Plasma Simulations Become Dramatically Faster with New Field-Aligned Modelling Technique

Researchers are continually striving to improve the accuracy and efficiency of simulating tokamak plasmas, crucial for advancing fusion energy development. Zhixin Lu, Guo Meng (Max Planck Institute for Plasma Physics), and Eric Sonnendruecker, alongside Hatzky et al., present a novel high-order piecewise field-aligned triangular finite element method for electromagnetic gyrokinetic particle simulations of plasmas featuring open field lines. This innovative approach utilises unstructured triangular meshes and locally field-aligned basis functions to substantially reduce computational cost while avoiding the limitations of conventional coordinate systems, particularly around the plasma separatrix. By accurately capturing key features of electromagnetic instabilities, including ion-temperature-gradient and kinetic ballooning modes, this method, implemented in the TRIMEG-C1 code, offers a robust framework for performing whole-volume electromagnetic gyrokinetic simulations in realistic and complex tokamak geometries.

Modelling turbulent plasmas with open field lines using high-order finite elements requires careful consideration of boundary conditions

Scientists have developed a new computational method for simulating the turbulent behaviour of plasmas within tokamak fusion reactors, a crucial step towards realising sustainable fusion energy. This work addresses a longstanding challenge in modelling plasmas with “open field lines”, a complex geometrical feature present in tokamak devices that previously hindered accurate, whole-volume simulations.
The innovative approach combines locally field-aligned finite element basis functions with unstructured triangular meshes, substantially reducing computational demands while maintaining precision. By accurately modelling these plasmas, researchers move closer to predicting and controlling the conditions necessary for efficient fusion reactions.

The research centres on a high-order piecewise field-aligned triangular finite element method implemented within the TRIMEG-C1 code. This method uniquely combines local field alignment of the computational basis with unstructured meshes in cylindrical coordinates, enabling simulations across the entire plasma volume with significantly reduced computational cost.
Avoiding the grid distortion inherent in globally field-aligned coordinate systems, the technique circumvents a common issue near the separatrix of diverted plasmas, a critical region for exhaust handling. The formulation is compatible with both δf and full-f models, offering flexibility in simulating different plasma regimes.

A key achievement of this work is the successful simulation of plasmas featuring “open field lines”, a particularly difficult aspect of tokamak geometry to model accurately in whole-volume simulations. The method employs mixed-variable representations and a generalized pullback scheme to effectively manage numerical cancellation in electromagnetic simulations, enhancing stability and reliability.

Demonstrations using linear and nonlinear electromagnetic simulations of the TCV-X21 configuration confirm the method’s ability to accurately capture key features of electromagnetic ion-temperature-gradient and kinetic ballooning mode physics. The results demonstrate accurate capture of crucial plasma behaviours, including those in the separatrix regions of the simulation domain.

This robust framework for whole-volume electromagnetic gyrokinetic simulations in realistic tokamak geometries represents a significant advancement in fusion energy research. By accurately modelling the complex interplay of electromagnetic forces and particle behaviour, this method provides a powerful tool for optimising reactor designs and predicting plasma performance. The ability to simulate these conditions with greater efficiency and accuracy accelerates the development of viable fusion power plants.

Implementation of a field-aligned triangular finite element method for tokamak plasma simulations is presented

A high-order piecewise field-aligned triangular finite element method forms the basis of a new approach to global electromagnetic gyrokinetic particle-in-cell simulations of tokamak plasmas. This method combines locally field-aligned finite element basis functions with unstructured C1 triangular meshes constructed in cylindrical coordinates, facilitating whole-volume simulations with reduced computational demands.

The technique avoids grid distortion inherent in globally field-aligned coordinate systems and circumvents the singularity typically found at the separatrix of diverted plasmas. Researchers implemented the formulation within the TRIMEG-C1 code, enabling simulations compatible with both δf and full-f models.

A mixed-variable representation, alongside a generalized pullback scheme, was employed to effectively control numerical cancellation within the electromagnetic simulations. This careful formulation ensures the stability and accuracy of the calculations, particularly when dealing with complex electromagnetic fields.

The study demonstrated the method’s capabilities using linear and nonlinear electromagnetic simulations of the TCV-X21 configuration. Crucially, the method successfully simulates plasmas with “open field lines”, a particularly challenging aspect of tokamak geometry previously difficult to model accurately in whole-volume simulations.

