arXiv subjects

Luis Chacon

Publications and source records attributed to Luis Chacon.

At least 19 recordsLinked to original sources

arXiv2026

An Energy-Conserving Unstaggered Electromagnetic-Potential Particle-in-Cell Method, Part I: Non-relativistic Generalized-Momentum Formulation

We develop an unstaggered, potential-based particle-in-cell method for the nonrelativistic Vlasov-Maxwell system in the Lorenz gauge. The field update is written as a Crank-Nicolson discretization of first-order wave systems for the scalar potential, the vector potential, and their time derivatives. The charge density is not deposited directly; instead, it is advanced from the discrete continuity equation using the current deposited from the particles. This opens up algorithmic flexibility with a range of innovation, including unstaggered mesh layouts that preserve the Lorenz gauge and Gauss's law at the discrete level. In the potential formulation, this source ordering also permits preservation of the Lorenz gauge and Gauss's law at the discrete level. To extend the paradigm to an energy-conserving formulation, we introduce a consistent orbit-averaged scatter, gather, and particle push. For energy consistency, the update of the canonical momentum is modified by replacing the pointwise midpoint derivative of the vector potential with an orbit-averaged discrete gradient of the mesh-interpolated vector potential consistent with the orbit-average maps. This construction satisfies an exact finite-difference chain rule along each particle orbit. As a result, the particle work equals the mesh work appearing in the Crank-Nicolson field-energy balance, yielding exact total-energy conservation up to nonlinear solver tolerance and roundoff. We demonstrate exact energy conservation of the method in 3D on the cold two-stream instability.

math.NA↗

arXiv2026

Comment on "Impact of particle number and cell-size in fully implicit charge- and energy-conserving particle-in-cell schemes" by N. Savard et al., Phys. Plasmas 32, 073903 (2025)

We take issue with the conclusions in the recent publication by Savard et al. In the study, the authors implement a fully nonlinear charge- and energy-conserving implicit particle-in-cell method (ECC-IPIC), and use it to study the impact of particle number in the quality of the ECC-IPIC solutions for several problems, including an ion acoustic shockwave (IASW) problem and several sheath problems in bounded plasmas. From the study, the authors concluded that ``to reproduce highly resolved convergent solutions, a higher amount of particles per cell need to be used in the implicit scheme for both periodic and bounded simulations when the cell size exceeds the Debye length.'' We demonstrate that, according to our analysis for the IASW test, this conclusion does not survive independent scrutiny. We have identified several diagnostics procedural issues that are at the root of their conclusion, which when fixed dramatically change the outcome of the study.

physics.plasm-ph↗

arXiv2025

Learning interpretable closures for thermal radiation transport in optically-thin media using WSINDy

We introduce an equation learning framework to identify a closed set of equations for moment quantities in 1D thermal radiation transport (TRT) in optically thin media. While optically thick media admits a well-known diffusive closure, the utility of moment closures in providing accurate low-dimensional surrogates for TRT in optically thin media is unclear, as the mean-free path of photons is large and the radiation flux is far from its Fickean limit. Here, we demonstrate the viability of using weak-form equation learning to close the system of equations for the energy density, radiation flux, and temperature in optically thin TRT. We show that the WSINDy algorithm (Weak-form Sparse Identification of Nonlinear Dynamics), together with an advantageous change of variables and an auxiliary equation for the radiation-energy-weighted opacity, enables robust and efficient identification of closures that preserve many desired physical properties from the high fidelity system, including hyperbolicity, rotational symmetry, black-body equilibria, and linear stability of black-body equilibria, all of which manifest as library constraints or convex constraints on the closure coefficients. Crucially, the weak form enables closures to be learned from simulation data with ray effects and particle noise, which then do not appear in simulations of the resulting closed moment system. Finally, we demonstrate that our closure models can be extrapolated in the key system parameters of drive temperature $T_{in}$ and scalar opacity $\gamma$, and this extrapolation is to an extent quantifiable by a Knudsen-like dimensionless parameter.

