arXiv subjects

Ammar Hakim

Publications and source records attributed to Ammar Hakim.

At least 19 recordsLinked to original sources

arXiv2026

Gyrokinetic equilibria of high temperature superconducting magnetic mirrors

High-temperature superconducting (HTS) magnets and other advances have led to renewed interest in magnetic mirrors for fusion energy. The non-Maxwellian nature of mirror plasmas necessitates kinetic modeling to predict, optimize and design mirrors. Explicit gyrokinetic full-f codes can be used to study instabilities and turbulent transport in tokamaks and mirrors, but they have been prohibitively expensive to integrate directly over the very long time scales required to compute kinetic plasma equilibrium. We demonstrate that these studies are now feasible thanks to novel multiscale methods delivering a 30,000X speed-up. The resulting kinetic equilibrium, electrostatic potential, and ion confinement time are consistent with analytic theory. This transformative capability opens the door to a new way of obtaining equilibria for mirrors, and we discuss how this technique may also accelerate calculations for tokamaks and stellarators. The models presented in this article address critical multiscale problems in modeling magnetic mirrors, opening a new research avenue for equilibrium studies using an explicit continuum gyrokinetic code.

physics.plasm-ph↗

arXiv2026

A Conservative Discontinuous Galerkin Algorithm for Particle Kinetics on Smooth Manifolds

A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using using both canonical and non-canonical Hamiltonian formulations. Our schemes apply to either formulations, but the canonical formulation results in a particularly efficient scheme that also conserves particle density and energy exactly. The collisionless update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for relaxation to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation of the manifold is incorporated by modifying the Hamiltonian while ensuring a canonical formulation. Several test problems, including a kinetic version of the classical Sod-shock problem, Kelvin-Helmholtz instability on the surfaces of a sphere and a paraboloid, with and without rotations, is presented. A prospectus for further development of this approach to simulation of kinetic theory in general relativity is presented.

physics.comp-ph↗

arXiv2026

From Weibel seeds to collisionless dynamos beyond pair-plasmas

Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetized electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of 100 for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll, which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropization and effectively sets the magnetic Reynolds number. We investigate how the strength of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a regime exhibiting dynamo behavior qualitatively similar to magnetohydrodynamics.

physics.plasm-ph↗

arXiv2026

Modeling of Relativistic Plasmas with a Conservative Discontinuous Galerkin Method

We present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic equation on a high-dimensional phase-space grid using a discontinuous Galerkin finite element approach, yielding a high-order, conservative numerical scheme that is free from the Poisson noise inherent to traditional Monte-Carlo methods. A novel and flexible velocity-space mapping technique enables the efficient treatment of the wide range of energy scales characteristic of relativistic plasmas, including QED pair-production discharges, instabilities in strongly magnetized plasmas surrounding neutron stars, and relativistic magnetic reconnection. Our noise-free approach is capable of providing unique insight into plasma dynamics, enabling detailed analysis of electromagnetic emission and fine-scale phase-space structure.

astro-ph.HE↗

arXiv2026

Capturing Secondary Kinetic Instabilities in Three-Dimensional Dayside Reconnection Using an Improved Gradient-Based Closure

Magnetic reconnection is a highly dynamic process that excites a wide variety of kinetic waves and instabilities. Transverse current sheet instabilities such as the lower-hybrid drift and secondary drift-kink instabilities in particular have been shown by kinetic simulations to modify the reconnection and introduce significant turbulence and mixing to the reconnection layer. Past studies using the ten-moment fluid model to capture important kinetic physics such as the electron inertia and full representation of the pressure tensor proved advantageous to a two-fluid representation of reconnection, but the model struggled when using a local relaxation closure for the heat flux to replicate the current sheet instabilities and subsequent mixing seen in kinetic simulations. This work uses the \texttt{Gkeyll} software framework to perform simulations of asymmetric reconnection based on the 16 October 2015 MMS crossing of a diffusion region, the Burch event. An improved gradient-based heat flux closure is implemented, showing significant improvement in secondary kinetic instabilities that grow in the current sheet. These instabilities generate turbulence which leads to growth of secondary magnetic islands and flux ropes.

physics.plasm-ph↗

arXiv2026

BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for Partial Differential Equations

