arXiv subjects

Opal Issan

Publications and source records attributed to Opal Issan.

11 recordsLinked to original sources

arXiv2026

Mixed Hermite-Legendre spectral method for kinetic plasma simulations

Kinetic collisionless plasma equations are commonly solved via spectral methods in velocity space. The most commonly used spectral method is based on Hermite polynomials with a Maxwellian weight, as this basis efficiently represents near-Maxwellian distributions with relatively few degrees of freedom. An alternative approach uses Legendre polynomials, which are better suited for resolving strongly non-Maxwellian features. In this paper, we propose a mixed method that combines the Hermite and Legendre expansions. The mixed method is particularly advantageous for problems in which non-Maxwellian features are localized in velocity space, such as beams and plateaus. We demonstrate analytically and numerically that the mixed method conserves total mass, momentum, and energy by imposing certain constraints. The numerical results show that, for the same number of degrees of freedom, the proposed mixed method can achieve improved accuracy in comparison to the individual Hermite or Legendre methods, while maintaining comparable computational cost.

physics.plasm-ph↗

arXiv2026

Secondary drift-driven instabilities in the presence of a parallel-propagating electromagnetic ion cyclotron wave and cold multi-component ions

Electromagnetic ion cyclotron (EMIC) waves are commonly observed in Earth's inner magnetosphere, particularly during geomagnetic storms driven by anisotropic ring-current protons. While their role in radiation belt scattering of hot ions is well established, their interaction with the cold (less than 100 eV) plasma remains less understood. This is partly due to limited magnetospheric cold ion observations, as spacecraft charging can prevent cold ions from reaching onboard instruments. It is well-known that the electric field of a parallel-propagating EMIC wave can drive inter-species perpendicular polarization drifts that excite lower-hybrid secondary instabilities. In multi-component plasmas, these include the modified two-stream and the ion-ion cross-field instabilities. In this paper, we study the impact of such secondary instabilities on the parallel-propagating EMIC wave and multi-component plasma via a fully kinetic particle-in-cell simulation and linear theory. We find that the secondary waves persist even at low EMIC amplitudes, provided the cold population remains sufficiently cold. The kinetic simulation demonstrates that these secondary modes produce anisotropic heating of cold protons and singly-charged oxygen ions, primarily in the direction perpendicular to the ambient magnetic field and of electrons in both parallel and perpendicular directions.

physics.plasm-ph↗

arXiv2025

Understanding cold electron impact on parallel-propagating whistler chorus waves via moment-based quasilinear theory

Earth's magnetosphere hosts a wide range of collisionless particle populations that interact through various wave-particle processes. Among these, cold electrons, with energies below 100eV, often dominate the plasma density but remain poorly characterized due to measurement challenges such as spacecraft charging and photoelectron contamination. Understanding the contribution of these cold populations to wave-particle interaction is of significant interest. Recent kinetic simulations identified a secondary drift-driven instability in which parallel-propagating whistler-mode chorus waves excite oblique electrostatic whistler waves near the resonance cone and Bernstein-mode turbulence. These secondary modes enable a new channel of energy transfer from the parallel-propagating whistler wave to the cold electrons. In this work, we develop a moment-based quasilinear theory of the secondary instabilities to quantify such energy exchange. Our results show that these secondary instabilities persist for a wide range of parameters and, in many cases, lead to nearly complete damping of the primary wave. Such secondary instability might limit the amplitude of parallel-propagating whistler waves in Earth's magnetosphere and might explain why high-amplitude oblique whistler or electron Bernstein waves are rarely observed simultaneously with high-amplitude field-aligned whistler waves in the inner magnetosphere.

physics.plasm-ph↗

arXiv2025

Conservative projection-based data-driven model order reduction of a fluid-kinetic spectral solver

Kinetic simulations are computationally intensive due to six-dimensional phase space discretization. Many kinetic spectral solvers use the asymmetrically weighted Hermite expansion due to its conservation and fluid-kinetic coupling properties, i.e., the lower-order Hermite moments capture and describe the macroscopic fluid dynamics and higher-order Hermite moments describe the microscopic kinetic dynamics. We leverage this structure by developing a parametric data-driven reduced-order model based on the proper orthogonal decomposition, which projects the higher-order kinetic moments while retaining the fluid moments intact. This approach can also be understood as learning a nonlocal closure via a reduced modal decomposition. We demonstrate analytically and numerically that the method ensures local and global mass, momentum, and energy conservation. The numerical results show that the proposed method effectively replicates the high-dimensional spectral simulations at a fraction of the computational cost and memory, as validated on the weak Landau damping and two-stream instability benchmark problems.

physics.plasm-ph↗

arXiv2024

Effects of Artificial Collisions, Filtering, and Nonlocal Closure Approaches on Hermite-based Vlasov-Poisson Simulations

Kinetic simulations of collisionless plasmas are computationally challenging due to phase space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related to limited velocity resolution in Hermite-based Vlasov-Poisson simulations: artificial collisions, filtering, and nonlocal closure approaches. We evaluate each method's performance in approximating the linear kinetic response function and suppressing recurrence in linear and nonlinear regimes. Numerical simulations of Landau damping demonstrate that artificial collisions, particularly higher orders of the Lenard-Bernstein collisional operator, most effectively recover the correct damping rate across a range of wavenumbers. Moreover, Hou-Li filtering and nonlocal closures underdamp high wavenumber modes in linear simulations, and the Lenard- Bernstein collisional operator overdamps low wavenumber modes in both linear and nonlinear simulations. This study demonstrates that hypercollisions offer a robust approach to kinetic simulations, accurately capturing collisionless dynamics with limited velocity resolution.

