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Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving…
We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker-Planck solver, with a…
Motivated by the particle acceleration problem in pulsars, we numerically investigate electrostatic instability of electron-positron pairs injected in an external electric field. The electric field is expected to be so strong that we cannot…
With the great development of parallel computing techniques, the particle-particle (PP) model has been successfully applied in a number of plasma applications. Comparing to particle-mesh (PM) models, for example the widely used…
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
Particle-mesh methods, such as the particle-in-cell (PIC) method, cannot retain exact pairwise interaction at sub-cell scales. For dense nonneutral relativistic electron bunches, this makes it difficult to accurately capture the…
In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
Magnetic reconnection in relativistic plasmas is well established as a fast and efficient particle accelerator, capable of explaining the most dramatic astrophysical flares. With particle-in-cell simulations, we demonstrate the importance…
A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an…
The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…
In a uniform radio-frequency (RF) plasma between a large electrode pair, the addition of an axial magnetic field induces diverse longitudinal filaments. To reveal its pattern dynamics, we conduct two-dimensional (2D) Particle-In-Cell (PIC)…
In the simulation of biological molecules, it is customary to impose constraints on the fastest degrees of freedom to increase the time step. The evaluation of the involved constraint forces must be performed in an efficient manner, for…
Particle in Cell (PIC) simulations are a widely used tool for the investigation of both laser- and beam-driven plasma acceleration. It is a known issue that the beam quality can be artificially degraded by numerical Cherenkov radiation…
We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In…
We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of…
The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…
The destabilizing role of neutrino beams on the Trivelpiece-Gould modes is considered, assuming electrostatic perturbations in a magnetized plasma composed by electrons in a neutralizing ionic background, coupled to a neutrino species by…
Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…