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Accueil > Recherche > Plasmas Spatiaux > Thématiques scientifiques > Collisionless shock waves

Collisionless shock waves

In gas we know the shock waves that occur before an obstacle in the path of a supersonic wind. In plasmas also, there are shock waves.

 LPP team :

P. Canu, D. Fontaine, P. Savoini

 Some significant articles :

 What is a shock wave ?

A shock wave is essentially an energy converter. It converts the energy of an incident wave (directional kinetic energy) into thermal energy (heating).

In a fluid, it is a localized area of strong gradients through which the fluid changes from a supersonic state (Vfluide > Vinfo) to a subsonic one (Vfluide ≤ Vinfo) where Vinfo is the characteristic velocity at which information can propagate. In an ordinary fluid, such as air or water, this velocity is the sound velocity and the collisions between particles are at the origine, at the microscopic level, of this dissipation. in a collisionless fluid as space plasmas are, the problem is different because this coupling via collisions is absent and wave-particle interactions, which are much more complex, do the work.

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Figure 1. Illustration de l’écoulement d’un fluide rencontrant un obstacle fixe. A gauche, le fluide est subsonique et donc l’information de la présence de l’obstacle peut être transmise au fluide, celui-ci s’écarte en arrivant dessus. A droite, le fluide est supersonique et aucune information ne peut parvenir au fluide, celui-ci percute alors l’obstacle, créant une zone où la densité, la température et la vitesse augmentent, la frontière extérieure de cette zone est l’onde de choc.
Source P. Savoini

The importance of these shock waves is evident when one remembers that the universe as a whole is made up of moving plasmas. There is a plasma stream, thus energy, between the planets, stars and galaxies. Shock waves exist in the Sun’s atmosphere (the corona) during solar flares and other active solar events. Flares and coronal mass ejections inject into the solar wind fast particles creating interplanetary shock waves that propagate through the solar system. Further way from us, we can find mass jets from active galaxies that can also generate such structures by interaction with the interstellar medium. During a star explosion (supernova), a huge amount of energy is deposited in a very short time in the interstellar medium, so that shock waves are formed and propagate outward, etc

 Earth bow shock

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Figure 2. Artist view representing the different characteristic regions of the collisionless shock of the Earth. The colored areas in front of the shock wave are the electronic foreshock (in yellow) and ion foreshock (red). The field lines of the interplanetary magnetic field are drawn in blue.
Source Tsurutani and Rodriguez, 1981

The LPP team mainly studies the Earth’s shocK wave, or bow shock, created by the interation of the solar wind, hot and diluate plasma in expansion, with the Earth magnetosphere. This particular shock wave has the hudge advantage of being in our close vicinity, allowing thus a comprehensive in situ study of its structure.

The experimental evidence of such a structure has been given in the years 1960 thanks to IMP-1 spacecraft ; its study has been pursued since then, using more and more powerful satellites, as Cluster fleet.
A compilation of the experimental data and of the numerical simulations results made it possible to demonstrate the two main characteristic parameters of the Earth shock wave :

  • the propagation angle : \Theta_{Bn} . This is the angle between the local normal to the shock and the interplanetary magnetic field.
    Two broad areas of propagation can be defined : :

(i) the quasi-perpendicular domain :

45 \leq \Theta_{Bn} \leq 90

which is characterized by a very clear jump of both the magnetic field and the density, over a narrow distance (Dchoc 100 km)
(ii) the quasi paralle domain :

0 \leq \Theta_{Bn} \leq 45

much more turbulent. It is characterized by fluctuations of great amplitude of the magnetic field and the density. It extends over a much larger spatial length Dshock (ranging from 1000 km to several terrestrial radii), which sometimes makes ambiguous to determine the very "shock" position.

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Figure 3. Synoptique d’un choc non-collisionnel similaire au choc magnétosphérique terrestre. La direction du champ magnétique interplanétaire (non perturbé) est indiquée sur la plate-forme de base. L’amplitude de B (perturbé) est représentée perpendiculairement par rapport à cette plateforme. La flèche rouge donne la direction du vent solaire.
Source Greenstadt and Fredricks, 1979

The shock is thus defined in figure 3 by the signature of the modulus of the magnetic field (ordinates) obtained in the ecliptic plane. The shock is of course curved (two-dimensional in the figure and three-dimensional in reality).