physics.plasm-ph↗

arXiv2024

Conservative Closures of the Vlasov-Poisson Equations Based on Symmetrically Weighted Hermite Spectral Expansion

We derive conservative closures of the Vlasov-Poisson equations discretized in velocity via the symmetrically weighted Hermite spectral expansion. The short note analyzes the conservative closures preservation of the hyperbolicity and anti-symmetry of the Vlasov equation. Furthermore, we verify numerically the analytically derived conservative closures on simulating a classic electrostatic benchmark problem: the Langmuir wave. The numerical results and analytic analysis show that the closure by truncation is the most suitable conservative closure for the symmetrically weighted Hermite formulation.

physics.comp-ph↗

arXiv2023

Anti-symmetric and Positivity Preserving Formulation of a Spectral Method for Vlasov-Poisson Equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

math.NA↗

arXiv2023

Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction

The ambient solar wind plays a significant role in propagating interplanetary coronal mass ejections and is an important driver of space weather geomagnetic storms. A computationally efficient and widely used method to predict the ambient solar wind radial velocity near Earth involves coupling three models: Potential Field Source Surface, Wang-Sheeley-Arge (WSA), and Heliospheric Upwind eXtrapolation. However, the model chain has eleven uncertain parameters that are mainly non-physical due to empirical relations and simplified physics assumptions. We, therefore, propose a comprehensive uncertainty quantification (UQ) framework that is able to successfully quantify and reduce parametric uncertainties in the model chain. The UQ framework utilizes variance-based global sensitivity analysis followed by Bayesian inference via Markov chain Monte Carlo to learn the posterior densities of the most influential parameters. The sensitivity analysis results indicate that the five most influential parameters are all WSA parameters. Additionally, we show that the posterior densities of such influential parameters vary greatly from one Carrington rotation to the next. The influential parameters are trying to overcompensate for the missing physics in the model chain, highlighting the need to enhance the robustness of the model chain to the choice of WSA parameters. The ensemble predictions generated from the learned posterior densities significantly reduce the uncertainty in solar wind velocity predictions near Earth.

physics.space-ph↗

arXiv2023

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A quadratization reveals new variables and structures of a model, which may be easier to analyze, simulate, control, and provides a convenient parametrization for learning. This paper presents novel theory, algorithms and software capabilities for quadratization of non-autonomous ODEs. We provide existence results, depending on the regularity of the input function, for cases when a quadratic-bilinear system can be obtained through quadratization. We further develop existence results and an algorithm that generalizes the process of quadratization for systems with arbitrary dimension that retain the nonlinear structure when the dimension grows. For such systems, we provide dimension-agnostic quadratization. An example is semi-discretized PDEs, where the nonlinear terms remain symbolically identical when the discretization size increases. As an important aspect for practical adoption of this research, we extended the capabilities of the QBee software towards both non-autonomous systems of ODEs and ODEs with arbitrary dimension. We present several examples of ODEs that were previously reported in the literature, and where our new algorithms find quadratized ODE systems with lower dimension than the previously reported lifting transformations. We further highlight an important area of quadratization: reduced-order model learning. This area can benefit significantly from working in the optimal lifting variables, where quadratic models provide a direct parametrization of the model that also avoids additional hyperreduction for the nonlinear terms. A solar wind example highlights these advantages.

cs.SC↗

arXiv2022

Predicting Solar Wind Streams from the Inner-Heliosphere to Earth via Shifted Operator Inference

Solar wind conditions are predominantly predicted via three-dimensional numerical magnetohydrodynamic (MHD) models. Despite their ability to produce highly accurate predictions, MHD models require computationally intensive high-dimensional simulations. This renders them inadequate for making time-sensitive predictions and for large-ensemble analysis required in uncertainty quantification. This paper presents a new data-driven reduced-order model (ROM) capability for forecasting heliospheric solar wind speeds. Traditional model reduction methods based on Galerkin projection have difficulties with advection-dominated systems -- such as solar winds -- since they require a large number of basis functions and can become unstable. A core contribution of this work addresses this challenge by extending the non-intrusive operator inference ROM framework to exploit the translational symmetries present in the solar wind caused by the Sun's rotation. The numerical results show that our method can adequately emulate the MHD simulations and outperforms a reduced-physics surrogate model, the Heliospheric Upwind Extrapolation model.

physics.comp-ph↗

arXiv2021

Deep Learning Enhanced Dynamic Mode Decomposition

Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of this infinite-dimensional operator can be difficult. The extended dynamic mode decomposition (EDMD) is one such method for generating approximations to Koopman spectra and modes, but the EDMD method faces its own set of challenges due to the need of user defined observables. To address this issue, we explore the use of autoencoder networks to simultaneously find optimal families of observables which also generate both accurate embeddings of the flow into a space of observables and submersions of the observables back into flow coordinates. This network results in a global transformation of the flow and affords future state prediction via the EDMD and the decoder network. We call this method the deep learning dynamic mode decomposition (DLDMD). The method is tested on canonical nonlinear data sets and is shown to produce results that outperform a standard DMD approach and enable data-driven prediction where the standard DMD fails.

cs.LG↗