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Plasma is a state of matter that emerges when a gas is heated to sufficiently high temperatures, prompting some electrons to become free from atoms. This state of matter has been the focus of many astrophysical studies, as predictions suggest that it would be found in the proximity of various cosmological objects, including pulsars and black holes.

Previous research findings suggest that the environment around these celestial objects is turbulent, which essentially means that magnetic fields and electric fields within it fluctuate chaotically across many scales. These chaotic fluctuations would in turn influence the movements and acceleration of particles.

Researchers have been trying to reproduce the turbulent environment associated with the emergence of plasma in space using numerical simulations. However, they were so far unable to realize a steady state in which a system's properties no longer change over time, such as that one might observe in real cosmic systems.

Researchers at KU Leuven and the Royal Belgian Institute for Space Astronomy report the first ever observation of a true steady state in simulated turbulent plasma. This remarkable observation, outlined in a paper in Â鶹ÒùÔºical Review Letters, was the result of 3D particle-in-cell simulations, computational simulations that can realistically reproduce both particles and electromagnetic fields.

"It is believed, with strong supporting evidence, that most plasma in space is turbulent," Evgeny Gorbunov, first author of the paper, told Â鶹ÒùÔº.

"Such turbulence heats the plasma and accelerates individual particles to very high energies: in other words, it acts as a universal cosmic particle accelerator. Understanding this process is crucial for explaining numerous astrophysical observations, such as radiation from accretion disks, cosmic-ray spectra, and others."

So far, the study of turbulence has primarily relied on numerical simulations, computer-based methods that rely on mathematical models to replicate physical processes or systems. When running these simulations, however, turbulence generally needs to be "stirred" via a constant injection of energy.

"In a closed simulation box, where energy dissipation cannot be modeled self-consistently, this approach has major shortcomings," said Gorbunov.

"A true steady state, in which dissipation balances energy injection, has never been observed. The injected energy typically ends up constantly accelerating particles, thus heating the plasma endlessly. In this work, we achieve for the first time a true steady state in turbulent simulations by allowing such energetic particles to escape the simulation domain."

As part of their study, Gorbunov and his colleagues ran 3D particle-in-cell simulations that meant to reproduce particle acceleration in turbulence. This simulation method allows particles to move freely inside the simulation "box," interacting via electromagnetic fields that are computed at fixed points on a regular grid.

"Turbulence simulations typically employ periodic boundaries; for example, if something crosses the top of the box, it reappears at the bottom," explained Gorbunov.

"We introduced an additional element to this standard setup. If a particle travels beyond a predefined distance, we consider it to have escaped the cosmic accelerator. It is then instantly replaced with a 'fresh' particle, its energy reset and sampled from a thermal population."

Essentially, the researchers coupled the turbulence in their simulation to a thermal particle reservoir. Particles enter the simulated accelerator, gain energy while they are inside it and eventually escape. This process mirrors what theories predict would occur in astrophysical environments.

"We observed that, regardless of the initial electromagnetic energy per particle, the system consistently evolves into a state where magnetic and kinetic pressures equilibrate," said Gorbunov.

"As a result, particle acceleration becomes limited, an effect which was not observed before. We also measured how the escape time of particles depends on their energy and found that it universally follows a very weak inverse power law, with important implications for explaining cosmic-ray observations."

This recent study and the team's observation of steady-state particle acceleration in turbulent plasma could open exciting possibilities for the modeling of various cosmological objects and physical phenomena. In the future, for instance, the simulation techniques they employed could be applied to the study of high-energy cosmic rays generated in turbulent astrophysical environments, potentially leading to new valuable insight.

"Turbulence in the universe occurs in many regimes," added Gorbunov. "For example, if particles radiate (as they typically do in astrophysical environments), how does this affect the steady state and particle spectra? What happens if the plasma contains multiple species, such as protons, electrons, and positrons, as in black-hole coronae?

"With the ability to reach a true steady state in simulations, many such questions can now be addressed. This method has the potential to transform how turbulence is studied."

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