Global Gyrokinetic Particle Simulations Research Articles

The performance of equilibrium radial electric field shear on microturbulence with different magnetic shears in tokamak plasmas

Global gyrokinetic particle simulations show that equilibrium radial electric field (E r ) shear reduces the linear growth rate, ion heat conductivity, and nonlinear turbulence amplitude for both the ion temperature gradient (ITG) and kinetic ballooning mode (KBM) microturbulence by tilting the poloidal mode structure. The increase in the magnetic shear enhances the stabilizing performance of the E r shear on linear growth rate for the ITG case but has no effect on that for the KBM case. The radial correlation length of the ITG turbulence is decreased by increasing the magnetic shear in a weak ion diamagnetic flow shear condition with low β, leading to a reduction in the effective E × B shearing rate, which weakens the suppression performance of the E r shear on the ITG turbulence amplitude. In contrast, under a larger ion diamagnetic shear flow for higher β, an increase in magnetic shear strengthens the suppression performance of the E r shear on the KBM turbulence amplitude due to an increase in the effective shearing rate by increasing the radial correlation length of the turbulence.

Effects of radial electric field on kinetic ballooning mode in toroidal plasma

Global gyrokinetic particle simulations show that the radial electric field (Er) shear can suppress the kinetic ballooning mode (KBM) in a toroidal plasma. The linear KBM growth rate reaches a maximum when the toroidal rotation induced by the ion diamagnetic shear is canceled by the E × B flow shear. High toroidal-mode-number (high-n) KBMs are more sensitive to the Er shear than low-n KBMs. Nonlinear simulations find that both the Er shear and a self-generated zonal flow can reduce the nonlinear KBM saturation level with smaller particle and ion heat transport. Meanwhile, the zonal flow can weaken the suppressing effects of the Er shear on KBM nonlinear saturation amplitude. The radial correlation length of the turbulence is reduced by the Er shear and the zonal flow.

Gyro-average method for global gyrokinetic particle simulation in realistic tokamak geometry

Gyro-average is a crucial operation to capturing the essential finite Larmor radius (FLR) effect in gyrokinetic simulation. In order to simulate strongly shaped plasmas, an innovative multi-point average method based on non-orthogonal coordinates has been developed to improve the accuracy of the original multi-point average method in gyrokinetic particle simulation. This new gyro-average method has been implemented in the gyrokinetic toroidal code (GTC). Benchmarks have been carried out to prove the accuracy of this new method. In the limit of concircular tokamak, ion temperature gradient (ITG) instability is accurately recovered for this new method and consistency is achieved. The new gyro-average method is also used to solve the gyrokinetic Poisson equation, and its correctness is confirmed in the long-wavelength limit for realistically shaped plasmas. The improved GTC code with the new gyro-average method is used to investigate the ITG instability with EAST magnetic geometry. The simulation results show that the correction induced by this new method in the linear growth rate is more significant for short-wavelength modes where the FLR effect becomes important. Due to its simplicity and accuracy, this new gyro-average method can find broader applications in simulating shaped plasmas in realistic tokamaks.

Global gyrokinetic particle simulations of microturbulence in W7-X and LHD stellarators

Global gyrokinetic particle simulations of electrostatic ion temperature gradient (ITG) instability show that the most unstable eigenmode is localized to some magnetic fieldlines or discrete locations on the poloidal plane in the Wendelstein 7-X (W7-X) stellarator due to its mirror-like magnetic fields, which vary strongly in the toroidal direction and induce coupling of more toroidal harmonics (n) to form the linear eigenmode than in the Large Helical Device (LHD) stellarator. Nonlinear electrostatic simulation results show that self-generated zonal flows are the dominant saturation mechanism for the ITG instabilities in both the LHD and W7-X. Furthermore, radial widths of the fluctuation intensity in both the LHD and W7-X are significantly broadened from the linear phase to the nonlinear phase due to turbulence spreading. Finally, nonlinear spectra in the W7-X are dominated by low-n harmonics, which can be generated both by nonlinear toroidal coupling of high-n harmonics and by linear toroidal coupling with large amplitude zonal flows due to the 3D equilibrium magnetic fields.

Gyrokinetic particle simulation of fast-electron driven beta-induced Aflvén eigenmode

The fast-electron driven beta-induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electron is described by the drift kinetic equation. The simulation shows that the e-BAE propagates in the fast electron diamagnetic direction and its polarization is close to an ideal MHD mode. The phase space structure shows that only the fast electron processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels, including transit, bounce, and processional resonance.

Gyrokinetic particle simulation of beta-induced Alfven-acoustic eigenmode

The beta-induced Alfven-acoustic eigenmode (BAAE) in toroidal plasmas is verified and studied by global gyrokinetic particle simulations. When ion temperature is much lower than electron temperature, the existence of the weakly damped BAAE is verified in the simulations using initial perturbation, antenna excitation, and energetic particle excitation, respectively. When the ion temperature is comparable to the electron temperature, the unstable BAAE can be excited by realistic energetic particle density gradient, even though the stable BAAE (in the absence of energetic particles) is heavily damped by the thermal ions. In the simulations with reversed magnetic shear, BAAE frequency sweeping is observed and poloidal mode structure has a triangle shape with a poloidal direction similar to that observed in tokamak experiments. The triangle shape changes the poloidal direction, and no frequency sweeping is found in the simulations with normal magnetic shear.

