A self organized criticalA self organized critical model of a highly correlated model of a highly correlated

flow-driven turbulent flow-driven turbulent magnetospheremagnetosphere

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 

Complex Magnetosphere

Energy release in the magnetosphere becomes apparent by geomagnetic and auroral perturbation

scale free distributionsE-( constant)

Normalized occurrence of spatiotemporal auroral perturbations

for different months J-F 1997-1998

Uri

tsky

et

al. 2

00

2

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 UTMarch 13th, 2007 (Fig 2., Donovan et al. 2008)

•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?

* 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

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 releasefrom the collapse?

Gaps in our knowledge of the relationship between magnetospheric

structures and energy release

What we do knowBright auroral arcs generated by energetic electron precipitation field-aligned currents (FACs) j

FAC and magnetopsheric current jObservations 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

• Bz(x,y,t)

• Incompressible fluid & uncorrelated v

• Bz(x,y,t0) linearly decreasing function of x

• The evolution of the magneticfield is:

x

y

z

Footpoint of Flux Tubes

B2

B1B3

B4

FIRST NEIGHBOURS

Perturbation & Redistribution Scheme

Critical Value: x B ~ j

B0 + B1 + B2 + B3 + B 45

Bi =

Redistribution rule:

Energy Released:

SANDPILE SOC MODEL

ForcingConstant

inputVelocity is prescribed

randomly at each node

Critical Value Static Friction Current

Redistribution

Sand grains rolling down

B-averaged with first neighbors

Energy Release

Gravitational Potential

Conservation of magnetic flux

Scheme

Simulation Results

N P E T

128 0.97 ± 0.06 1.15 ± 0.03 1.41 ± 0.05

256 1.09 ± 0.06 1.15 ± 0.02 1.37 ± 0.05

Polar UVI (Uristky 2002)

1.25 – 1.6 ~ 2

Probability density functions

Liu et al. (2010) JGR

Currents Filaments

MultiscalarHighly filamentary

At the Onset After the Onset

The avalanche did not erase the underlying pattern although there was energy removal

Memoryeffect

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

256 0.77± 0.06 0.29± 0.08 0.91± 0.15 1.71 1.16± 0.1 2.06

128 0.67 ± 0.06 0.31 ± 0.08 1.12 ± 0.15 1.81 1.18 ± 0.1 2.00± 0.14

Exp(1) 0.41 0.42 1.84 1.23 1.83

Exp (2) -0.36 1.23 2.04

(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.

Area covered by the avalanches

t0 t=

tmax

Integrated time area

Hig

hly

Corre

late

dH

ighly

Corre

late

dWhat are

the options to

improvethe model?

More realistic

description of

velocity

Final Remarkso 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…!