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A self organized critical model of a highly correlated flow-driven turbulent magnetosphere

A self organized critical model of a highly correlated flow-driven turbulent magnetosphere L. F. Morales 1 , W.W. Liu 1,2 , P. Charbonneau 3 , V. M. Uritsky 4,5 & J. Manuel 1. (1) Space Science and Technology Branch, CSA, Saint Hubert, QC, Canada

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A self organized critical model of a highly correlated flow-driven turbulent magnetosphere

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  1. A self organized critical model of a highly correlated flow-driven turbulent magnetosphere L. F. Morales1, W.W. Liu1,2, P. Charbonneau3, V. M. Uritsky4,5 & J. Manuel1 (1) Space Science and Technology Branch, CSA, Saint Hubert, QC, Canada (2) College of Electronic Information, Wuham University, Wuham, China. (3) Département de Physique, Université de Montréal, Montréal, QC, Canada. (4) Department of Physics and Astronomy, University of Calgary, Calgary, AB, Canada. (5) CUA at NASA Goddard Space Flight Center, Greenbelt, Maryland, USA 

  2. Complex Magnetosphere

  3. Energy release in the magnetosphere becomes apparent by geomagnetic and auroral perturbation • scale free distributions • E- ( constant) Uritsky et al. 2002 Normalized occurrence of spatiotemporal auroral perturbations for different months J-F 1997-1998 Probability distribution p(S) characterizing dynamics of auroral active region during a major storm & entire month

  4. A possible interpretation: the active magnetosphere is a state of Self Organized Criticality (SOC) Theoretical + numerical studies produced scale-free distributions (Chapman et al, 1998; Klimas et al., 2000, 2004; Uritsky et al., 2001) Model = MHD + kinetic + anomalous component resistivity

  5. Active aurora is dominated by discrete arcs • Disruption of auroral equatorward arcs lies at the • heart of auroral substorm onset (Akasofu, 1964) Themis ASI data Auroral onset at 0507 UT March 13th, 2007 (Fig 2., Donovan et al. 2008)

  6. What do we know about this arcs? Although the structuring of auroral arcs has not been completely resolved as an observational problem it is generally agreed that the scale distribution of aurora is not smooth but has multiple peaks.

  7. But arcs .... • Longitudinal length of several thousand of km ~ magnetosphere size • Lifetime of arcs ~ 1 min (Alfven transit time) • Can explain processes in the auroral acceleration region (1-2 RE) • Can't be formed without organization of the magnetosphere

  8. MOREOVER …. • Arcs are a solution of quasistatic convection • problem? (Rice Convection model) Not found Structures do not arise naturally in global MHD models

  9. Gaps in our knowledge of the relationship between magnetospheric structures and energy release How do meta-stable arc-like structures form in a turbulent magnetosphere? What make this structures collapse? What is the distribution of energy release from the collapse?

  10. What we do know Bright auroral arcs generated by energetic electron precipitation field-aligned currents (FACs)j FAC and magnetopsheric current j Observations showed that there is close correlation between auroral arcs and currents in the CPS + Power-law observations (SOC)

  11. y z x Model • Footpoints undergo slow quasi-random motions • Straight field lines • Bz(x,y,t) • Incompressible fluid & uncorrelated v • Bz(x,y,t0) linearly decreasing function of x • The evolution of the magnetic • field is: Footpoint of Flux Tubes

  12. B4 B3 B1 B2 Perturbation & Redistribution Scheme Critical Value: x B ~ j Redistribution rule: B0 + B1 + B2 + B3 + B 4 Bi = 5 Energy Released: FIRST NEIGHBOURS  

  13. Simulation Results

  14. Probability density functions Liu et al. (2010) JGR

  15. Currents Filaments Multiscalar Highly filamentary

  16. At the Onset After the Onset The avalanche did not erase the underlying pattern although there was energy removal Memory effect

  17. Spreading Exponents Number of unstable nodes at time t Probability of existence at t Size of an avalanche ‘death’ by t k Probability of an avalanche to reach a size S b

  18. Spreading Exponents (1) Uritsky, V. et al, GRL, 2001; (28), 19, 3809-3812 (2) Uritsky, V. M. & Klimas, A.J.,2004; Substorms-7 Proceedings of the 7th International conference of substorms.

  19. Area covered by the avalanches t0 t=tmax Integrated time area

  20. What are the options to improve the model? Highly Correlated More realistic description of velocity Highly Correlated

  21. Final Remarks • We explorate an alternative view of energy storage and release in the CPS. • The system can reach a critical state. • The distribution of avalanches over total energy, peak energy and avalanche duration are scale free. • Found correlation between parameters. • We calculated the spreading exponents  and . We verified that they satisfy the mutual numerical relationship expected for SOC systems. • We are still working…!

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