tao Xiao

Explicit Runge–Kutta integrator with Hamiltonian correction for long-time simulations of guiding-center orbit in tokamak configurations

Hamiltonian correction method is proposed to improve the variable time-step fourth-order Runge–Kutta methods in computing guiding-center orbits in a tokamak. It is found that the new method can significantly improve the computation efficiency of the conventional Runge–Kutta method in simulation of the long-time behavior of the guiding-center orbits.

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.

Numerical simulation of geodesic acoustic modes in a multi-ion system

Based on the semi-Lagrangian method, a δf drift kinetic continuum code incorporating magnetic flux coordinate was developed and applied to investigate the geodesic acoustic mode (GAM) oscillation in a multi-ion plasma system. This work proves clearly that the effective ion mass number affects the GAM in a multi-ion system. In this simulation, GAM frequency and damping rate are seen to vary with the proportion of impurity ions. The numerical result is consistent with the theoretical prediction in terms of both frequency and damping rate.

Kinetic effect of toroidal rotation on the geodesic acoustic mode

Kinetic effects of the toroidal rotation on the geodesic acoustic mode are theoretically investigated. It is found that when the toroidal rotation increases, the damping rate increases in the weak rotation regime due to the rotation enhancement of wave-particle interaction, and it decreases in the strong rotation regime due to the reduction of the number of resonant particles. Theoretical results are consistent with the behaviors of the geodesic acoustic mode recently observed in DIII-D and ASDEX-Upgrade. The kinetic damping effect of the rotation on the geodesic acoustic mode may shed light on the regulation of turbulence through the controlling the toroidal rotation.

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.

Ion orbit loss and pedestal width of H-mode tokamak plasmas in limiter geometry

A simple analytical model is proposed to analyze the effects of ion orbit loss on the edge radial electric field in a tokamak with limiter configuration. The analytically predicted edge radial electric field is consistent with the H-mode experiments, including the width, the magnitude, and the well-like shape. This model provides an explanation to the H-mode pedestal structure. Scaling of the pedestal width based on this model is proposed.

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.

Simulation of the alpha particle heating and the helium ash source in an International Thermonuclear Experimental Reactor-like tokamak with an internal transport barrier

A guiding center orbit following code, which incorporates a set of non-singular coordinates for orbit integration, was developed and applied to investigate the alpha particle heating in an ITER-like tokamak with an internal transport barrier. It is found that a relatively large q (safety factor) value can significantly broaden the alpha heating profile in comparison with the local heating approximation; this broadening is due to the finite orbit width effects; when the orbit width is much smaller than the scale length of the alpha particle source profile, the heating profile agrees with the source profile, otherwise, the heating profile can be significantly broadened. It is also found that the stagnation particles move to the magnetic axis during the slowing-down process, thus the effect of stagnation orbits is not beneficial to the helium ash removal. The source profile of helium ash is broadened in comparison with the alpha source profile, which is similar to the heating profile.

Neoclassical polarization drift of collisionless single ion in tokamaks with arbitrary time-varying radial electric field

An improved theory for the neoclassical polarization drift of the collisionless single ion with the arbitrary time-varying radial electric field is presented. A guiding-center motion code is used to numerically study the neoclassical polarization drift of a collisionless single ion in a model tokamak geometry. The results from the improved theory are compared with the numerical results and they agree with each other very well. The improved theory can be used to study the neoclassical polarization drift due to the fast time-varying radial electric field.

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...