math.DS↗

arXiv2025

A Multiscale Eulerian Vlasov-Rosenbluth-Fokker-Planck Algorithm for Thermonuclear Burning Plasmas

Accurate treatment of energetic fusion byproducts in laboratory plasmas often requires a kinetic description, owing to their large birth kinetic energy and long mean-free-paths compared with the characteristic system scale lengths. For example, alpha particles produced by deuterium--tritium fusion reactions are born at high energies (\SI{3.5}{MeV}) and predominantly slow down through interactions with electrons traveling at comparable speeds. As an alpha particle slows, its distribution collapses near the background ion-thermal speed, forming a sharp structure in velocity space. Such sharp features pose numerical challenges in grid-based Eulerian methods: capturing the full alpha-particle energies demands a large velocity domain, while resolving the near-thermal region requires a sufficiently fine mesh. Inspired by the work of Peigney et al.[J. Comput. Phys. 278 (2014)], we present a two-grid approach that splits the alpha-particle distribution into energetic (suprathermal) and ash (thermal) components. A Gaussian-based sink term transfers particles from the energetic population to the ash population as they slow to the thermal regime, and a conservative projection scheme ensures that mass, momentum, and energy of the alpha and ash interactions are preserved. Unlike the formulation of Peigney, our method does not require a strict asymptotic separation of velocity scales, which can, in principle, be arbitrary. We demonstrate the robustness of this approach on challenging multiscale problems, including a surrogate for an igniting inertial confinement fusion capsule.

physics.plasm-ph↗

arXiv2025

Aligning Thermal and Current Quenches with a High Density Low-Z Injection

The conventional approach for thermal quench mitigation in a tokamak disruption is through a high-Z impurity injection that radiates away the plasma's thermal energy before it reaches the wall. The downside is a robust Ohmic-to-runaway current conversion due to the radiatively clamped low post-thermal-quench electron temperature. An alternative approach is to deploy a low-Z (either deuterium or hydrogen) injection that aims to slow down the thermal quench, and ideally aligns it with the current quench. This approach has been investigated here via 3D MHD simulations using the PIXIE3D code. By boosting the hydrogen density, a fusion-grade plasma is dilutionally cooled at approximately the original pressure. Energy loss to the wall is controlled by a Bohm outflow condition at the boundary where the magnetic field intercepts a thin plasma sheath at the wall, in addition to Bremsstrahlung bulk losses. Robust MHD instabilities proceed as usual, while the collisionality of the plasma has been greatly increased and parallel transport is now in the Braginskii regime. The main conclusion of this study is that the decreased transport loss along open field lines due to a sufficient low-Z injection slows down the thermal quench rate to the order of 20 ms, aligned with the current quench timescale for a 15 MA ITER plasma.

physics.plasm-ph↗

arXiv2024

Sylvester-Preconditioned Adaptive-Rank Implicit Time Integrators for Advection-Diffusion Equations with Variable Coefficients

We consider the adaptive-rank integration of {2D and 3D} time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with an adaptive-rank algorithm structured around three key strategies: {(i) constructing dimension-wise subspaces based on an extended Krylov strategy, (ii) developing an effective preconditioner for the reduced coefficient matrix, and (iii) efficiently computing the residual of the equation without explicitly reverting to the full-rank form. {The low-rank decomposition is performed in 2D using SVD, and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format.} The computational complexity of the proposed approach {is demonstrated numerically to} be comparable to the constant-coefficient case [El Kahza et al, J. Comput. Phys., 518 (2024)], scaling as $\mathcal{O}(N {r^2} + {r^{d+1}})$ for $d$-dimensional problems (here, $d = 2$ or $3$), with $N$ the resolution in one dimension and $r$ the maximal rank during the Krylov iteration (which we find to be largely independent of $N$). We present numerical examples that illustrate the computational efficacy and complexity of our algorithm.}

math.NA↗

arXiv2024

Exact local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete \emph{local} energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature \citep{xiao2017local}, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

math.NA↗

arXiv2024

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla \times \nabla \times$ operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

physics.plasm-ph↗

arXiv2023

An implicit, conservative electrostatic particle-in-cell algorithm for paraxial magnetic nozzles

