Plasma Transport and Entropy Considerations
at the Magnetospheric Flanks
Antonius Otto
Outline:
 Basic Issues
 Basic processes
 Properties of the cold dense plasma sheet
 Lobe/cusp reconnection
 Diffusion
 Kelvin-Helmholtz modes
 Summary
What physical
processes provide the
plasma of the plasma
sheet?
Specific questions:
• What are the processes that transport the plasma from the magnetosheath into
the magnetosphere on closed field lines?
• How is this plasma processed and transported deeper into the magnetotail?
Focus: Northward IMF Conditions
Basic Processes at the Magnetopause
Magnetic reconnection (Dungey,1961)
Viscous interaction (Axford and Hines, 1961)
• Diffusion (Micro-instabilities, turbulence)
• Kelvin-Helmholtz instability
(Impulsive penetration (Lemaire and Roth, 1978))
Observations I – Strong Correlation of Plasma Sheet and Solar Wind
Properties
Fujimoto et al. (1998): Neutral sheet temperature
and density versus solar wind conditions.
Borovsky et al. (1998): Plasma sheet
density correlates with solar wind
 Cold dense plasma sheet for
Northward IMF!
density.
4
Observations II – DMSP plasma sheet flanks for northward IMF
Wing et al. (2006): Flank plasma sheet density and temperature evolution
for Feb 4-5, 1998
4
Observations III – DMSP average plasma sheet properties
for northward IMF
Wing et al. (2006): Average plasma sheet density and occurrence for
two-component Maxwellian for extended northward IMF periods.
4
Observations IV – DMSP median plasma sheet evolution
for northward IMF
Properties:
dawn
dusk
• Rapid decrease of temperature at flank
boundaries
• Increase of density first at flanks
• Timescale of density and temperature
changes in the midnight meridian ~10 hr
• Asymmetries of the dawn-dusk flanks
(distribution, density, temperature)
=> Plasma entry from magnetosheath along
the flank boundaries
Wing et al. (2006
4
Cusp Reconnection (Crooker, '79; Song and Russell, '92; ..)
Dorelli et al, 2007
Cusp Reconnection
Observations (Fuselier, Phan, Trattner, Wang, Lavraud, ..)
 Ground based (lobe reconnection cells, particle signatures)
 In-situ spacecraft observations
 Remote particle signatures
Trattner et al, 2004
Cusp Reconnection – Global simulation
Li et al., '05
Cusp Reconnection – Comparison with Cluster Data
Good agreement for density
temperature and magnetic field at
cluster location
Oieroset et al., '05
Cusp Reconnection
Dayside Hybrid Simulations (Lin and Wang, ’06)
Cusp Reconnection - mass transfer potential:
c 
Potential to generate closed magnetic flux:
Change of the total number of
particles due to the added flux:
dN
ps

dt
d
dt
n sh AL ft



  B A
B  d a  sh

 c n sh L ft
B sh
dn ps
 V ps
dt
Potential required to cause an average plasma density increase of dn ps dt
 c  B sh
V ps
dn ps
n sh L ft
dt
=>  c  30 kV
Typical parameters:
V ps  10
B sh  30 nT
n sh  10 cm
3
25
m
3
L ft  25 R E
dn ps dt  0 . 5 cm
3
hr
1
Diffusion/Viscosity at the LLBL
Processes:
 Kelvin-Helmholtz modes
 Microinstabilities (LHD turbulence, ion
acoustic, ion cyclotron,..)
 Kinetic Alfven waves (KAW)
Microinstabilities:
 Many observations of wave turbulence at the
magnetopause and LLBL
 Estimated maximum diffusion coefficient (LHD)
D = 109m2s-1
But: Instabilities require high current densities or
gradients to be excited –> Widening of the LLBL
switches off instability and diffusion is limited to very
narrow layers!
Required Diffusion coefficient:
D = 109m2s-1
(Sonnerup, 1980?)
Diffusion at the LLBL - 2
Kinetic Alfven Waves (Hasegawa
1976; Lee et al.,1994; Johnson and
Cheng, 1997; ..)
k i  1
Courtesy: J. Johnson
Lin and Wang, 2005
Kelvin-Helmholtz Modes:
Observations (Scopke, Fairfield, Fujimoto, Hasegawa, Nykyri, etc.)
Simulation (Miura, Belmont, Wu, Wei, ..)
Miura: Viscous diffusion (momentum transport) coefficient: D=109m2s-1
Mass transport (Otto, Nykyri, Fujimoto)

