a self organized critical model of a highly correlated model of a highly correlated flow-driven...
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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…!