An electrostatic, implicit particle-in-cell (PIC) model for collisionless, fully magnetized, paraxial plasma expansions in a magnetic nozzle is introduced with exact charge, energy, and magnetic moment conservation properties. The approach is adaptive in configuration space by the use of mapped meshes, and exploits the strict conservation of the magnetic moment to reduce the dimensionality of velocity space. A new particle integrator is implemented, which allows for particle substepping without the need to stop particle motion at every cell for charge conservation. Particle suborbits are determined from accuracy considerations, and are allowed to span multiple cells. Novel particle injection and expansion-to-infinity boundary conditions are developed, including a control loop to prevent the formation of spurious sheaths at the edges of the domain. The algorithm is verified in a periodic magnetic mirror configuration, a uniform plasma test case (to test particle injection), and a propulsive magnetic nozzle. The algorithm's computational complexity is shown to scale favorably with timestep, and linearly with the number of particles and mesh cells (unlike earlier implicit PIC implementations, which scaled quadratically with the number of mesh cells in one dimension). Numerical experiments demonstrate that the proposed algorithm outperforms both explicit PIC and semi-Lagrangian Vlasov codes by more than an order of magnitude.

physics.plasm-ph↗

arXiv2021

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in [Chacon, et al, JCP 2002] to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime ($\ge 10^7$) with the successful resolution of plasmoid instabilities and thin current sheets.

physics.comp-ph↗

arXiv2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

physics.plasm-ph↗

arXiv2020

An Adaptive EM Accelerator for Unsupervised Learning of Gaussian Mixture Models

We propose an Anderson Acceleration (AA) scheme for the adaptive Expectation-Maximization (EM) algorithm for unsupervised learning a finite mixture model from multivariate data (Figueiredo and Jain 2002). The proposed algorithm is able to determine the optimal number of mixture components autonomously, and converges to the optimal solution much faster than its non-accelerated version. The success of the AA-based algorithm stems from several developments rather than a single breakthrough (and without these, our tests demonstrate that AA fails catastrophically). To begin, we ensure the monotonicity of the likelihood function (a the key feature of the standard EM algorithm) with a recently proposed monotonicity-control algorithm (Henderson and Varahdan 2019), enhanced by a novel monotonicity test with little overhead. We propose nimble strategies for AA to preserve the positive definiteness of the Gaussian weights and covariance matrices strictly, and to conserve up to the second moments of the observed data set exactly. Finally, we employ a K-means clustering algorithm using the gap statistic to avoid excessively overestimating the initial number of components, thereby maximizing performance. We demonstrate the accuracy and efficiency of the algorithm with several synthetic data sets that are mixtures of Gaussians distributions of known number of components, as well as data sets generated from particle-in-cell simulations. Our numerical results demonstrate speed-ups with respect to non-accelerated EM of up to 60X when the exact number of mixture components is known, and between a few and more than an order of magnitude with component adaptivity.

cs.LG↗

arXiv2020

An Eulerian Vlasov-Fokker-Planck Algorithm for Spherical Implosion Simulations of Inertial Confinement Fusion Capsules

We present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov-Fokker-Planck (VFP) simulation of an inertial confinement fusion (ICF) capsule implosion. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma's evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: 1) an elastic moving wall boundary; 2) a time-dependent Maxwellian Dirichlet boundary; and 3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems --the first-ever reported using a Vlasov-Fokker-Planck model.

physics.comp-ph↗

arXiv2019

A conservative phase-space moving-grid strategy for a 1D-2V Vlasov-Fokker-Planck Equation

We develop a conservative phase-space grid-adaptivity strategy for the Vlasov-Fokker-Planck equation in a planar geometry. The velocity-space grid is normalized to the thermal speed and shifted by the bulk-fluid velocity. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The grid adaptation ensures discrete conservation of the collisional invariants (mass, momentum, and energy). The conservative grid-adaptivity strategy provides an efficient scheme which resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity.

physics.plasm-ph↗

arXiv2018

A multi-dimensional, moment-accelerated deterministic particle method for time-dependent, multi-frequency thermal radiative transfer problems

