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NASA NTRS1986

Linearly polarized magnetic fluctuations at comet Giacobini-Zinner

The fully electromagnetic linear Vlasov dispersion equation for instabilities in a homogeneous, magnetized plasma is solved. Parameters appropriate to conditions observed during the ICE encounter with comet Giacobini-Zinner are used to study the polarization of electromagnetic instabilities driven by the relative streaming of two ion components. If the ion/ion relative drift is near the Alfven speed, the associated long-wavelength modes may be approximately linearly polarized at relatively small angles of propagation with respect to the magnetic field. The relatively inhomogeneous plasma background of the comet may impose such oblique propagation, so that this result provides an alternate explanation to the observations of linearly polarized waves near the comet.

Gary, S. Peter↗

NASA NTRS1987

Electron/ion whistler instabilities and magnetic noise bursts

Two whistler instabilities are investigated by means of the linear Vlasov dispersion equation. They are called the electron/ion parallel and oblique whistler instabilities, and are driven by electron/ion relative drifts along the magnetic field. It is demonstrated that the enhanced fluctuations from these instabilities can explain several properties of magnetic noise bursts in and near the plasma sheet in the presence of ion beams and/or field-aligned currents. At sufficiently high plasma beta, these instabilities may affect the current system in the magnetotail.

Akimoto, K.↗

NASA NTRS1993

Ion anisotropy instabilities in the magnetosheath

Recent observations in Earth's magnetosheath have delineated several different kinds of magnetic fluctuation spectra below the proton cyclotron frequency. This paper provides a theoretical interpretation for some of these observations describing solutions of the linear Vlasov dispersion equation for fully electromagnetic instabilities for particle distributions which model those observed in the magnetosheath. This model yields three growing modes: the proton cyclotron anisotropy the helium cyclotron anisotropy, and the mirror instabilities. The results show very good agreement with the observations of mirror-like and proton-cyclotron-like events. This agreement with observations implies that the transition between cyclotron and mirror fluctuation dominance is consistent with linear theory.

Gary, S. P.↗

NASA NTRS1993

Superposition of nonlinear plasma waves

We report results showing that spatially periodic Bernstein-Greene-Kruskal (BGK) waves, which are exact nonlinear traveling wave solutions of the Vlasov-Maxwell equations for collisionless plasmas, satisfy a nonlinear principle of superposition in the small amplitude limit. The analysis explicates the notion of superimposed BGK waves which, as recent numerical calculations suggest, is crucial in the proper description of the time-asymptotic state of a plasma when a large amplitude electrostatic wave undergoes nonlinear Landau damping.

Buchanan, Mark↗

NASA NTRS1995

A new approach to the linear theory of single-species tearing in two-dimensional quasi-neutral sheets

We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component B(sub n) normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Omega(sub n) is comparable to the Harris neutral sheet growth rate. A cross-tail B(sub y) component has little effect on the growth rate for B(sub y) approximately = B(sub n). Even in the limit B(sub y) much greater than B(sub n), the mode is strongly stabilized by B(sub n). We report than random pitch angle scattering can overcome the stabilizing effect of B(sub n) and drive the growth rate up toward the Harris neutral sheet (B(sub n) = 0) value when the pitch angle diffusion rate is comparable to Omega(sub n).

Brittnacher, M.↗

NASA NTRS1995

Mirror Instability in the Solar Wind: The Theory Revisited

"Magnetic holes", localized depressions in the interplanetary magnetic field, have been identified in Ulysses data over a range of several AU and as far as 23 degrees south in latitude by Winterhalter et al., who concluded that these structures are most likely the remnants of structures caused by occasional mirror-mode instability in the solar wind. However, these authors, like a number of previous investigators, used the mirror stability criterion derived from the kinetic theory under very special assumptions. On the other hand, theoretical investigations using the fully self-consistent kinetic theory (Vlasov-Maxwell equations) have shown that the mirror stability criterion is more complicated when electrons and ions have different anisotropies, as is normally the case in the solar wind. Winterhalter et al used an instability criterion of the form R is greater than 1, where R is a function of the thermal anisotropy; the correct criterion (for bi-Maxwellian distributions) is R R is greater than 1 - x(exp 2), where x is a real quantity that depends on both the proton anisotropy and electron anisotropy. So nonzero x would modify the Winterhalter et al results in the direction of reinforcing their conclusions. We have revisited the instability criterion in its most general form, allowing for (a) non-Maxwellian velocity distributions, (b) multiple ion species, and (c) interparticle streaming. These results should give sound theoretical grounding for future observational studies related to the mirror instability, by Ulysses and other spacecraft.

