arXiv subjects

Manaure Francisquez

Publications and source records attributed to Manaure Francisquez.

17 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

An explicit multiscale pseudo orbit-averaging time integration algorithm

We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a phased time integrator for cases where the boundaries of dynamical scales are known: one phase solves the unmodified equation, while the other freezes part of phase-space and slows down the evolution of the fast dynamics. This algorithm is applied to reduced kinetic models of plasmas in magnetic mirrors, which feature a distinct boundary between a region dominated by rapid particle transit and a region characterized by slow collisions. Two representative model problems are presented that decompose the dynamics of the magnetic mirror into a simpler, computationally inexpensive form. The model problems demonstrate a speedup by a factor of order $ω/ ν_c$, where $ω$ is the fast oscillation frequency and $ν_c$ is the slow damping rate. This is a 30,000$\times$ speedup for a case of practical interest.

physics.plasm-ph↗

arXiv2026

Super Time Stepping Methods for Diffusion using Discontinuous-Galerkin Spatial Discretizations

Super-time-stepping (STS) methods provide an attractive approach for enabling explicit time integration of parabolic operators, particularly in large-scale, higher-dimensional kinetic simulations where fully implicit schemes are impractical. In this work, we present an explicit STS framework tailored for diffusion operators in gyrokinetic models, motivated by the fact that constructing and storing a Jacobian is often infeasible due to strong nonlocal couplings, high dimensionality, and memory constraints. We investigate the performance of several STS methods, including Runge-Kutta-Chebyshev (RKC) and Runge-Kutta-Legendre (RKL) schemes, applied to a diffusion equation discretized using both discontinuous Galerkin (DG) and finite-difference methods. To support time adaptivity, we introduce a novel error norm designed to more accurately track temporal error arising from DG spatial discretizations, in which degrees of freedom contribute unevenly to the solution error. Finally, we assess the performance of an automatic eigenvalue estimation algorithm for determining the required number of STS stages and compare it against an analytical estimation formula.

math.NA↗

arXiv2026

Conservative velocity mappings for discontinuous Galerkin kinetics

Continuum computational kinetic plasma models evolve the distribution function of a plasma species $f_s$ on a phase-space grid over time. In many problems of interest the distribution function has limited extent in velocity space; hence, using a uniform, highly refined mesh would be costly and slow. Nonuniform velocity grids can reduce the computational cost by placing more degrees of freedom where $f_s$ is appreciable and fewer where it is not. In this work we introduce a first-of-its kind discontinuous Galerkin approach to nonuniform velocity-space discretization using mapped velocity coordinates. This new method is presented in the context of a gyrokinetic model used to study magnetized plasmas. We create discretizations of collisionless and collisional terms using mappings in a way that exactly conserves particles and energy. Numerical tests of such properties are presented, and we show that this new discretization can reproduce earlier gyrokinetic simulations using grids with up to 6-60 times fewer cells and 22X-60X speed-ups depending on dimensionality, geometry and plasma parameters.

physics.plasm-ph↗

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

General kinetic ion induced electron emission model for metallic walls applied to biased Z-pinch electrodes

A kinetic ion induced electron emission (IIEE) model for general applications is developed to obtain the emitted electron energy spectrum for a distribution of ion impacts on a metallic surface. We assume an ionization cascade mechanism and use empirical models for the ion and electron stopping powers. The emission spectrum and the secondary electron yield (SEY) are validated for a variety of materials. The IIEE model is used to study the effect of IIEE on the plasma-material interactions of Z-pinch electrodes. Un-magnetized Boltzmann-Poisson simulations are performed for a Z-pinch plasma doubly bounded by two biased copper electrodes with and without IIEE at bias potentials from 0 to 9 kV. At the anode, the SEY decreases from 0 to 1 kV, but then increases at higher bias potentials. At the cathode, the SEY is much larger due to higher energy ion bombardment and grows with bias potential. As the bias potential increases, the emitted cathode electrons are accelerated to higher energies into the domain collisionally heating the plasma. Above 1 kV, the heating is strong enough to increase the plasma potential. Despite SEY greater than 1, only a classical sheath forms as opposed to a space-charge limited or inverse sheath due to the emitted electron flux not reaching the space charge current saturation limits. Furthermore, the current in the emissionless cases saturates to a value lower than experiment. With IIEE, the current does not saturate and continues to increase with the 4 kV case matching most closely with experiment.

