arXiv subjects

A. Hakim

Publications and source records attributed to A. Hakim.

15 recordsLinked to original sources

arXiv2026

High-throughput full-f gyrokinetics of the tokamak boundary

Full-f global gyrokinetic simulations of the plasma boundary have until now required heroic computational efforts and case-by-case expert intervention, precluding systematic parameter scans. Here we demonstrate a paradigm shift: hundreds of independent, concurrent, and unsupervised full-f boundary gyrokinetic simulations in a geometry inspired by the Tokamak \`a Configuration Variable (TCV), covering both the closed flux surface region and the open-field-line scrape-off layer (SOL) while scanning triangularity, elongation, and heating power. All simulations are evolved much longer than the turbulence relaxation time until the steady state is reached. Analysis of the steady-state profiles reveals that the impact of plasma shaping on confinement is strongly power dependent: at low power, triangularity primarily controls the SOL ion temperature, while at high power it mostly affects the edge ion temperature gradient. The low-power hot SOL observed for positive triangularity is explained by a neoclassical trapped-ion mechanism in which triangularity modifies the field-line arc length between banana turning points and the high-field-side limiter, altering the interaction with cold neutral-ionization regions. Fingerprint analysis of turbulent transport categorize the simulations in a regime dominated by ion temperature gradient (ITG) or trapped electron modes (TEMs), confirmed by dedicated local linear gyrokinetic calculations. The generated open data represents a previously unobtainable resource. It can serve both as a benchmark for boundary transport models, and as a training dataset for data-driven methods in fusion foundation and surrogate models.

physics.plasm-ph↗

arXiv2025

Towards fully predictive gyrokinetic full-f simulations: validation and triangularity studies in TCV

Designing economical magnetic confinement fusion power plants motivates computational tools that can estimate plasma behavior from engineering parameters without direct reliance on experimental measurement of the plasma profiles. In this work, we present full-$f$ global gyrokinetic (GK) turbulence simulations of edge and scrape-off layer turbulence in tokamaks that use only magnetic geometry, heating power, and particle inventory as inputs. Unlike many modeling approaches that employ free parameters fitted to experimental data, raising uncertainties when extrapolating to reactor scales, his approach directly simulates turbulence and resulting profiles through GK without such empirical adjustments. This is achieved via an adaptive sourcing algorithm in Gkeyll that strictly controls energy injection and emulates particle sourcing due to neutral recycling. We show that the simulated kinetic profiles compare reasonably well with Thomson scattering and Langmuir probe data for Tokamak \`{a} Configuration Variable (TCV) discharge #65125, and that the simulations reproduce characteristic features such as blob transport and self-organized electric fields. Applying the same framework to study triangularity effects suggests mechanisms contributing to the improved confinement reported for negative triangularity (NT). Simulations of TCV discharges #65125 and #65130 indicate that NT increases the $E \times B$ flow shear (by about 20% in these cases), which correlates with reduced turbulent losses and a modest change in the distribution of power exhaust to the vessel wall. While the physical models contain approximations that can be refined in future work, the predictive capability demonstrated here, evolving multiple profile relaxation times with kinetic electron and ion models in hundreds of GPU hours, indicates the feasibility of using Gkeyll to support design studies of fusion devices.

physics.plasm-ph↗

arXiv2025

Axisymmetric Gyrokinetic Simulation of ASDEX-Upgrade Scrape-off Layer Using a Conservative Implicit BGK Collision Operator

