Maxwell Prize: 35 years of Computer Simulations of 5D Plasma Turbulence in Tokamaks*

Major progress has been made in computer simulations of turbulence in tokamaks over the past 35 years, from early gyro-Landau-fluid models to the sophisticated 5D gyrokinetics of the current state of the art. Part of this was enabled by a factor of 10 million growth in computer power, but it also required the design of efficient algorithms and effective formulation of models with enough physics to be realistic enough for the problems at hand while being tractable. This line of work began in an era when many thought turbulence was an intractable problem. The community relied upon empirical scalings, hoping for reliable extrapolations. Many people have contributed to progress since then, in theoretical formulations, simulation complexity and algorithms, and testing with experiments. Direct gyrokinetic simulations are now able to quantitatively predict turbulence and temperature and density profiles in the main core plasma region of many experiments. Turbulence determines how large a device needs to be to reach Lawson's criterion for high fusion gain. Modest reductions in turbulence levels could lead to significantly cheaper fusion devices. We will discuss some highlights of what has been learned about the nature of tokamak turbulence, including counterintuitive implications of critical gradient thresholds, which can cause the core plasma to depend sensitively on the edge plasma. There has been important work on simulations of the much harder edge region of tokamaks, but this remains a critical area where more work is needed, to be able to reliably predict the height of the H-mode pedestal, heat loads on surfaces, etc., and to conduct detailed testing with experiments and independent codes. AI/ML can greatly help with turbulence studies, such as by searching through the high dimensional space of tokamak and stellarator designs to optimize them. Some of the simulation techniques developed for fusion are also useful for astrophysical plasma turbulence, and vice versa.