ASYMMETRIC THIN CURRENT SHEETS: A 1-D TEST

PARTICLE MODEL AND COMPARISON WITH SW DATA

J. Chen1 and R. A. Santoro2

1 Plasma Physics Division, Naval Research Laboratory

2 Lockheed Martin Management and Data System

The Second Workshop on Thin Current Sheets

19—21 April 2004 University of Maryland

NRL Plasma Physics Division

COLLISIONLESS CURRENT SHEETS

Observations of Collisionless Current Sheets

• Extensively observed in the magnetosphere (also in laboratory)

– Plasma and magnetic field data

– Key new observations: CLUSTER

• Model-data comparisons using magnetospheric data

– But, no in situ data in the corona or astrophysical plasmas

Objective: Construct a quantitative model of asymmetric collisionless

current sheets and test it against solar wind data

– Observational identifiers—magnetic field and plasma particle properties

– Collilsionless but generally asymmetric

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BASIC STRUCTURE

Current Sheets in Space Plasmas

• Collisionless:

• Magnetotail current sheet observations: e.g., Fairfield [1984], McPherron et al. [1987],

Mitchell et al. [1990], Lui et al. [1992], Sergeev et al. [1993], Asano et al. [2003]

– Thickness: “Thin”

, ( )i i i mfp sysL L

a

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MODELS AND PARAMETERS

Symmetric Current Sheets

• Analytic Harris model: [Harris, 1962]

– magnetic field with Bn = 0

– Sharply peaked particle density:

– Uniform average velocity in the current sheet

• Important parameters: particle distributions of the asymptotic sources

1. Two basic regimes:

2. The form of f, in particular, the size

of the high-energy tail;

e.g., the distribution

/ 1 . / 1D th D thv v v v v

tanh( / )z 2

0 sech ( / )n n z

Sf

function

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PREVIOUS WORK (1)

The vD/vth > 1 Regime

• Harris-like models: [e.g., Eastwood 1972, 1974; Francfort and Pellat 1976; Burkhart et al.

1992; Pritchett and Coroniti 1992]

– magnetic field

– Sharply peaked particle density

–

tanh( / )z

/ 0.5D thv v

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PREVIOUS WORK (2)

The vD/vth << 1 Regime [Holland and Chen 1993; Sitnov et al. 2000]

• Current sheet properties—non-Harris-like

– magnetic field

– Particle density is nearly constant (10—20%)

– Velocity is peaked in the current sheet

– Pressure tensor is nondiagonal and anisotropic

• Observed quiet-time magnetotail current sheet properties

[McComas et al. 1986; Sergeev et al. 1993]

– Magnetic field:

– Particle density is nearly constant

– Velocity is peaked in the current sheet

• New work: Extend Holland and Chen [1993] to asymmetric current sheets

tanh( / )z

tanh( / )z

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MODEL: 1-D Asymmetric Thin Current Sheets

IONS: Vlasov Equilibrium

• Individual ion trajectories are calculated

– Static magnetic (and electric) field with

– Motion is nonintegrable: transient, stochastic, and integrable orbits

• Ion contributions to J(x3), n(x3), V(x3) are calculated on a grid

• Obtain new B(x3). Iterate until convergence.

ELECTRONS:

• Mass-less fluid equations

– Momentum equation (me = 0)

– Quasi-neutrality

– Polytropic equation of state

0nB

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MODEL

MODEL SPECIFICATION

• Asymptotic source particle distributions

– : both are -function distributions; n0, U

• Parameters: Bn/Ba and Ti / Te for each asymptotic region

MODEL OUTPUT

• Converged B1(x3), J(x3), n(x3), T(x3), P(x3)

• is satisfied

f f

aB

1=0

c J B P

nB

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MODEL RESULTS

SS

Demand that the solution satisfy specified n, T, V, and B.

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FORCE BALANCE: PRESSURE TENSOR

Pressure tensor: nondiagonal and anisotropic inside the current sheet

Anisotropic and nearly diagonal outside

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SOLAR WIND DATA

Time resolution: 3 sec (diamonds). 0.044 sec (thin line)

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MODEL—DATA COMPARISON

Model: lines. Data: diamonds

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MODE—DATA COMPARISON

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NONLOCAL NATURE

• “Kinetic thinning” [Harold and Chen 1996]

– Source distributions: Increase vD/vth, more field-aligned, increased high-energy

tail in f thinner current sheets

– Bifurcated current sheets

• Increase asymmetry, , of the sources (this work)

thinner current sheets

• Increasing fraction of transient orbits [Chen and Palmadesso 1986]

f f

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SUMMARY

• Current sheet current:

• For Te ~ Ti in the solar wind, J2e is ~50% of J2i.

• It is possible to match both magnetic field and plasma data with good agreement

– Force balance is satisfied in all three directions

• Current sheets are not Harris-like: density is relatively flat, pressure tensor is

nondiagonal inside the current sheet

• Current sheet structure can be “remotely” determined via source distributions

– A purely kinetic effect

– Associated with increased flows, more field-line aligned distribution

– Formation of bifurcated current sheets

• Implications: anisotropic (ion) tearing mode can be strongly unstable [Chen and

Palmadesso, 1984]

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i

TJ J

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