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Taking the Temperature of the Solar Wind with Simulations

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photograph of earth's aurora taken from the international space station
The sparse plasma of the solar wind fills the solar system, constantly buffets the planets, and provides the particles that generate auroras on Earth and other planets. [NASA]

Researchers have applied a powerful simulation tool to a fundamental question about the solar wind: how do sparse plasmas exchange energy?

A Tenuous Topic

Earth and the solar wind

This artist’s impression of the solar wind shows a constant torrent of particles filling the heliosphere and streaming past Earth. [NASA Goddard’s Conceptual Image Lab/Greg Shirah]

In a dense plasma, particles exchange energy through collisions and eventually reach thermal equilibrium. Space plasmas, however, aren’t dense enough to trade much energy in this way — at Earth’s location, the solar wind is less dense than the best vacuum we can create on Earth.

Particles bounce around equally in all directions in a substance in thermal equilibrium, but in a tenuous, magnetized plasma like the solar wind, the particles can move at very different speeds parallel and perpendicular to the magnetic field. Since temperature is a measure of the average kinetic energy of a collection of particles, this means the temperature of a plasma can be different in the direction parallel to the magnetic field lines than it is perpendicular to them!

Early plasma theory predicted that the solar wind plasma would be tens of times hotter parallel to the magnetic field than perpendicular to it. In reality, at Earth’s location, the temperature parallel to the magnetic field is, on average, just 20% hotter than the temperature perpendicular to the field lines. With few to no collisions to help the plasma come to thermal equilibrium, how is this possible?

An Unstable Solution

photograph of clouds exhibiting the kelvin-helmholtz instability

The Kelvin–Helmholtz instability, which plays an important role in the atmospheres of stars and planets alike, is revealed by rare, wave-like patterns in clouds. [UCAR]

In a new publication, a team led by Rodrigo López (University of Santiago, Chile) used simulations to explore the impact of a plasma instability on the temperature of solar wind plasma. Plasma instabilities kick in when certain physical conditions are present, and they can have a big impact on a plasma’s large-scale characteristics, like temperature and density. While instabilities might seem abstract, they actually play a role in many common situations; weather systems, volcanic clouds, and lava lamps are all examples of instabilities at work. In each of these cases, what we observe is the result of the system spiraling away from equilibrium when it is disturbed.

Similar to these examples, instabilities can arise in a plasma in which the temperature parallel to the magnetic field is much higher than the temperature perpendicular to the magnetic field. In today’s article, López and collaborators investigated what happens to this setup when the fire hose instability comes into play. Previous work has explored the impact of the fire hose instability in plasmas where the electrons or the protons have a much higher temperature parallel than perpendicular, but relatively little work has explored what happens when both types of particles have this feature.

Approaching Equilibrium

plot of simulation results

The change in the perpendicular to parallel temperature ratio over time for the simulated electrons (top) and protons (bottom). In Case 1, the electrons start out with a temperature ratio of 1. In Cases 2 and 3, the electron temperature ratios are 0.4 and 0.3, respectively. [Adapted from López et al. 2022]

Using plasma physics equations and two-dimensional particle-in-cell simulations, López and coauthors found that when solar wind protons and electrons have much higher temperatures in the parallel direction, the fire hose instability takes hold of the protons much faster than it would if only the protons had this feature, while the electrons behave similarly regardless of what the protons are up to. In addition, the protons’ parallel and perpendicular temperatures draw closer when the electrons undergo the fire hose instability as well, suggesting that the electrons’ behavior is an important factor in explaining the observed temperatures in the solar wind.

Overall, the authors’ findings confirm that the fire hose instability plays an important role in moderating the temperature of the solar wind plasma, and future work should consider the influence that electrons have on the behavior of protons in the solar wind and other sparse plasmas.

Citation

“Mixing the Solar Wind Proton and Electron Scales. Theory and 2D-PIC Simulations of Firehose Instability,” R. A. López et al 2022 ApJ 930 158. doi:10.3847/1538-4357/ac66e4