Drawn into a Whirlpool: A New Way to Stop Dangerous Fast Electrons in a Fusion Device

A new phenomena forms vortices that trap particles, impeding electron avalanches that harm fusion reactors.

Distribution of runaway electrons and the directions in which they are flowing. The top figures show the results without fan instabilities (left), with a large population of electrons running into a high-energy regime (right). The bottom figures show the results with fan instabilities that trap runaway electrons in vortices, pushing them back to lower energy and making the whole distribution fan-shaped.

The Science

As the density, temperature, and currents in the hot ionized gas, known as plasma, inside experimental fusion devices reach the point where hydrogen ions fuse to form helium and huge amounts of energy are released, the electric currents become increasingly difficult to control. If control is lost, the plasma disrupts. A dangerous avalanche of fast electrons is continuously accelerated by a self-generated electric field. These electrons can escape and melt “hot spots” in the wall. In addition to avoidance strategies, the scientists that operate future fusion reactors need mitigation strategies to reduce the damage. A new approach exploits a fan instability first observed in electromagnetic waves in the Earth’s atmosphere.

The Impact

Because of this fan instability, the fast electron beam moves chaotically as it passes through the background plasma, just as water flowing through a flexible hose causes it to move as a snake does. This process excites a “whistler wave” in which the frequency drops from high to low, just like a slide whistle. Scientists have found whistler waves in both Earth’s radiation belt (thanks to NASA’s Van Allen Probes) and in the DIII-D National Fusion Facility. In a big step forward for using whistler waves in mitigation strategies, scientists have accurately simulated their interaction with electron beams both theoretically and numerically using advanced computational models.


Just like when pushing a playground swing, energy is only transferred from the electron beam to the whistler wave when the “pushing” and “swinging” are at the same frequency (that is, in resonance). But in tokamaks (fusion devices that contain the plasma), the electron rotation frequency is much larger than that of the whistler wave. So how can there be a resonant energy transfer that diffuses electron energy?

The continuous acceleration of the electrons means they get faster and faster until their speed approaches the speed of light. Then, Einstein’s theory of relativity kicks in. The mass of the electrons increases, time seems to slow down, and the resonance condition changes.

To better understand this process, scientists at the Princeton Plasma Physics Laboratory have developed a numerical simulation code that fully utilizes modern multi-core processors. When the resonance condition is satisfied, the electrons are drawn away from their original trajectories and trapped inside whirlpool-like vortices formed by the whistler waves. The energy is diffused and the momentum scattered; this is exactly what is required for mitigation: impede the relativistic electrons before they hit the wall.

Simulations of existing experiments show the importance of this fan instability in the suppression of avalanches and the enhancement of radiation (that is, cooling) from the runaway electrons. Scientists are now testing this idea as a mitigation strategy in ITER, where the whistler waves are either caused by self-excited fan instability or by the use of external antennas, to limit the damage caused by disruptions.


Chang Liu
Princeton Plasma Physics Laboratory


This work was supported by the Department of Energy, Office of Science, Fusion Energy Sciences.


C. Liu, E. Hirvijoki, G.Y. Fu, D.P. Brennan, A. Bhattacharjee, and C. Paz-Soldan, “Role of kinetic instability in runaway-electron avalanches and elevated critical electric fields.” Physical Review Letter 120, 265001 (2018). [DOI: 10.1103/PhysRevLett.120.265001]

C. Liu, L. Shi, E. Hirvijoki, D.P. Brennan, A. Bhattacharjee, C. Paz-Soldan, and M.E. Austin, “The effects of kinetic instabilities on the electron cyclotron emission from runaway electrons.” Nuclear Fusion 58, 096030 (2018). [DOI: 10.1088/1741-4326/aacc9b]

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