physics.plasm-ph↗

arXiv2023

Towards continuum gyrokinetic study of high-field mirrors

High-temperature superconducting (HTS) magnetic mirrors under development exploit strong fields with high mirror ratio to compress loss cones and enhance confinement, and may offer cheaper, more compact fusion power plant candidates. This new class of devices could exhibit largely unexplored interchange and gradient-driven modes. Such instabilities, and methods to stabilize them, can be studied with gyrokinetics given the strong magnetization and prevalence of kinetic effects. Our focus here is to: a) determine if oft-used gyrokinetic models for open field lines produce the electron-confining (Pastukhov) electrostatic potential; b) examine and address challenges faced by gyrokinetic codes in studying HTS mirrors. We show that a one-dimensional limit of said models self-consistently develops a potential qualitatively reaching the analytical Pastukhov level. Additionally, we describe the computational challenges of studying high mirror ratios with open field line gyrokinetic solvers, and offer a force softening method to mitigate small time steps needed for time integration in colossal magnetic field gradients produced by HTS coils, providing a 19X speedup.

physics.plasm-ph↗

arXiv2022

Improved multispecies Dougherty collisions

The Dougherty model Fokker-Planck operator is extended to describe nonlinear full-f collisions between multiple species in plasmas. Simple relations for cross-species interactions are developed which obey conservation laws, and reproduce familiar velocity and temperature relaxation rates. This treatment of multispecies Dougherty collisions, valid for arbitrary mass ratios, satisfies the H-Theorem unlike analogous Bhatnagar-Gross-Krook operators.

physics.plasm-ph↗

arXiv2021

Turbulent field fluctuations in gyrokinetic and fluid plasmas

A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbulent field fluctuations between electrostatic two-fluid theory and electromagnetic gyrokinetic modelling with good overall agreement found in magnetized helical plasmas at low normalized pressure. This framework is readily adaptable to experimental and astrophysical environments, and presents a new technique for the numerical validation and discovery of reduced global plasma turbulence models.

physics.plasm-ph↗

arXiv2021

Mapped discontinuous Galerkin interpolations and sheared boundary conditions

Translations or, more generally, coordinate transformations of scalar fields arise in several applications, such as weather, accretion disk and magnetized plasma turbulence modeling. In local studies of accretion disks and magnetized plasmas these coordinate transformations consist of an analytical mapping and enter via sheared-shift boundary conditions. This work introduces a discontinuous Galerkin algorithm to compute these coordinate transformations or boundary conditions based on projections and quadrature-free integrals. The procedure is high-order accurate, preserves certain moments exactly and works in multiple dimensions. Tests of the proposed approach with increasing complexity are presented, beginning with translations of one and two dimensional fields, followed by 3D and 5D simulations with sheared (twist-shift) boundary conditions. The results show that the algorithm is (p+1)-order accurate in the DG representation and (p+2)-order accurate in the cell averages, with p being the order of the polynomial basis functions. Quantification of the algorithm's diffusion and, for shearing boundary conditions, discussion of aliasing errors are provided.

