Publication: Study of Magnetically Confined Plasma Dynamics with Cellular Automata
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2018-09
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2018-10-09
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Abstract
Nuclear fusion has many chances to become the primary energy source of the future.
The great energy density of fusion reactions, together with the environmental and safety
benefits that it encloses makes it a powerful alternative to existing energy sources and a
smart response to the increase in energy demand.
Up to now, research has designated tokamaks as the best alternative to obtain fusion
energy. However, their reliability has not yet been proved. To this matter, ITER, the most
ambitious energy project in human history, is being built to demonstrate the viability of
fusion energy by producing net positive energy in a giant tokamak.
Fusion plasmas inside Tokamaks are known to be turbulent. The instabilities created
in the plasma by the great gradients they are subjected to, turn the issue of their confinement
into a difficult goal to achieve. Part of the plasma escapes from the confinement
volume, reducing the density in its core and decreasing the efficiency of the fusion reaction
as well as the energy obtained from it. As a consequence, the net fusion energy
produced may not be sustainable. More energy is used in the process than the one that
is extracted from it. If fusion reactors are meant to be a reliable source of energy in the
future, effective solutions to mitigate the effects of turbulence are a critical necessity.
Various confinement modes exist in a tokamak as the power of the heating source is
increased. The most well-known one is the L-mode (Low confinement mode), but it is
only the H-mode (High confinement mode) the one that brings some hope to the idea of
industrial fusion processes. Still, there are many unknowns to the dynamic processes that
take part in this last regime.
In H-mode, a transport barrier created by the poloidal rotation of the plasma is known
to appear at the edge of the tokamak section. The differences in radial velocities in this
barrier, create zonal shear flows that shear apart turbulent eddies, reducing the transport of
particles out of the tokamak. It is this mechanism that makes H-mode the most reasonable
regime in which a fusion reactor would operate.
Still, the transport dynamics of H-mode are not fully understood. In order to make
effective predictions on confinement control strategies as well as the cost and size of a future
fusion energy plant, the ultimate concepts on the interaction of shear with turbulence
have to be clarified. It is a proved fact that the dynamics of transport in fusion plasmas
is not diffusive. Instead, the transport regime operating in L-mode appears to be similar
to ”SOC dynamics” (SOC = Self Organized Criticality), characterized by the existence of
memory as well as the absence of characteristic scales or times. This absence makes the
quest for an effective coefficient of diffusion a useless work. As a first step towards the understanding on how the relations between turbulence
and shear change the transport dynamics in H-mode, the present project aims to create
an abstract model of radial turbulent transport inside tokamaks. This model needs to be
versatile enough to introduce and detect essential changes and fundamental relations in
the transport dynamics of the system. With it, fundamental questions such as the search
for a proper effective description of transport beyond usual diffusion could be investigated
in the future.
For this purpose, the running sandpile, a model that attempted to capture the basic
dynamics of the plasma in L-mode introduced in the 1990’s, is used and modified by
introducing in it a new variable, shear. By doing this an ”extended sandpile model” is
created. In order to introduce the interactions of the shear with the other variables in
the model in a way inspired by the actual physics in H-mode, new dynamic rules are
implemented and included in a newly designed algorithm created with the software tool
Matlab. This ”Extended sandpile model” has then been tested by analyzing data retrieved
from its continued operation.
The tool that has been used to examine the validity of this extended model is known as
”transfer entropy”, a tool capable of determining the direction and importance of causal
flows between variables. Variables such as the instantaneous variance of the average
shear, the instantaneous variance of the average gradient and the instantaneous number
of unstable cells have been tested by this tool, revealing reverted relations in causality
between the model with shear and the one without. Moreover, in the extended running
sandpile the results show that shear can be made to become the most influential factor,
something that was intended, since it is what actually happens in H-mode plasmas.
As a conclusion for these results follow that the procedures here conducted have been
able to produce a model that is able to capture the essence of near-marginal transport in
the presence of shear in a few rules and parameters. Furthermore, transfer entropy has
been proved to be able to detect these changes afterwards.
As content of future research one could mention that a thorough exploration of the parameter
space that defines the extended model should be carried out before selecting the
operational point that would set the system closer to actual H-mode transport dynamics.
Once done, this could serve as the starting point of investigations aiming at finding appropriate
effective transport equations that, from previous experience with the usual running
sandpile, would probably have to be based on the use of the integro-differential operators
usually known as fractional derivatives.
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Keywords
Nuclear fusion, Plasma, Tokamak, Sandpile, Transfer entropy, Shear, Turbulence