Collisions play an important role in turbulence and transport of fusion plasmas. For kinetic simulations, as the collisionality increases in the domain of interest, the size of the time step to resolve the collisional physics can become overly restrictive in an explicit time integration scheme, leading to high computational cost. With the aim of overcoming such restriction, we have implemented an implicit Bhatnagar-Gross-Krook (BGK) collision operator for use in the discontinuous Galerkin (DG) full-f gyrokinetic solver within the Gkeyll framework, which, when combined with Gkeyll's traditional explicit time integrator for collisionless advection, can significantly increase the time step in gyrokinetic simulations of highly collisional regimes. To ensure conservation of density, momentum, and energy, we utilize an iterative scheme to correct the discretized approximation to the equilibrium Maxwellian distribution to which the BGK collision operator relaxes. We have further generalized the BGK infrastructure, both the implicit scheme and the correction routine, to handle cross species collisions. This improved implicit and conservative BGK operator is benchmarked against the more accurate but more computationally expensive Lenard-Bernstein-Dougherty (LBD) operator which has been utilized in prior studies with Gkeyll. The implicit BGK operator enables 2D axisymmetric simulations of the ASDEX-Upgrade scrape-off layer to run 56 times faster to completion than the simulations with the LBD operator, because the BGK operator is more robust and converges at a lower resolution than is required by the LBD operator. Additionally, in this more collisional limit, we demonstrate that the results of our simulations utilizing the implicit BGK operator agreed well with simulations utilizing the more computationally expensive LBD operator.

physics.plasm-ph↗

arXiv2025

Direct Comparison of Gyrokinetic and Fluid Scrape-Off Layer Simulations

Typically, fluid simulations are used for tokamak divertor design. However, fluid models are only valid if the SOL is highly collisional, an assumption that is valid in many present day experiments but is questionable in the high-power scenarios envisioned for burning plasmas and fusion pilot plants. This paper reports on comparisons between fluid and kinetic simulations of the scrape off layer (SOL) for parameters and geometry representative of the Spherical Tokamak for Energy Production (STEP) fusion pilot plant. The SOLPS-ITER (fluid) and Gkeyll (gyrokinetic) codes are operated in a two-dimensional (2D) axisymmetric mode, which replaces turbulence with ad-hoc diffusivities. In kinetic simulations, we observe that the ions in the upstream SOL experience significant mirror trapping. This substantially increases the upstream temperature and has important implications for impurity dynamics. We show that the mirror force, which is excluded in SOLPS's form of fluid equations, enhances the electrostatic potential drop along the field line in the SOL. We also show that the assumption of equal main ion and impurity temperatures, which is made in commonly used fluid codes, is invalid. The combination of these effects results in superior confinement of impurities to the divertor region in kinetic simulations, consistent with our earlier predictions. This effect can be dramatic, reducing the midplane impurity density by orders of magnitude. These results indicate that in reactor-like regimes the tolerable downstream impurity densities may be higher than would be predicted by fluid simulations, allowing for higher radiated power while avoiding unacceptable core contamination. Our results highlight the importance of kinetic simulations for divertor design and optimization for fusion pilot plants.

physics.plasm-ph↗

arXiv2022

Turbulent broadening of electron heat-flux width in electromagnetic gyrokinetic simulations of a helical scrape-off layer model

We demonstrate that cross-field transport in the scrape-off layer (SOL) can be moderately increased by electromagnetic effects in high-beta regimes, resulting in a broader electron heat-flux width on the endplates. This conclusion is taken from full-$f$ electromagnetic gyrokinetic simulations of a helical SOL model that roughly approximates the SOL of the National Spherical Torus Experiment (NSTX). The simulations have been performed with the Gkeyll code, which recently became the first code to demonstrate the capability to simulate electromagnetic gyrokinetic turbulence on open magnetic field lines with sheath boundary conditions. We scan the source rate and thus $β$ so that the normalized pressure gradient (the MHD ballooning parameter $α\propto \partial β/ \partial r \propto β/ L_p$) is scanned over an experimentally-relevant range, $α= 0.3-1.5$. While there is little change in the pressure gradient scale length $L_p$ near the midplane as beta is increased, a 10% increase in cross-field transport near the midplane results in an increase in the electron heat-flux width $λ_q$ and a 25% reduction of the peak electron heat flux to the endplates.

