Kinetische simulaties van magnetische reconnectie en scheurmodusinstabiliteit in botsingsvrij plasma

Magnetic reconnection is an omnipresent phenomenon in astrophysical and laboratory plasmas and is widely regarded as the fundamental mechanism underlying various astrophysical and laboratory events, including solar flares, coronal mass ejections (CMEs), geomagnetic storms and substorms, as well as sawtooth crashes in fusion devices [Biskamp, 2000, Goedbloed et al., 2019, Hesse and Cassak, 2020]. During magnetic reconnection, magnetic field lines break and reconnect, altering the magnetic topology and converting magnetic energy into plasma kinetic and thermal energy. In this thesis, we investigate magnetic reconnection and tearing mode instabilities in collisionless plasmas using fully kinetic Particle-in-Cell (PIC) simulations. The fully kinetic PIC approach, a firstprinciples-based method, enables the resolution of the finest temporal and spatial scales in plasmas, making it a powerful tool for simulating magnetic reconnection and its associated instabilities. In our work, we employ a semi-implicit PIC method [Lapenta, 2017, 2023], which enables us to conserve energy exactly. Additionally, the semi-implicit approach allows us not to resolve the Debye length and the electron plasma frequency, thereby reducing computational cost while maintaining numerical stability simultaneously [Colonna and D'Angola, 2016a]. The main findings and conclusions of this thesis are summarized below. We explore the potential of using the fully kinetic PIC method to study tearing mode instability in fusion tokamak plasmas. Tearing mode is a detrimental instability in tokamaks and it is closely connected with magnetic reconnection. This instability can compromise plasma confinement and may even result in disruptions that damage devices by releasing energetic particles to the surrounding walls [Bateman, 1978]. Conventional simulation approaches for studying fusion plasma tearing mode include magnetohydrodynamics (MHD), gyrokinetic method, and relevant hybrid methods. Although significant progress has been made in this domain, its underlying mechanism and methods for its control are still not fully understood [Hornsby et al., 2015a]. Compared to methods such as MHD and gyrokinetic approaches, the fully kinetic method can resolve finer spatial and temporal scales and has the potential to uncover new physics. In addition, recent advancements in PIC algorithms and supercomputing have brought new promise to the application of the fully kinetic PIC method to the instability study in fusion tokamak plasmas. We begin with mapping an analytical MHD equilibrium with a circular crosssection profile onto the grids for our fully kinetic simulations. We conduct both 2-dimensional and 3-dimensional simulations. The 3-dimensional simulations model the full tokamak geometry using a method called 'λ damping' to set its boundary conditions. The 3-dimensional simulations successfully capture the formation and evolution of magnetic islands as well as the deformation of magnetic flux surfaces, contributing to understanding their generation in tokamaks. However, we found that current computational resources are insufficient to conduct fully kinetic PIC simulations over durations comparable to MHD simulations, which renders direct comparisons challenging at present. We discuss the main obstacles in applying the fully kinetic PIC method to fusion tokamak plasma research and propose potential solutions to overcome these challenges, including the development of more advanced fully kinetic PIC algorithms and the use of more appropriate coordinate systems, such as magnetic flux or cylindrical coordinates, to reduce computational costs and improve accuracy. Then we study electron-only reconnection under varying strengths of guide fields using 2-dimensional fully kinetic PIC simulations, with a particular focus on electron heating and electron velocity distribution functions (EVDFs). Electron-only reconnection, observed in Earth's magnetosheath, plays a crucial role in energy transfer and dissipation within turbulence. The presence of guide fields delays the onset of electron-only reconnection and reduces the reconnection rate, aligning with findings from previous studies on standard ion-coupled reconnection [Pritchett, 2005, Birn and Priest, 2007]. The absence of ion outflow jets in the simulations confirms that the reconnection occurs in the electron-only regime. As the guide field intensifies, the density enhancements and cavities, as well as the quadrupolar out-of-plane magnetic field structures, become more localized. This narrowing is likely tied to non-ideal kinetic effects occurring at electron gyroradius scales. Consistent with previous experimental studies, electron temperature anisotropy along