The origin of high-energy particles in the Universe, whether atomic nuclei, electrons, photons or neutrinos, represents a key enigma in multi-messenger astrophysics. Recent work carried out by a team from the IAP and the CEA provides insight into the mechanism by which turbulent astrophysical plasmas act as particle accelerators. This work notably proposes a theoretical model that implements in a modern framework the pioneering idea of the famous physicist Enrico Fermi.

Modern instrumental techniques for astronomy now allow us to probe the Universe beyond the visible band to which our eyes are sensitive, meaning X-rays and gamma rays, or even high-energy gamma rays. Light in that frequency range is made up of photons[1] with energies of the order of 1 tera, or one thousand billion electron volts (noted TeV) to 1 peta, or 1 million billion electron volts (noted PeV), that is to say approximately 1012 to 1015 times higher than the energy carried by red light. High energy radiation also differs from visible radiation in its origin, as it results from various radiative processes, called Bremsstrahlung[2], synchrotron[3], Compton[4] or hadronic[5] which charged particles - be they electrons[6] or atomic nuclei, or even positrons[7] – undergo after having been accelerated to high energies in tenuous (i.e. not very dense) astrophysical plasmass[8], by a mechanism that remains to be elucidated.

Figure 1: The Centaurus-A radio galaxy in two frequency bands Figure 1 : The Centaurus-A radio galaxy seen in two different frequency bands. In the visible range on the left: one can see the diffuse halo of stars of the elliptical type galaxy (white color), and the thick band of dust which crosses it in its center and obscures the light emitted by the stars; in X-rays on the right: the ejections of matter composed of very energetic particles are visible in blue in the form of diffuse lobes, and of linear jets.
Credits: ESO/WFI/M. Rejkuba et al., NASA/CXC/CfA/R. Kraft et al.

Common stars, nebulae or galaxies are absent from the high-energy sky, because the objects which are visible there must harbor physical processes that are sufficiently dynamic and violent to accelerate particles to the observed energies: black holes[9], microquasars[10], gamma-ray bursts[11], radio galaxies[12], etc. This is illustrated by the image of the radio galaxy Centaurus A (Figure 1) which compares the appearance of this object in two frequency bands: in X-rays (right) and in the visible domain (left). The X-ray image reveals the presence of jets of matter that move away from the central nucleus of the galaxy in opposite directions. These ejections are composed of high energy particles, a testimony of acceleration processes at work. Another example is GRB221009, a very recent gamma-ray burst[11] (detected on October 9, 2022), which has produced photons in the gamma-ray range with energies close to 20 TeV.

Understanding the mechanism by which these sources become particle accelerators is a key question in the field of so-called multi-messenger astrophysics, which aims to probe the cosmos by detecting photons of any energy, or neutrinos[13], or cosmic rays (atomic nuclei moving at velocities approaching the speed of light, and therefore of high energy), or gravitational waves [14].

Enrico Fermi (1901 - 1954), a famous 20th century physicist and pioneer of nuclear and particle physics, was the first to seek an answer to this question. In a seminal paper in 1949, he studied the possibility of accelerating particles in tenuous astrophysical plasmas by repeated collisions with dynamic, i.e. moving, "magnetized clouds". These magnetized clouds are localized regions of space in which magnetic fields are present. When charged particles (atomic nuclei or electrons) propagate in an assembly of such dynamic magnetized structures, they gain (or lose) energy from the electromagnetic fields that those structures carry. More simply, one can depict this process by assimilating the particle to a tennis ball which undergoes, along its path, arbitrary racket strokes. If the stroke is a drop shot, the particle loses energy, otherwise it gains energy. In the end, the energy of each particle evolves in a random way, so that some particles end up accelerated to high energy, while others become decelerated.

This mechanism, brought to light by Fermi and called "stochastic" or "turbulent", represents the basis of theoretical models that seek to describe the origin of high energy particles in astrophysics. However, a formal description of this process under realistic astrophysical conditions has remained a challenge to this day. This is due in particular to the fact that the picture of "dynamic magnetized clouds" remains a simplified description of a complex phenomenon, magnetized turbulence[15] which represents a field of research in its own right. Moreover, in high-energy astrophysical sources, this turbulence takes an extreme form, because the characteristic speed of magnetic vortices approaches the speed of light.

