arXiv subjects

Luis Chacón

Publications and source records attributed to Luis Chacón.

16 recordsLinked to original sources

arXiv2026

Fully-implicit Particle-in-Cell model of a Magnetic Nozzle with electromagnetic power deposition

A fraction of the electromagnetic power used to generate and heat the plasma in helicon sources and electrodeless plasma thrusters can leak into the outer expansion region, interacting with the plasma in the magnetic nozzle and affecting the performance of the device. This work analyzes the properties of the plasma in a convergent-divergent magnetic nozzle when right-hand polarized waves of varying amplitude propagate into it. This is accomplished with a 1D3V fully-implicit, Vlasov-Darwin particle-in-cell model of the collisionless ion and electron plasma in a magnetic tube. The code exactly conserves charge locally and energy globally. It features a nonuniform grid and an enhanced substepping routine for the particle trajectories. The requirement that the expansion be current-free is satisfied thanks to linear closed-loop controllers on the injection and downstream boundary conditions. Wave heating increases the electron perpendicular temperature, especially in the vicinity of an electron cyclotron resonance surface, always present inside the magnetic nozzle of a helicon device. The energized electrons become anisotropic, and drive a more pronounced potential drop and a higher ion acceleration than in the absence of waves, at the expense of the wave power. The computed moments of the ion and electron distributions reveal the dominant balance of the electron thermal terms, electrostatic terms, and ion inertial terms in the momentum and energy equations. Wave heating helps populate otherwise-inaccessible regions of the electrons phase space and modifies the doubly-trapped electron population found in the purely electrostatic case...

physics.plasm-ph↗

arXiv2026

Implementation and Verification of Toroidal Resistive Wall Boundary Conditions in the PIXIE3D MHD code using a Boundary Integral Method

We present the complete formulation of resistive wall boundary conditions in axisymmetric toroidal geometries as implemented in the PIXIE3D extended magnetohydrodynamics (MHD) code, along with a complete suite of analytical verification examples that demonstrate correctness in the implementation. The formulation centers around a thin wall approximation and a Boundary Integral Method to solve for the magnetic scalar potential in the immediately surrounding vacuum. This requires specialized quadrature rules derived from existing literature to handle the numerical integration of singular and hypersingular integrands (the Green's function of Laplace's equation and its derivatives), for which we provide the nodes and weights. Further, we describe an extension to the formalism to include the effect of a perfectly conducting second, outer wall exterior to the resistive (plasma-facing) wall and separated by vacuum, and exterior to the computational plasma mesh proper. Lastly, we describe an extension to include the effect of current-carrying coils also defined exterior to the plasma mesh in the resistive wall boundary condition treatment. For most aspects of the method, we present self-contained verification examples using analytic solutions in axisymmetric toroidal geometries (with both 2D and 3D plasmas) and show it to be accurate to second order. We demonstrate the algorithm with a vertical displacement event (VDE) using the ITER tokamak geometry.

physics.plasm-ph↗

arXiv2026

A Structure-Preserving Penalization Method for the Single-species Rosenbluth-Fokker-Planck Equation

The Rosenbluth-Fokker-Planck (RFP) equation describes Coulomb collisional dynamics within and across species in plasmas. It belongs to the broader class of anisotropic-diffusion-advection equations, whose numerical approximation is highly-nontrivial due to its nonlinearity, stiffness, and structural properties such as conservation and entropy dissipation (hence with the Maxwellian distribution as the equilibrium state). In this paper, we propose a structure-preserving penalization scheme for the stiff, single-species RFP equation. The scheme features three novel components: 1) a novel generalization of the well-known Chang-Cooper discretization for the RFP equation that is equilibrium-preserving and enables positivity while preserving mass, momentum, and energy; 2) an easy-to-invert isotropic variable-coefficient penalization operator to deal with the temporal stiffness without resorting to a fully implicit scheme, borrowing ideas from explicit-implicit-null (EIN) methods, and 3) an adaptive timestepping strategy that preserves the positivity of the full penalized scheme. The resulting scheme conserves mass, momentum, and energy strictly, is unconditionally stable, and robustly positivity preserving. The scheme is demonstrated with linear and nonlinear anisotropic diffusion examples of increasing complexity, including several single-species RFP examples.

