Gyrokinetic Particle Simulation Research Articles

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.

Unlike-particle collision operator for gyrokinetic particle simulations

Plasmas in modern tokamak experiments contain a significant fraction of impurity ion species in addition to main deuterium background. A new unlike-particle collision operator for δf particle simulation has been developed to self-consistently study the non-local effects of impurities on neoclassical transport in toroidal plasmas. A new algorithm for simulation of cross-collisions between different ion species includes test-particle and conserving field-particle operators. The field-particle operator is designed to enforce conservation of number, momentum and energy. It was shown that the new operator correctly simulates the thermal equilibration of different plasma components. It was verified that the ambipolar radial electric field reaches steady state when the total radial guiding center particle current vanishes.

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.

Gyrokinetic δf particle simulations of toroidicity-induced Alfvén eigenmode

Gyrokinetic δf particle simulation is used to investigate toroidicity-induced Alfvén 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 Alfvén waves is well resolved and the damping rate is compared to and found to agree well with analytical theory.

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.

Full-f gyrokinetic particle simulation of centrally heated global ITG turbulence from magnetic axis to edge pedestal top in a realistic tokamak geometry

Global electrostatic ITG turbulence physics, together with background dynamics, has been simulated in a realistic tokamak core geometry using XGC1, a full-function 5D gyrokinetic particle code. An adiabatic electron model has been used. Some verification exercises of XGC1 have been presented. The simulation volume extends from the magnetic axis to the pedestal top inside the magnetic separatrix. Central heating is applied, and a number, momentum and energy conserving linearized Monte Carlo Coulomb collision is used. In the turbulent region, the ion temperature gradient profile self-organizes globally around R/LT = (Rd logT/dr = major radius on the magnetic axis/temperature gradient length) ≃6.5–7, which is somewhat above the conventional nonlinear criticality of ≃6. The self-organized ion temperature gradient profile is approximately stiff against variation of heat source magnitude. Results indicate that the relaxation to a self-organized state proceeds in two phases, namely, a transient phase of excessively bursty transport followed by a 1/f avalanching phase. The bursty types of behaviour are allowed by the quasi-periodic collapse of local E × B shearing barriers.

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.

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 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.

Compressed ion temperature gradient turbulence in diverted tokamak edge

It is found from a heat-flux-driven full-f gyrokinetic particle simulation that there is ion temperature gradient (ITG) turbulence across an entire L-mode-like edge density pedestal in a diverted tokamak plasma in which the ion temperature gradient is mild without a pedestal structure, hence the normalized ion temperature gradient parameter ηi=(d log Ti/dr)/(d log n/dr) varies strongly from high (>4 at density pedestal top/shoulder) to low (<2 in the density slope) values. Variation of density and ηi is in the same scale as the turbulence correlation length, compressing the turbulence in the density slope region. The resulting ion thermal flux is on the order of experimentally inferred values. The present study strongly suggests that a localized estimate of the ITG-driven χi will not be valid due to the nonlocal dynamics of the compressed turbulence in an L-mode-type density slope. While the thermal transport and the temperature profile saturate quickly, the E×B rotation shows a longer time damping during the turbulence. In addition, a radially in-out mean potential variation is observed.

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.

Gyrokinetic particle simulations of toroidal momentum transport

Simulations of toroidal angular momentum transport have been carried out using global toroidal gyrokinetic particle-in-cell code. The significant redistribution of toroidal momentum is observed, driven by the ion temperature gradient turbulence with adiabatic electrons, resulting in a peaked momentum profile in the central region of the radial domain. Cases with rigid and sheared plasma rotation are considered. Diffusive and off-diagonal (pinchlike) fluxes are identified. Toroidal momentum diffusivity is calculated by subtracting pinch contribution from the total momentum flux, and compared to quasilinear estimates. It is found that the ratio of momentum to heat conductivity is smaller than unity even after subtracting pinch contribution when wave-particle resonance energy is larger than thermal energy.

