Clarifying the mechanism of coupled plasma fluctuations using simulations

Background
In nature, phenomena in which multiple fluctuations occur in a coupled manner are frequently observed. For example, in large earthquakes, cases of them occurring consecutively in adjacent regions have been reported. When multiple fluctuations occur in this coupled way, compared to a single fluctuation, the coupled ones release more energy, leading to larger-scale phenomena. In fusion plasmas, fluctuations caused by energetic particles exist and are known to degrade the confinement of energetic particles. On the other hand, these fluctuations are expected to play a role in transferring the energy of the energetic particles to fusion fuel ions for heating. Thus, fluctuations caused by energetic particles are an important issue in fusion research, and among them, fluctuations that occur in a coupled manner are particularly noteworthy because they can develop into large-scale phenomena.

At the ASDEX Upgrade device in Germany, two fluctuations occurring in a coupled manner were observed. Although these fluctuations were attributed to energetic particles, the underlying mechanism of their coupling remained unclear.

Results
Researchers from the National Institute for Fusion Science (NIFS) and the Max Planck Institute for Plasma Physics (IPP) have collaborated on a simulation study to clarify the physical mechanism by which two fluctuations occur in a coupled manner.

NIFS has developed a code named "MEGA" to simulate plasma fluctuations caused by energetic particles. This is called a "hybrid simulation"^*3 because it performs coupled and simultaneous calculations for particles and fluid. The MEGA code has been applied to experimental devices in Japan and overseas, with its effectiveness demonstrated through comparisons with various experimental results. This time, Assistant Professor Hao Wang of NIFS and others conducted a simulation using MEGA on a supercomputer and succeeded in reproducing the phenomenon observed in the ASDEX-Upgrade device, in which two fluctuations occur in a coupled manner. In the simulation, the first fluctuation with a frequency of 103 kHz was initially caused by energetic particles, followed by the generation of a second fluctuation with a frequency of 51 kHz, which developed into a larger amplitude than the first (see figure). This simulation result is consistent with the experimental results.

To understand the generation mechanism of the second fluctuation, researchers investigated the time evolution of the distribution function of energetic particles. This describes how many particles with what velocities and energies exist at each location in the plasma. The shape of this distribution function can strongly influence the development of fluctuations and conversely, fluctuations can deform the distribution function. Assistant Professor Hao Wang and his collaborators performed a detailed analysis of the simulation results. They found that as the first fluctuation grew, the distribution function of energetic particles was significantly deformed, and this deformation caused the second fluctuation to occur (see figure). In other words, they revealed that the two fluctuations occurred in a coupled manner via the deformation of the energetic particle distribution function.

Significance and future work

Achieving fusion energy requires energetic particles generated by fusion reactions to heat plasma and sustain these reactions. For this purpose, it is crucial to efficiently confine these energetic particles within the plasma. Coupled fluctuations can lead to significant losses of energetic particles. By utilizing the knowledge of the physical mechanism clarified in this study, it will be possible to contribute to the development of methods to suppress the coupled generation of fluctuations. Furthermore, this physical mechanism may allow us to generate the second fluctuation — which is difficult to excite directly — from the first. This could contribute to heating fuel ions. Moreover, even in space plasmas, although the types of waves differ, coupled fluctuations caused by energetic particles have been observed. The analysis method of the energetic particle distribution function developed in this study is also expected to be applicable to space plasmas.

In the future, we plan to conduct simulations that calculate both energetic particles and fuel ions to investigate the role of the latter and the energy transfer to them in coupled energetic particle driven fluctuations.

Glossary

*1 ASDEX-Upgrade
The ASDEX-Upgrade is a magnetic confinement fusion facility based on the tokamak concept operated by the Max-Planck-Institute for plasma physics in Garching, Germany. The full name of ASDEX is “Axially Symmetric Divertor EXperiment”. The ASDEX-Upgrade has a major radius of 1.65 meters, a plasma volume of 13 cubic meters, and a plasma current of 1.4 megaamperes.

*2 Distribution Function

In simplified models, statistical quantities such as averages are commonly used to describe key parameters. However, a distribution function provides more detailed information about variations within the data. For example, two cups of coffee may have the same average concentration of coffee grounds, but the distribution of those grounds within each cup can differ. In one cup, the grounds might be concentrated at the bottom, resulting in a weaker taste at the top; in the other, the grounds might be more evenly distributed, resulting in a consistent taste throughout. This difference in the distribution of coffee grounds, and consequently in taste, can be effectively described by a distribution function. Just as different distribution functions within coffee cups lead to different tastes and flavors due to variations in concentration, those of particles in a plasma can lead to different physical phenomena by affecting factors such as energy transfer and interparticle interactions.

*3 Hybrid Simulation

Computational models (equations) describing plasma behavior vary depending on the time and spatial scales of interest. A magnetohydrodynamic (MHD) model treats the plasma as a whole, calculating the time evolution of plasma density, fluid velocity, pressure, and electromagnetic fields. Conversely, a particle model calculates the equations of motion for individual particles constituting the plasma. At the National Institute for Fusion Science (NIFS), a hybrid simulation code has been developed. This code uses the MHD model for background plasma and the particle model for energetic and bulk ions, tracking their evolution over time and coupling the two models in a physically consistent manner.

Acknowledgements

This work was partially supported by MEXT as a “Program for Promoting Research on the Supercomputer Fugaku (Exploration of burning plasma confinement physics, JPMXP1020200103)”, JSPS KAKENHI Grant Nos. JP18K13529, JP18H01202, JP21H04973, and “PLADyS”, JSPS Core-to-Core Program, A. Advanced Research Networks. Also, this work was partially supported by the National Institutes of Natural Sciences program of Promoting Research by Networking among Institutions (Grant Number 01422301) and by the International Research Exchange Support Program of NINS. In addition, this work was partially carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200 - EUROfusion).

Numerical computations were performed on the “Plasma Simulator” (NEC SX-Aurora TSUBASA) of the National Institute for Fusion Science (NIFS) with the support and under the auspices of the NIFS Collaboration Research program (NIFS19KNXN397, NIFS20KNST156, NIFS21KNST196, and NIFS22KIST025), the JFRS-1 supercomputer system at the Computational Simulation Centre of International Fusion Energy Research Centre (IFERC-CSC), and the Supercomputer Fugaku provided by the RIKEN Center for Computational Science (Project IDs: hp200127, hp210178, hp220165).