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Magnetospheric physics

Turbulence on a small scale

The four-spacecraft Cluster mission has identified small-scale vortices in Earth's magnetosphere. The observation reveals processes that transfer energy and momentum from the solar wind to the magnetosphere.

Turbulence is ubiquitous. It can be seen by gently stirring cream into coffee, or by observing the white caps and surf at the beach, and it causes the drag on cars and aeroplanes. The phenomenon is also widespread in magnetized plasmas — ionized gases that contain a magnetic field — such as the interstellar and intergalactic media, the solar wind and Earth's magnetosphere.

Although magnetic fields complicate the description of turbulence, certain characteristics, among them vortices, can arise in fluid and magnetofluid turbulence. On page 825 of this issue, Sundkvist et al.1 report the detection of small vortices in the ‘dayside cusp’ of Earth's magnetosphere by the four-spacecraft Cluster, a joint European Space Agency and NASA mission. The authors describe their observations as evidence for a phenomenon known as drift–kinetic Alfvénic turbulence.

The solar wind is the extension of the corona, the hot outer atmosphere of the Sun, into interplanetary space. Near Earth, the speed of the solar wind is typically around 400 kilometres per second, with variations of a couple of hundred kilometres per second that depend on solar activity. That speed exceeds by about a factor of ten the speed of sound and the speed of the most common magnetic waves, known as Alfvén waves. (Alfvén waves are highly correlated fluctuations in both the fluid-velocity and magnetic fields.)

As the supersonic, super-Alfvénic solar wind encounters Earth's magnetic field, a bow shockwave is produced at about 10–15 Earth radii in front of Earth (Fig. 1). Behind the bow shock, the hot solar-wind plasma can flow down towards the ionosphere through the dayside cusp. This cusp forms the boundary between magnetic field lines that are closed on the dayside (the side of Earth exposed to the Sun) and magnetic field lines that are open and have been swept back into the lobes of the nightside magnetosphere.

Figure 1: Transverse cut of Earth's magnetosphere.
figure1

A two-dimensional cut through the magnetosphere, with the Sun to the left. Solar-wind plasma is heated as it passes through the bow shock caused by its encounter with Earth's magnetic field. Some of the plasma is funnelled down the dayside cusps into the Northern and Southern Hemispheres. The Cluster orbits are shown as they appear in February/March of each year, the time period of the observations reported by Sundkvist et al.1. When the four spacecraft are on the dayside, they pass through the cusp regions; when near apogee on the nightside, they cross the magnetotail and neutral sheet. (The diagram is not to scale; in reality, the apogee of Cluster's orbits occurs at some 19 Earth radii.)

The flow of plasma down the funnel-like cusp has been conjectured either to excite turbulence locally or to amplify the turbulence carried by the shocked solar-wind plasma. Savin et al.2 noted that the flow down the cusp should generate vortices. Nykyri et al.3 found, using Cluster magnetometer data from March 2001, evidence that the cusp contained magnetic turbulence.

Cluster's four spacecraft orbit such that, at the point where they are farthest from Earth — at apogee — their positions form a regular tetrahedron (Fig. 1). This formation is ideal for distinguishing between unchanging spatial features and features that evolve with time. In the spring of 2002, at the time of Sundkvist and colleagues' measurements1, the separation of the spacecraft at apogee was about 100 kilometres (compared with around 500 kilometres for earlier Cluster measurements3), allowing the resolution of smaller spatial features. When the spacecraft entered the cusp, they were still relatively close together, but no longer traced out the points of a regular tetrahedron (see Fig. 3e on page 827).

Turbulence is often described as a process in which large-scale eddies cascade down to smaller-scale eddies until a scale is reached at which dissipation sets in. In magnetized plasmas, because of the large variety of possible small-scale wave modes, it is not clear how that cascade progresses to the dissipation range. Understanding these processes would enable us to determine how energy flows in a turbulent magnetofluid from large scales to the smaller, kinetic scale — and thus heats Earth's ambient plasma. Furthermore, where vortices form, materials in initially separate regions of space become mixed, which transfers energy, momentum and material from one region of the magnetosphere to another.

In the solar wind itself, measurements from single spacecraft4,5 indicate that as the scales of the turbulent fluctuations approach the dissipation scale, the kinetic Alfvén wave becomes the predominant wave mode. The distinguishing characteristic of such waves is that they have a small electric field that is parallel to the direction of the local magnetic field. Sundkvist and colleagues1 have now analysed the temporal evolution of the magnetic field in the dayside cusp region. There they show that kinetic Alfvén waves interact nonlinearly with so-called drift waves caused by gradients in plasma density and magnetic fields, and provide evidence that this interaction produces distinctive small-scale turbulent features known as drift–kinetic Alfvén vortices. Measurements of the velocity shears across the plasma flow direction made by Cluster's thermal plasma instrument indicate amplitudes that exceed those required for vortex production. The authors' interpretation is further bolstered by a vortex model constructed by the authors that accurately reproduces the observed behaviour of the magnetic field.

The Cluster observations are the first measurements in space to indicate that small-scale vortices are formed as eddies reach the dissipation scale. At the time of the observations, Cluster 1 and 2 were aligned with the plasma flow. Data from those two spacecraft indicated that the observed structures were quasi-stationary. The other two spacecraft were not aligned with the flow and could be used to deduce that the transverse radial scales of the structures were a few proton gyroradii (the radius of the circle described by a proton moving across a background magnetic field — in this region of the cusp, about 25 kilometres).

The small spatial scales involved make measurements of a turbulent cascade's dissipation — and of the transfer of the energy contained in magnetic fields and particle motion into the heating of the ambient plasma — difficult in both terrestrial laboratories and in space. Cluster observations indicate the existence of a turbulent vortical boundary layer that enhances the transfer of momentum and energy from the solar wind to the magnetosphere. The four-spacecraft Cluster, with its ability to distinguish between spatial and temporal effects, has opened a new window on the study of turbulence, both in the magnetosphere and in the solar wind. In the near future, missions such as Magnetospheric Multiscale (MMS), with its even smaller spacecraft separation and higher time-resolution for plasma measurements, will further enhance our understanding of the generation and dissipation of magnetofluid turbulence.

References

  1. 1

    Sundkvist, D. et al. Nature 436, 825–828 (2005).

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    Nykyri, K. et al. Ann. Geophys. 22, 2413–2429 (2004).

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    Bale, S. et al. Phys. Rev. Lett. 94, 215002 (2005).

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Goldstein, M. Turbulence on a small scale. Nature 436, 782–783 (2005). https://doi.org/10.1038/436782a

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