arXiv subjects

Z. X. Lu

Publications and source records attributed to Z. X. Lu.

10 recordsLinked to original sources

arXiv2025

Comparison of MHD and gyrokinetic simulations of linear instabilities at the q = 1 surface

Accurate modeling of core instabilities in tokamak plasmas is essential to understand the underlying physical mechanisms and their impact on plasma confinement. The ideal stability of the internal kink mode and the m = 1 collisionless tearing mode are analyzed numerically both with gyrokinetic and MHD codes. We compare the different models implemented in the codes and show that the gyrokinetic equations without collisions inherently contain the ideal MHD limit. The simulation results show that the stability of the internal kink mode strongly depends on the choice of several setup parameters like the inclusion of parallel magnetic field fluctuations, the tokamak aspect ratio, the drift- or gyrokinetic treatment of the ions and the electron mass. Furthermore, we demonstrate the stabilization of the instabilities by diamagnetic effects. Our results indicate that gyrokinetic and MHD models can be reconciled in the description of the internal kink mode by careful consideration of the simulation setup and model assumptions, but instabilities like the collisionless tearing mode require a more advanced treatment beyond MHD.

physics.plasm-ph↗

arXiv2021

The development of an implicit full f method for electromagnetic particle simulations of Alfvén waves and energetic particle physics

In this work, an implicit scheme for particle-in-cell/Fourier electromagnetic simulations is developed and applied to studies of Alfvén waves in one dimension and three-dimensional tokamak plasmas. An analytical treatment is introduced to achieve efficient convergence of the iterative solution of the implicit field-particle system. First, its application to the one-dimensional uniform plasma demonstrates its applicability in a broad range of $β/m_e$ values. Second, toroidicity induced Alfvén eigenmodes (TAE) are simulated in a three-dimensional axisymmetric tokamak plasma, using the widely studied case defined by the International Tokamak Physics Activity (ITPA) Energetic Particle (EP) Topical Group. The real frequency and the growth (or damping) rate of the TAE with (or without) EPs agree with previous results reasonably well. The full f electromagnetic particle scheme established in this work provides a possible natural choice for EP transport studies where large profile variation and arbitrary particle distribution functions need to be treated in kinetic simulations.

physics.plasm-ph↗

arXiv2020

Global linear and nonlinear gyrokinetic modelling of Alfvén eigenmodes in ITER

Linear and nonlinear modelling of Alfvénic instabilities, most notably toroidal Alfvén eigenmodes (TAEs), obtained by using the global nonlinear electromagnetic gyrokinetic model of the code ORB5 are presented for the 15 MA scenario of the ITER tokamak. Linear simulations show that elliptic Alfvén eigenmodes and odd-parity TAEs are only weakly damped but not excited by alpha particles, whose drive favours even-parity TAEs. Low mode number TAEs are found to be global, requiring global treatment. Nonlinearly, even with double the nominal EP density, single mode simulations lead to saturation with negligible EP transport however multi-mode simulations predict that with double the nominal EP density, enhanced saturation and significant EP redistribution will occur.

physics.plasm-ph↗

arXiv2020

Development and testing of an unstructured mesh method for whole plasma gyrokinetic simulations in realistic tokamak geometry

In this work, we have formulated and implemented a mixed unstructured mesh-based finite element (FE)-Fourier decomposition scheme for gyrokinetic simulations in realistic tokamak geometry. An efficient particle positioning (particle-triangle mapping) scheme for the charge deposition and field scattering using an intermediate grid as the search index for triangles has been implemented and a significant speed-up by a factor of $\sim30$ is observed as compared with the brute force scheme for a medium-size simulation. The TRIMEG (TRIangular MEsh based Gyrokinetic) code has been developed. As an application, the ion temperature gradient (ITG) mode is simulated using the simplified gyrokinetic Vlasov-Poisson model. Our simulation and that using the ORB5 code for the DIII-D Cyclone case show reasonable agreement. As an additional application, ITG simulations using an ASDEX Upgrade equilibrium have been performed with density and temperature gradient profiles similar to the Cyclone case. Capabilities of the TRIMEG code for simulations with realistic experimental equilibria in the plasma core and in the whole plasma volume with open field lines are demonstrated.

physics.plasm-ph↗

arXiv2019

ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes.

physics.plasm-ph↗

arXiv2018

Global gyrokinetic simulations of intrinsic rotation in ASDEX Upgrade Ohmic L-mode plasmas