Since 2019, a team consisting of Virginia Bresci (PhD student at IAP), Martin Lemoine (senior researcher at CNRS) and Laurent Gremillet (researcher at the Commissariat à l’énergie atomique et aux énergies renouvelables, CEA) has tackled this problem through high-performance numerical simulations[16] (Bresci et al. 2022), as well as through the development of theoretical models (Lemoine 2021, Lemoine 2022). Video 1 presents a visualization of such a simulation, in two spatial dimensions, conducted with the CALDER (Lefebvre et al. 2003) “particle-in-cell”[17] code. This simulation allows to reproduce in a computer the development of magnetized turbulence in extreme conditions, representative of those of astrophysical systems, and to study the acceleration of particles therein. The gray levels trace the magnetic field intensity, while the green symbols follow some of the billions of particles that make up this simulation. The size of the symbol, which increases with the energy of the particle, allows to visualize the acceleration at work: by interacting with the moving magnetic vortices, the particles gain energy according to the mechanism described above. Figure 2 shows a visualization of the velocity field (measured in units of the speed of light) in a similar simulation, this time conducted in three spatial dimensions (Bresci et al. 2022).

Figure 2 : Visualisation en trois dimensions de la vitesse du plasma dans une simulation de turbulence magnétisée. La carte de couleur indique la valeur de cette vitesse v en unité de c, vitesse de la lumière.

Video 1: Animation from a numerical simulation of magnetized turbulence in two dimensions, conducted with the particle-in-cell code CALDER. In black and white: the magnetic field intensity, increasing with the brightness. In green: the positions of a few tens of particles chosen at random in the turbulence, among the billion particles present in the simulation; the size of the symbol increases with the energy of the particle. The simulation evolves here on a time scale comparable to several times the time needed to observe the turn-around of a vortex of maximum size (this maximum size corresponds to about one third of a side of the simulation box).
Credit: V. Bresci, L. Gremillet, M. Lemoine

Figure 2 : Visualization in three dimensions of the plasma velocity in a magnetized turbulence simulation. The colored map indicates the value of this velocity v in unit of c, the speed of light. Credit: Bresci et al. 2022

In parallel, this team has generalized and formalized Fermi's original model in the context of magnetized turbulence, in conditions representative of those astrophysical sources (Lemoine 2021, Lemoine 2022). A study, carried out in collaboration with Camilia Demidem (former PhD student at IAP, currently post-doctoral fellow at the University of Colorado at Boulder) and a team from Columbia University has allowed to confront this model to the numerical experiments described above, and thereby, to confirm it (Bresci et al. 2022). This analysis indeed reveals that most of the energy gained by the particles results from their interaction with the moving magnetic structures, and not from the interaction with electromagnetic waves present in the turbulence, as proposed by other modern scenarios.

The more recent study (Lemoine 2022) proposes a formal approach that aims at describing, from first principles, how a collection of particles draws energy from magnetized turbulence. In detail, it provides an equation that allows to follow the time evolution of the energy distribution of the ensemble of particles. The key issue is to characterize in a rigorous way the statistical properties of the random electromagnetic fields that control the acceleration process. This study relates these statistics to the so-called "intermittent" nature of the turbulence, i.e., the fact that when one zooms in on small spatial scales, the quantities tend to take on large values in localized regions, which can furthermore vary rapidly with time. Such statistics can be captured by so-called “multi-fractal”[18] models, proposed by Uriel Frisch and Giorgio Parisi (Nobel Prize 2021). Making use of those tools, the study opens a new connection between the fundamental properties of magnetized turbulence and the efficiency of the Fermi acceleration process that takes effect therein.

In fine, these theoretical and numerical results shed light on how and under which conditions turbulent plasmas can act as particle accelerators. Eventually, the tools developed can be used to model particle acceleration in a variety of astrophysical environments, from the solar atmosphere to the more extreme plasmas of relativistic astrophysical sources, with the goal of progressing in our quest for the origin of high energy particles in the Universe.