physics.plasm-ph↗

arXiv2022

Kinetic modeling of neutral transport for a continuum gyrokinetic code

We present the first-of-its-kind coupling of a continuum full-f gyrokinetic turbulence model with a 6D continuum model for kinetic neutrals, carried out using the Gkeyll code. Our objective is to improve the first-principles understanding of the role of neutrals in plasma fueling, detachment, and their interaction with edge plasma profiles and turbulence statistics. Our model includes only atomic hydrogen and incorporates electron-impact ionization, charge exchange, and wall recycling. These features have been successfully verified with analytical predictions and benchmarked with the DEGAS2 Monte Carlo neutral code. We carry out simulations for a scrape-off layer (SOL) with simplified geometry and NSTX parameters. We compare these results to a baseline simulation without neutrals and find that neutral interactions reduce the normalized density fluctuation levels and associated skewness and kurtosis, while increasing auto-correlation times. A flatter density profile is also observed, similar to the SOL density shoulder formation in experimental scenarios with high fueling.

physics.plasm-ph↗

arXiv2021

Reduction of transport due to magnetic shear in gyrokinetic simulations of the scrape-off layer

The effect of varying magnetic shear on scrape-off layer turbulence and profiles is studied via electromagnetic gyrokinetic simulations of a helical scrape-off layer model. We develop a model helical geometry with magnetic shear and a corresponding field-aligned coordinate system, which is used for simulations with the Gkeyll code. We find that perpendicular transport is reduced in cases with stronger shear, resulting in higher peak particle and heat fluxes to the endplates. Electromagnetic effects slightly increase transport in strong shear cases.

physics.plasm-ph↗

arXiv2020

Noise-Induced Magnetic Field Saturation in Kinetic Simulations

Monte Carlo methods are often employed to numerically integrate kinetic equations, such as the particle-in-cell method for the plasma kinetic equation, but these methods suffer from the introduction of counting noise to the solution. We report on a cautionary tale of counting noise modifying the nonlinear saturation of kinetic instabilities driven by unstable beams of plasma. We find a saturated magnetic field in under-resolved particle-in-cell simulations due to the sampling error in the current density. The noise-induced magnetic field is anomalous, as the magnetic field damps away in continuum kinetic and increased particle count particle-in-cell simulations. This modification of the saturated state has implications for a broad array of astrophysical phenomena beyond the simple plasma system considered here, and it stresses the care that must be taken when using particle methods for kinetic equations.

physics.plasm-ph↗

arXiv2020

Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods

We present an energy-conserving discontinuous Galerkin scheme for the full-$f$ electromagnetic gyrokinetic system in the long-wavelength limit. We use the symplectic formulation and solve directly for $\partial A_\parallel/\partial t$, the inductive component of the parallel electric field, using a generalized Ohm's law derived directly from the gyrokinetic equation. Linear benchmarks are performed to verify the implementation and show that the scheme avoids the Ampère cancellation problem. We perform a nonlinear electromagnetic simulation in a helical open-field-line system as a rough model of the tokamak scrape-off layer using parameters from the National Spherical Torus Experiment (NSTX). This is the first published nonlinear electromagnetic gyrokinetic simulation on open field lines. Comparisons are made to a corresponding electrostatic simulation.

physics.plasm-ph↗

arXiv2019

Discontinuous Galerkin schemes for a class of Hamiltonian evolution equations with applications to plasma fluid and kinetic problems

In this paper we present energy-conserving, mixed discontinuous Galerkin (DG) and continuous Galerkin (CG) schemes for the solution of a broad class of physical systems described by Hamiltonian evolution equations. These systems often arise in fluid mechanics (incompressible Euler equations) and plasma physics (Vlasov--Poisson equations and gyrokinetic equations), for example. The dynamics is described by a distribution function that evolves given a Hamiltonian and a corresponding Poisson bracket operator, with the Hamiltonian itself computed from field equations. Hamiltonian systems have several conserved quantities, including the quadratic invariants of total energy and the $L_2$ norm of the distribution function. For accurate simulations one must ensure that these quadratic invariants are conserved by the discrete scheme. We show that using a discontinuous Galerkin scheme to evolve the distribution function and ensuring that the Hamiltonian lies in its continuous subspace leads to an energy-conserving scheme in the continuous-time limit. Further, the $L_2$ norm is conserved if central fluxes are used to update the distribution function, but decays monotonically when using upwind fluxes. The conservation of density and $L_2$ norm is then used to show that the entropy is a non-decreasing function of time. The proofs shown here apply to any Hamiltonian system, including ones in which the Poisson bracket operator is non-canonical (for example, the gyrokinetic equations). We demonstrate the ability of the scheme to solve the Vlasov--Poisson and incompressible Euler equations in 2D and provide references where we have applied these schemes to solve the much more complex 5D electrostatic and electromagnetic gyrokinetic equations.