physics.plasm-ph↗

arXiv2021

Uncovering turbulent plasma dynamics via deep learning from partial observations

One of the most intensely studied aspects of magnetic confinement fusion is edge plasma turbulence which is critical to reactor performance and operation. Drift-reduced Braginskii two-fluid theory has for decades been widely applied to model boundary plasmas with varying success. Towards better understanding edge turbulence in both theory and experiment, we demonstrate that physics-informed neural networks constrained by partial differential equations can accurately learn turbulent fields consistent with the two-fluid theory from just partial observations of a synthetic plasma's electron density and temperature in contrast with conventional equilibrium models. These techniques present a novel paradigm for the advanced design of plasma diagnostics and validation of magnetized plasma turbulence theories in challenging thermonuclear environments.

physics.plasm-ph↗

arXiv2020

Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

A conservative discontinuous Galerkin scheme for a nonlinear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it has a non-decreasing entropy functional, and conserves particles, momentum and energy. Discretely these conservative properties are maintained exactly as well, independent of numerical resolution. In this work the phase space discretization is performed using a novel version of the discontinuous Galerkin scheme, carefully constructed using concepts of weak equality and recovery. Discrete time advancement is carried out with an explicit time-stepping algorithm, whose stability limits we explore. The formulation and implementation within the long-wavelength gyrokinetic solver of Gkeyll are validated with relaxation tests, collisional Landau-damping benchmarks and the study of 5D gyrokinetic turbulence on helical, open field lines.

physics.plasm-ph↗

arXiv2020

Generalized slab universal instability and its appearance in pair plasma

A generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron-ion plasma, while Debye shielding strongly stabilizes this instability when $λ_D$ approaches $ρ_i$ ($λ_D$ is the Debye length and $ρ_i$ is the ion gyro-radius). In particular, we examine the stability criterion for this instability in electron-positron pair plasmas, and find that the instability persists in this simplest plasma system as long as the pair plasma number density exceeds the critical value $n_c=B^2/(8πm_e c^2)$.

physics.plasm-ph↗

arXiv2020

Fluid & Gyrokinetic turbulence in open field-line, helical plasmas

Two-fluid Braginskii codes have simulated open-field line turbulence for over a decade, and only recently has it become possible to study these systems with continuum gyrokinetic codes. This work presents a first-of-its-kind comparison between fluid and (long-wavelength) gyrokinetic models in open field-lines, using the GDB and Gkeyll codes to simulate interchange turbulence in the Helimak device at the University of Texas (T. N. Bernard, et. al., Phys. of Plasmas 26, 042301 (2019)). Partial agreement is attained in a number of diagnostic channels when the GDB sources and sheath boundary conditions (BCs) are selected carefully, especially the heat-flux BCs which can drastically alter the temperature. The radial profile of the fluctuation levels is qualitatively similar and quantitatively comparable on the low-field side, although statistics such as moments of the probability density function and the high-frequency spectrum show greater differences. This comparison indicates areas for future improvement in both simulations, such as sheath BCs, as well as improvements in GDB like particle conservation and spatially varying thermal conductivity, in order to achieve better fluid-gyrokinetic agreement and increase fidelity when simulating experiments.

physics.plasm-ph↗

arXiv2020

Dynamo in weakly collisional nonmagnetized plasmas impeded by Landau damping of magnetic fields

We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale. In simulations we thus observe decaying magnetic fields where resistive MHD would predict a dynamo.

physics.plasm-ph↗

arXiv2018

Gyrokinetic theory of slab universal modes and the non-existence of the Gradient Drift Coupling (GDC) instability

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on $k_\parallel=0$ universal (or entropy) modes driven by plasma gradients at small and large plasma $β$. These are small scale non-MHD instabilities with growth rates that typically peak near $k_\perpρ_i\sim 1$ and vanish in the long wavelength $k_\perp\to 0$ limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate $γ= \sqrt{β/[2(1+β)]} C_s/|L_p|$ with $C_s^2=p_0/ρ_0$ for $k_\perp\to 0$ and is universally unstable for $1/L_p\neq 0$. We show the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance $p_0+B_0^2/(8π)=\text{constant}$, which renders the assumption $B_0'=0$ inconsistent if $p_0'\neq 0$.

physics.plasm-ph↗