Kinetic Simulations of Astrophysical and Solar Plasma Turbulence
Max-Planck-Institute for Solar System Research, Göttingen
Local Project ID:
HPC Platform used:
SuperMUC and SuperMUC-NG
The hot and dilute collisionless plasmas near the Earth and in the solar-wind are very turbulent. Astrophysical plasmas, e.g., in accretion disks around stars, in supernovae, the interstellar medium (ISM) or in galaxy clusters are turbulent. Despite of the omnipresence of turbulence in the plasma Universe, its properties and consequences are not well understood, yet. The reason is the complicated kinetic nature of the collective collisionless plasma phenomena at the end of the turbulence cascade, where the energy is dissipated. A kinetic, particle description is required to describe the energy dissipation in turbulence, so that non-thermal effects and wave-particle interactions are taken into account.
Turbulence is inherently linked with two fundamental processes of energy conversion in the Universe which are the focus of this SuperMUC-NG project . These fundamental processes are shock waves and magnetic reconnection.
In shock waves plasma flow energy is converted into thermal energy (heating) and the acceleration of particles while the plasma flow is decelerated. In the upstream region of shock waves the plasma may become highly turbulent. Shock waves are observed in situ at space plasma boundaries, e.g. between the solar wind and magnetospheres or other heliospheric obstacles and, indirectly, between exploding supernovae and the interstellar medium (ISM). They are assumed to be behind gamma-ray bursts as well. The latter are known to occur in highly relativistic plasmas.
In the first of our SuperMUC-NG sub-project we investigated the efficiency of particle acceleration by shock waves in gamma-ray bursts and the role of self-generated turbulence in this highly energetic process. The obtained particle energy spectra are used as input for models of the non-thermal emission due to, e.g., synchrotron radiation from gamma-ray bursts.
The second fundamental process of energy conversion in the Universe, closely linked to turbulence, is magnetic reconnection. In the course of magnetic reconnection, magnetic energy is converted into plasma flows, thermal energy and the acceleration of highly energetic particles. The understanding of magnetic reconnection processes is crucial for the understanding of the heating of cosmic plasmas, e.g. of stellar coronae, the release of magnetic energy in solar and stellar flares, as well as of the dynamics and consequences of the energization of the ISM. Reconnection and turbulence are related to each other in several different ways: reconnection can proceed if turbulence allows non-ideal plasma responses, it can generate secondary turbulence itself by causing plasma instabilities, small scale current sheets are formed in turbulent plasmas trough which reconnection happens. The latter process is the focus of our second SuperMUC-NG sub-project.
A number of studies of these processes have been carried out using different plasma models. In particular we concentrated our studies on the not well understood role of the electrons in the energy dissipation, plasma heating and acceleration processes. Our studies compared the consequences of different ways to reduce the plasma models. The results of our investigations are important to better understand the energy dissipation and heating in astrophysical plasmas from the Earth’s magnetosheath to the solar wind and the interstellar medium.
Results and Methods
To tackle the outstanding astrophysical problems of collisionless shocks and reconnection in turbulence kinetically, the method of choice are fully-kinetic plasma simulations in which the full sets of Vlasov- and Maxwell equations are self-consistently solved together with the action of the electromagnetic fields on the charged plasma particles. For this sake we carried out Particle-in-Cell (PIC) simulations which describe the particle motion by a Lagrangian approach and solves for the electromagnetic fields by an Eulerian description allocated on a mesh. The particle distribution functions are the main variables to be obtained by solving Vlasov equations. Hence, the PIC-method relies on a sufficiently large number of many macro-particles, in order to statistically reliable reconstruct the particle distribution functions. Such PIC-code simulations are, therefore, computationally very demanding: they have to trace in the order of 109-1011 macro-particles on a mesh consisting about 108 grid points in 3D simulations. This implies that a single particle snapshot requires a memory in the order of one Terabyte, hence one has to make the particle output as sparse in time as possible. Grid data (e.g., electromagnetic fields) is comparably less heavy, but this data output should be carried out more frequently in order to correctly understand the evolution of the system. The resulting output field sizes are in the order of a significant fraction of a Terabyte for large production runs.
