Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Vlasov equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

The coupling of Alfven and compressional waves

The article studies the hydromagnetic wave propagation characteristics in a mixture of cold and hot plasma in the presence of an inhomogeneous magnetic field. Electron and ion distribution functions with a temperature anisotropy and a density gradient are used to obtain the dispersion equation by solving the Vlasov equation and Maxwell equations. From the solutions of the dispersion equation we find that the Alfven waves can couple to unstable drift mirror waves under certain conditions. The polarization of the coupled waves is studied for varying parameters of temperature anisotropy and the cold to hot density ratio. From detailed comparison of the theoretical results with the low-frequency wave properties observed in the magnetosphere we propose that the storm-associated magnetic field oscillations with periods of 100-600 s might be caused by the coupling of Alfven waves and the unstable drift mirror waves.

Lin, C. S.↗
NASA NTRS1984

Theory and modeling of atmospheric turbulence, part 2

Two dimensional geostrophic turbulence driven by a random force is investigated. Based on the Liouville equation, which simulates the primitive hydrodynamical equations, a group-kinetic theory of turbulence is developed and the kinetic equation of the scaled singlet distribution is derived. The kinetic equation is transformed into an equation of spectral balance in the equilibrium and non-equilibrium states. Comparison is made between the propagators and the Green's functions in the case of the non-asymptotic quasi-linear equation to prove the equivalence of both kinds of approximations used to describe perturbed trajectories of plasma turbulence. The microdynamical state of fluid turbulence is described by a hydrodynamical system and transformed into a master equation analogous to the Vlasov equation for plasma turbulence. The spectral balance for the velocity fluctuations of individual components shows that the scaled pressure strain correlation and the cascade transfer are two transport functions that play the most important roles.

Chen, C. M.↗
NASA NTRS2000

Generalized Langmuir Waves in Magnetized Kinetic Plasmas

The properties of unmagnetized Langmuir waves and cold plasma magnetoionic waves (x, o, z and whistler) are well known. However, the connections between these modes in a magnetized kinetic plasma have not been explored in detail. Here, wave properties are investigated by numerically solving the dispersion equation derived from the Vlasov equations both with and without a beam instability present. For omega(sub p)>Omega(sub e), it is shown that the generalized Langmuir mode at oblique propagation angles has magnetic z-mode characteristics at low wave numbers and thermal Langmuir mode characteristics at high wave numbers. For omega(sub p)<Omega(sub e), it is shown that the (oblique) Langmuir mode instead connects to the whistler mode at low wave numbers. The transition from the Langmuir/z mode to the Langmuir/whistler mode near omega(sub p) = Omega(sub e) is rapid. In addition, the effects on wave dispersion and polarization after adding a beam are investigated. Applications of this theory to magnetized Langmuir waves in Earth's foreshock and the solar wind, to waves observed near the plasma frequency in the auroral regions, and to solar type III bursts are discussed.

Willes, A. J.↗
NASA NTRS1977

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

Stern, D. P.↗
DOE OSTI2022

The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space

Helicity, a topological degree that measures the winding and linking of vortex lines, is preserved by ideal (barotropic) fluid dynamics. In the context of the Hamiltonian description, the helicity is a Casimir invariant characterizing a foliation of the associated Poisson manifold. Casimir invariants are special invariants that depend on the Poisson bracket, not on the particular choice of the Hamiltonian. The total mass (or particle number) is another Casimir invariant, whose invariance guarantees the mass (particle) conservation (independent of any specific choice of the Hamiltonian). In a kinetic description (e.g., that of the Vlasov equation), the helicity is no longer an invariant (although the total mass remains a Casimir of the Vlasov’s Poisson algebra). The implication is that some “kinetic effect” can violate the constancy of the helicity. To elucidate how the helicity constraint emerges or submerges, we examine the fluid reduction of the Vlasov system; the fluid (macroscopic) system is a “sub-algebra” of the kinetic (microscopic) Vlasov system. In the Vlasov system, the helicity can be conserved if a special helicity symmetry condition holds. To put it another way, breaking helicity symmetry induces a change in the helicity. We delineate the geometrical meaning of helicity symmetry and show that for a special class of flows (the so-called epi-two-dimensional flows), the helicity symmetry is written as ∂γ = 0 for a coordinate γ of the configuration space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Interplanetary gas dynamics.

Observations of the interplanetary medium are considered together with the structure of the solar atmosphere and the kinetic properties of the interplanetary plasma. Methods of gas kinetics and continuum flows are examined, taking into account microscopic and macroscopic representations, the kinetic flow equations, the formal solution of the Vlasov equation, and the continuum flow equations. The collective particle behavior of that interplanetary gas is discussed along with the hydrodynamic coronal expansion, a wave-pump problem, the free expansion phenomenon, and a generalized free expansion problem.