An Integrated Exploration Approach to Visualizing Multivariate Particle Data

The authors describe a data exploration system that visualizes time-varying, multivariate, point-based data from gyrokinetic particle simulations. By using two interaction modes, their system lets researchers explore collections of densely packed particles and discover interesting aspects, such as the location and motion of particles trapped in turbulent plasma flow.

Nonlinear saturation of mirror instability

Mechanism of the nonlinear saturation of compressible electromagnetic mirror instability is studied using the gyrokinetic particle simulation. Phase‐space particle trapping due to the mirror force is found to be the dominant saturation mechanism in the simulation of a single mirror mode with relatively weak drive. At the nonlinear saturation, the phase‐space island of the distribution function is formed. The oscillation frequency of the saturated perturbation amplitude is close to the bounce frequency of the trapped particles, which is comparable to the linear growth rate of the mirror mode. Scaling of the saturation amplitude is consistent with the onset of the particle trapping. With strong instability drive, relaxation toward marginal stability dominates the nonlinear saturation of the mirror instability. Phase‐space trapping, however, persists after the saturation and continues to regulate the nonlinear evolution of the mirror mode.

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.

Large-scale gyrokinetic particle simulation of microturbulence in magnetically confined fusion plasmas

As the global energy economy makes the transition from fossil fuels toward cleaner alternatives, nuclear fusion becomes an attractive potential solution for satisfying growing needs. Fusion, the power source of the stars, has been the focus of active research since the early, 1950s. While progress has been impressive--especially for magnetically confined plasma devices called tokamaks--the design of a practical power plant remains an outstanding challenge. A key topic of current interest is microturbulence, which is believed to be responsible for the unacceptably large leakage of energy and particles out of the hot plasma core. Understanding and controlling this process is of utmost importance for operating current devices and designing future ones. In addressing such issues, the Gyrokinetic Toroidal Code (GTC) was developed to study the global influence of microturbulence on particle and energy confinement. It has been optimized on the IBM Blue Gene/L™ (BG/L) computer, achieving essentially linear scaling on more than 30,000 processors. A full simulation of unprecedented phase-space resolution was carried out with 32,768 processors on the BG/L supercomputer located at the IBM T. J. Watson Research Center, providing new insights on the influence of collisions on microturbulence.

Global gyrokinetic particle simulations with kinetic electrons

A toroidal, nonlinear, electrostatic fluid-kinetic hybrid electron model is formulated for global gyrokinetic particle simulations of driftwave turbulence in fusion plasmas. Numerical properties are improved by an expansion of the electron response using a smallness parameter of the ratio of driftwave frequency to electron transit frequency. Linear simulations accurately recover the real frequency and growth rate of toroidal ion temperature gradient (ITG) instability. Trapped electrons increase the ITG growth rate by mostly not responding to the ITG modes. Nonlinear simulations of ITG turbulence find that the electron thermal and particle transport are much smaller than the ion thermal transport and that small scale zonal flows are generated through nonlinear interactions of the trapped electrons with the turbulence.

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.

Visual interrogation of gyrokinetic particle simulations

Gyrokinetic particle simulations are critical to the study of anomalous energy transport associated with plasma microturbulence in magnetic confinement fusion experiments. The simulations are conducted on massively parallel computers and produce large quantities of particles, variables, and time steps, thus presenting a formidable challenge to data analysis tasks. We present two new visualization techniques for scientists to improve their understanding of the time-varying, multivariate particle data. One technique allows scientists to examine correlations in multivariate particle data with tightly coupled views of the data in both physical space and variable space, and to visually identify and track features of interest. The second technique, built into SCIRun, allows scientists to perform range-based queries over a series of time slices and visualize the resulting particles using glyphs. The ability to navigate the multiple dimensions of the particle data, as well as query individual or a collection of particles, enables scientists to not only validate their simulations but also discover new phenomena in their data.