Jianying Lang

Role of zonal flows in trapped electron mode turbulence through nonlinear gyrokinetic particle and continuum simulation

Trapped electron mode (TEM) turbulence exhibits a rich variety of collisional and zonal flow physics. This work explores the parametric variation of zonal flows and underlying mechanisms through a series of linear and nonlinear gyrokinetic simulations, using both particle-in-cell and continuum methods. A new stability diagram for electron modes is presented, identifying a critical boundary at ηe=1, separating long and short wavelength TEMs. A novel parity test is used to separate TEMs from electron temperature gradient driven modes. A nonlinear scan of ηe reveals fine scale structure for ηe≳1, consistent with linear expectation. For ηe 1, zonal flows are weak, and TEM transport falls inversely with a power law in ηe. The role of zonal flows appears to be connected to linear stability properties. Particle and continuum methods are compared in detail over a range of ηe=d ln Te/d ln ne values from zero to fiv...

Gyrokinetic δf particle simulation of trapped electron mode driven turbulence

The linear instabilities and nonlinear transport driven by collisionless trapped electron modes (CTEM) are systematically investigated using three-dimensional gyrokinetic δf particle-in-cell simulations. Scalings with local plasma parameters are presented. Simulation results are compared with previous simulations and theoretical predictions. The magnetic shear is found to be linearly stabilizing, but nonlinearly the transport level increases with increasing magnetic shear. This is explained by the changes in radial eddy correlation lengths caused by toroidal coupling. The effect of zonal flows in suppressing the nonlinear CTEM transport is demonstrated to depend on electron temperature gradient and electron to ion temperature ratio. Zonal flow suppression is consistent with the rate of E×B shearing of the ambient turbulence and radial spectra broadening. Strong geodesic acoustic modes (GAM) are generated along with zonal flows.

Nonlinear saturation of collisionless trapped electron mode turbulence: Zonal flows and zonal density

Gyrokinetic δf particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter-sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear, and electron temperature gradient. For parameters where zonal flow is found to be unimportant, zonal density (purely radial density perturbations) is generated and expected to be the dominant saturation mechanism. A toroidal mode-coupling theory is presented that agrees with simulation in the initial nonlinear saturation phase. The mode-coupling theory predicts the nonlinear generation of the zonal density and the feedback and saturation of the linearly most unstable mode. Inverse energy cascade is also observed in CTEM turbulence simulations and is reported here.Gyrokinetic δf particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter-sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear, and electron temperature gradient. For parameters where zonal flow is found to be unimportant, zonal density (purely radial density perturbations) is generated and expected to be the dominant saturation mechanism. A toroidal mode-coupling theory is presented that agrees with simulation in the initial nonlinear saturation phase. The mode-coupling theory predicts the nonlinear generation of the zonal density and the feedback and saturation of the linearly most unstable mode. Inverse energy cascade is also observed in CTEM turbulence simulations and is reported here.

Gyrokinetic δf particle simulations of toroidicity-induced Alfvén eigenmode

Gyrokinetic δf particle simulation is used to investigate toroidicity-induced Alfven eigenmodes (TAEs). Both thermal ions and energetic particles are fully kinetic, but a reduced fluid model is used for the electrons. Simulation of a single n=2 global TAE is carefully analyzed and benchmarked with an eigenmode analysis, and a very good agreement is achieved in both mode structure and mode frequency. The instability of the mode in the presence of energetic particles is demonstrated. In particular, gyrokinetic simulations demonstrate the kinetic damping effect of thermal ions, where the finite radial structure of kinetic Alfven waves is well resolved and the damping rate is compared to and found to agree well with analytical theory.

Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code

As an alternative option to kinetic electrons, the gyrokinetic total-f particle-in-cell (PIC) code XGC1 has been extended to the MHD/fluid type electromagnetic regime by combining gyrokinetic PIC ions with massless drift-fluid electrons analogous to Chen and Parker [Phys. Plasmas 8, 441 (2001)]. Two representative long wavelength modes, shear Alfvén waves and resistive tearing modes, are verified in cylindrical and toroidal magnetic field geometries.

Arbitrary plasma shape and trapped electron modes in the GEM gyrokinetic electromagnetic turbulence simulation code

Here the recent developments in GEM, a quite comprehensive Gyrokinetic Electromagnetic (GEM) turbulence code are described. GEM is a δf particle turbulence simulation code that has kinetic electrons and electromagnetic perturbations. The key elements of the GEM algorithm are: (1) the parallel canonical formulation of the gyrokinetic system of equations (1); (2) an adjustable split-weight scheme for kinetic electrons (2); and (3) a high-β algorithm for the Amperes equation (3). Additionally, GEM use a two-dimensional (2D) domain decomposition and runs efficiently on a variety of high performance architectures. GEM is now extended to include arbitrary toroidal equilibrium profiles and flux-surface shapes (4). The domain is an arbitrarily sized toroidal slice with periodicity assumed in the toroidal direction. It is global radially and poloidally along the magnetic field. Results are presented that demonstrate the effect of plasma shaping on the Ion-Temperature-Gradient (ITG) driven instabilities. An example of nonlinear simulation of the finite-β modified ITG turbulence in general geometry is also given. Finally, collisionless Trapped Electron Modes (TEM) are investigated and shown here is the transition from the TEM dominated core region to the Drift-Wave dominated edge region as the density gradient increases.