The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in which one often wishes to solve PDEs in regimes far beyond anything which can be experimentally or analytically validated. In this paper, we show how it is possible to circumvent these limitations by constructing formally-verified neural network solvers for PDEs, with rigorous convergence, stability, and conservation properties, whose correctness can therefore be guaranteed even in extrapolatory regimes. By using the method of characteristics to predict the analytical properties of PDE solutions a priori (even in regions arbitrarily far from the training domain), we show how it is possible to construct rigorous extrapolatory bounds on the worst-case L^inf errors of shallow neural network approximations. Then, by decomposing PDE solutions into compositions of simpler functions, we show how it is possible to compose these shallow neural networks together to form deep architectures, based on ideas from compositional deep learning, in which the large L^inf errors in the approximations have been suppressed. The resulting framework, called BEACONS (Bounded-Error, Algebraically-COmposable Neural Solvers), comprises both an automatic code-generator for the neural solvers themselves, as well as a bespoke automated theorem-proving system for producing machine-checkable certificates of correctness. We apply the framework to a variety of linear and non-linear PDEs, including the linear advection and inviscid Burgers' equations, as well as the full compressible Euler equations, in both 1D and 2D, and illustrate how BEACONS architectures are able to extrapolate solutions far beyond the training data in a reliable and bounded way. Various advantages of the approach over the classical PINN approach are discussed.

cs.LG↗

arXiv2025

Gyrokinetic Simulations of a Low Recycling Scrape-off Layer without a Lithium Target

Low-recycling regimes are appealing because they entail a high edge temperature and low edge density which are good for core confinement. However, due to considerably enhanced heat flux, the exhaust problems become severe. In addition, in the low-recycling regime, the conventional fluid simulations may not capture the physics of the Scrape-Off Layer (SOL) plasma that lies in the long mean free path regime; kinetic calculations become necessary. In this paper, by performing both Kinetic and fluid simulations, we explore the feasibility of a low-recycling regime in the magnetic geometry of the Spherical Tokamak for Energy Production (STEP); kinetic effects come out to be crucial determinants of the SOL dynamics. The simulation results indicate that a high SOL temperature and low SOL density could be achieved even when the divertor target is not made of a low recycling material. This can be done by using a low recycling material as a wall material. This is an important step towards demonstrating the feasibility of a low-recycling scenario. Lithium, a commonly used low recycling material, tends to evaporate at high heat fluxes which counteracts the desired high temperature, low density regime, and materials that can handle high heat fluxes are generally high recycling. Comparisons of gyrokinetic and fluid simulation results indicate that one can take advantage of kinetic effects to address some of the issues associated with a low-recycling SOL. Specifically, kinetic simulations show better confinement of impurities to the divertor region and greater broadening of the heat flux width due to drifts when compared with fluid simulations. Impurity confinement would help prevent core contamination from sputtering, and a broader heat flux width would help reduce the peak heat load at the target in the absence of detachment.

physics.plasm-ph↗

arXiv2025

Constructing Field Aligned Coordinate Systems for Gyrokinetic Simulations of Tokamaks in X-point Geometries

Structures in tokamak plasmas are elongated along the direction of the magnetic field and short in the directions perpendicular to the magnetic field. Many tokamak simulation codes take advantage of this by using a field aligned coordinate system. However, field aligned coordinate systems have a coordinate singularity at magnetic X-points where the poloidal magnetic field vanishes, which makes it difficult to use field aligned coordinate systems when simulating the core and scrape-off layer (SOL) simultaneously. Here we present an algorithm for computing geometric quantities in a standard field aligned coordinate system that avoids the singularity and allows one to conduct 2D axisymmetric simulations in X-point geometries. We demonstrate the efficacy of this algorithm with an example simulation of the Spherical Tokamak for Energy Production (STEP).

physics.plasm-ph↗

arXiv2025

Beyond GRMHD: A Robust Numerical Scheme for Extended, Non-Ideal General Relativistic Multifluid Simulations

The equations of general relativistic magnetohydrodynamics (GRMHD) have become the standard mathematical framework for modeling high-energy plasmas in curved spacetimes. However, the fragility of the primitive variable reconstruction operation in GRMHD, as well as the difficulties in maintaining strong hyperbolicity of the equations, sharply limit the applicability of the GRMHD model in scenarios involving large Lorentz factors and high magnetizations, such as around neutron stars. Non-ideal effects, such as electron inertia and Hall terms, are also neglected, and the absence of an explicitly evolved electric field precludes the self-consistent modeling of the strong poloidal fields found around spinning black holes, which are known to be crucial for jet formation. Here, we present a general relativistic multifluid model which strictly generalizes the GRMHD equations, consisting of an arbitrary number of relativistic fluid species interacting with a shared electromagnetic field via an explicit coupling of their source terms, thus allowing for the incorporation of non-ideal effects. We sketch how our model may be derived from general relativistic kinetics (via moments of the relativistic Boltzmann-Vlasov equation), as well as how GRMHD may be recovered in the single-fluid limit as the mobility of charge carriers goes to infinity. We present a numerical scheme for solving the general relativistic multifluid equations, and validate it against the analogous scheme for the GRMHD equations. Since the primitive variable reconstruction operation for our multifluid model is purely hydrodynamic, and therefore independent of the magnetic field, the resulting solver is highly robust, and able to simulate significantly larger Lorentz factors and higher magnetizations (across both black hole and neutron star spacetimes) than GRMHD without loss of either accuracy or stability.

