2023 THEMIS SCIENCE NUGGETS
THEMIS Takes the lead in Observing Rayleigh-Taylor Instability at the Magnetopause
Guang Qing Yan
Geovis Environment Technology Company, Limited
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| Artist rendition of the Rayleigh-Taylor Instability at Earth's Magnetopause, when the solar wind dynamic pressure suddenly drops. Credit: G.Q. Yan |
Introduction
Rayleigh-Taylor instability can be excited at an interface between two fluids of different densities causing turbulent mixing of the two fluids. To generate such an unstable process, the lighter fluid needs to support the heavier one against the gravity or push the heavier one into an accelerated motion. The instability is named after the two contributors, Lord Rayleigh and Sir Geoffrey Ingram Taylor. This phenomenon is common in our everyday life: the spreading of a drop of ink in a cup of water, and turbulent diffusion of cold milk into a cup of hot coffee. Other examples include the interface of water suspended upon oil in a gravity field or the instability created by the motion of Earth's mantle, or the expansion of a nebula in cosmic space.
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| Figure 1. Illustration of the spacecraft crossing of the magnetopause and the Rayleigh-Taylor instability at the magnetopause. |
At the magnetopause, the outer edge of the Earth's intrinsic magnetic field that separates the shocked solar wind and the magnetosphere, the Rayleigh-Taylor instability occurs because the magnetopause is always in motion. The Rayleigh-Taylor unstable conditions lie in two aspects, the different densities at the two sides of the interface and gravity. The first one is naturally satisfied because the solar wind is much denser than the matter inside the magnetosphere. The matter near the magnetopause is much more dilute than the air we breathe on the ground and the atoms are fully ionized into a conducting plasma of negative and positive charges. The local gravity is about only one millionth of the electromagnetic force there. In such a situation, the acceleration of the interface is another necessary condition that plays the role of effective gravity. Early theoretical analysis has indicated that the Rayleigh-Taylor instability should be observable at the magnetopause when the dynamic pressure of the solar wind suddenly drops, with an outward accelerated motion of the interface. However, such a process at the magnetopause was not verified by satellites during the 66-year space era until THEMIS observations.
Results
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| Figure 2. The abrupt drop in the solar wind dynamic pressure and the expansion of the magnetosphere. |
NASA's Advanced Composition Explorer (ACE) spacecraft at the L1 point (about 1.5 million kilometers upstream of Earth) observed a sudden drop in solar wind dynamic pressure. With the time lag from L1 to the Earth's magnetopause accounted for by NOAA's GOES 13, 14, 15 spacecraft at geosynchronous orbit, decrease of the geomagnetic field was observed, indicating the outward expansion of the Earth's magnetosphere due to the decrease of solar wind dynamic pressure. The outward expansion results in an outward acceleration of the magnetopause, i.e., lighter magnetospheric plasma pushes the denser solar wind into outward accelerated motion.
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| Figure 3. The periodical disturbances at the magnetopause. |
At the same time, one probe, THEMIS-D, was crossing the magnetopause and encountered the interface 7 times periodically within ten minutes. The magnetic field and plasma at the magnetopause are periodically disturbed by the ripple-like structure at the boundary. The magnetic field is periodically compressed along the dominant direction and meanders along the deformed wavy magnetopause, with hot plasma from the magnetosphere and cold plasma from solar wind mixing together. To investigate the true physics happening here, some special processing needs to be done in the observed data, including removing the convective electric field and mean electric field, and then converting the vectors into a kind of local magnetopause coordinate system called LMN.
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| Figure 4. The unique signals of the Rayleigh-Taylor instability's attendant electrostatic field and the periodical compressions and meandering in the magnetic field. |
The truths are uncovered in the appropriate coordinate system, LMN. On one hand, the periodical compressions in the dominant direction of the magnetic field and the meandering in the perpendicular directions now more clear features. On the other hand, by riding the plasma frame and observing the electric field along with the motion of the plasma, the sinusoidal features appear in the electric field perturbations in the perpendicular directions, even with a phase difference of 90 degrees between them. This is an astonishingly consistent with the theoretical formations of the Rayleigh-Taylor instability's attendant electrostatic field, predicted in 1957 at the beginning of space era. It is not by chance that the electric field perturbations are so small along the magnetic field while so large and regular in the perpendicular directions. The electrostatic field is generated by separated charges in the plasma due to the accelerated motion of the magnetopause. The outward pushing force of the magnetosphere causes a kind of drift of the positive and negative charges in opposite directions and in speeds proportional to the charge's mass. Hence, the charges are separated to generate the electrostatic field. The electrostatic field drives the surrounding negative charges to drift in the same direction and same speed. Such electric drift, characterized by motions of both negative and positive charges perpendicular to the magnetic field, is evidenced in the observation of pitch-angle distributions and the phase space distribution of the plasmas. The electric drift is how the solar wind plasmas move across the shielding magnetopause into the magnetosphere.
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| Figure 5. The Ion Pitch-Angle distribution measured by THEMIS-D, indicating the transverse motion of the cold plasma across the magnetic field. |
It is an interesting collective behavior in plasmas that only a small portion of the charges are separated from their counterpart charges, and that the electrostatic field of the separated charges could only drive the surrounding charges rather than drive themselves to drift across the magnetic field. Based on observations, it is estimated that approximately one of 30 ions “divorces” its nearby electron in the Rayleigh-Taylor process.
Conclusion
The Rayleigh-Taylor instability at the magnetopause was predicted and theoretically analyzed for many years, but had not been observed in spacecraft observations. By using a set of unique analysis techniques, the first observational evidence of the Rayleigh-Taylor instability is captured by a single spacecraft of the THEMIS mission. The observations are shown to agree with predictions from earlier theoretical work, with some new and important elements such as the unique attendant electrostatic field in the form of sinusoidal signals, and the quantitative estimate of charge separation.
References
Yan, G. Q., Parks, G. K., Mozer, F. S., Goldstein, M. L., Chen, T., and Liu, Y. (2023). Rayleigh-Taylor instability observed at the dayside magnetopause under northward interplanetary magnetic field. Journal of Geophysical Research: Space Physics, 128, e2023JA031461Biographical Note
Professor Guang Qing Yan is the Chief Scientist Officer of Geovis Environment Technology Company, Limited. His research focuses on the mechanisms of solar wind transport into the magnetosphere, and the interaction of the solar wind with the magnetosphere.
Professor George K. Parks is the author of the text book "Physics of Space Plasmas: An Introduction" and a Research Scientist in Space Physics at the Space Science Laboratory, University of California, Berkeley. His research widely covers magnetosphere physics and beyond.
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