Barnes, A.↗

DOE OSTI2026

Higher-order space-charge stability in anisotropic beams: Vlasov-Poisson derivation, refined dispersion relations, and stability charts

The Hofmann stability chart is used to screen working points in space-charge-dominated linacs. We identify two errors in its published higher-order dispersion relations: missing $(1\mp2\hatη^2/α)$ factors in the third-order $S^4$ coupling residues, and a sign error in the stated isotropic reduction of the fourth-order relation. Both corrections follow from Hofmann's Vlasov-Poisson equations without fitted parameters. They reproduce coherent tune-shift coefficients in the author's later monograph that the printed forms miss by 24% and 127%. Mode-resolved figures from a published application agree with the corrected relations and reject the printed forms, indicating an inconsistency between the 1998 equations and the calculations underlying those tested figures. We quantify the effect on the non-oscillatory stability chart. Inside the adopted $S^2\le10$ comparison domain, printed and corrected forms disagree on 0.73-2.11% of cells, with no preferred direction. Among excluded cells, disagreement reaches 22%, and the printed relation over-predicts instability at every sampled anisotropy. This concentration may help explain why the errors persisted, although it does not establish their historical cause. For PIP-II, the corrected chart flags four of thirty-two evaluable periods, including one on a third-order odd branch missed by a second-order screen. This count covers non-oscillatory modes only and remains conditional on an unresolved factor-five disagreement between two codes on transverse emittance growth.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗

DOE OSTI2023

An extended Vlasov–Fokker–Planck approach for kinetic simulations of laser plasmas

Vlasov–Fokker–Planck simulation codes occupy an important niche in modeling laser-produced plasmas, since they are well suited to studying the effect of collisions on electron kinetic phenomena, especially energy transport. One of the most important elements of energy transport is the absorption of laser light by the plasma; however, simulating this in detail requires resolving oscillations of the laser light, whose characteristic timescale is orders of magnitude shorter than the simulation time needed to study transport physics. For this reason, most Vlasov–Fokker–Planck codes used to study electron transport in laser plasmas rely on simplified models of the laser–plasma coupling. Their underlying assumptions nominally preclude their use for modeling laser light having short-scale structure in space or time, such as broadband lasers. In this work, we derive a more general computational framework suitable for arbitrarily structured laser fields. Furthermore, our approach is based on an extended set of Vlasov–Fokker–Planck equations that separately solve for the low- and high-frequency plasma response. We implement these extended Vlasov–Fokker–Planck equations in the spherical harmonic code K2 and demonstrate the performance of the method on several laser absorption test problems, with particular attention to the judicious selection of time steps, time integrators, and spherical harmonic truncation, according to the intensity and spectrum of the laser light under consideration. Comparison with the widely used Langdon absorption operator shows the Langdon operator performs remarkably well for predicting laser heating in the simple cases considered here, even in situations that would seem to violate its underlying assumptions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Theories derived from Haissinski equation and their applications to electron storage rings

As a stationary solution of the Vlasov–Fokker–Planck equation, the Haissinski equation predicts the equilibrium line density of a bunch that circulates in a storage ring for a given wake function. The research in this paper shows that some equations regarding the centroid shift of the bunch, the peak position of the bunch profile, bunch length, and the impedance from the bunch profile can be derived from the Haissinski equation in a self-consistent manner. Specifically, a generalized quadratic equation for potential-well bunch lengthening is derived to accommodate any arbitrary impedance model (that is, the impedance spectrum under consideration can take any form). This expands upon Zotter's cubic equation, which is primarily applicable to inductive impedance. The equations derived in this paper are tested using computed impedance models for some electron storage rings, showing machine-dependent properties of impedance effects. We conclude that these equations can be employed in electron storage rings to effectively bridge the gap between impedance computations and beam-based measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Structure preservation using discrete gradients in the Vlasov-Poisson-Landau system

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is an accurate model for studying hot plasma dynamics at a kinetic scale where small-angle Coulomb collisions dominate. Our scheme guarantees conservation of mass, momentum and energy as well as preservation of the monotonicity of entropy production in both the time-continuous and discrete systems. We employ the conservative integrator for both the Hamiltonian Vlasov-Poisson equations and the dissipative Landau equation using the PETSc library (www.mcs.anl.gov/petsc) to showcase structure-preserving properties.

