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
Borovsky et al. (1998): Plasma sheet
density correlates with solar wind
density.
Fujimoto et al. (1998): Neutral sheet temperature
and density versus solar wind conditions.
Cold dense plasma sheet for
Northward IMF!
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, 19984
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
Wing et al. (20064
dawndusk
Properties:
• 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
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
Oieroset et al., '05
Good agreement for density
temperature and magnetic field at
cluster location
Cusp Reconnection
Dayside Hybrid Simulations (Lin and Wang, ’06)
Cusp Reconnection - mass transfer potential:
AB
adBdt
d shc
dt
dnV
B
LnALn
dt
dN psps
sh
ftshcftshps
Potential to generate closed magnetic flux:
Change of the total number of
particles due to the added flux:
dtdnpsPotential required to cause an average plasma density increase of
Typical parameters: nTBsh 30dt
dn
Ln
VB ps
ftsh
psshc
32510 mVps 310 cmnsh Eft RL 25
135.0 hrcmdtdnps=> kVc 30
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; ..) 1 ik
Courtesy: J. Johnson
Lin and Wang, 2005
Kelvin-Helmholtz and Reconnection - 2D Three-Dimensional Dynamics Entropy Considerations Conclusions
2
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)
Magnetic Reconnection vs. Kelvin-Helmholtz Modes
Process
Requires Magnetic Shear Yes No
Requires Velocity Shear No Yes
Momentum Transport Yes Yes
Energy Transport Yes Yes
Plasma Transport Yes No
Magnetic Reconnection
Kelvin-Helmholtz Mode
• KH modes unstable for v > vA along k vector of the KH mode.
• Magnetic reconnection can operate for v < vA based on the antiparallel magnetic field components.
Stability:
Two-Dimensional Dynamics
3
Observations – Large Perturbations
at the Magnetospheric
Flanks for Northward IMF
Fairfield et al. (2000)
Bx
By
Bz
B
T
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!
Two-Dimensional Dynamics - A
5
Agreement between 2D Simulation and Observation
Bx
By
Bz
T
Fairfield et al. (2000)Otto and Fairfield (2000)
Magnetic Reconnection in 2D KH Vortices
Plasma density, velocity and magnetic field lines
(Nykyri and Otto, 2001, 2003)
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!
6
Two Basic Mechanisms for Reconnection in KH Vortices
- Mass transport rate consistent with observed plasma transport for northward IMF.
- Mass transport occurs always from the high density into the low density region!
Mass transport rate:
- 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 pre-
existing current layer (magnetic shear)!
7
Two-dimensional dynamics - B
● 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
Anti-parallel magnetic field along the KH k vector
Nakamura et al., 20068
Three-Dimensional Dynamics: Open Questions
Possible Differences of 2D and 3D Kelvin-Helmholtz Modes
• Stabilization• Coupling along magnetic field lines + line tying• Reconnection in 3D• Mass transport?• Signatures
In general k vectors of tearing (reconnection) and KH modes are not aligned except for singular cases!=> Dynamics in general 3D?
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:
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
• 3D MHD (Hall) Simulation • Leapfrog/Dufort-Frankel + FCT,• 2nd order accuracy, low dissipation
Local Properties
16
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
Example: Magnetic shear 10o
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
17Borovsky, GEM’06
Entropy density of plasma sheet populations
Cold dense plasma sheet:
Only of magnetosheath origin?
or
Mixture of magnetosheath and
magnetospheric plasma
Entropy:
The great Alaska Earthquake from Nov 4, 2002
T = T0 + 1hr
Entropy - 1
Entropy - 2
u
Entropy - 3
pVH 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)
/ps is conserved only in MHD except for nonadiabatic
processes!
Entropy change for switch-off shocks:
18
Entropy changes associated with magnetic reconnection/slow
switch-off shocks:
Compression:
Pressure increase:
Entropy increase:
=> Local entropy can increase
significantly only for very low
plasma
Magnetic Field Lines:
=>
=> =>
=>
MSP
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
16
Filamentary current layers Well ordered parallel electric field distribution
Integrated:
VelocityParallel Electric Field
Parallel Current Density
Parallel Current and Electric Field
16
Reconnection within the KH vortices
Mass Transport:• Parallel `Potential’:
• Specific Flux Tube Mass:
16
Mass and Entropy Transport - 45 sec later
16
Positive Potential Negative PotentialFlux Tube Mass Entropy
• Rapid change of the topological boundary• Location of boundary agrees excellent with location of the potential
Flux Tube Mass and Entropy Mapped to Southern Boundary
16
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.
Parallel Potential and Magnetic Foot Print Displacement
15
Parallel Potential FT Footprint coordinate at northern boundary
• Potential + reconnection are present along flux tubes strongly distorted by the KH vortex motion
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
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Summary - KH
2D Dynamics:
KH modes unstable for v>vA,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
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