The Spectral Method Of Kinetic Equation In Plasma Landau Damping

The study of kinetic model is important in the plasma physics.The kinetic equation involves seven independent variables x,y,z,vx,vy,vz and t.It can describe the interaction between plasma and electromagnetic field coupled with Maxwell equations.But it's difficult to solve it analytically because of its high dimensionality and complex physical process.The numerical solution is especially critical in the study of plasma physicsIn Chapter ?,we briefly review common numerical methods in the solution of kinetic equation,including the PIC method and semi-Lagrangian method and give a comparison of their advantages and disadvantages.In Chapter ?,we derive different types of Vlasov equations.The details of semi-Lagrangian solver are demonstrated by solving a guiding-central Vlasov equation.Also the finite volume solver for plasma physics is demonstrated by UGKS for Vlasov-BGK model.In Chapter ?.we study the spectral solver for collisional Vlasov-BGK-Poisson equations,and use it to simulate the free-streaming model and Landau damping model.The numerical simulation corresponds well with the theoretical results.Hermite basis has the similar shape with Maxwellian function,so it has giant advantage in the simulation of Maxwellian shape functions.With a proper velocity-scaled factor,the number of Hermite polynomials can be reduced in the simulation.In Chapter ?,we give a conclusion of our paper and an expectation of future work.We will use our algorithm study the two-stream instability and more complex physical process coupled with Maxwell equations.