On application of stochastic differential equations for simulation of nonlinear wave-particle resonant interactions

A. S. Lukin; A. V. Artemyev; A. A. Petrukovich

doi:10.1063/5.0058054

Home/Archive/arXiv

arXiv · 2105.05819

On application of stochastic differential equations for simulation of nonlinear wave-particle resonant interactions

A. S. Lukin·A. V. Artemyev·A. A. Petrukovich

View original source ↗Read source document ↗Export metadata ↓

Abstract

Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and electron adiabatic heating/transport by mesoscale plasma flows. Examples of such systems are Earth's radiation belts and Earth's bow shock, where ion-scale plasma injections and cross-shock electric fields determine the general electron energization, whereas electron scattering by waves relax anisotropy of electron distributions and produces small populations of high-energy electrons. The applicability of stochastic differential equations is a promising approach for including effects of resonant wave-particle interaction into codes of electron tracing in global models. This study is devoted to test of such equations for systems with nondiffusive wave-particle interactions, i.e. systems with nonlinear effects of phase trapping and bunching. We consider electron resonances with intense electrostatic whistler-mode waves often observed in the Earth's radiation belts. We demonstrate that nonlinear resonant effects can be described by stochastic differential equations with the non-Gaussian probability distribution of random variations of electron energies.

Explore related subjects

physics.plasm-ph physics.space-ph

Keep this discovery

BibTeX RIS

A. S. Lukin, A. V. Artemyev, A. A. Petrukovich. 2021-05-12. On application of stochastic differential equations for simulation of nonlinear wave-particle resonant interactions. https://doi.org/10.1063/5.0058054

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Particle-resolved pathways to energetic-ion formation in a fluctuating low-current hollow-cathode plume

Energetic-ion formation in a low-current hollow-cathode plume is investigated using experiments, self-consistent electrostatic particle-in-cell (PIC) simulation, and particle-resolved analysis. Retarding potential analyzer measurements show a substantial energetic-ion population over discharge currents of 0.8-3.5 A, while probe measurements reveal broadband plume fluctuations. Two-point phase-derived frequency-wavenumber measurements do not resolve a continuous ion-acoustic dispersion branch within the principal apparent-wavenumber interval. Because the inferred wavenumber is obtained from a cross-spectral phase defined modulo 2pi, the fluctuation diagnostics do not provide an unambiguous modal attribution for the energetic-ion population. A representative PIC plume, used as a qualitative kinetic reference, likewise develops broadband time-dependent electrostatic fluctuations together with a nonthermal energetic-ion population. Particle-resolved analysis shows that the energetic outflow is dominated by ions generated through ionization inside the plume, while source localization biases access to distinct trajectory and escape families. Matched field controls further show that time-averaged and frozen fields strongly suppress access to high-energy trajectories relative to the full time-dependent field over the analyzed interval. At the single-particle level, ion kinetic-energy gain is determined by electrostatic-field work accumulated along the actual trajectory, with different escape families exhibiting distinct radial and axial work contributions. These results establish a source-trajectory-field-work pathway for energetic-ion formation that can be identified without first assigning the fluctuating plume to a unique resolved plasma mode.

physics.plasm-ph↗

arXiv2026

kobra: a new Vlasov code intended for plasma-wall modeling

In a fusion device plasma-wall interactions \edit{on the sheath scale} can be modeled as a collisionless problem. When modeling these regions particle-in-cell codes suffer from statistical error originating from undersampling the velocity space. On the other hand, Vlasov codes do not have this issue as they evolve the full distribution function. Here, we present a new finite-volume Vlasov code, kobra, equipped with adaptive-mesh refinement to reduce computational effort. Currently, the code solves the Vlasov-Poisson equations. We validate our code in 1d1v and 1d2v using established benchmarks, i.e. the two-stream instability, Landau damping, the Dory-Guest-Harris instability, and also a classical electrostatic plasma sheath. We find that the code reproduces the theoretical properties of these problems well. More importantly, the adaptive grid provides a computational gain that is likely to scale to higher dimensional, plasma-wall simulations.

physics.plasm-ph↗

arXiv2026

Physics-Informed Neural Networks to Infer the Perpendicular Energy Conductivity in the Scrape-Off Layer of Stellarator Devices

In this work, we develop an inverse Physics-Informed Neural Network (PINN) framework to infer the dependence of the scrape-off layer (SOL) perpendicular heat conductivity on plasma density and temperature, $\kappa_\perp(n,T)$. The method combines radial profile measurements of electron density and temperature with the residual of a reduced one-dimensional SOL transport equation, so that the inferred conductivity is constrained by both the measurements and the underlying transport model. Three neural networks are trained simultaneously: two reconstruct the temperature and density profiles as functions of the radial coordinate and transported power, while a third represents the effective conductivity as a function of the local density and temperature. The framework is first validated using synthetic data generated from a prescribed conductivity function, allowing the inferred $\kappa_\perp(n,T)$ to be compared directly with the ground truth. The model recovers the imposed functional dependence with errors below $10~\%$ in the data-constrained region. Bootstrap resampling is shown to provide a practical indicator of prediction reliability and consistency. A scan in the number of plasma profiles used for training and the number of radial measurement positions per profile identifies a practical trade-off between reconstruction accuracy and data availability. Finally, the method is applied to an experimental dataset from the TJ-II stellarator obtained with the helium-beam diagnostic. This exploratory application provides an initial estimate of the effective SOL conductivity and illustrates the potential of inverse PINNs for extracting transport information from plasma edge measurements.

physics.plasm-ph↗