Geometric methods of kinetic theory and simulation

Title: Geometric methods of kinetic theory and simulationAuthor: on governanceDegree awarded: China University of Science and TechnologyKeywords: Kinetic;; differential geometry;; particle simulation;; swing center standard kinetic;; magnetically confined plasmas;; radio waves;; computational electromagnetics;; finite difference time domain methodSummary:Physical nature of the problem is geometric problems. Objective physical laws should be used no specific coordinate system on the "geometric" language to express. Simulation of a physical system should be in their space-time geometry of reproduction, only when the simulation algorithms and discrete structures consistent with the physical geometry of the system when, in order to reproduce the correct and effective evolution of the physical system. In this paper, neodymium magnets summarize, sum up the geometric kinetic magnetized plasma on the basis of the basic theoretical framework is presented to convert it into a numerical simulation algorithm generalized way; and verified through simulation geometry kinetic method and the traditional classical kinetic theory of consistent of.Kinetic theory of geometric language of differential geometry to describe the plasma kinetic system. Plasma particles in the electromagnetic field on the role of macro reflected Poincaré-Cartan-Einstein 1 - form, along the particle world line of the Poincaré-Cartan-Einstein 1 - electromagnetic fields in the form of points you can get the action of charged particles. Macro-particle phase space distribution function describes the particle world line in the phase space of the macro-distribution, the distribution function along the world line is a constant. The role of space in the amount of charged particles and electromagnetic fields to be added to the action of the Vlasov-Maxwell system has been the role of volume. By the least action principle, the variational method is given by the Hamilton equation of particle motion and Maxwell's equations describe the evolution of electromagnetic fields. Further, with the Lie coordinate transformation method, by introducing the gauge field S decomposition of multi-particle trajectory perturbations scale structure of space-time.In geometry, based on the kinetic theory, this paper gives a general geometric kinetic simulation algorithms. Phase-space distribution function from configuration space to the fiber points, and the electromagnetic field from the configuration space to phase space back to the transformation, can be said to include the full Dirac-δ function space integral presentation. http://www.chinamagnets.biz/Neodymium/Ball-Neodymium-Magnets.php In order to resolve the shape of the function instead of the Dirac-δ function, integral presentation by Monte-Calor integration method into a discrete sum. Essentially, numerical simulation of the interpolation, the speed differential and integral function can be interpreted as a discrete form of integral representation. As the particles only through the current density field acting on the electromagnetic fields, kinetic particle simulation should be based on the discrete velocity integral, rather than discrete functions on phase space.According to Maxwell's equations, the evolution of the electromagnetic field is a local process, this means that the algorithm can be local parallelism. Finite-difference time-domain (FDTD) Maxwell equations will be written about the time of partial differential equations, iterative methods by extrapolating the evolution of electromagnetic fields. According to the electromagnetic field A geometric meaning of the potential function along the sampling grid points on a connection between their sample, and thus build the electromagnetic field of space-time difference grid. Maxwell equations in the Ampere's law can be broken down into two separate electric field E and on the electromagnetic vector potential A first-order partial differential equation of time, the scalar potential? The time evolution of the specific conditions of use of the electromagnetic specifications determined. Cold plasma in the current density field on the electromagnetic response time can be written as partial differential equations, which is in the form of Ohm's law. In this paper, Maxell equations and Ohm's law difference scheme for a limited time, and nothing to regulate the form of Ampere's law gives the calculation of the PML region format.Cyclotron center standard (G-Gauge) kinetic is kinetic geometry in the realization of magnetically confined plasmas. As the G-Gauge kinetic theory is introduced to the Lie perturbation, the perturbation of its velocity integral part of the phase space distribution function that contains both F and G-Gauge function S two phase space functions. Function of sampling phase space in order to Kruskal ring as the basic unit, the sampling points uniformly distributed in the ring, each ring has a set of phase space coordinates, a set of partial derivatives of F and F the number of samples, and a number of S samples. Use step by step integration method, the velocity integral in retaining only S, eliminate all the partial derivatives of S. So that each sampling point only need to push a variable S, the G-Gauge algorithm than direct particle simulation algorithm has a smaller amount of computation. In this paper, uniformly magnetized plasma, magnetic field perpendicular to the propagation of radio waves has been simulated, the complete reproduction of a uniform plasma waves and electron Bernstein wave X dispersion curve, and reproduction of the non-uniform plasma in the X-wave electron Bernstein wave The mode conversion process, especially given the almost complete conversion of the XB-mode simulation results. G-Gauge algorithm for the first time starting from first principles, to achieve the targeted radio waves in magnetically confined plasma particles interact with the physical simulation.Geometry described in this paper methods of kinetic theory and simulation is essentially a system of plasma kinetic description of the geometry and reproduction, is a modern geometric point of view to re-examine the classic kinetic. Geometry of the plasma kinetic theory description of the system is complete and multi-time scale, it will complex plasma kinetic system is decomposed into a few relatively simple subsystems, without loss of physical information of the condition, reducing the problem complexity. Relative to the classical kinetic approach, geometric kinetic constraints can reveal more deeply the geometric structure of the plasma, which help us understand the complex kinetic phenomena.Degree Year: 2009