In our project we utilized the optimum MPI-parallelized codes OSIRIS (http://epp.tecnico.ulisboa.pt/osiris) and ACRONYM (http://plasma.nerd2nerd.org/). These codes were proven to run efficiently on the SuperMUC-NG machine. The largest simulations carried out were in the order of a few million core-hours, while parametric studies are done with runs in the order of a significant fraction of a million core-hours. A typical run requires between a few to tens of thousands of cores.
With the OSIRIS code we performed the first PIC simulations of relativistic, weakly magnetized electron-ion-positron shock waves and compared them with shocks in a pure electron-ion plasma. Our simulation results apply to gamma-ray bursts, where the released radiation is thought to produce electron-positron pairs in the external medium upstream of the shock, i.e. in the unperturbed plasma flow ahead of the shock wave. In those environments, a critical parameter that controls the energization process is the magnetization parameter Sigma, the ratio of the upstream magnetic energy to the ion rest mass energy. We studied the dependence of the shock properties on this parameter. The shock is numerically generated by pushing against one of the reflective boundaries of the 2D simulation domain a cold stream of plasma. This kind of numerical setup is prone to a numerical instability known as Cherenkov radiation, which is taken care of by means of a modified Maxwell solver implemented in the OSIRIS code (see further details about the initial conditions in ).
We illustrate a particular result in Figure 1, showing the downstream energy spectra in a unmagnetized shock composed of a mixture of electrons, ions, and positrons. We find that the shock can efficiently accelerate particles via scattering of the small-scale turbulence. More generally, we studied the dependence on the plasma composition (mixed electron-ion-positron versus pure electron-ion) and on Sigma, determining the conditions when electron-ion-positron shocks accelerate particles.
With the code ACRONYM we simulated a turbulent plasma by imposing initial velocity and magnetic field fluctuations at large-scales. The fluctuations evolve in time, transferring energy to smaller and smaller scales, until it is finally dissipated at the smallest (electron-) kinetic scales. During the first period of our SuperMUC-NG project we have already found by utilizing the OSIRIS code that the turbulent fluctuations match the theoretical predictions of the so-called kinetic Alfvén wave turbulence, characterized by a specific correlation of density and perpendicular magnetic field fluctuations . We then started to investigate the properties of current sheet structures that are formed in the turbulence. The current sheets release magnetic energy via magnetic reconnection. They seem to determine the energy dissipation in a kinetically turbulent collsionless plasmas (Figure 2).
On-going Research / Outlook
In the first sub-project (relativistic shock waves) we found the conditions under which electro-ion-positron shocks can efficiently accelerate particles.
In the second sub-project (reconnection in turbulence) the question of the influence of the electron fluid with / without mass on the energy dissipation via current sheet reconnection is still open. For the sake of a better understanding of the role of the electrons, comparative simulations for different plasma models are necessary using, other than fully kinetic PIC codes, hybrid-PIC simulations with and without electron inertia  which will allow to directly assess the influence of the electron dynamics.
References and Links
 Sironi, L., Spitkovsky, A., & Arons, J. 2013, ApJ, 771,
54, doi: 10.1088/0004-637X/771/1/54
 Grošelj, D., Mallet, A., Loureiro, N. F., & Jenko, F. (2018). Physical Review Letters, 120(10), 105101. doi: 10.1103 PhysRevLett. 120.105101
 Jain, N., Büchner, J., Comişel, H., & Motschmann, U. (2020). Free energy sources in current sheets in collisionless turbulence. http://arxiv.org/abs/2008.13206
Jörg Büchner1,2,Daniel Grošelj3, Frank Jenko4, Patricio Muñoz2
1Max-Planck-Institut für Sonnensystemforschung (MPS), Göttingen, Germany
3Columbia University, New York, USA
4Max-Planck-Institut für Plasmaphysik, Garching, Germany
Prof. Dr. Jörg Büchner
Max-Planck-Institute for Solar System Research
Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany)
LRZ project ID: pr74vi