Discrete gradients↗

NASA NTRS1984

Wave-particle transport from density drift instabilities - A comparison of local and nonlocal theories

Second-order Vlasov theory is used to compute the dissipation rates of plasma irregularities with a variety of shapes. A derivation of the nonlocal dispersion equation using linearized Vlasov theory is presented. Expressions for the normalized amplitudes of the first-order plasma density and electrostatic potential fluctuations are derived. Expressions are given for the saturation amplitudes of the electrostatic eigenmodes. The wave-particle transport and irregularity dissipation rate are computed by using formulas whose derivation is presented. Computational results for specific density variations are shown, and conclusions on the validity of the local theory as opposed to the nonlocal theory are given.

Bernhardt, P. A.↗

NASA NTRS1977

Implications of Navier-Stokes turbulence theory for plasma turbulence

The methodology of Navier-Stokes fluid turbulence theory is reviewed, with emphasis placed on the relevance of the Navier-Stokes concepts for understanding plasma turbulence. After a brief consideration of the three-dimensional case, two-dimensional problems are discussed. In addition, MHD turbulence and turbulence in Vlasov plasmas are treated. In particular, the direct interaction approximation developed by Kraichnan (1959) is generalized from Navier-Stokes turbulence theory to produce a computable set of differentio-integral equations for a Vlasov plasma.

Montgomery, D.↗

DOE OSTI2024

A physics-informed deep learning description of Knudsen layer reactivity reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov–Fokker–Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, the predictions from the Vlasov–Fokker–Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot, thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov–Fokker–Planck PINN and the results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile, demonstrating that the Vlasov–Fokker–Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A Physics-Informed Deep Learning Description of Knudsen Layer Reactivity Reduction

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

On a Spectral Method for β -particle Bound Excitation Collisions in Kilonovae

The interaction of β-particles with the weakly ionized plasma background is an important mechanism for powering the kilonova (KN) transient signal from neutron star mergers. For this purpose, we present an implementation of the approximate fast-particle collision kernel, described by Inokuti following the seminal formulation of Bethe, in a spectral solver of the Vlasov–Maxwell–Boltzmann equation. In particular, we expand the fast-particle plane-wave atomic excitation kernel into coefficients of the Hermite basis, and derive the relevant discrete spectral system. In this fast-particle limit, the approach permits the direct use of atomic data, including optical oscillator strengths, normally applied to photon–matter interaction. The resulting spectral matrix is implemented in the MASS-APP spectral solver framework, in a way that avoids full matrix storage per spatial zone. We numerically verify aspects of the matrix construction, and present a proof-of-principle 3D simulation of a 2D axisymmetric KN ejecta snapshot. Our preliminary numerical results indicate that a reasonable choice of Hermite basis parameters for β-particles in the KN is a bulk velocity parameter u = 0, a thermal velocity parameter α = 0.5c, and a 9 × 9 × 9 mode velocity basis set (Hermite orders of 0–8 in each dimension). For interior-ejecta sample zones, we estimate that the ratio of thermalization from large-angle (≳2fdg5) bound excitation scattering to total thermalization is ~0.002–0.003.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

Approximations to the plasma dispersion function

Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.

Brinca, A. L.↗

NASA NTRS1980

Some features of inverted-V events as seen from simulated double layers

Results from a numerical simulation of a double layer show some features similar to those of inverted-V events. The strong heating of thermal and precipitating electrons is observed along with extremely low frequency fluctuations found during inverted-V events. It is suggested that after the acceleration of auroral electrons by the double layer, the precipitating free electrons are heated by the nonlinear effects of the electron beam plasma instability. Fluctuations and pulsations of auroral electron fluxes during auroral events are caused by a relaxation type of oscillation. The finite extent of one dimensional plasma is simulated by solving the Vlasov and Poisson equations as an initial and boundary value problem.

Singh, N.↗

NASA NTRS1981

The plasma wake of mesosonic conducting bodies. I - An experimental parametric study of ion focusing by the plasma sheath

The experimental investigation considered is concerned with the deflection of ion streams resulting from the interaction of conducting test bodies with an unmagnetized, mesosonic (supersonic with respect to ions but subsonic with respect to electrons) plasma stream. The investigation is, therefore, limited to plasma-electrostatic interactions. The experimental conditions are similar to those of the spacecraft-ionospheric interaction in that the ionic mass and number density, the electron temperature, and the plasma drift velocity ranges include values appropriate for small satellites or diagnostic probes at 200 to 400 km altitude. The study provides direct observations of deflected ion streams for cylindrical test bodies and gives a detailed description of the effects of the governing, dimensionless parameter ratios obtained from the steady-state, nonmagnetic Maxwell-Vlasov system of equations.

Stone, N. H.↗