The mission of the U.S. Fusion Energy Science Program is to acquire the knowledge base needed for an economically and environmentally attractive fusion energy source.
Overview of Fusion and Plasma Science Computing:
Plasma, sometimes called the 4th state of matter, is a gas of such high temperature that the atoms have Dis-associated into their component parts of electrons and charged nuclei. Plasmas play a key role in controlled fusion and in space physics, as well as in other applications and disciplines such as material processing, particle accelerators, and astrophysics. Many of these applications involve plasmas in strong electric and magnetic fields. To simulate (or model) the behavior of plasmas, a system of mathematical equations and boundary conditions is formulated that describes the plasma and the electromagnetic field. Different mathematical models arise from different approximation techniques and hence have different regions of validity. For example the ideal MHD equations provide a simplified set of equations suitable for describing a wide range of global plasma instabilities, but these completely neglect all dissipative effects, which are not important for this class of global, fast time scale instabilities described well by ideal MHD. Other classification schemes sometimes used are that of microscopic and macroscopic models, which are appropriate for describing the small-scale and the large-scale features, respectively, and that of classification according to the typical time scales of the plasma phenomena being addressed.
As an illustration of the richness of this field, we show in
figure 22 a range of time scales spanning fifteen
orders of magnitude that are of relevance to a modern magnetic fusion
experiment. On that figure, we also indicate many of the equation
sets that are appropriate to describe phenomena occurring on those
time scales, and some of the computational plasma models that have been
developed to address these. These models include sets of linear and
nonlinear equations, and both fluid and particle-in-cell based
representations. Within each time scale category, plasma models may
also be distinguished by their physical and corresponding mathematical
complexity, and by their need to be supplemented with experimentally
measured parameters. Because of the complexity of the physical model,
the geometry, the boundary conditions, and/or the nonlinear phenomena,
these equations can only be solved on the most powerful computers.
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During the last few decades, remarkable progress has been made in
measuring, understanding and in predicting many aspects of plasma behavior
in the laboratory as well as in space. Many simulation models, such as
those referred to here, have been developed that accurately describe many
facets of plasma behavior. In magnetized fusion physics, the tokamak
configuration has emerged as the leading candidate to serve as the
embodiment of the first fusion-powered electrical power plant. Because of
it's importance to the program, an extensive system of tokamak specific
simulation and analysis codes have been developed by the fusion community.
We illustrate this system, which consists of over 50 separate stand-alone
codes in figure 23. A typical project to optimize the design of a
new fusion device would use most if not all of these codes to define the
configuration, analyze its stability and confinement properties, develop
heating and current-sustainment methods, and analyze potentially
destructive failure modes.
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The system of codes shown in this figure illustrate the impressive achievements that have been made, but they also hint at some of the needs for improvement. Present emphasis is on extending the range of validity of existing simulation models so that realistic fusion parameters can be addressed, and also in developing models that span wider ranges in time and space scales for more comprehensive simulations of complex phenomena. This direction would eventually lead to a complete physics based predictive simulation model of fusion and space plasma behavior, and there is reason to believe that such comprehensive simulation capabilities are now within reach. The creation of such fundamental simulation models would have dramatic implications for fusion, as well as for related fields such as space sciences.
In fusion, more comprehensive simulation models would provide better guidance for the design and operation of experiments. In this new paradigm, experiment and theory will work in tandem in the validation of the fundamental principles, thereby providing the high scientific confidence required to design and construct the next generation of experimental devices. A credible-physics-based simulation model also holds forth the promise of enabling the discovery of a breakthrough advance in fusion science. An example would be one that would radically increase the obtainable fusion core power density and hence the economic attractiveness of a fusion power plant.
It now appears that a complete physics-based predictive simulation model could result from an appropriate combination and extension of 3D simulation models that now exist. This integrated modeling would involve solving the appropriate equations on both the microscopic and macroscopic spatial and temporal scales and developing efficient algorithms for coupling the simulations. On the microscopic scales, the Numerical Tokamak Turbulence Grand Challenge has produced near first-principles 3D gyrokinetic and gyrofluid simulation models that are now making realistic predictions of the turbulent transport of plasma and energy in localized regions and in simplified geometry. These models need to be extended by increasing the order of the fundamental mathematical equations and by increasing the generality and the spatial extent of the geometry they are applied to, including extending them to the plasma edge. In the integrated modeling, the geometry for the microscopic model would be defined by the macroscopic model that would be solved concurrently. The need for effective coupling algorithms can be illustrated by a simple example that shows 3D micro-turbulence calculations cannot be applied directly to macroscopic problems in the near future. A 10 msec full torus simulation with 36,000 modes would require 50 Terabytes of fast memory, generate 27 Petabytes of data, and take 80 hours of CPU time on a Teraflop computer.
On the macroscopic scale, great progress has been made in solving the 3D magnetohydrodynamic (MHD) equations accurately, including the effects of plasma resistivity. As viscous hydrodynamics is characterized by the Reynolds number R, resistive MHD is characterized by a dissipation parameter S called the magnetic Reynolds number. Present MHD simulations are generally limited to S values of 104, whereas values of 108 would be more typical of fusion plasmas. Also, today's macroscopic codes normally utilize relatively simple idealized boundary conditions, and need to be supplied with empirical ``transport coefficients'' to describe the sub-grid scale turbulent phenomena. The implementation of more realistic boundary conditions is relatively straightforward and would open up a whole host of new capabilities. The integrated modeling would in effect self- consistently determine these transport coefficients from the microscopic simulation model.
Other major modeling and simulation issues include the development of optimization methods to design compact helical or toroidally symmetric plasmas that simultaneously have good confinement, MHD pressure limits, and position control characteristics with a realizable set of external coils and acceptable plasma access. Several different approaches to this design problem have begun in the last few years and are leading to a new generation of proposals for advanced confinement experiments that could significantly enhance the attractiveness of a fusion power plant.