The Heating Rate in the Magnetic Environment around the Earth Estimated for the First Time

Researchers at the Laboratory of Plasma Physics (UPSud/CNRS/École Polytechnique/Sorbonne University/Paris Observatory) and the Swedish Institute of Space Physics (IRF) have for the first time estimated the energy dissipation rate of turbulence in the magnetosheath, a key region lying between the solar wind and the magnetic bubble protecting the Earth. With the aid of theoretical tools developed by the LPP and data collected by the Cluster and Themis space probes, the values found are at least 100 times greater than those obtained in the solar wind. The results of this study constitute a major advance in this field, and could be applicable to other distant astrophysical regions.


Turbulence the Terrestrial Magnetosheath

The solar wind is a supersonic plasma (stream of charged particles, mainly protons and electrons) which is emitted continuously by the Sun. It propagates through interplanetary space and interacts with the planets of the solar system. In the case of planets which have an intrinsic magnetic field, a magnetosphere is formed around the planet and acts as a barrier against the flow of solar wind. The solar wind/magnetosphere interaction then generates a shock, followed by a highly turbulent region referred to as the magnetosheath, in which the solar wind slows, becoming denser and hotter (Figure 1). The plasma turbulence in the magnetosheath is considered to be a key factor in understanding the heat transfer and the penetration of solar wind particles into the magnetosphere, processes which are responsible for numerous dynamic phenomena such as the polar aurorae.

Left (©SOHO/LASCO/EIT NASA, ESA): Image showing the interaction of the solar wind with the magnetosphere; Right (©James Burch): Various key regions resulting from this interaction, including the magnetosheath (the subject of this study). Key: Sun, Solar Wind, Magnetosphere, Shock, Magnetopause, Magnetosheath


Heating and Astrophysical Regions

Despite several decades of research into plasma turbulence in the magnetosheath, many of its fundamental properties remain poorly understood. One of these unknowns is the average rate at which energy is dissipated, i.e. converted into heat, in the region. In a turbulent fluid (air, water in a river), large vortices of similar size collide, fragment and create smaller vortices, until reaching even smaller scales at which the kinetic energy of the vortices is converted into heat (dissipation). The rate at which this dissipation takes places the same as the rate at which the energy of the large vortices is transferred to the smaller vortices (Figure 2). In the magnetosheath, this cascade may cover scales ranging from 100,000 km to 1 km. The energy involved is that of the electric and magnetic fields, and its dissipation leads to heating, i.e. acceleration, of the particles of the plasma. These processes occur in many astrophysical plasmas (heating of the solar corona, acceleration of cosmic rays, etc.). 

View (simplified) of the process of energy turbulence cascade from large scales (injection) to small scales (dissipation) with a constant flux E. Key: Energy injection, Energy cascade, Energy dissipation

Major Advance

The LPP and IRF researchers have made significant progress in the understanding of turbulence in the terrestrial magnetosheath, by obtaining the first estimate of the energy dissipation rate. Because of the complex nature of this turbulence and the extent of the density fluctuations, it had not previously been possible to obtain this estimate by using the incompressible turbulence model widely used for the solar wind. More complete new theoretical models have recently been developed at the LPP in order to resolve this problem. Applying these to a wide sample of data acquired using the space probes Cluster (ESA) and Themis (NASA) from the terrestrial magnetosheath has made it possible to obtain this energy dissipation rate. The values found are at least 100 times higher than those previously estimated in the solar wind.

This work has also made it possible to obtain an initial empirical law which shows that the flunctuations of density and magnetic field amplify the heating rate. If this law is universal, it could be applicable to more distant astrophysical regions, such as the magnetospheres of other planets or interstellar space, for which in-situ measurements are rare or non-existent (Fig. 3). The processes by which the energy of the turbulence is dissipated remain an open question, which future studies will attempt to answer.

Artist’s impression of the edge of the solar system and its interaction with the interstellar wind. The system is very similar to that of Figure 1 (particularly with the formation of the heliosheath, which is a highly turbulent region). © NASA. Key: Interstellar wind, Shock, Heliosphere, Heliosheath, Heliopause, Solar system, Terminal shock)

These results were published in the journal Physical Research Letters, 29 January 2018.

Lina Z. Hadid, Swedish Institute of Space Physics (IRF) Uppsala, Sweden (lina @
Fouad Sahraoui, LPP/CNRS, (fouad.sahraoui @