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 the dominant saturation mechanism, and TEM transport is insensitive to ηe. 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 five. Linear growth rate spectra, transport fluxes, fluctuation wavelength spectra, zonal flow shearing spectra, and correlation lengths and times are in close agreement. In addition to identifying the critical parameter ηe for TEM zonal flows, this paper takes a challenging step in code verification, directly comparing very different methods of simulating simultaneous kinetic electron and ion dynamics in TEM turbulence.

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.

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. The suppression effect is consistent with the rate of shearing on turbulent eddies due to zonal flows and the radial sprectra broadening. Strong geodesic acoustic modes (GAM) are generated along with zonal flows.

A hybrid gyrokinetic ions/massless fluid electron model is used to study the stability of high-n toroidal Alfvén eigenmodes (TAEs) in ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)]. The hybrid model has been implemented in the particle-in-cell turbulence simulation code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)]. The adequacy of the hybrid model for simulating TAEs has been previously demonstrated [J. Lang et al., Phys. Plasmas 16, 102101 (2009)] by comparing the simulated TAE mode frequency and structure with an eigenmode analysis, and the thermal ion kinetic damping effect with analytic theory. By using a global particle-in-cell code the effects of large orbit width and nonlocal mode structures can be accurately included. Damping rate due to numerical filtering is carefully monitored, and convergence with respect to particle number, grid resolution, etc., is thoroughly tested. The simulations show that the most unstable modes in ITER lie in the rage of 10&lt;n&lt;20. Thermal ion pressure effect and alpha particle nonperturbative effect are important in determining the mode radial location and stability threshold. The thermal ion Landau damping rate and radiative damping rate from the simulations are compared with analytical estimates. The thermal ion Landau damping is the dominant damping mechanism. Plasma elongation has a strong stabilizing effect on the alpha driven TAEs. The central alpha particle pressure threshold for the most unstable n=15 mode is about βα(0)=0.7% for the fully shaped ITER equilibrium.

Kinetic/magnetohydrodynamic hybrid simulations are carried out to investigate the nonlinear dynamics of energetic particle-driven toroidal Alfvén eigenmode with collision and source/sink. For cases well above marginal stability, the mode saturation is approximately steady state with finite collision frequency. The calculated scaling of saturation level with collision frequency agrees well with analytic theory. For cases near-marginal stability at low collision rates, the mode saturation exhibits pulsation behavior with frequency chirps up and down.