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:

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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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