math.NA↗

arXiv2024

Krylov-based Adaptive-Rank Implicit Time Integrators for Stiff Problems with Application to Nonlinear Fokker-Planck Kinetic Models

We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of solutions with significantly reduced computational costs. We further introduce an efficient mechanism for residual evaluation and an adaptive rank-seeking strategy that optimizes low-rank settings based on a comparison between the residual size and the local truncation errors of the time-stepping discretization. We demonstrate our approach with the challenging Lenard-Bernstein Fokker-Planck (LBFP) nonlinear equation, which describes collisional processes in a fully ionized plasma. The preservation of {the equilibrium state} is achieved through the Chang-Cooper discretization, and strict conservation of mass, momentum and energy via a Locally Macroscopic Conservative (LoMaC) procedure. The development of implicit adaptive-rank integrators, demonstrated here up to third-order temporal accuracy via diagonally implicit Runge-Kutta schemes, showcases superior performance in terms of accuracy, computational efficiency, equilibrium preservation, and conservation of macroscopic moments. This study offers a starting point for developing scalable, efficient, and accurate methods for high-dimensional time-dependent problems.

math.NA↗

arXiv2024

Validation of hydrodynamic and kinetic simulations with a plasma interpenetration ICF hohlraum experiment

We report on simulations of counter-propagating laser-produced plasmas in an inertial confinement fusion (ICF) hohlraum surrogate, aiming to replicate observations reported by Le Pape et. al in recent work. The conditions of the colliding plasmas are relevant to ICF hohlraums used for indirect-drive ignition, and are obtained both with and without low-density He-gas fill. We compare experimental diagnostics to outputs from simulations using the 1D-2V Vlasov-Fokker-Planck kinetic code iFP and the xRAGE radiation-hydrodynamics code. These include the inferred radial lineouts of inferred ion number fraction and ion and electron temperatures, as well as the reported experimental Thomson-scattering (TS) spectra (compared via synthetic TS diagnostics). We observe that 1D kinetic simulations capture the plasma states reported in the experimental diagnostics quite well. Counter-intuitively, the kinetic simulations capture the gas-fill experiment (expected to be more `hydro-like') better than the vacuum experiment, while the reverse is observed for hydrodynamic simulations. This is attributed to the presence of non-trivial multi-dimensional hydrodynamic effects which are more dominant in the vacuum experiment. These effects are somewhat inhibited in the gas-fill experiment, permitting quasi-1D kinetic plasma transport to play more of a role in producing plasma interpenetration. Differences between the effects of Maxwellian vs. non-Maxwellian (`full f') synthetic TS diagnostics are investigated for the kinetic simulations. We find non-Maxwellian TS spectra differ non-trivially from Maxwellian spectra, which suggests caution may be warranted when applying Maxwellian TS models to infer plasma conditions via backward modeling when kinetic effects may be present.

physics.plasm-ph↗

arXiv2023

Asymptotic-preserving gyrokinetic implicit particle-orbit integrator for arbitrary electromagnetic fields

We extend the asymptotic preserving and energy conserving time integrator for charged-particle motion developed in [Ricketson & Chacón, JCP, 2020] to include finite Larmor-radius (FLR) effects in the presence of electric-field length-scales comparable to the particle gyro-radius (the gyro-kinetic limit). We introduce two modifications to the earlier scheme. The first is the explicit gyro-averaging of the electric field at the half time-step, along with an analogous modification to the current deposition, which we show preserves total energy conservation in implicit PIC schemes. The number of gyrophase samples is chosen adaptively, ensuring proper averaging for large timesteps, and the recovery of full-orbit dynamics in the small time-step limit. The second modification is an alternating large and small time-step strategy that ensures the particle trajectory samples gyrophases evenly. We show that this strategy relaxes the time-step restrictions on the scheme, allowing even larger speed-ups than previously achievable. We demonstrate the new method with several single-particle motion tests in a variety of electromagnetic field configurations featuring gyro-scale variation in the electric field. The results demonstrate the advertised ability to capture FLR effects accurately even when significantly stepping over the gyration time-scale.

