Research On Gyrokinetic Theory And Simulation

The turbulent transport is one of the most important physical questions in the tokamak magnetized plasma research. Because the turbulent transport will degrade the confinement of the plasma. The turbulence in tokamaks is mainly the low frequency microturbulence, which can be studied by gyrokinetic theory and simulation.In this thesis, we study on the gyrokinetic theory and simulation. Firstly, we reviewed the nonlinear gyrokinetic theory.Secondly, we have discussed the properties of the Lie-transform in the gyroki-netic theory for the Hamiltonian gyrocenter model. The first property is that the gyrocenter Jacobian is formally the same as the guiding-center Jacobian. The sec-ond property is that the coordinate transform between two sets of the gyrocenter coordinates is the same as the coordinate transform between two corresponding sets of the guiding-center coordinates. The third property is that although the generating vectors are non-Hamiltonian flows, they are incompressible flows in the phase space, which is consistent with the first property.Thirdly, we have discussed the electromagnetic gauge invariance of the non-linear gyrokinetic theory for the Hamiltonian gyrocenter model. We have demon-strated that the electromagnetic gauge invariance of the nonlinear gyrokinetic theory is kept with the systematic truncation of the gyrokinetic equations by us-ing "R-I" decomposition. For an arbitrary truncation, the electromagnetic gauge invariance is broken. For the nonlinear gyrokinetic theory, the guiding-center dis-tribution function is an electromagnetic gauge invariant with all the second-order terms in the gyrokinetic Vlasov equation and in the pull-back transformation of the gyrocenter distribution function kept.Finally, we have obtained the linear gyrokinetic theory in terms of the exact canonical variables from the properties of the Lie-transform in the gyrokinetic theory. Next, we have demonstrated the equivalence of the gyrocenter equations of motion and the usual guiding-center equations of motion with the linear and drift approximation. Then, we have developed the numerical code GYCAVA based on the linear gyrokinetic theory in terms of the exact canonical variables. The code can be used to compute the guiding-center orbit of the charged particles with an arbitrary electromagnetic fields in tokamaks. We have discussed the guiding-center orbits computed by GYCAVA in a static magnetic island.