Numerical Lie-transform Method And The Nonlinear Simulation Study Of The Vlasov System

Turbulence transport is an important and difficult problem in plasma physics.The quasilinear theory is widely used to investigate the turbulence transport.However,the transport in quite a lot of cases is still significantly different from the theory prediction.Numerical simulations now play a major role in the investigation of the low-frequency plasma turbulence.In this thesis,first,a new code based on the numerical Lie-transform method for nonlinear kinetic simulation in a one-dimensional collisionless system is developed.This new code solves I-transform formulations by using the continuum approach and the characteristic line method,which reduces the noise of the simulation and keeps the numerical stability of the code.Further,the computation of the multi-dimensional interpolation is avoided in simulation by using the ?-transform fomulations.The new numerical Lie-transform code can be used to simulate the nonlinear evolution of the system by using the mulitple-step transform method.In numerical cases of the Landau damping and the bump-on-tail instability,the simulation results computed by using the new code well match the results computed by using the traditional numerical method.Then,we use the new code to analyze the transport in cases of the random per-turbed field and the bump-on-tail instability.By using the intermediate variables of the new code,we compute the transport flux and diffusion coefficient directly.In cases of the random perturbed field and quasilinear transport,the diffusion flux in velocity is successfully demonstrated by using the new code.And it is found that the nonlinear transport cannot be well-described by a simple diffusion model due to the strong particle trapping.Next,the coarse-grain averaged distribution function of the one-dimensional Vlasov system is obtained in numerical simulation.By using the coarse-grain averaged distri-bution function,we compute the entropy production in cases of the random field,the linear Landau damping and the bump-on-tail instability.The computed entropy produc-tion is converged with increasing length of coarse-grain average.When the distribution function differs slightly from a Maxwellian distribution,the converged value agrees with the result computed by using the definition of thermodynamic entropy.The rela-tion between the average length for computing the coarse-grain averaged distribution function and the computed entropy production by using this coarse-grain averaged dis-tribution function is discussed.Finally,the issues of particle-conservation and nonlinear filter in the gyrokinetic simulation code NLT are discussed.