gr-qc↗

arXiv2025

Discontinuous Galerkin Representation of the Maxwell-Jüttner Distribution

Kinetic simulations of relativistic gases and plasmas are critical for understanding diverse astrophysical and terrestrial systems, but the accurate construction of the relativistic Maxwellian, the Maxwell-Jüttner (MJ) distribution, on a discrete simulation grid is challenging. Difficulties arise from the finite velocity bounds of the domain, which may not capture the entire distribution function, as well as errors introduced by projecting the function onto a discrete grid. Here we present a novel scheme for iteratively correcting the moments of the projected distribution applicable to all grid-based discretizations of the relativistic kinetic equation. In addition, we describe how to compute the needed nonlinear quantities, such as Lorentz boost factors, in a discontinuous Galerkin (DG) scheme through a combination of numerical quadrature and weak operations. The resulting method accurately captures the distribution function and ensures that the moments match the desired values to machine precision.

physics.plasm-ph↗

arXiv2025

A Parallel-Kinetic-Perpendicular-Moment Model for Magnetized Plasmas

We describe a new model for the study of weakly-collisional, magnetized plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle dynamics parallel to the magnetic field while approximating the perpendicular dynamics through a spectral expansion in the perpendicular degrees of freedom, analogous to moment-based fluid approaches. In so doing, a hybrid approach is obtained which is computationally efficient enough to allow for larger-scale modeling of plasma systems while eliminating a source of difficulty in deriving fluid equations applicable to magnetized plasmas. We connect this system of equations to historical asymptotic models and discuss advantages and disadvantages of this approach, including the extension of this parallel-kinetic-perpendicular-moment beyond the typical region of validity of these more traditional asymptotic models. This paper forms the first of a multi-part series on this new model, covering the theory and derivation, alongside demonstration benchmarks of this approach including shocks and magnetic reconnection.

physics.plasm-ph↗

arXiv2025

Effects of oxidation and impurities in lithium surfaces on the emitting wall plasma sheath

Use of lithium as a surface coating in fusion devices improves plasma performance, but the change in wall properties affects the secondary electron emission properties of the material. Lithium oxidizes easily, which drives the emission yield well above unity. We present here simulations demonstrating the change in sheath structure from monotonic to the nonmonotonic space-charge limited sheath using an energy-dependent data-driven emission model which self-consistently captures both secondary emission and backscattering populations. Increased secondary electron emission from the material has ramifications for the degradation and erosion of the wall. Results shows that the oxidation leads to an increased electron flux into the wall, and a reduced ion flux. The net transfer of energy to the surface is significantly greater for the oxidized case than for the pure lithium case. High reflection rates of low-energy backscattered particles leads to a high re-emission rate at the wall.

physics.plasm-ph↗

arXiv2025

Hydrodynamic and Electromagnetic Discrepancies between Neutron Star and Black Hole Spacetimes

The exterior spacetime geometry surrounding an uncharged, spinning black hole in general relativity depends only upon its mass and spin. However, the exterior geometry surrounding any other rotating compact object, for example a neutron star, will generally depend upon higher moments in its multipole expansion, which will in turn be dependent upon the object's equation of state. Using general relativistic hydrodynamics and electrodynamics simulations, we illustrate that the presence or absence of these higher moments (assuming a physically realistic neutron star equation of state) has a significant qualitative effect near the surface of the compact object on the dynamics of unmagnetized accretion, and a smaller quantitative effect on the electromagnetic field configuration of its magnetosphere. In some places, the discrepancies in energy-momentum density are found to reach or exceed 50%, with electric field strength discrepancies in excess of 10%. We argue that many of these differences are likely to be amplified by the inclusion of more sophisticated plasma physics models, and are therefore likely to be relevant for the dynamics of gravitational collapse, and potentially also for particle acceleration and jet launching. These discrepancies suggest important limitations regarding the use of the Kerr metric when performing numerical simulations around neutron stars.

gr-qc↗

arXiv2025

Improved Dimensionality Reduction for Inverse Problems in Nuclear Fusion and High-Energy Astrophysics

Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional parameter scans and large ensembles of simulations to be performed. Such inverse problems typically involve large uncertainties, both in the measurement parameters being inverted and in the underlying physics models themselves. Monte Carlo sampling, when combined with modern non-linear dimensionality reduction techniques such as autoencoders and manifold learning, can be used to reduce the size of the parameter spaces considerably. However, there is no guarantee that the resulting combinations of parameters will be physically valid, or even mathematically consistent. In this position paper, we advocate adopting a hybrid approach that leverages our recent advances in the development of formal verification methods for numerical algorithms, with the goal of constructing parameter space restrictions with provable mathematical and physical correctness properties, whilst nevertheless respecting both experimental uncertainties and uncertainties in the underlying physical processes.

cs.LG↗

arXiv2025

A Tetrad-First Approach to Robust Numerical Algorithms in General Relativity

General relativistic Riemann solvers are typically complex, fragile and unwieldy, at least in comparison to their special relativistic counterparts. In this paper, we present a new high-resolution shock-capturing algorithm on curved spacetimes that employs a local coordinate transformation at each inter-cell boundary, transforming all primitive and conservative variables into a locally flat spacetime coordinate basis (i.e., the tetrad basis), generalizing previous approaches developed for relativistic hydrodynamics. This algorithm enables one to employ a purely special relativistic Riemann solver, combined with an appropriate post-hoc flux correction step, irrespective of the geometry of the underlying Lorentzian manifold. We perform a systematic validation of the algorithm using the Gkeyll simulation framework for both general relativistic electromagnetism and general relativistic hydrodynamics, highlighting the algorithm's superior convergence and stability properties in each case when compared against standard analytical solutions for black hole magnetosphere and ultra-relativistic black hole accretion problems. However, as an illustration of the generality and practicality of the algorithm, we also apply it to more astrophysically realistic magnetosphere and fluid accretion problems in the limit of high black hole spin, for which standard general relativistic Riemann solvers are often too unstable to produce useful solutions.

gr-qc↗

arXiv2025

Shock with Confidence: Formal Proofs of Correctness for Hyperbolic Partial Differential Equation Solvers

First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock waves, electromagnetic interactions, and even general relativistic phenomena. Such equations are often challenging to solve numerically in the non-linear case, due to their tendency to form discontinuities even for smooth initial data, which can cause numerical algorithms to become unstable, violate conservation laws, or converge to physically incorrect solutions. In this paper, we introduce a new formal verification pipeline for such algorithms in Racket, which allows a user to construct a bespoke hyperbolic PDE solver for a specified equation system, generate low-level C code which verifiably implements that solver, and then produce formal proofs of various mathematical and physical correctness properties of the resulting implementation, including L^2 stability, flux conservation, and physical validity. We outline how these correctness proofs are generated, using a custom-built theorem-proving and automatic differentiation framework that fully respects the algebraic structure of floating-point arithmetic, and show how the resulting C code may either be used to run standalone simulations, or integrated into a larger computational multiphysics framework such as Gkeyll.

cs.LO↗

arXiv2024

Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations

One of the most promising applications of machine learning (ML) in computational physics is to accelerate the solution of partial differential equations (PDEs). The key objective of ML-based PDE solvers is to output a sufficiently accurate solution faster than standard numerical methods, which are used as a baseline comparison. We first perform a systematic review of the ML-for-PDE solving literature. Of articles that use ML to solve a fluid-related PDE and claim to outperform a standard numerical method, we determine that 79% (60/76) compare to a weak baseline. Second, we find evidence that reporting biases, especially outcome reporting bias and publication bias, are widespread. We conclude that ML-for-PDE solving research is overoptimistic: weak baselines lead to overly positive results, while reporting biases lead to underreporting of negative results. To a large extent, these issues appear to be caused by factors similar to those of past reproducibility crises: researcher degrees of freedom and a bias towards positive results. We call for bottom-up cultural changes to minimize biased reporting as well as top-down structural reforms intended to reduce perverse incentives for doing so.

math.NA↗

arXiv2024

Plasma sheath studies using a physical treatment of electron emission from a dielectric wall

When a plasma sheath forms next to a dielectric wall, material properties determine electron absorption and reflection from the surface, impacting the sheath formation and structure. The low energy regime of this interaction is often not considered rigorously in emissive sheath simulations, but may be modeled from quantum mechanical first principles, and has important applications to plasma thrusters and fusion devices. In this work, low energy electron reflection from the wall is implemented as a boundary condition in a continuum kinetic framework and the sheath is simulated for dielectric material parameters in high and low emission cases. The results presented here demonstrate that the material parameters can have significant effect on the resulting sheath profile and particle distribution functions. Surfaces with high reflection rates see the formation of a space-charge limited sheath.

physics.plasm-ph↗