Relativistic magnetic reconnection in collisionless ion-electron plasmas explored with particle-in-cell simulations

Magnetic reconnection is a leading mechanism for magnetic energy conversion and high-energy non-thermal particle production in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas (e.g., microquasars or AGNs) - a regime where first principle studies are scarce. We present 2D particle-in-cell (PIC) simulations of low $\beta$ ion-electron plasmas under relativistic conditions, i.e., with inflow magnetic energy exceeding the plasma rest-mass energy. We identify outstanding properties: (i) For relativistic inflow magnetizations (here $10 < \sigma_e < 360$), the reconnection outflows are dominated by thermal agitation instead of bulk kinetic energy. (ii) At large inflow electron magnetization ($\sigma_e > 80$), the reconnection electric field is sustained more by bulk inertia than by thermal inertia. It challenges the thermal-inertia-paradigm and its implications. (iii) The inflows feature sharp transitions at the entrance of the diffusion zones. These are not shocks but results from particle ballistic motions, all bouncing at the same location, provided that the thermal velocity in the inflow is far smaller than the inflow E cross B bulk velocity. (iv) Island centers are magnetically isolated from the rest of the flow, and can present a density depletion at their center. (v) The reconnection rates are slightly larger than in non-relativistic studies. They are best normalized by the inflow relativistic Alfv\'en speed projected in the outflow direction, which then leads to rates in a close range (0.14-0.25) thus allowing for an easy estimation of the reconnection electric field.Comment: Submitted to A&

The energetics of relativistic magnetic reconnection: ion-electron repartition and particle distribution hardness

Collisionless magnetic reconnection is a prime candidate to account for flare-like or steady emission, outflow launching, or plasma heating, in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas. But the fate of the initial magnetic energy in a reconnection event remains poorly known: what is the amount given to kinetic energy, the ion/electron repartition, and the hardness of the particle distributions? We explore these questions with 2D particle-in-cell simulations of ion-electron plasmas. We find that 45 to 75% of the total initial magnetic energy ends up in kinetic energy, this fraction increasing with the inflow magnetization. Depending on the guide field strength, ions get from 30 to 60% of the total kinetic energy. Particles can be separated into two populations that only weakly mix: (i) particles initially in the current sheet, heated by its initial tearing and subsequent contraction of the islands; and (ii) particles from the background plasma that primarily gain energy via the reconnection electric field when passing near the X-point. Particles (ii) tend to form a power-law with an index $p=-d\log n(\gamma)/d\log\gamma$, that depends mostly on the inflow Alfv\'en speed $V_A$ and magnetization $\sigma_s$ of species $s$, with for electrons $p=5$ to $1.2$ for increasing $\sigma_e$. The highest particle Lorentz factor, for ions or electrons, increases roughly linearly with time for all the relativistic simulations. This is faster, and the spectra can be harder, than for collisionless shock acceleration. We discuss applications to microquasar and AGN coronae, to extragalactic jets, and to radio lobes. We point out situations where effects such as Compton drag or pair creation are important.Comment: 15 pages, submitted to A&

Apar-T: code, validation, and physical interpretation of particle-in-cell results

We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests: spectra from simulations of thermal plasmas, linear growth rates of the relativistic tearing instability and of the filamentation instability, and non-linear filamentation merging phase. For the filamentation instability we show that the effective growth rates measured on the total energy can differ by more than 50% from the linear cold predictions and from the fastest modes of the simulation. Second, we detail a new method for initial loading of Maxwell-J\"uttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. Third, we scrutinize the question of what description of physical plasmas is obtained by PIC models. These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p~10^10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e., quantities depending on p. They derive from the PIC plasma parameter Lambda^{PIC}, which we show to scale as 1/p. We explore two implications. One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p~10^10 smaller than in real plasmas. The other is that the level of electric field fluctuations scales as 1/Lambda^{PIC} ~ p. We provide a corresponding exact expression. Fourth, we compare the Vlasov-Maxwell theory, which describes a phase-space fluid with infinite Lambda, to the PIC model and its relatively small Lambda.Comment: 24 pages, 14 figures, accepted in Astronomy & Astrophysic

Collisionless magnetic reconnection in relativistic plasmas with particle-in-cell simulations

