To make fusion energy a viable resource for the world's energy grid,
researchers need to understand the turbulent motion of plasmas: a mix of
ions and electrons swirling around in reactor vessels. The plasma particles,
following magnetic field lines in toroidal chambers known as tokamaks, must
be confined long enough for fusion devices to produce significant gains in
net energy, a challenge when the hot edge of the plasma (over 1 million
degrees Celsius) is just centimeters away from the much cooler solid walls
of the vessel.
Abhilash Mathews, a Ph.D. candidate in the Department of Nuclear Science and
Engineering working at MIT's Plasma Science and Fusion Center (PSFC),
believes this plasma edge to be a particularly rich source of unanswered
questions. A turbulent boundary, it is central to understanding plasma
confinement, fueling, and the potentially damaging heat fluxes that can
strike material surfaces—factors that impact fusion reactor designs.
To better understand edge conditions, scientists focus on modeling
turbulence at this boundary using numerical simulations that will help
predict the plasma's behavior. However, "first principles" simulations of
this region are among the most challenging and time-consuming computations
in fusion research. Progress could be accelerated if researchers could
develop "reduced" computer models that run much faster, but with quantified
levels of accuracy.
For decades, tokamak physicists have regularly used a reduced "two-fluid
theory" rather than higher-fidelity models to simulate boundary plasmas in
experiment, despite uncertainty about accuracy. In a pair of recent
publications, Mathews begins directly testing the accuracy of this reduced
plasma turbulence model in a new way: he combines physics with machine
learning.
"A successful theory is supposed to predict what you're going to observe,"
explains Mathews, "for example, the temperature, the density, the electric
potential, the flows. And it's the relationships between these variables
that fundamentally define a turbulence theory. What our work essentially
examines is the dynamic relationship between two of these variables: the
turbulent electric field and the electron pressure."
In the first paper, published in Physical Review E, Mathews employs a novel
deep-learning technique that uses artificial neural networks to build
representations of the equations governing the reduced fluid theory. With
this framework, he demonstrates a way to compute the turbulent electric
field from an electron pressure fluctuation in the plasma consistent with
the reduced fluid theory. Models commonly used to relate the electric field
to pressure break down when applied to turbulent plasmas, but this one is
robust even to noisy pressure measurements.
In the second paper, published in Physics of Plasmas, Mathews further
investigates this connection, contrasting it against higher-fidelity
turbulence simulations. This first-of-its-kind comparison of turbulence
across models has previously been difficult—if not impossible—to evaluate
precisely. Mathews finds that in plasmas relevant to existing fusion
devices, the reduced fluid model's predicted turbulent fields are consistent
with high-fidelity calculations. In this sense, the reduced turbulence
theory works. But to fully validate it, "one should check every connection
between every variable," says Mathews.
Mathews' advisor, Principal Research Scientist Jerry Hughes, notes that
plasma turbulence is notoriously difficult to simulate, more so than the
familiar turbulence seen in air and water. "This work shows that, under the
right set of conditions, physics-informed machine-learning techniques can
paint a very full picture of the rapidly fluctuating edge plasma, beginning
from a limited set of observations. I'm excited to see how we can apply this
to new experiments, in which we essentially never observe every quantity we
want."
These physics-informed deep-learning methods pave new ways in testing old
theories and expanding what can be observed from new experiments. David
Hatch, a research scientist at the Institute for Fusion Studies at the
University of Texas at Austin, believes these applications are the start of
a promising new technique.
"Abhi's work is a major achievement with the potential for broad
application," he says. "For example, given limited diagnostic measurements
of a specific plasma quantity, physics-informed machine learning could infer
additional plasma quantities in a nearby domain, thereby augmenting the
information provided by a given diagnostic. The technique also opens new
strategies for model validation."
Mathews sees exciting research ahead. "Translating these techniques into
fusion experiments for real edge plasmas is one goal we have in sight, and
work is currently underway," he says. "But this is just the beginning."
Reference:
A. Mathews et al, Uncovering turbulent plasma dynamics via deep learning
from partial observations, Physical Review E (2021).
DOI: 10.1103/PhysRevE.104.025205
A. Mathews et al, Turbulent field fluctuations in gyrokinetic and fluid
plasmas, Physics of Plasmas (2021).
DOI: 10.1063/5.0066064
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