Applications Of Relativistic Structure-preserving Particle Algorithms In Multi-scale Plasma Processes

As typical multi-body systems,plasmas contain massive charged particles which are coupled with inner and outer electromagnetic fields.It is difficult to describe such complex systems through pure theoretical methods,especially for nonlinear and multi-scale plasma processes.Thus,the numerical simulation has become a widely-used tool for researchers especially after the rapid boost of computer technology in last decades.But,the simulations of multi-scale phenomena are still hampered by limited compu-tation resources and accumulation of numerical errors.Nowadays,the peak compu-tational ability of the fastest supercomputer in the world has reached 120PFlops.In the future,the computation resources of human world will undoubtedly keep growing,which brings hopes to the large-scale numerical studies of plasmas.To achieve efficient and accurate usages of future massive computation resources,algorithms with long-term stability are also needed.The structure-preserving algorithms,through preserving geometric structures of physical systems,can effectively control the global numerical errors during multi-scale simulations.In this thesis,the structure-preserving particle algorithms for relativistic plasma systems are discussed.Several relativistic structure-preserving particle algorithms are constructed and studied theoretically.Physical results of runaway electrons in tokamak,a typical relativistic multi-scale process,are obtained via large-scale applications of structure-preserving algorithms.The development of extensible software platform for structure-preserving particle algorithms is also intro-duced.In this thesis,the relativistic volume-preserving algorithm(VPA)for charged par-ticles is constructed by use of the splitting method.The Lorentz covariance of discrete systems is defined and studied.A convenient procedure for constructing Lorentz covari-ant symplectic algorithms is summarized,based on which an explicit Lorentz covari-ant canonical symplectic algorithm(LCCSA)is built.Compared with non-covariant and non-symplectic-preserving algorithms,the covariant symplectic algorithm shows long-term stability as well as the reference independency.Meanwhile,the built-in energy-based adaptive time step of LCCSA can improve the efficiency and the cor-rectness of simulations for energy-varying processes.Based on the covariant Hamilto-nian of charged particles,the construction of high-order explicit symplectic algorithms for time-dependent systems is studied by use of the generation-function method and the Hamiltonian splitting method.For the relativistic Vlasov-Maxwell system,a relativistic canonical symplectic Particle-in-Cell(PIC)algorithm is developed.As a typical relativistic multi-scale plasma process,the runaway electron physics in tokamak plays an important role in the safe operation of fusion devices.In this thesis,the multi-scale full-orbit dynamics of runaway electrons is studied through large-scale application of the relativistic volume-preserving algorithm.The gyro-center assump-tion is proved to be invalid for describing energetic runaways.And,correspondingly,a collisionless pitch-angle scattering effect is discovered,which results from the toroidal geometric configuration of tokamak field.This effect causes the break of magnetic moment conservation and new rules of energy limit different from predictions of gyro-center theory.The fine physical pictures of runaway dynamics in different time-scales are provided.The influences of initial phase space sampling as well as the device pa-rameters of tokamaks on the runaway secular momentum evolution,the energy inte-grate behavior,the energy balance time,and the collisionless pitch-angel scattering are discussed.Under the parameters of ITER,a large-scale runaway dynamical simulation with 117 samples and 1011 time steps is done on the Sunway TaihuLight supercomputer,which shows the positive effects of magnetic ripple perturbations on the confinement of runaway electrons.To boost the development and the large-scale application of structure-preserving particle algorithms,a modularized,standardized,and extensible software platform,the Accurate Particle Tracer(APT),is designed.APT supports standard I/O format and several parallelization implementations.It has been integrated with various geometric algorithms and physical modules.The APT code has been distributed on the Sunway TaihuLight supercomputer.As a platform,the extensible module of APT provides a convenient environment for adding new algorithms or physical modules,which can boost the communication of research results from different fields.