Kelvin-Helmholtz and Reconnection - 2D

Three-Dimensional Dynamics

Entropy Considerations

Conclusions
2
Two-Dimensional Dynamics
Magnetic Reconnection vs.
Kelvin-Helmholtz Modes
Proces s
Magnetic
Reconnection
Kelvin-Helmholtz
Mode
Requires Magnetic S hear
Yes
No
Requires Velocity S hear
No
Yes
Momentum Trans port
Yes
Yes
Energy Trans port
Yes
Yes
Plas ma Trans port
Yes
No
Stability:
• KH modes unstable for Dv > vA
along k vector of the KH mode.
• Magnetic reconnection can
operate for v < DvA based on
the antiparallel magnetic field
components.
3
Bx
Observations –
Large Perturbations
at the
Magnetospheric
Flanks for
Northward IMF
By
Bz
B
Fairfield et al. (2000)
T
Two-Dimensional Dynamics - A
Approach: Kelvin-Helmholtz with a k
vector not exactly perpendicular to B
=> Small magnetic field component in
the plane of the KH wave
Strong amplification of the magnetic
field in the KH plane.
● Intense current layers in
the KH vortex. Current does not
neet to be present in the initial
conditions!
●
5
Agreement between 2D Simulation and Observation
Bx
By
Bz
T
Otto and Fairfield (2000)
Fairfield et al. (2000)
Magnetic Reconnection
in 2D KH Vortices
Plasma velocity, density, and magnetic
field projected into KH plane for 3
different times.
Yellow line and asteriks (fluid tracers)
mark original plasma boundary.
Plasma filaments are reconnected and
become detached from the high
density region!
Plasma density, velocity and magnetic field lines
(Nykyri and Otto, 2001, 2003)
6
Two Basic Mechanisms for Reconnection in KH Vortices
- Nonlinear KH modes stretch the surface
of the plasma boundary ~n (number of
rotations) => Pre-existing current layer
density intensified ~n!
- If initial conditions contains B0 || k =>
Vortex motion generates anti-parallel
magnetic field. Current density ~ n,
B0. This does not require a preexisting current layer (magnetic
shear)!
Mass transport rate:
- Mass transport rate consistent with observed
plasma transport for northward IMF.
- Mass transport occurs always from the high
density into the low density region!
7
Two-dimensional dynamics - B
Anti-parallel magnetic field along the KH k vector
●
Reconnection of the anti-parallel magnetic
field in the KH plane.
●
Plasma mixing in the tearing island
●
But: Unclear whether plasma is
transported onto closed geomagnetic flux
Nakamura et al., 2006
8
Three-Dimensional Dynamics: Open Questions
In general k vectors of tearing (reconnection) and KH modes are
not aligned except for singular cases!
=> Dynamics in general 3D?
Possible Differences of 2D and 3D Kelvin-Helmholtz
Modes
• Stabilization
• Coupling along magnetic field lines + line tying
• Reconnection in 3D
• Mass transport?
• Signatures
9
Three-Dimensional Simulation: Basic
Approach
• Simulation with application to the flank magnetospheric
boundaries (close to equatorial plane)
- Small magnetic shear
- `Sub-Alfvenic' shearflow
• Current dependent resistivity
• Initial velocity perturbation to seed Kelvin- Helmholtz
modes
• System size:
- Perpendicular to boundary (here x): 4 RE
- North/South: 8 RE
- Tailward: 3 RE(= KH wavelength)
• Density asymmetry nmsh = 3nmsp
Magnetosphere
(line tying)
Magnetosheath
10
Numerical Method:
• 3D MHD (Hall) Simulation
• Leapfrog/Dufort-Frankel + FCT,
• 2nd order accuracy, low dissipation
KH waves with a finite size along the north/south
direction:
• Magnetosphere: Field-line curvature + line-tying =>
limited interaction region
• Simulation: Line-tying by frictional drag increasing
toward the min and max boundaries in z (north and
southward from equatorial plane):
- maintains initial shearflow
- absorbs velocity perturbations (wave damping)
Normalization: Typical properties at the magnetopause:
B0 = 25nT, n0 = 4cm−3, L0 = 600km, vA = 250km/s,
and A = 22s.
11
Local Properties
Example: Magnetic shear 10o
 Properties similar to 2D Kelvin Helmholtz modes; vortex plasma has either
high (MSH) or low (MSP) density.
 Stabilization for wavelength larger than the width of the interaction region
16
Three-Dimensional Dynamics Localization
Cuts at x = 0 = original
boundary;
In- and outward plasma
motion due to KH
Perturbation of the
magnetic field normal
to the initial boundary
13
Issue: Entropy of
cold dense plasma
sheet
Entropy density of plasma sheet populations
Cold dense plasma sheet:
Only of magnetosheath origin?
or
Mixture of magnetosheath and
magnetospheric plasma
Borovsky, GEM’06
17
Entropy:
The great Alaska Earthquake from Nov 4, 2002
T = T0 + 1hr
Entropy - 1
Entropy - 2
u
Entropy - 3
H  pV

