Approaching the unexplored “plasma phase-space” with data science

A paper summarizing the results of this research was published in the Proceedings of the National Academy of Sciences on November 8.

Fusion energy is being researched and developed as a new source of electric power that will contribute to the realization of a carbon-neutral society. At the National Institute for Fusion Science, research on magnetically confined plasma is being conducted using the Large Helical Device*2 (LHD). The major difference between plasma and other gases is its low density. The density of magnetically confined plasma is only about one millionth that of the atmosphere, and collisions between constituent particles occur only rarely. As a result, the histogram of particle motion, called the velocity distribution function*3, is distorted. Distortions in the velocity distribution function can cause unexpected plasma dynamics, such as sudden changes in plasma temperature and the generation of currents; therefore, an understanding of the background physics is desired.

Spectroscopy, which measures the light emitted from plasma, is often used to determine the plasma velocity distribution function. Because the total amount of light is limited, spatial resolution has to be given up in order to measure the time variation of the velocity distribution function. On the other hand, knowing the change in phase-space distribution of the plasma, resolved in velocity and space coordinates, is essential to predict and control the plasma and to realize a fusion power reactor.

A research group led by Associate Professor Tatsuya Kobayashi, Assistant Professor Mikiro Yoshinuma, and Professor Katsumi Ida of the National Institute for Fusion Science has successfully achieved a high-speed measurement of plasma phase distribution with high precision, by utilizing tomography technology used in the medical field. 

They newly installed a “high-speed luminescence intensity monitor” in addition to the existing “high-resolution spectrometer” and “high-speed spectrometer,” and performed a coordinated operation of the three types of instruments. The obtained data were integrated and tomographic analysis was done to reconstruct the original plasma phase-space distribution. As a result, it became possible for the first time in the world to measure the plasma phase-space distribution at a high speed of 10,000 Hz (10,000 times per second). This is a 50-fold improvement over the previous two hundred hertz. 

Phase-space tomography was applied to the observation of energy exchange between plasma particles and beam particles via waves in the LHD experiment, and revealed evolutions in the plasma phase-space distribution. It is known that particles moving at velocities close to those of waves are accelerated by the waves and gain energy (wave-particle interaction). This phenomenon is analogous to how surfers accelerate by moving simultaneously with waves. Plasma heating via waves is an essential element in achieving highly efficient fusion energy. It has been observed that waves travel primarily in the toroidal direction and interact with the plasma. Phase-space tomography has newly discovered cases where rightward and leftward waves occur simultaneously. Those waves accelerate more particles, which is thought to lead to more efficient plasma heating (Figure 2).

This research has demonstrated that simultaneous operation of different diagnostic systems and integrating data can provide measurement performance that exceeds that from each instrument. It is expected that this measurement technique will be utilized in future research on fusion energy experiments to find a way to control plasmas according to information from the plasma phase-space distribution. Collisionless plasmas are commonly found not only in magnetic confinement plasmas but also in astronomical objects, the sun, and auroras. Therefore, detailed measurements of plasma phase-space distribution are desired for these different systems as well. Phase-space tomography is expected to play a role in different fields in the future.

Glossary

*1 Tomography

An analysis method that infers the internal structure of objects that are difficult to observe directly, such as the human body, historical cultural properties, and products before shipment, by combining observations from multiple directions. For example, in medical tomography, projection imaging using X-rays or proton beams is performed from multiple directions, and the internal structure is estimated from the results. In plasma diagnostics, signal integration is performed in time, space, and velocity directions to increase the signal level. The resolution lost in this process is recovered by tomographic techniques. This method is called phase-space tomography.

*2 Large Helical Device (LHD)

LHD is an experimental device of the National Institute for Fusion Science. LHD is one of the world's largest plasma confinement devices using superconducting coils. LHD started experiments in 1998. Recently, experiments have been conducted in collaboration with researchers from other fields, such as, astrophysics and life sciences. 

*3 Velocity distribution function

In gases and plasmas composed of a large number of particles, it is important to know the statistical properties of the constituent particles, rather than focusing on the dynamics of each particle individually. A histogram of particle velocity, the velocity distribution function, is often used to describe the statistical properties of a gas or plasma. Figure 3 shows an example. The velocity distribution function is described by taking the particle velocity on the horizontal axis and showing the number of particles in that velocity range on the vertical axis. The width of the histogram narrows when particle motion is moderate and widens when it is intense. It is known that when particle collisions are frequent, the shape of the velocity distribution function becomes the normal distribution (Maxwell distribution in physics terminology). In this case, density, temperature, and flow velocity correspond to the area, width, and peak position of the distribution, respectively. In high-temperature plasmas with rare collisions, the velocity distribution function may deviate from the normal distribution and become distorted. In such a situation, the physical properties of the plasma, namely, thermal and electrical conductivity, are considered to drastically change. The plasma distribution resolved in space and velocity coordinates is called plasma phase-space distribution. Experimental observations are underway to understand the physical properties of plasma with a distorted plasma phase space distribution.