1. ASYMMETRIC THIN CURRENT SHEETS: A 1-D TEST PARTICLE MODEL AND COMPARISON WITH SW DATA J. Chen 1 and R. A. Santoro 2 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

2. 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

3. NRL Plasma Physics Division 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”

4. NRL Plasma Physics Division MODELS AND PARAMETERS Symmetric Current Sheets Analytic Harris model: [Harris, 1962] – magnetic field with B n = 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

5. NRL Plasma Physics Division PREVIOUS WORK (1) The v D /v th > 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 –

6. NRL Plasma Physics Division PREVIOUS WORK (2) The v D /v th << 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

7. NRL Plasma Physics Division 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(x 3 ), n(x 3 ), V(x 3 ) are calculated on a grid Obtain new B(x 3 ). Iterate until convergence. ELECTRONS: Mass-less fluid equations –Momentum equation (m e = 0) –Quasi-neutrality –Polytropic equation of state

8. NRL Plasma Physics Division MODEL MODEL SPECIFICATION Asymptotic source particle distributions – : both are -function distributions; n 0, U Parameters: B n /B a and T i / T e for each asymptotic region MODEL OUTPUT Converged B 1 (x 3 ), J(x 3 ), n(x 3 ), T(x 3 ), P(x 3 ) is satisfied

9. NRL Plasma Physics Division MODEL RESULTS Demand that the solution satisfy specified n, T, V, and B.

10. NRL Plasma Physics Division FORCE BALANCE: PRESSURE TENSOR Pressure tensor: nondiagonal and anisotropic inside the current sheet Anisotropic and nearly diagonal outside

11. NRL Plasma Physics Division SOLAR WIND DATA Time resolution: 3 sec (diamonds). 0.044 sec (thin line)

12. NRL Plasma Physics Division MODEL—DATA COMPARISON Model: lines. Data: diamonds

13. NRL Plasma Physics Division MODE—DATA COMPARISON

14. NRL Plasma Physics Division NONLOCAL NATURE “Kinetic thinning” [Harold and Chen 1996] –Source distributions: Increase v D /v th, 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]

15. NRL Plasma Physics Division SUMMARY Current sheet current: For T e ~ T i in the solar wind, J 2e is ~50% of J 2i. 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]