physics.comp-ph↗

arXiv2019

Drift instabilities in thin current sheets using a two-fluid model with pressure tensor effects

The integration of kinetic effects in fluid models is important for global simulations of the Earth's magnetosphere. We use a two-fluid ten moment model, which includes the pressure tensor and has been used to study reconnection, to study the drift kink and lower hybrid drift instabilities. Using a nonlocal linear eigenmode analysis, we find that for the kink mode, the ten moment model shows good agreement with kinetic calculations with the same closure model used in reconnection simulations, while the electromagnetic and electrostatic lower hybrid instabilities require modeling the effects of the ion resonance using a Landau fluid closure. Comparisons with kinetic simulations and the implications of the results for global magnetospheric simulations are discussed.

physics.space-ph↗

arXiv2019

Temperature-dependent Saturation of Weibel-type Instabilities in Counter-streaming Plasmas

We present the first 2X2V continuum Vlasov-Maxwell simulations of interpenetrating, unmagnetized plasmas to study the competition between two-stream, Oblique, and filamentation modes in the weakly relativistic regime. We find that after nonlinear saturation of the fastest-growing two-stream and Oblique modes, the effective temperature anisotropy, which drives current filament formation via the secular Weibel instability, has a strong dependence on the internal temperature of the counter-streaming plasmas. The effective temperature anisotropy is significantly more reduced in colder than in hotter plasmas, leading to orders of magnitude lower magnetization for colder plasmas. A strong dependence of the energy conversion efficiency of Weibel-type instabilities on internal beam temperature has implications for determining their contribution to the observed magnetization of many astrophysical and laboratory plasmas.

astro-ph.HE↗

arXiv2017

Discontinuous Galerkin algorithms for fully kinetic plasmas

We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge-Kutta method. Since the Vlasov equation in the Vlasov-Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.

physics.plasm-ph↗

arXiv2017

Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma

3D2V continuum gyrokinetic simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using the full-$f$ discontinuous-Galerkin code Gkeyll. These simulations include the basic elements of a fusion-device scrape-off layer: localized sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath model boundary conditions. The set of sheath boundary conditions used in the model allows currents to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device (LAPD), a linear device featuring straight magnetic field lines, are presented.

physics.plasm-ph↗

arXiv2016

Scrape-Off Layer Turbulence in Tokamaks Simulated with a Continuum Gyrokinetic Code

We are developing a new continuum gyrokinetic code, Gkeyll, for use in edge plasma simulations, and here present initial simulations of turbulence on open field lines with model sheath boundary conditions. The code implements an energy conserving discontinuous Galerkin scheme, applicable to a general class of Hamiltonian equations. Several applications to test problems have been done, including a calculation of the parallel heat-flux on divertor plates resulting from an ELM crash in JET, for a 1x/1v SOL scenario explored previously, where the ELM is modeled as a time-dependent intense upstream source. Here we present initial simulations of turbulence on open field lines in the LAPD linear plasma device. We have also done simulations in a helical open-field-line geometry. While various simplifications have been made at present, this still includes some of the key physics of SOL turbulence, such as bad-curvature drive for instabilities and rapid parallel losses with sheath boundary conditions. This is useful for demonstrating the overall feasibility of this approach and for initial physics studies of SOL turbulence. We developed a novel version of DG that uses Maxwellian-weighted basis functions while still preserving exact particle and energy conservation. The Maxwellian-weighted DG method achieves the same error with 4 times less computational cost in 1v, or 16 times lower cost in the 2 velocity dimensions of gyrokinetics (assuming memory bandwidth is the limiting factor).

physics.plasm-ph↗