Thermal Radiative Transfer (TRT) is the dominant energy transfer mechanism in high-energy density physics with applications in inertial confinement fusion and astrophysics. The stiff interactions between the material and radiation fields make TRT problems challenging to model. In this study, we propose a multi-dimensional extension of the deterministic particle (DP) method. The DP method combines aspects from both particle and deterministic methods. If the emission source is known \apriori, and no physical scattering is present, the intensity of a particle can be integrated analytically. This introduces no statistical noise compared to Monte-Carlo methods, while maintaining the flexibility of particle methods. The method is closely related to the popular method of long characteristics. The combination of the DP-method with a discretely-consistent, nonlinear, gray low-order system enables an efficient solution algorithm for multi-frequency TRT problems. We demonstrate with numerical examples that the use of a linear-source approximation based on spatial moments improves the behavior of our method in the thick diffusion limit significantly.

physics.comp-ph↗

arXiv2018

Wavelet Methods for Studying the Onset of Strong Plasma Turbulence

Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed turbulence from a laminar state. Originally applied to neutral fluid turbulence, an iterative wavelet technique decomposes the field into coherent and incoherent contributions. In contrast to Fourier power spectra, finite time Lyapunov exponents (FTLE), and simple measures of intermittency such as non-Gaussian statistics of field increments, the wavelet technique is found to provide a quantitative measure for the onset of turbulence and to track the transition to fully developed turbulence. The wavelet method makes no assumptions about the structure of the coherent current sheets or the underlying plasma model. Temporal evolution of the coherent and incoherent wavelet fluctuations is found to be highly correlated with the magnetic field energy and plasma thermal energy, respectively. The onset of turbulence is identified with the rapid growth of a background of incoherent fluctuations spreading across a range of scales and a corresponding drop in the coherent components. This is suggestive of the interpretation of the coherent and incoherent wavelet fluctuations as measures of coherent structures (e.g., current sheets) and dissipation, respectively. The ratio of the incoherent to coherent fluctuations $R_{ic}$ is found to be fairly uniform across different plasma models and provides an empirical threshold for turbulence onset. The technique is illustrated through examples. First, it is applied to the Kelvin--Helmholtz instability from different simulation models including fully kinetic, hybrid (kinetic ion/fluid electron), and Hall MHD simulations. Second, it is applied to the development of turbulence downstream of the bowshock in a magnetosphere simulation.

physics.plasm-ph↗

arXiv2017

Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas

Strong collisional shocks in multi-ion plasmas are featured in many environments, with Inertial Confinement Fusion (ICF) experiments being one prominent example. Recent work [Keenan ${\it et \ al.}$, PRE ${\bf 96}$, 053203 (2017)] answered in detail a number of outstanding questions concerning the kinetic structure of steady-state, planar plasma shocks, e.g., the shock width scaling by Mach number, $M$. However, it did not discuss shock-driven ion-species stratification (e.g., relative concentration modification, and temperature separation). These are important effects, since many recent ICF experiments have evaded explanation by standard, single-fluid, radiation-hydrodynamic (rad-hydro) numerical simulations, and shock-driven fuel stratification likely contributes to this discrepancy. Employing the state-of-the-art Vlasov-Fokker-Planck code, iFP, along with multi-ion hydro simulations and semi-analytics, we quantify the ion stratification by planar shocks with arbitrary Mach number and relative species concentration for two-ion plasmas in terms of ion mass and charge ratios. In particular, for strong shocks, we find that the structure of the ion temperature separation has a nearly universal character across ion mass and charge ratios. Additionally, we find that the shock fronts are enriched with the lighter ion species, and the enrichment scales as $M^4$ for $M \gg 1$.

physics.plasm-ph↗

arXiv2017

An Adaptive, Implicit, Conservative 1D-2V Multi-Species Vlasov-Fokker-Planck Multiscale Solve in Planar Geometry

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comp. Phys., 318, 391-420, (2016)] to a spatially inhomogeneous system. In this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker-Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

physics.plasm-ph↗