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## Self-Organization in a Plasma Transport model in the Magnetotail

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**Self-Organization in a Plasma**Transport model in the Magnetotail J. A. Valdivia Colaboradores A. J. Klimas D. Vassiliadis A. S. Sharma A. Chian J. Takalo J. Rogan L. Gomberoff M. Hesse K. Papadopoulos D. Baker etc.**0th Order Magnetosphere**• The Magnetosphere, Model 0 • The Magnetosphere, Model 1 • Globally coherent • Repetitive • The Magnetosphere, Model 2 • Problems in the “magnetotail” • Turbulence in the “Plasma Sheet” • Self-similarity of events • Self-organization • Mode of attack**Instability?**T. I. Pulkkinen FMI 1st Order Magnetosphere • The Magnetosphere, Model 0 • The Magnetosphere, Model 1 • Globally coherent • Repetitive • The Magnetosphere, Model 2 • Problems in the “magnetotail” • Turbulence in the “Plasma Sheet” • Self-similarity of events • Self-organization • Mode of attack**Low Dimensional (Caos?)**Useful for prediction “Low dimensional” Models Space weather**2nd Order Magnetosphere**• The Magnetosphere, Model 0 • The Magnetosphere, Model 1 • Globally coherent • Repetitive • The Magnetosphere, Model 2 • Problems in the “magnetotail” • Turbulence in the “Plasma Sheet” • Self-similarity of events • Self-organization • Mode of attack**PROBLEMS -> SO? I**• (1) Turbulence - Near Earth Plasma Sheet (~20RE) • All phases • elementary transport eevents • Ohtani et la., [1998]: fractal D? • (2) Busty Bulk Flows (BBF) • restricted size (~ 1RE) • Sporadic (intermittent) • Consistent with localized reconnection Borovsky et al., [1997]: Baumjohann et al. [1990]; Angepoulos et al.[1992,1996], Fairfield et al. [1998] Nagai et al., [1998] How can we connect this observations with the Coherence and repeatability of the Magnetosphere?**PROBLEMS -> SO? II**• (3) Power law distribution of events: • Auroral geomagnetic disturbances • Distribution of auroral dissipation fs(s) • Distribution de duration ft(T) • Power spectrum S(w) • (4) Pi2 Pulsations • Contains signature of turbulence • in the plasma sheet and possibly SOC? (Consolini et al)**PROBLEMS -> SO? III**(5) Low dimensional Magnetospheric Dynamics (6) Energy output from Polar UVI images (Uritsky et al) (Liu et al, GRL 2000) (Liu et al, GRL 2000)**PROBLEMS -> SO? IV**Energy release in the form of plasmoid is similar to a crisis in stock prices • The definition of SOC’s almost describes the phenomena of “substorms” • … it is the natural state to which driven dissipative systems evolve … (Lu [1995]) • A variable is conserved • Dissipation through a localized instability Theoretical guideline (1) Sand pile (or type) models (2) Milovanov et al. [1996] Self Similar percolation of flux tube (3) SOC a la Tom Chang (4) SOC from generalized MHD Klimas, Valdivia, et al., [2000] (5) Antonnova**nth Order Magnetosphere**• The Magnetosphere, Model 0 • The Magnetosphere, Model 1 • Globally coherent • Repetitive • The Magnetosphere, Model 2 • Problems in the “magnetotail” • Turbulence in the “Plasma Sheet” • Self-similarity of events • Self-organization • Mode of attack**Self-organized criticality**Discrete intuition: -> J. Takalo et al (1998, 1999,etc) But plasma models are continuous**Continuous Models?**Intermittent turbulence Localized reconnection? Self-similarity? Self-organization?**Continuous models?**TO START: FROZEN IN and Beyond MHD B field is frozen with the plasma when Reconnection -> how the Frozen in condition is broken**Hysteresis**Q(J) Dmax Dmin bk k Bx(z) z 0 Approximation I Z**Approximation I**Reconnection (BBF) Chaos -> driver is constant in t Renormaliztion group & spatio-temporal chaos**Approximation I**MOVIE I**More**Plasma Physics Learning Experience 1D Magnetic annihilation 2D Magnetic field model Bx(z) Turbulence? z More D 0 1D Plasma model (Reconnection?) 2D resistive MHD model (Reconnection?) • 2D Plasma • model • Reconnection? • Turbulence? • Self-similarity?**Aproximacion II**Magnetic flux Y Turbulent vs. self-organization? X**Aproximacion II**Turbulence V = 0.1 k = 4**More**Plasma Physics It is a learning experience and fun! 1D Magnetic annihilation 2D Magnetic field model Bx(z) Turbulence? z More D 0 1D Plasma model (Reconnection?) 2D resistive MHD model (Reconnection?) • 2D Plasma • model • Reconnection? • Turbulence? • Self-similarity?**Aproximacion III**Z X**Approximation III**E=VzBx Z MOVIE III outgoing X Symmetric Petscheck type of Picture … WORK IN PROGRESS ...**Model of the Dynamics**• The Magnetosphere, Model 0 • The Magnetosphere, Model 1 • Globally coherent • Repetitive • The Magnetosphere, Model 2 • Problems in the “magnetotail” • Turbulence in the “Plasma Sheet” • Self-similarity of events • Self-organization • Mode of attack