is conserved except for losses into the ionosphere
and nonadiabatic processes (in MHD)!
Particle drifts and/or perpendicular heatflux can also
alter entropy (important in inner magnetosphere)
s p/

is conserved only in MHD except for nonadiabatic
processes!
Entropy changes associated with magnetic reconnection/slow
switch-off shocks:
Compression:
Pressure increase:
Entropy increase:
Entropy change for switch-off shocks:
=> Local entropy can increase
significantly only for very low
plasma b.
18
MSP
Magnetic Field Lines:
MSP
=>
=>
=>
=>
MSP
MSP
Interchange motion moves MSP flux into MSH and vice versa.
However, finite size of interaction region => at large distances field line
move unperturbed, i.e., magnetosheath field moves large distance
along the boundary
 Interaction region must decouple or KH must be stabilized
 Decoupling (magnetic reconnection, E||) must occur at boundaries
of interaction region in a systematic manner.
14
Parallel Current and Electric Field
Integrated:
Velocity
Parallel Electric
Field
Parallel Current
Density
 Filamentary current
layers
 Well ordered parallel
electric field distribution
16
Parallel Current and Electric Field
 Reconnection within the KH vortices
16
Mass Transport:
•
Parallel `Potential’:
•
Specific Flux Tube Mass:
16
Mass and Entropy Transport - 45 sec later
Flux Tube Mass
Entropy
Positive Potential
Negative Potential
• Rapid change of the topological boundary
• Location of boundary agrees excellent with location of the potential
16
Flux Tube Mass and Entropy Mapped to Southern Boundary
Time=175 s
Time=220 s
- Average mass transport velocity 2 to 5 km/s
=> Diffusion coefficient of 2 to 4 x109 m2/s
- (Average) entropy of newly captured plasma average between MSP and MSH values.
16
Parallel Potential and Magnetic Foot Print Displacement
• Potential + reconnection are
present along flux tubes strongly
distorted by the KH vortex motion
Parallel Potential
FT Footprint coordinate
at northern boundary
15
Transport within the plasma sheet
Time scale for transport to the noon-midnight meridian: 10 hrs
Convection: 3 km/s
Diffusion coefficient: D=3x1011m2s-1
Plasma sheet turbulence (Borovsky and Funsten, 2003)
Diffusion coefficient: D=2.6x1011m2s-1
Summary
Mass diffusion rate for entry consistent for lobe reconnection
3D KH mass transport mechanism:
• consistent with required rate
• very different from 2D
• qualitatively consistent with mixed plasma entropy observed for cdps
Issues:
• Asymmetries
• Transport mechanism and path for transport within the plasma sheet
22
Summary - KH
2D Dynamics:
 KH modes unstable for Dv>v
A,typ along the k vector of the mode.
 Nonlinear modes twist boundary, generate thin current layers, and can cause
reconnection in the KH vortices either of type A or B
 Mass transport rate for northward IMF is consistent with observations.
3D Dynamics:
 The KH mode radiates energy and momentum out of the unstable region along
magnetic field lines.
 Stabilization for wavelength larger than the width of the interaction region.
 Nonlinear KH vortices require reconnection at interaction region boundaries:
• The required parallel electric fields are generated mainly close to the boundary of
the interaction region.
• Northern and southern potentials are similar but not identical => generation of
open and re-closed magnetic flux (different from 2D)
 Material transport across a boundary onto ‘closed’ field lines requires reconnection of
the ‘same’ field line at different locations (but not necessarily at the same time)
 Entropy of cold dense plasma sheet better consistent with 3D KH/reconnection.
 Mass transport corresponding to average velocity of 2 to 5 km/s or a diffusion rate of
2 to 4x109 m2/s
22