A self organized critical model of a highly correlated 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 (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

Complex Magnetosphere

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

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

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

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. What do we know about this arcs?

*L ongitudinal 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 R E ) * Can't be formed without organization of the magnetosphere But arcs....

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

1. How do meta-stable arc-like structures form in a turbulent magnetosphere? 2. What make this structures collapse? 3. What is the distribution of energy release from the collapse? Gaps in our knowledge of the relationship between magnetospheric structures and energy release

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) +

Model Footpoints undergo slow quasi- random motions Straight field lines B z (x,y,t) Incompressible fluid & uncorrelated v B z (x,y,t 0 ) linearly decreasing function of x The evolution of the magnetic field is: x y z Footpoint of Flux Tubes

B2B2 B1B1 B3B3 B4B4 FIRST NEIGHBOURS Perturbation & Redistribution Scheme Critical Value:  x B ~ j B 0 + B 1 + B 2 + B 3 + B 4 5 B i = Redistribution rule: Energy Released:  

SANDPILESOC MODEL Forcing Constant input Velocity is prescribed randomly at each node Critical ValueStatic FrictionCurrent Redistribution Sand grains rolling down B-averaged with first neighbors Energy Release Gravitational Potential Conservation of magnetic flux Scheme

Simulation Results

N PP EE TT ± ± ± ± ± ± 0.05 Polar UVI (Uristky 2002)1.25 – 1.6~ 2 Probability density functions Liu et al. (2010) JGR

Currents Filaments Multiscalar Highly filamentary

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

Spreading Exponents Number of unstable nodes at time t Probability of existence at t   Size of an avalanche ‘death’ by t Probability of an avalanche to reach a size S

Spreading Exponents N      ± ± ± ± ± ± ± ± ± 0.14 Exp(1) Exp (2) (1) Uritsky, V. et al, GRL, 2001; (28), 19, (2) Uritsky, V. M. & Klimas, A.J.,2004; Substorms-7 Proceedings of the 7 th International conference of substorms.

Area covered by the avalanches t0t0 t= t max Integrated time area

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

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