[1] The photon is the quantum of energy associated with electromagnetic waves (ranging from radio waves to gamma rays through visible light), which behaves as an elementary particle. When two electrically charged particles interact, this interaction can be regarded as an exchange of photons.

[2] Bremsstrahlung radiation, or braking radiation, is produced when an electron undergoes acceleration due to its attraction by an atomic nucleus.

[3] Synchrotron radiation follows from the deflection of an electron by a magnetic field.

[4] Compton radiation results from the interaction between an electron and electromagnetic radiation.

[5] Hadronic interactions take place between atomic nuclei, or between a nucleus and radiation. This interaction leads to the production of many secondary particles, including photons.

[6] Among charged particles, the electron is that of the smallest mass, and it is one of the components of the atom, together with protons and neutrons, which compose the nucleus of the atom.

[7] The positron is an anti-electron, i.e. a particle with the same characteristics as the electron, but an electric charge of opposite sign.

[8] Plasma is one of the four states of matter (in addition to the solid state, the liquid state or the gaseous state). A plasma is composed of electrons and ions (atoms or molecules carrying an electric charge) which makes it sensitive to the action of electromagnetic fields. The flame of a candle, the lightning, the sun are plasmas.

[9] A black hole is an object so compact that no form of matter or radiation cannot escape from its gravity field. This object is therefore black because it cannot shine.

[10] A microquasar is a binary system composed of an ordinary star orbiting at a short distance from a black hole. The atmosphere of the star is torn apart by the black hole, which leads to the production of matter jets and the emission of high energy radiation.

[11] A gamma-ray burst appears to us as an intense and brief emission (for one to a few tens of seconds) of photons in the gamma-ray frequency band. These events result from the fusion of neutron stars or black holes, or from the end of the life of a very massive star.

[12] A radio galaxy is endowed with jets of matter that travel distances much larger than the size of the galactic nucleus. These jets were first detected in the radio domain, whence the denomination. These jets are produced in the environment of the central black hole of the galaxy, and they are also visible at higher frequencies (infrared, ultraviolet and X-ray).

[13] The neutrino is an electrically neutral elementary particle that interacts weakly with matter.

[14] Highlight on the IAP's website: “First joint detection of gravitational and electromagnetic emissions from a neutron stars merger”

[15] Turbulence refers to a state of fluid flow, in which the velocity at any point varies rapidly in intensity and direction, leading to a highly disordered appearance on many spatial and temporal scales. Magnetized turbulence characterizes such a turbulent flow for a plasma in a magnetic field.

[16] High performance numerical computing allows to perform simulations, or complex calculations, using a large number of computers in parallel. The simulations discussed here have used up to 27000 computing cores on the Irene machine of the Très Grand Centre de Calcul (TGCC, for “Very Large Computing Center”) of the CEA.

[17] The “particle-in-cell” numerical method is used to model the behavior of a plasma and electromagnetic fields. It describes the plasma as an assembly of a large number of charged particles subjected to the forces exerted by electromagnetic fields, including those generated by these particles.

[18] An object with fractal geometry exhibits a similar structure at all scales. A multi-fractal geometry has a multitude of intertwined fractal behaviors.


puce  Article in Physical Review D106, 023028: Virginia Bresci, Martin Lemoine, Laurent Gremillet, Luca Comisso, Lorenzo Sironi, Camilia Demidem, 2022, « Nonresonant particle acceleration in strong turbulence: Comparison to kinetic and MHD simulations » (Public version)

puce  Article in Physical Review D104, 063020: Martin Lemoine, 2021, « Particle acceleration in strong MHD turbulence » (Public version)

puce  Article in Physical Review Letters, 129, 215101: Martin Lemoine, 2022, « First-principles Fermi acceleration in magnetized turbulence » (Public version)

puce  Editors' highlighted articles for Volume 129, Issue 21, 18 November 2022 of Physical Review Letters

puce  News of INSU/CNRS, scientific result in the theme “Universe” (in French), November 30, 2022 : Les plasmas astrophysiques turbulents, accélérateurs de particules

puce  Article in Nuclear Fusion, 43, 629: E. Lefebvre et al., 2003, « Electron and photon production from relativistic laser–plasma interactions »

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