Non-linear, radially global, turbulence simulations of ASDEX Upgrade (AUG) plasmas are performed and the nonlinear generated intrinsic flow shows agreement with the intrinsic flow gradients measured in the core of Ohmic L-mode plasmas at nominal parameters. Simulations utilising the kinetic electron model show hollow intrinsic flow profiles as seen in a predominant number of experiments performed at similar plasma parameters. In addition, significantly larger flow gradients are seen than in a previous flux-tube analysis (Hornsby et al {\it Nucl. Fusion} (2017)). Adiabatic electron model simulations can show a flow profile with opposing sign in the gradient with respect to a kinetic electron simulation, implying a reversal in the sign of the residual stress due to kinetic electrons. The shaping of the intrinsic flow is strongly determined by the density gradient profile. The sensitivity of the residual stress to variations in density profile curvature is calculated and seen to be significantly stronger than to neoclassical flows (Hornsby et al {\it Nucl. Fusion} (2017)). This variation is strong enough on its own to explain the large variations in the intrinsic flow gradients seen in some AUG experiments. Analysis of the symmetry breaking properties of the turbulence shows that profile shearing is the dominant mechanism in producing a finite parallel wave-number, with turbulence gradient effects contributing a smaller portion of the parallel wave-vector.

physics.plasm-ph↗

arXiv2017

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from drift kinetic equation is used to time advance electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, shear Alfvén wave dispersion relation in shearless slab and continuum damping in sheared cylinder have been recovered. The new scheme overcomes the stringent requirement in conventional perturbative simulation method that perpendicular grid size needs to be as small as electron collisionless skin depth even for the long wavelength Alfvén waves. The new scheme also avoids the problem in conventional method that an unphysically large parallel electric field arises due to the inconsistency between electrostatic potential calculated from the perturbed density and vector potential calculated from the perturbed canonical flow. Finally, the gyrokinetic particle simulations of the Alfvén waves in sheared cylinder have superior numerical properties compared with the fluid simulations, which suffer from numerical difficulties associated with singular mode structures.

physics.plasm-ph↗

arXiv2017

Comparisons and Applications of Four Independent Numerical Approaches for Linear Gyrokinetic Drift Modes

To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on integral equation, Euler initial value simulation, Euler matrix eigenvalue solution and Lagrangian particle simulation, respectively, are used to solve the linear gyrokinetic electrostatic drift modes equation in Z-pinch with slab simplification and in tokamak with ballooning space coordinate. We identify that these approaches can yield the same solution with the difference smaller than 1\%, and the discrepancies mainly come from the numerical convergence, which is the first detailed benchmark of four independent numerical approaches for gyrokinetic linear drift modes. Using these approaches, we find that the entropy mode and interchange mode are on the same branch in Z-pinch, and the entropy mode can have both electron and ion branches. And, at strong gradient, more than one eigenstate of the ion temperature gradient mode (ITG) can be unstable and the most unstable one can be on non-ground eigenstates. The propagation of ITGs from ion to electron diamagnetic direction at strong gradient is also observed, which implies that the propagation direction is not a decisive criterion for the experimental diagnosis of turbulent mode at the edge plasmas.

physics.plasm-ph↗

arXiv2014

Particle simulation of lower hybrid waves in tokamak plasmas

Global particle simulations of the lower hybrid waves have been carried out using fully kinetic ions and drift kinetic electrons with a realistic electron-to-ion mass ratio. The lower hybrid wave frequency, mode structure, and electron Landau damping from the electrostatic simulations agree very well with the analytic theory. Linear simulation of the propagation of a lower hybrid wave-packet in the toroidal geometry shows that the wave propagates faster in the high field side than the low field side, in agreement with a ray tracing calculation. Electromagnetic benchmarks of lower hybrid wave dispersion relation are also carried out. Electromagnetic mode conversion are observed in toroidal geometry, slow waves are launched at the plasma boundary and converts to fast waves at the mode conversion layer, which is consistent with linear theory.

physics.plasm-ph↗

arXiv2011

Theoretical and numerical studies of wave-packet propagation in tokamak plasmas

Theoretical and numerical studies of wave-packet propagation are presented to analyze the time varying 2D mode structures of electrostatic fluctuations in tokamak plasmas, using general flux coordinates. Instead of solving the 2D wave equations directly, the solution of the initial value problem is used to obtain the 2D mode structure, following the propagation of wave-packets generated by a source and reconstructing the time varying field. As application, the 2D WKB method is applied to investigate the shaping effects (elongation and triangularity) of tokamak geometry on the lower hybrid wave propagation and absorbtion. Meanwhile, the Mode Structure Decomposition (MSD) method is used to handle the boundary conditions and simplify the 2D problem to two nested 1D problems. The MSD method is related to that discussed earlier by Zonca and Chen [Phys. Fluids B 5, 3668 (1993)], and reduces to the well-known "ballooning formalism" [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40, 396 (1978)], when spatial scale separation applies. This method is used to investigate the time varying 2D electrostatic ITG mode structure with a mixed WKB-full-wave technique. The time varying field pattern is reconstructed and the time asymptotic structure of the wave-packet propagation gives the 2D eigenmode and the corresponding eigenvalue. As a general approach to investigate 2D mode structures in tokamak plasmas, our method also applies for electromagnetic waves with general source/sink terms, either by an internal/external antenna or nonlinear wave interaction with zonal structures.

physics.plasm-ph↗