Properties of toroidal Alfvén eigenmode in DIII-D plasma

Linear properties of the toroidal Alfvén eigenmode (TAE) excited by energetic particles (EP) in a DIII-D tokamak experiment have been studied in global gyrokinetic particle simulations treating self-consistently kinetic effects of EP, thermal ions, and electrons. Simulation results of the TAE frequency and mode structure agree very well with the experimental measurements. The non-perturbative EP contribution induces a radial localization of the TAE mode structure, a break-down of mode radial symmetry, as well as a frequency dependence on the toroidal mode number. The simulations further demonstrate the dependence of the growth rate and mode structure on EP pressure gradients. The in-out asymmetry of the mode structure and the experimental identification of the poloidal harmonics have also been clarified.

Verification of gyrokinetic particle simulation of current-driven instability in fusion plasmas. II. Resistive tearing mode

Global gyrokinetic particle simulation of resistive tearing modes has been developed and verified in the gyrokinetic toroidal code (GTC). GTC linear simulations in the fluid limit of the kink-tearing and resistive tearing modes in the cylindrical geometry agree well with the resistive magnetohydrodynamic eigenvalue and initial value codes. Ion kinetic effects are found to reduce the radial width of the tearing modes. GTC simulations of the resistive tearing modes in the toroidal geometry find that the toroidicity reduces the growth rates.

Comparison of toroidicity-induced Alfvén eigenmodes and energetic particle modes by gyrokinetic particle simulations

This work reports on linear global gyrokinetic particle simulations of the excitation of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes (EPM), and the comparison between these two modes. The TAE excitation by antenna clarifies the magnetohydrodynamic (MHD) mode structure and the discrete eigenmode exists in the gap between the upper and lower accumulation points. The TAE excitation by fast ions modifies the MHD mode structure because of radial symmetry breaking and the eigenmode frequency moves towards the lower accumulation point. The phase space structure of fast ions shows that both passing and trapped particles contribute to the TAE excitation and that trapped particles dominate the wave-particle resonance in our simulations. The growth rate of TAE is sensitive to the fast ion energy, density, and density gradient, which are also important factors contributing to the transition of the TAE to the EPM. The gyrokinetic particle simulations also confirm the excitation of EPM when the drive is stronger. The frequency of the EPM is determined by the characteristic frequencies of fast ion motion in toroidal geometry.

Verification of electromagnetic fluid-kinetic hybrid electron model in global gyrokinetic particle simulation

The fluid-kinetic hybrid electron model is verified in global gyrokinetic particle simulation of linear electromagnetic drift-Alfvenic instabilities in tokamak. In particular, we have recovered the β-stabilization of the ion temperature gradient mode, transition to collisionless trapped electron mode, and the onset of kinetic ballooning mode as βe (ratio of electron kinetic pressure to magnetic pressure) increases.

Global gyrokinetic particle simulation of toroidal Alfvén eigenmodes excited by antenna and fast ions

Linear properties of toroidal Alfvén eigenmode (TAE) is studied in global gyrokinetic particle simulations using both fast ion and antenna excitations. A synthetic antenna provides a precise measurement of the Alfvén continuum gap width and the TAE eigenmode frequency, damping rate, and mode structures. The measured gap width exhibits a linear dependence on the aspect ratio, in agreement to a local analytic theory. The TAE frequency and mode structure excited by fast ions show a significant radial symmetry breaking relative to the ideal magnetohydrodynamic theory due to the non-perturbative contributions from the fast ions. The electromagnetic capability of the global gyrokinetic toroidal code (GTC) is verified through these global gyrokinetic simulations of Alfvén eigenmode in cylindrical and toroidal geometries.

Convective motion in collisionless trapped electron mode turbulence

Global gyrokinetic particle simulation of collisionless trapped electron mode turbulence in toroidal plasmas finds both diffusive and convective electron motion using a Lagrangian analysis. The convective motion is identified using simulation and analytic theory to arise from the conservation of the second invariant when resonant trapped electrons lose kinetic energy to the drift wave. A resonance broadening model fits well the diffusive and convective electron motion.

Gyrokinetic particle simulation of beta-induced Alfvén eigenmode

The beta-induced Alfvén eigenmode (BAE) in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic (MHD) accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.