Results indicate accurate capture of key features of electromagnetic ion-temperature-gradient and kinetic ballooning mode physics, including detailed representation of the separatrix regions. This demonstrates a robust framework for whole-volume electromagnetic gyrokinetic simulations in realistic tokamak geometries, offering a significant improvement in simulation capability.

The use of unstructured triangular meshes provides geometric flexibility, allowing for accurate representation of the complex magnetic field topology within a tokamak. High-order basis functions further enhance numerical accuracy, reducing the computational cost associated with resolving the fine-scale features of plasma turbulence. By aligning basis functions locally with magnetic field lines within each toroidal subdomain, the method preserves continuity along field lines and minimizes errors related to parallel dynamics.

Field-aligned triangular finite elements enable robust global gyrokinetic simulations of tokamak plasmas with high accuracy and efficiency

Researchers have developed a high-order piecewise field-aligned triangular finite element method for global electromagnetic gyrokinetic particle-in-cell simulations of plasmas, successfully modelling plasmas with open field lines. This new approach utilizes locally field-aligned finite element basis functions with unstructured triangular meshes in cylindrical coordinates, substantially reducing computational effort in whole-volume simulations.

The method avoids grid distortion associated with globally field-aligned coordinates and the singularity present at the separatrix of diverted plasmas, providing a robust framework for realistic tokamak geometries. The work demonstrates accurate capture of key features of electromagnetic ion-temperature-gradient and kinetic ballooning mode physics, including the separatrix regions within the simulation domain.

This is achieved through a formulation compatible with both δf and full-f models, employing mixed-variable representations and a generalized pullback scheme to control numerical cancellation in electromagnetic simulations. The method was implemented within the TRIMEG-C1 code and validated using linear and nonlinear electromagnetic simulations of the TCV-X21 configuration.

Notably, the method successfully simulates plasmas with “open field lines”, a particularly challenging aspect of tokamak geometry previously difficult to model accurately in whole-volume simulations. This represents a significant improvement in simulation capability and opens avenues for more detailed investigations of plasma behaviour in these regions.

The use of high-order C1 finite elements on triangular meshes in the poloidal cross section further enhances the accuracy and efficiency of the simulations. The research incorporates generalized pullback schemes and an efficient iterative treatment of Ampère’s law, contributing to the robustness of the method.

By employing a piecewise field-aligned approach, the simulations utilize an identical mesh structure at different toroidal locations, differing from previous implementations. This advancement facilitates the study of microinstabilities and turbulence in magnetically confined fusion plasmas, including ion-temperature-gradient modes and kinetic ballooning modes, particularly at finite plasma pressure.

High order field aligned simulations of open field line tokamak plasmas are computationally challenging

Researchers have developed a new computational method for simulating the behaviour of plasmas within tokamak fusion reactors, achieving a significant advancement in modelling capability. This technique employs a high-order piecewise field-aligned triangular finite element method, enabling more efficient and accurate whole-volume simulations of plasmas with complex electromagnetic fields.

The approach successfully simulates plasmas featuring “open field lines”, a notoriously difficult aspect of tokamak geometry to model accurately, representing a substantial improvement over existing methods. The new method combines locally field-aligned finite element basis functions with unstructured triangular meshes in cylindrical coordinates, reducing computational demands while avoiding distortions associated with traditional coordinate systems.

By utilising mixed-variable representations and a generalized pullback scheme, the simulation effectively manages numerical cancellation in electromagnetic calculations, enhancing the robustness of the model. Validated through linear and nonlinear electromagnetic simulations of the TCV-X21 configuration, the method accurately captures key features of ion-temperature-gradient and kinetic ballooning mode physics, including behaviour in the separatrix regions.

The authors acknowledge that the approximation used in calculating the perturbed magnetic field introduces a slight deviation from exact zero divergence, which could be refined in future work. Further research will focus on extending the method to more complex plasma scenarios and incorporating additional physical effects. Nevertheless, this advancement provides a robust framework for whole-volume electromagnetic gyrokinetic simulations in realistic geometries, accelerating progress towards viable nuclear fusion energy by enabling more accurate and efficient modelling of tokamak plasmas.