Multi-Scale, Multi-Rate, and Multi-Fidelity Methods to Predict Fusion Plasma Performance and Opportunities for Collaboration
Darin Ernst
Massachusetts Institute of Technology
Plasma Science and Fusion Center
Fusion energy development has entered a golden era with over $15B in unprecedented private funding among 77 fusion companies worldwide, with over half of this funding in the U.S., amounting to approximately 5 times the annual $1.5B allocated to fusion by the U.S. Dept. of Energy. For the first time, the direct numerical simulation of gyrokinetic plasma turbulence and collisional transport (albeit limited to the core region) has been used to guide or validate the designs of next-generation fusion machines.
The DOE Fusion Innovation Research Engine (FIRE) Collaboratory, “Advanced Profile Prediction for Fusion Pilot Plant Design (APP-FPP)”, will help bridge the gap to leverage federally funded progress to inform next generation machine designs in industry. The project is comprised of eleven institutions, with the primary goal of developing the first whole-device performance predictions based on gyrokinetic simulations of plasma turbulence. The predictions will feature practical edge gyrokinetic profile predictions and include kinetic plasma-wall and neutral interactions to simultaneously predict impurity density profiles, which strongly influence fusion yield. To achieve practical and useful integrated simulations, the component codes must be further developed, accelerated and integrated using a range of approaches. These include multi-rate time-stepping, GPU acceleration, and multi-fidelity and machine learning models for key physical process including turbulence, kinetic neutrals, plasma sheaths, and plasma-materials interactions. Multi-scale approaches which are used to couple short turbulence spatial and temporal scales with larger and slower transport timescales, over which density and temperature profiles evolve, are being extended to the plasma boundary. Multi-scale turbulence spanning electron and ion gyroradius scales (a factor of ~60 in space and time) are being included using multi-rate and multi-scale approaches, leveraging both reduced models and direct gyrokinetic simulations, with strong cross-scale nonlinear coupling.
The temperatures and densities in the core, where fusion power is produced, are highly sensitive to their values at the edge, where transport timescales are often two orders of magnitude shorter. However, the edge, where densities and temperatures fall off rapidly, is more difficult to predict. Scale lengths which are comparable to the both the orbit widths of the ions and turbulence eddy sizes often preclude the “local”, small-fluctuation approach used in the plasma core. In the edge, particles “leak” from one nested magnetic flux surface to the next before they can equilibrate within a flux surface. Thus, edge temperatures and densities can vary strongly on a flux surface and the diffusion equations are no longer one-dimensional. Collisional transport plays a more significant role and requires accurate global approaches including strong flows. Turbulent fluctuations in the edge are generally much stronger than in the core and a fully nonlinear calculation is required. Gyrokinetic codes which include these effects as well as atomic physics such as kinetic neutral ionization and radiation are being developed and have matched some results from experiments. These approaches are being further developed in APP-FPP, leveraging collaborations and building on methods which promise a factor of ~500 speedup to complete simulations in hours rather than weeks.
Acknowledgments: Work supported by DOE Awards DE-SC0025853 (MIT, UT-Austin, UC-Boulder, UI-Urbana, UMd-Baltimore, ExoFusion, Jubilee), DE-AC52-07NA27344 (LLNL), and DE-AC05-00OR22725 (ORNL) and in collaboration with the Max Planck Institute for Plasma Physics, Garching and General Atomics.