  • the Mach number : This parameter is defined as the ratio between the plasma flow velocity upstream of the shock wave and the associated characteristic velocity. It is a direct measurement of the energy brought by the solar wind and that has to be dissipated by the shock wave. As one would expect, the higher the Mach number, the greater the energy available, and the more the shock wave has spectacular properties. In the solar system, the shocks that can be found there have Mach numbers between 1 and 20. More generally, these numbers may be larger under certain circumstances and even reach factors of the order of 1000 in remnants of supernovae. It is interesting to note that beyond a certain critical value MA * ( 3-4), the shock wave reflects a part of the ions which causes a non-stationary behavior as illustrated by FIG. 4, behavior predicted by numerical simulations before being observed experimentally.
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    Figure 4. Simulation auto-cohérente d’une onde de choc perpendiculaire montrant l’espace des phases des ions (leur vitesse Px le long de la normal au choc) au cours du temps. Le profil du champ magnétique associé est reporté en mauve. Source P. Savoini

 Ionic pre-shock studies performed at LPP :

As its name indicates, this region, in red in figure2, is upstream of the shock, but is magnetically connected to it. This pre-shock is essential in the morphology of planetary and interplanetary shock waves and is peculiar to non-collisional shocks. Indeed, this pre-shock may seem paradoxical since the shock wave should be considered as a "horizon", that is to say the limit beyond which no information can propagate (see Figure 1). This paradox can be solved by remembering that in a collisionless plasma (and only in this type of plasma !) particles can have any velocities (but of course less than the light velocity). This region of the pre-shock is thus populated by ions having been reflected by the shock wave, after being accelerated at very high velocities.
Such particles carry a lot of energy, interact with the environment and produce a multitude of waves (instabilities), making pre-shock a very rich bestiary composed of different types of particles and waves.
Recent simulations of quasi-perpendicular shock have yielded information on the different populations of upstream reflected ions, namely the Field-Aligned Beam (or FAB) and the Gyro-Phase bunched population (or GPB), which are characterized by distribution functions as illustrated in Figure 5. This study is in progress, but it has been shown that the shock wave itself could be at the origin of these two populations thanks to a common acceleration mechanism [Savoini and Lembège, 2015].

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Figure 5. Différent types de population d’ions réfléchis sont présentes dans le préchoc ionique : les FAB et les GPB. Observés à la fois expérimentalement par CLUSTER [Meziane et al., 2004, 2005] et dans les simulations numériques 2D PIC [Savoini et Lembège, 2013, 2015].
Source P. Savoini

 Studies on the interaction between a magnetic cloud and the Earth shock wave performed at LPP :

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Figure 6. Représentation schématique d’un nuage magnétique dans le plan de l’écliptique
Source Zurbuchen et Richardson (2006).

The idea that solar flares release plasma clouds which then propagate in the interplanetary medium was proposed by Sidney Chapman in 1929. These structures are called coronal mass ejections. Magnetic clouds are a special case, characterized by a well-defined magnetic structure. At the Earth level, about one-third of the observed coronal mass ejections are magnetic clouds that play a central role in Sun-Earth relations, notably because they are at the origin of the most intense geomagnetic storms.
The study of their interaction with the terrestrial environment is therefore of major interest because it raises more fundamental questions, such as the way in which the coupling between solar wind and magnetosphere occurs.
It has thus been shown that if the crossed over shock is in quasi-perpendicular regime, the magnetic structure of the magnetic cloud is little modified in the magnetosheath, while it varies greatly in the crossing of a quasi-parallel shock [Turc et al ., 2013, 2014, 2015]. Thus, downstream of a quasi-parallel shock, the direction of the magnetic field varies by more than 50◦ compared to that observed in the solar wind. In this shock regime, the simulation results give the fluctuations of density and magnetic field observed by Cluster. The simulations show, however, that the magnetic cloud modifies the large-scale structure of these regions of the planetary environment. In particular, the magnetic tension due to the drape of the field lines around the magnetopause tends to accelerate the particles in the sectors of the magnetosheath perpendicular to the magnetic field upstream of the shock. Due to the slow rotation of the magnetic field within the magnetic cloud, these regions move as it passes through. Moreover, the arrival of the magnetic cloud also has an important impact on the zone of the pre-shock which sees its dynamics totally modified by the arrival of the cloud, undergoing a strong attenuation due to the decrease of the Alfvén Mach number, and also an overall rotation due to the orientation of the magnetic field which rotates in the cloud.

These results show that it is essential to take the magnetosheath into account in order to reach a deeper understanding of the impact of these structures on the terrestrial environment. Indeed the orientation of their magnetic field can vary significantly downstream of the shock, the plasma can be accelerated at velocities which may be greater than that of the solar wind on the flanks of the magnetosphere, and turbulent regions may appear in the vicinity of the quasi-parallel shock, upstream as well as downstream.

CNRS Ecole Polytechnique Sorbonne Université Université Paris-Saclay Observatoire de Paris
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Hébergeur : Laboratoire de Physique des Plasmas, Ecole Polytechnique route de Saclay F-91128 PALAISEAU CEDEX
Directeur de la publication : Dominique Fontaine (Directrice)