the separatrices is identified, primarily driven by changes in parallel temperature. It is noted that the variations in parallel temperature are stronger than those in perpendicular temperature in our simulations. The intensity of guide fields has a pronounced effect on the spatial distribution of parallel electron temperature. Stronger guide fields narrow temperature variation regions and result in various structures. Specifically, as the guide field increases, a transition from a quadrupolar to a hexapolar (six-polar) to an octopolar (eight-polar) structure is observed in the parallel electron temperature and temperature anisotropy results. EVDFs are analyzed at multiple locations across the three simulation cases. The perpendicular velocity components show a nearly gyrotropic distribution across all cases. The parallel velocity components, especially those of electrons in the outflow regions, are strongly influenced by the presence of guide fields. The EVDF shapes vary significantly with changes in guide field strength. Intense electron heat fluxes along the parallel direction are observed at the X-point, along the separatrices, and inside magnetic islands. Our simulations indicate they fall within a transition regime between the Boltzmann response and the CGL (Chew-Goldberger-Low) theory. As the guide field strength increases, they show increasing consistency with the CGL theory, which explains the electron parallel temperature variations and the shape of the EVDFs observed along the separatrices in all three cases. We also investigate the spontaneous evolution from electron-only to traditional ion-coupled magnetic reconnection in the presence of a guide field through 2-dimensional PIC simulations. This study focuses on the transition mechanism and the effect of ion temperature on this shift from electron-only towards ion-coupled reconnection. Previous simulations and observations have indicated that electron-only reconnection may act as a transitional phase between a quiet current sheet and traditional ion-coupled reconnection [Lu et al., 2020b, 2022, Hubbert et al., 2022]. However, these studies focused on externally driven reconnection in their simulations, raising the question of whether electron-only reconnection might play a similar intermediary role in spontaneous reconnection. In this study, we address this gap by demonstrating that electron-only reconnection can indeed play this transitional role in spontaneous reconnection with guide fields. In our simulations, we analyze the spontaneous evolution from electron-only to ion-coupled reconnection. In the initial phase, electrons promptly respond to magnetic field changes, accompanied by noticeable electron outflows and electron heating, while the ion response remains either negligible or entirely absent. These observations align well with features of electron-only reconnection. As reconnection develops, the degree of ion coupling to the reconnection process increases and the reconnection transits to the ion-coupled reconnection regime, with distinct ion outflows and heating. This is because the spatial and temporal conditions necessary for ion acceleration and heating are met due to the growth of magnetic islands. We also found that the Hall electric field drives ion acceleration, with the pressure gradient term intensifying as ion velocities increase, contributing to ion heating. The influence of ion temperature on this transition is also examined by conducting a simulation with higher ion thermal velocities. Notable differences manifest in the ion response. Specifically, no ion outflows or ion heating are observed, indicating that the system stays within the electron-only regime. This finding is consistent with the results of Guan et al. [2023], where the ratio (L/2)/ρi ≈ 3.54 (with L divided by 2 because there are two current sheets in our simulation box) was inadequate to induce ion coupling. We propose that guide field strength may influence the reconnection transition, as it is related to the scale of electron and ion motion in guide-field reconnection. This factor, along with the ion-to-electron mass ratio, presents a promising direction for future research. When the mass ratio is larger, i.e. electrons are lighter, the electron response to changes in magnetic field topology is expected to be quicker. Consequently, the electric field structure and ion dynamics would be affected. Further studies are needed to explore the effects of guide field strength and mass ratio. Additionally, a similar transition role occurring in anti-parallel reconnection is another intriguing area for further study. The characteristic ion motion scale in anti-parallel reconnection differs from that in guide-field reconnection [Guan et al., 2024] and the ion responses could vary between these two configurations.