interaction of many islands over a volume
– Remains a hypothesis based on our 2-D understanding
• Averaging over these islands leads to a kinetic equation
describing the production of energetic electrons that has
similarities to that in particle acceleration in shocks
• Particle distributions of energetic electrons take the form of
powerlaws
– The initial electron pressure dominantly controls the spectral indices of the
energy distributions
• Low initial pressure as in the solar corona yields harder spectra than in the
magnetosphere
• Electrons gain a substantial fraction of the energy released during magnetic
reconnection
The MHD Reconnection Rate Problem
• Reconnection rates too slow to explain observations
– solar and stellar flares
– sawtooth crash in fusion experiments
– Storms in the Earth’s magnetosphere
• Ongoing scientific issue since the late 1950’s
• The solution: non-MHD physics at the small spatial scales
drives fast reconnection
– The one-fluid MHD model breaks down in the narrow boundary layers
that develop during magnetic reconnection
– The motion of electrons and ions in the narrow boundary layers where
magnetic field lines break decouples  Hall reconnection
• New class of “dispersive” waves facilitates fast reconnection
• Physics is confirmed in magnetospheric satellite observations and in
laboratory reconnection experiments.
Quiet-time tails of the form j = jo E -1.5 or equivalently f = fov -5 are often observed
Decker et al., Science (2005)
Krimigis et al., AGU (Fall 2003)
~85 AU
~45 AU
j = joE-1.5
Accelerated
Pickup Ions
Voyager 1 LECP
2004:352-2005:144
CRS
CRS
ACR
101
100
-5
10-1
f(w) = f w
o
10-2
10-3
10-4
Pickup H
core
+
quiet time
tail
1996.5-2000.5
-5
10
1
2
W
3
4
FW corr <=1
<FW> cnts(W>2.39, <=1
109
FW corr <=400
+
sum core+tail baseline
sum core+tail quiet
7
412.3
10
M21H1d|w 2.00-2.39|M/Q1.00-1.00|
*FWcore
FW corr <=1
FW corr <=400
105
Solar
5
6 7 8 9
Ion Speed/Solar Wind Speed
SWICS Ulysses
H
(s 3/km6)
3
H+
~5 AU
F(W) Phase Space Density
102
6
Phase Space Density (s /km )
SWICS Ulysses
1997.108-1999.108
5.26 AU
(x27.7)
Wind
1H1t|w 0.8
ccM21H1d
*1H1t
*ccM21H1
ccM21H1d
5.26^2*cc
H+peak co
*H+peak c
FWH+
ACEtail
*ULStail
FWH+_UL
103
101
F(W) = F W
–5
o
10-1
Suprathermal
Pickup Ion Tail
10-3
1
W
2
4
7
(Proton speed/Solar Wind speed)
10
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
Positron-Electron Reconnection
• No decoupling of the motion of the two species
– No dispersive whistler waves
• Displays Sweet-Parker structure but reconnection rate is high (Hesse,
Bessho and Bhattacharjee).
• Scaling of reconnection rate to large systems?
Why is reconnection explosive?
• Slow Sweet-Parker reconnection and fast Hall reconnection are
valid solutions for the same parameters
Ez

Cassak et al
2005

• Sweet-Parker solution does not exist below a critical resistivity
 For the solar corona the critical temperature is around 100 eV and the
reconnection rate will jump a factor of 105
Particle Scattering
• Increase of v|| within
island
• Nearly constant vL
within island
• Scattering from v|| to
vL near the
separatrix
• Isotropic particle
distributions at high
energy?
Powerlaw spectra
•
Solve the kinetic equation in reconnection geometry
– Fermi drive balances convective loss
•
Powerlaw spectra -- as often seen in both solar and magnetospheric observations
v
 1
up

0
f (v) 
  1
•
 1
v
3 y
x A
The energy integral diverges
 dv' f
 1
(v')v'
3 y
 yi
 x  Gi

 xi
– Spectral index depends on the ratio of the aspect ratio of the island region (~0.1) to the
mean aspect ratio of individual islands.
– In the strongly driven regime,  < 3, the energy content of energetic electrons diverges
• Energy budget of electrons is important
• Feedback of the energetic component on the reconnection process must be calculated