Sandpiles as a Paradigm for Turbulent Transport
In order to understand the complex dynamics of
turbulent (anomalous) transport in magnetic confinement devices a
simple Self Organized Criticality (SOC) model based on the dynamics
of avalanches down a running sandpile has been used. The cellular
automata rules governing the system are simply: if the local gradient
(Zn) is greater than a critical gradient the sandpile
become locally unstable and a given number (Nf) of grains
fall down to the next site down. This simple model displays
remarkably rich dynamics which have many characteristics in common
with the observed transport dynamics in magnetic confinement devices.
Therefore this type of model is used to explore the interaction
between this avalanche like transport and the sheared flows which are
so important in plasma confinement. From this model useful insight
has been gained into the transport dynamics and the two apparent
transport regimes in plasma confinement devices
In the animations below, you will be looking at the face of the
sandpile (like the face of the sandpile on the left). The light
colored squares, in the animation, are unstable (avalanching) sites
while the dark colored squares (the rest) are stable sites. The
system is periodic across the pile, closed at the top and open at the
bottom. You will be able to see avalanches of all sizes (a
characteristic feature of SOC systems) as well as unstable sites
propagating up the pile (again something characteristic of SOC
systems).
Animation of a running sandpile with and without sheared
flow
No Shear in the system 
Shear in middle
3rd of system
Note how the transport events (the avalanches) span
all sizes in the unsheared system. This leads to very efficient
transport (a bad thing if you are trying to confine a plasma).
However in the sheared region the large transport events are torn
apart which reduces the effective transport and therefore improves
the confinement.
A simulation of a turbulent system used to validate the
SOC model
This 3-D nonlinear computation is of Resistive G-mode
turbulence driven by the pressure gradient. The figure on the left
shows the density in which the long, transport event, scalelengths
are visible. The figure on the right shows the potential in which the
smaller, fluctuation, scalelengths are apparent. This agrees with the
simple SOC model.
For more information see
The Dynamics of Marginality and Self-organized
Criticality as a Paradigm for Turbulent Transport, D. E. Newman,
B. A. Carreras, P. H. Diamond and T. S. Hahm, Phys. Plasmas 3 (5) May
1996.
The Dynamics of Sand piles with sheared flow, D. E. Newman,
B. A. Carreras and P. H. Diamond Phys. Letters A 218 July (1996).
A Model Realization of
Self-Organized Criticality for Plasma Confinment, B. A.
Carreras, D. E. Newman, V. E. Lynch, and P. H. Diamond, Phys. Plasmas
3 (8) August 1996.
Home
Last changed on 11 Nov
1998
This page is maintained by David
Newman