L'objectif de cette thèse est l'étude de la reconnexion magnétique dans les plasmas non-collisionels et relativistes. De tels plasmas sont présents dans divers objets astrophysiques (MQs, AGNs, GRBs...), où la reconnexion pourrait expliquer la production de particules et de radiation de haute énergie, un chauffage, ou des jets. Une compréhension fondamentale de la reconnexion n'est cependant toujours pas acquise, en particulier dans les plasmas relativistes ion-électron. Nous présentons d'abord les bases de la reconnexion magnétique. Nous démontrons des résultats particuliers à la physique des plasmas relativistes, concernant par exemple la distribution de Maxwell-Jüttner. Ensuite, nous réalisons une étude détaillée de l'outil numérique utilisé : les simulations particle-in-cell (PIC). Le fait que le plasma réel contienne beaucoup plus de particules que le plasma PIC a des conséquences importantes (collisionalité, relaxation, bruit) que nous décrivons. Enfin, nous étudions la reconnexion magnétique dans les plasmas ion-électron et relativistes à l'aide de simulations PIC. Nous soulignons des points spécifiques : loi d'Ohm (l'inertie de bulk dominante), zone de diffusion, taux de reconnexion (et sa normalisation relativiste). Les ions et les électrons produisent des lois de puissance, avec un index qui dépend de la vitesse d'Alfvén et de la magnétisation, et qui peut être plus dur que dans le cas des chocs non-collisionels. De plus, les ions peuvent avoir plus ou moins d'énergie que les électrons selon la valeur du champ guide. Ces résultats fournissent une base solide à des modèles d'objets astrophysiques qui, jusque là, supposaient a priori ces résultats.The purpose of this thesis is to study magnetic reconnection in collisionless and relativistic plasmas. Such plasmas can be encountered in various astrophysical objects (microquasars, AGNs, GRBs...), where reconnection could explain high-energy particle and photon production, plasma heating, or transient large-scale outflows. However, a first principle understanding of reconnection is still lacking, especially in relativistic ion-electron plasmas. We first present the basis of reconnection physics. We derive results relevant to relativistic plasma physics, including properties of the Maxwell-Jüttner distribution. Then, we provide a detailed study of our numerical tool, particle-in-cell simulations (PIC). The fact that the real plasma contains far less particles than the PIC plasma has important consequences concerning relaxation times or noise, that we describe. Finally, we study relativistic reconnection in ion-electron plasmas with PIC simulations. We stress outstanding properties: Ohm's law (dominated by bulk inertia), structure of the diffusion zone, energy content of the outflows (thermally dominated), reconnection rate (and its relativistic normalization). Ions and electrons produce power law distributions, with indexes that depend on the inflow Alfvén speed and on the magnetization of the corresponding species. They can be harder than those produced by collisionless shocks. Also, ions can get more or less energy than the electrons, depending on the guide field strength. These results provide a solid ground for astrophysical models that, up to now, assumed with no prior justification the existence of such distributions or of such ion/electron energy repartition

Reconnexion magnétique non-collisionelle dans les plasmas relativistes et simulations particle-in-cell

The purpose of this thesis is to study magnetic reconnection in collisionless and relativistic plasmas. Such plasmas can be encountered in various astrophysical objects (microquasars, AGNs, GRBs...), where reconnection could explain high-energy particle and photon production, plasma heating, or transient large-scale outflows. However, a first principle understanding of reconnection is still lacking, especially in relativistic ion-electron plasmas. We first present the basis of reconnection physics. We derive results relevant to relativistic plasma physics, including properties of the Maxwell-Jüttner distribution. Then, we provide a detailed study of our numerical tool, particle-in-cell simulations (PIC). The fact that the real plasma contains far less particles than the PIC plasma has important consequences concerning relaxation times or noise, that we describe. Finally, we study relativistic reconnection in ion-electron plasmas with PIC simulations. We stress outstanding properties: Ohm's law (dominated by bulk inertia), structure of the diffusion zone, energy content of the outflows (thermally dominated), reconnection rate (and its relativistic normalization). Ions and electrons produce power law distributions, with indexes that depend on the inflow Alfvén speed and on the magnetization of the corresponding species. They can be harder than those produced by collisionless shocks. Also, ions can get more or less energy than the electrons, depending on the guide field strength. These results provide a solid ground for astrophysical models that, up to now, assumed with no prior justification the existence of such distributions or of such ion/electron energy repartition.L'objectif de cette thèse est l'étude de la reconnexion magnétique dans les plasmas non-collisionels et relativistes. De tels plasmas sont présents dans divers objets astrophysiques (MQs, AGNs, GRBs...), où la reconnexion pourrait expliquer la production de particules et de radiation de haute énergie, un chauffage, ou des jets. Une compréhension fondamentale de la reconnexion n'est cependant toujours pas acquise, en particulier dans les plasmas relativistes ion-électron. Nous présentons d'abord les bases de la reconnexion magnétique. Nous démontrons des résultats particuliers à la physique des plasmas relativistes, concernant par exemple la distribution de Maxwell-Jüttner. Ensuite, nous réalisons une étude détaillée de l'outil numérique utilisé : les simulations particle-in-cell (PIC). Le fait que le plasma réel contienne beaucoup plus de particules que le plasma PIC a des conséquences importantes (collisionalité, relaxation, bruit) que nous décrivons. Enfin, nous étudions la reconnexion magnétique dans les plasmas ion-électron et relativistes à l'aide de simulations PIC. Nous soulignons des points spécifiques : loi d'Ohm (l'inertie de bulk dominante), zone de diffusion, taux de reconnexion (et sa normalisation relativiste). Les ions et les électrons produisent des lois de puissance, avec un index qui dépend de la vitesse d'Alfvén et de la magnétisation, et qui peut être plus dur que dans le cas des chocs non-collisionels. De plus, les ions peuvent avoir plus ou moins d'énergie que les électrons selon la valeur du champ guide. Ces résultats fournissent une base solide à des modèles d'objets astrophysiques qui, jusque là, supposaient a priori ces résultats