physics.comp-ph↗

arXiv2023

An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields

We introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC implementations with a new asymptotic-preserving particle-push scheme that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all particle drifts, while recovering the full orbit for small timesteps. The scheme allows for a seamless, efficient treatment of particles with coexisting magnetized and unmagnetized species, and conserves energy and charge exactly without spoiling implicit solver performance. We demonstrate by numerical experiment with several problems of variable species magnetization (diocotron instability, modified two-stream instability, and drift instability) that orders of magnitude wall-clock-time speedups vs. the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution accuracy.

physics.comp-ph↗

arXiv2021

Fully kinetic simulations of strong steady-state collisional planar plasma shocks

We report on the first steady-state simulations of strong plasma shocks with fully kinetic ions and electrons, independently confirmed by two fully kinetic codes (an Eulerian continuum and a Lagrangian particle-in-cell). While kinetic electrons do not fundamentally change the shock structure as compared with fluid electrons, we find an appreciable rearrangement of the preheat layer, associated with nonlocal electron heat transport effects. The electron heat flux profile qualitatively agrees between kinetic and fluid electron models, suggesting a certain level of "stiffness", though substantial nonlocality is observed in the kinetic heat flux. We also find good agreement with nonlocal electron heat-flux closures proposed in the literature. Finally, in contrast to the classical hydrodynamic picture, we find a significant collapse in the "precursor" electric-field shock at the preheat layer edge, which correlates with the electron-temperature gradient relaxation.

physics.plasm-ph↗

arXiv2021

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

We propose an unsupervised machine-learning checkpoint-restart (CR) lossy algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm features a particle compression stage and a particle reconstruction stage, where a continuum particle distribution function is constructed and resampled, respectively. To guarantee fidelity of the CR process, we ensure the exact preservation of charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. We demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm on physical problems of interest, with compression factors $\gtrsim75$ with no appreciable impact on the quality of the restarted dynamics.

cs.DC↗

arXiv2020

An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

We consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

physics.plasm-ph↗

arXiv2019

A fully implicit, scalable, conservative nonlinear relativistic Fokker-Planck 0D-2P solver for runaway electron

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic runaway electrons (MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. For this purpose, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker-Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron-ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham-Lorentz-Dirac reaction term. However, our implementation improves on these earlier studies by 1) ensuring exact conservation properties for electron collisions, 2) strictly preserving positivity, and 3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams-Karney potentials [Braams and Karney, Phys. Rev. Lett. 59, 16 (1987)], and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

physics.comp-ph↗

arXiv2019

An energy-conserving and asymptotic-preserving charged-particle orbit implicit time integrator for arbitrary electromagnetic fields

We present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit motion in the small time-step limit, but also recovers all the first-order guiding center drifts as well as the correct gyroradius when stepping over the gyration time-scale. In contrast to previous efforts in this direction, the new scheme also features exact energy conservation. In the derivation of the scheme, we find that a new numerical time-scale is introduced. This scale is analyzed and the resulting restrictions on time-step are derived. Based on this analysis, we develop an adaptive time-stepping strategy the respects these constraints while stepping over the gyration scale when physically justified. It is shown through numerical tests on single-particle motion that the scheme's energy conservation property results in tremendous improvements in accuracy, and that the scheme is able to transition smoothly between magnetized and unmagnetized regimes as a result of the adaptive time-stepping.