Gyrokinetic particle simulations of reversed shear Alfvén eigenmode excited by antenna and fast ions

Global gyrokinetic particle simulations of reversed shear Alfvén eigenmode (RSAE) have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially suppressed, the mode amplitude shows a near-linear growth. With kinetic thermal ions, the mode amplitude eventually saturates due to the thermal ion damping. The damping rates measured from the antenna excitation and from the initial perturbation simulation agree very well. The RSAE excited by fast ions shows an exponential growth. The finite Larmor radius effects of the fast ions are found to significantly reduce the growth rate. With kinetic thermal ions and electron pressure, the mode frequency increases due to the elevation of the Alfvén continuum by the geodesic compressibility. The nonperturbative contributions from the fast ions and kinetic thermal ions modify the mode structure relative to the ideal magnetohydrodynamic (MHD) theory. The gyrokinetic simulations have been benchmarked with extended hybrid MHD-gyrokinetic simulations.

Trapped electron damping of geodesic acoustic mode

Global gyrokinetic particle simulation finds that the collisionless damping rate of the geodesic acoustic mode (GAM) in tokamak is greatly enhanced by trapped electrons in the high-q region of tokamak (q is the safety factor). The electron damping has been identified to arise from the resonance of the GAM oscillation with the trapped electron bounce motion. The contribution of passing electrons to the GAM collisionless damping is much smaller than the trapped electrons. The residual level of the zonal flow is not sensitive to the trapped electron resonance.

Fluctuation characteristics and transport properties of collisionless trapped electron mode turbulence

The collisionless trapped electron mode turbulence is investigated by global gyrokinetic particle simulation. The zonal flow dominated by low frequency and short wavelength acts as a very important saturation mechanism. The turbulent eddies are mostly microscopic, but with a significant portion in the mesoscale. The ion heat transport is found to be diffusive and follows the local radial profile of the turbulence intensity. However, the electron heat transport demonstrates some nondiffusive features and only follows the global profile of the turbulence intensity. The nondiffusive features of the electron heat transport is further confirmed by nonlognormal statistics of the flux-surface-averaged electron heat flux. The radial and time correlation functions are calculated to obtain the radial correlation length and autocorrelation time. Characteristic time scale analysis shows that the zonal flow shearing time and eddy turnover time are very close to the effective decorrelation time, which suggests that the trapped electrons move with the fluid eddies. The fluidlike behaviors of the trapped electrons and the persistence of the mesoscale eddies contribute to the transition of the electron turbulent transport from gyro-Bohm scaling to Bohm scaling when the device size decreases.

Electromagnetic formulation of global gyrokinetic particle simulation in toroidal geometry

The fluid-kinetic hybrid electron model for global electromagnetic gyrokinetic particle simulations has been formulated in toroidal geometry using magnetic coordinates, providing the capabilities to describe low frequency processes in electromagnetic turbulence with electron dynamics. In the limit of long wavelength and no parallel electric field our equations reduce to the ideal magnetohydrodynamic equations. The formulation has been generalized to include equilibrium flows. The equations for zonal components of electrostatic and vector potentials have been derived, demonstrating the electron screening of the zonal vector potential.

Properties of microturbulence in toroidal plasmas with reversed magnetic shear

Electrostatic drift wave turbulence in tokamak plasmas with reversed magnetic shear is studied using global gyrokinetic particle simulations. The linear eigenmode of the ion temperature gradient (ITG) instability exhibits a mode gap around the minimum safety factor (qmin) region, particularly when qmin is an integer, due to the rarefaction of rational surfaces. The collisionless trapped electron mode (CTEM) instability is suppressed in the negative-shear region due to the reversal of the toroidal precessional drift of trapped electrons. However, after nonlinear saturation, the ITG gap is filled up by the turbulence spreading and the CTEM fluctuation propagates into the stable negative-shear region. The steady state turbulence occupies the whole volume without any identifiable gap or coherent structures of the heat conductivity, perturbed temperature, or zonal flows in the qmin location or the reversed shear region. Our finding indicates that the electrostatic drift wave turbulence itself does not support either linear or nonlinear mechanism for the formation of internal transport barriers in the reversed magnetic shear when qmin crossing an integer.

Turbulent Transport of Trapped-Electron Modes in Collisionless Plasmas

Global gyrokinetic particle simulations of collisionless trapped-electron mode turbulence in toroidal plasmas find that electron heat transport exhibits a device size scaling with a gradual transition from Bohm to gyro-Bohm scaling. A comprehensive analysis of spatial and temporal scales shows that the turbulence eddies are predominantly microscopic because of zonal flow shearing, but the presence of mesoscale structures drives a nondiffusive component in the electron heat flux due to the weak nonlinear detuning of the precessional resonance that excites the linear instability.

Excitation of low-n toroidicity induced Alfvén eigenmodes by energetic particles in global gyrokinetic tokamak plasmas

The first linear global electromagnetic gyrokinetic particle simulation on the excitation of toroidicity induced Alfvén eigenmode (TAE) by energetic particles is reported. It is shown that the long wavelength magnetohydrodynamic instabilities can be studied by the gyrokinetic particle simulation. With an increase in the energetic particle pressure, the TAE frequency moves down into the lower continuum together with an increase in the linear growth rate.