Yingfeng Xu

Linear gyrokinetic theory and computation of the gyrocenter motion based on the exact canonical variables for axisymmetric tokamaks

Linear gyrokinetic theory based on the Lie-transform perturbation method is presented in terms of the exact canonical variables. In the linear drift approximation, it is shown that the gyrocenter equations of motion based on the canonical variables are equivalent to the usual guiding-center equations of motion. A numerical code is developed to advance the gyrocenter motion in terms of the exact canonical variables with arbitrary perturbations. It is found that a static magnetic island in a tokamak has little effect on the trapped particle orbits due to the conservation of the longitudinal invariant; and it induces the island structure of passing particle orbits due to the fact that the longitudinal invariant for the passing particles is broken by the asymmetric perturbation.

Nonlinear gyrokinetic theory based on a new method and computation of the guiding-center orbit in tokamaks

The nonlinear gyrokinetic theory in the tokamak configuration based on the two-step transform is developed; in the first step, we transform the magnetic potential perturbation to the Hamiltonian part, and in the second step, we transform away the gyroangle-dependent part of the perturbed Hamiltonian. Then the I-transform method is used to decoupled the perturbation part of the motion from the unperturbed motion. The application of the I-transform method to the computation of the guiding-center orbit and the guiding-center distribution function in tokamaks is presented. It is demonstrated that the I-transform method of the orbit computation which involves integrating only along the unperturbed orbit agrees with the conventional method which integrates along the full orbit. A numerical code based on the I-transform method is developed and two numerical examples are given to verify the new method.

A gyrokinetic continuum code based on the numerical Lie transform (NLT) method

In this work, we report a novel gyrokinetic simulation method named numerical Lie transform (NLT), which depends on a new physical model derived from the I-transform theory. In this model, the perturbed motion of a particle is decoupled from the unperturbed motion. Due to this property, the unperturbed orbit can be computed in advance and saved as numerical tables for real-time computation. A 4D tensor B-spline interpolation module is developed and applied with the semi-Lagrangian scheme to avoid operator splitting. The NLT code is verified by the Rosenbluth-Hinton test and the linear ITG Cyclone test.

A new continuum approach for nonlinear kinetic simulation and transport analysis

A numerical code based on the I-transform approach is developed to solve the nonlinear Vlasov equation and carry out the transport analysis. The numerical results given by the I-transform approach agree with the conservative semi-Lagrangian approach in the Landau damping case and the bump-on-tail instability case. The diffusivities induced by the random fields and the quasilinear transport are also successfully demonstrated by using the new approach. It is found that the nonlinear transport in the one-dimensional Langmuir turbulence cannot be well-described by a simple diffusion model, due to the strong particle trapping at the nonlinear stage.

Electromagnetic gauge invariance of the nonlinear gyrokinetic theory and its implication for the truncation in gyrokinetic simulations

The exact electromagnetic gauge invariance of the nonlinear gyrokinetic theory is discussed. It is shown that the guiding-center distribution function is an electromagnetic gauge invariant with all the terms in the nonlinear gyrokinetic equations retained. δ is the amplitude ordering parameter of the perturbations. All the terms have to be retained in the nonlinear gyrokinetic simulation to guarantee the electromagnetic gauge invariance.

Transport induced by ion cyclotron range of frequencies waves

The Vlasov equation, which includes the effect of the ion cyclotron range of frequencies (ICRF) waves, can be written as the Fokker-Planck equation which describes the quasilinear transport in phase space by using the Lie-transform method. The radial transport fluxes of particle, energy and parallel momentum driven by ICRF waves in the slab geometry have been derived. The results show that the ICRF-induced radial redistributions of particle, energy and parallel momentum are driven by the inhomogeneity in energy of the equilibrium distribution function, and related to the correlation between the excursion in the real space and the excursion in energy. For the case with strong asymmetry of ky spectrum, the ICRF-induced radial transport driven by the energy inhomogeneity dominates the ICRF-induced radial transport driven by the spatial inhomogeneity.

Ion heat pinch due to the magnetic drift resonance with the ion temperature gradient instability in a rotating plasma

The ion heat pinch due to the magnetic drift resonance with the ion temperature gradient instability is investigated by using the Lie-transform method. In a tokamak plasma with an equilibrium parallel flow, the total heat flux is found to direct inward with a strong flow shear. The proposed heat pinch can provide possible explanations for some experimental observations.

Nonlinear gyrokinetic theory and its application to computation of the gyrocenter motion in ripple field

The nonlinear gyrokinetic equation with full electromagnetic potential perturbations is derived by using the two-step transform procedure. The second-order transformed Hamiltonian can be simplified as 12δA∥2, instead of 12δA2 in the long-wave-length limit. A numerical code based on the I-transform method is improved to compute the gyrocenter orbit in the TFTR tokamak with a ripple field, and the numerical results indicate that the collisionless stochastic diffusion criterion agrees well with the theoretical prediction.

Influence of mean radial electric field on particle transport induced by RMPs in tokamak plasmas

The quasi-linear theory of the particle diffusion coefficient including the finite Larmor radius effect and the mean radial electric field ( E r without shear) in a stochastic magnetic field is derived. The theory has been verified by comparing with test particle simulations and previous theory. It is found that E r can shift the wave-particle resonance position. The Er-shift effect mainly modifies the ion diffusion coefficients and leads to the modification of ion particle flux. By using the ambipolar condition, we obtained the balanced flux at the edge of a tokamak plasma and found good agreement with recent experimental observations.The quasi-linear theory of the particle diffusion coefficient including the finite Larmor radius effect and the mean radial electric field ( E r without shear) in a stochastic magnetic field is derived. The theory has been verified by comparing with test particle simulations and previous theory. It is found that E r can shift the wave-particle resonance position. The Er-shift effect mainly modifies the ion diffusion coefficients and leads to the modification of ion particle flux. By using the ambipolar condition, we obtained the balanced flux at the edge of a tokamak plasma and found good agreement with recent experimental observations.

Loss and redistribution of energetic passing ions with resonant magnetic perturbations

The effects of resonant magnetic perturbations (RMPs) and the magnetic drift on the loss and redistribution of passing ions are investigated numerically by the upgrade version of the orbit following code GYCAVA. The drift island structures of passing ion orbits induced by RMPs and the magnetic drift are consistent with the given toroidal and poloidal mode numbers of RMPs in the orbit simulations. The redistribution and loss of energetic and thermal passing ions with and without RMPs are numerically studied and compared with each other. The redistribution near the edge is due to the loss induced by RMPs and the magnetic drift. The extra loss of passing ions induced by RMPs is related to the drift island structure induced by RMPs and the magnetic drift and the stochasticity induced by overlap of magnetic islands. The loss of passing ions with n = 1 RMPs is larger than that with n = 4 RMPs for the same perturbation amplitude parameter, which is due to the fact that the magnetic islands produced by n = 1 RMPs...