physics.comp-ph↗

arXiv2019

A semi-implicit, energy- and charge-conserving particle-in-cell algorithm for the relativistic Vlasov-Maxwell equations

Conventional explicit electromagnetic particle-in-cell (PIC) algorithms do not conserve discrete energy exactly. Time-centered fully implicit PIC algorithms can conserve discrete energy exactly, but may introduce large dispersion errors in the light-wave modes. This can lead to intolerable simulation errors where accurate light propagation is needed (e.g. in laser-plasma interactions). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce an exactly energy- and charge-conserving relativistic electromagnetic PIC algorithm. Specifically, we employ the leap-frog method for Maxwell's equations, and the Crank-Nicolson method for the particle equations. The semi-implicit algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm employs a new particle pusher designed to maximize efficiency and minimize wall-clock-time impact vs. the explicit alternative. It has been implemented in a code named iVPIC, based on the Los Alamos National Laboratory VPIC code (\url{https://github.com/losalamos/vpic}). We present numerical results that demonstrate the properties of the scheme with sample test problems: relativistic two-stream instability, Weibel instability, and laser-plasma instabilities.

physics.comp-ph↗

arXiv2017

Formation and Evolution of Target Patterns in Cahn-Hilliard Flows

We study the evolution of the concentration field in a single eddy in the 2D Cahn-Hilliard system to better understand scalar mixing processes in that system. This study extends investigations of the classic studies of flux expulsion in 2D MHD and homogenization of potential vorticity in 2D fluids. Simulation results show that there are three stages in the evolution: (A) formation of a jelly roll pattern, for which the concentration field is constant along spirals; (B) a change in isoconcentration contour topology; and (C) formation of a target pattern, for which the isoconcentration contours follow concentric annuli. In the final target pattern stage, the isoconcentration bands align with stream lines. The results indicate that the target pattern is a metastable state. Band merger process continues on a time scale exponentially long relative to the eddy turnover time. The band merger process resembles step merger in drift-ZF staircases; this is characteristic of the long-time evolution of phase separated patterns described by the Cahn-Hilliard equation.

physics.flu-dyn↗

arXiv2011

An efficient mixed-precision, hybrid CPU-GPU implementation of a fully implicit particle-in-cell algorithm

Recently, a fully implicit, energy- and charge-conserving particle-in-cell method has been proposed for multi-scale, full-f kinetic simulations [G. Chen, et al., J. Comput. Phys. 230,18 (2011)]. The method employs a Jacobian-free Newton-Krylov (JFNK) solver, capable of using very large timesteps without loss of numerical stability or accuracy. A fundamental feature of the method is the segregation of particle-orbit computations from the field solver, while remaining fully self-consistent. This paper describes a very efficient, mixed-precision hybrid CPU-GPU implementation of the implicit PIC algorithm exploiting this feature. The JFNK solver is kept on the CPU in double precision (DP), while the implicit, charge-conserving, and adaptive particle mover is implemented on a GPU (graphics processing unit) using CUDA in single-precision (SP). Performance-oriented optimizations are introduced with the aid of the roofline model. The implicit particle mover algorithm is shown to achieve up to 400 GOp/s on a Nvidia GeForce GTX580. This corresponds to 25% absolute GPU efficiency against the peak theoretical performance, and is about 300 times faster than an equivalent serial CPU (Intel Xeon X5460) execution. For the test case chosen, the mixed-precision hybrid CPU-GPU solver is shown to over-perform the DP CPU-only serial version by a factor of \sim 100, without apparent loss of robustness or accuracy in a challenging long-timescale ion acoustic wave simulation.

physics.plasm-ph↗

arXiv2011

An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm

This paper discusses a novel fully implicit formulation for a 1D electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson formulation), ours is based on a nonlinearly converged Vlasov-Ampère (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (CFL) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical roundoff for arbitrary implicit time steps. While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling. The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton-Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.

physics.comp-ph↗