Liu, V. C.↗
DOE OSTI2022

Verification of a fully kinetic ion model for electromagnetic simulations of high-frequency waves in toroidal geometry

For the research of high-frequency electromagnetic waves in tokamaks, an electromagnetic simulation model, in which the ion dynamics is described by a six-dimensional Vlasov equation and the electron dynamics is described by a drift kinetic equation, is formulated and implemented in the global gyrokinetic toroidal code (GTC). Analytic dispersion relations are derived in reduced systems and compared with various theories to verify the model. Linear simulations of a generalized ion Bernstein wave and ion cyclotron emission are verified by comparing the GTC simulation results with analytic dispersion relation theory and magnetoacoustic cyclotron instability theory, respectively, in cylindrical geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electromagnetic formalism

This is a companion paper to the previous work [P. H. Yoon, Phys. Plasmas 31, 032309 (2024)] in which the nonlinear susceptibilities of weakly turbulent magnetized plasma are derived under a simplifying assumption of electrostatic interaction. The present paper extends the analysis to a general situation of electromagnetic interaction. The main novelty of the previous and present papers is that by employing the Bessel function addition theorem, the mathematical definitions for the susceptibilities are substantially simplified, a procedure that has not been discussed in the existing literature. In the present paper, a full set of Maxwell’s equations are considered in conjunction with the nonlinear Vlasov equation, which is solved by a perturbative method. The result is a fully general nonlinear susceptibility, given in tensorial form, which is applicable for weakly turbulent magnetized plasmas.

Materials Science↗
NASA NTRS1989

Oxygen acoustic solitary waves in a magnetized plasma

Ion-acoustic solitary waves in a magnetized plasma containing an arbitrary mixture of H(+) and O(+) ions are studied. A nonlinear wave equation has been derived from the Poisson-Vlasov equations, including a uniform magnetic field and dissipation due to reflected electrons. When dissipation is ignored, the equation has soliton solutions associated with both oxygen and hydrogen acoustic modes, which can be either rarefactive or compressive depending on the ion concentrations and the electron/ion temperature ratio and, more weakly, on the bulk drifts of the species. If electron reflection is included, the solitary wave can be intensified. Under somewhat restrictive conditions the oxygen solitary wave is rarefactive and propagates with a velocity comparable to that observed by the Viking satellite. The three-dimensional solitons obey a relation of scales parallel to the magnetic field and in the transverse direction. Computer simulations of one-dimensional versions of the nonlinear wave equation are presented.

Qian, S.↗
DOE OSTI2022

Modelling general-relativistic plasmas with collisionless moments and dissipative two-fluid magnetohydrodynamics

ABSTRACT Relativistic plasmas are central to the study of black hole accretion, jet physics, neutron star mergers, and compact object magnetospheres. Despite the need to accurately capture the dynamics of these plasmas and the implications for relativistic transients, their fluid modelling is typically done using a number of (overly) simplifying assumptions, which do not hold in general. This is especially true when the mean free path in the plasma is large compared to the system size, and kinetic effects start to become important. Going beyond common approaches used in the literature, we describe a fully relativistic covariant 14-moment based two-fluid system appropriate for the study of electron–ion or electron–positron plasmas. This generalized Israel-Stewart-like system of equations of motion is obtained directly from the relativistic Boltzmann–Vlasov equation. This new formulation can account for non-ideal effects, such as anisotropic pressures and heat fluxes, not present in previous formulations of two-fluid magnetohydrodynamics. We show that a relativistic two-fluid plasma can be recast as a single fluid coupled to electromagnetic fields with (potentially large) out-of-equilibrium corrections. We keep all electron degrees of freedom, which provide self-consistent evolution equations for electron temperature and momentum. The out-of-equilibrium corrections take the form of a collisional 14-moment closure previously described in the context of viscous single fluids. The equations outlined in this paper are able to capture the full two-fluid character of collisionless plasmas found in black hole accretion and flaring processes around compact objects, as well Braginskii-like two-fluid magnetohydrodynamics applicable to weakly collisional plasmas inside accretion discs.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

Dynamics of localized ion-acoustic waves in a magnetized plasma

The evolution of negative potential pulses in a magnetized plasma is studied. A three-dimensional nonlinear ion-acoustic wave equation, including nonstationary effects of reflected electrons, has been derived from the Poisson-Vlasov equations with uniform magnetic field. The studies show that a negative potential pulse can be enhanced by drifting electrons. The growing pulse develops asymmetrically with an oscillatory precursor and a local potential jump resembling the early phase of weak double layer formation.

Qian, S.↗
DOE OSTI2022

Gaussian Mixture Model Solvers for the Boltzmann Equation

This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1971

Kinetic theory of a two-dimensional magnetized plasma.

Several features of the equilibrium and nonequilibrium statistical mechanics of a two-dimensional plasma in a uniform dc magnetic field are investigated. The charges are assumed to interact only through electrostatic potentials. The problem is considered both with and without the guiding-center approximation. With the guiding-center approximation, an appropriate Liouville equation and BBGKY hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially nonuniform situation, a guiding-center Vlasov equation is discussed and solved in special cases. For the nonequilibrium, nonguiding-center case, a Boltzmann equation, and a Fokker-Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral which must be cut off on physical grounds. Several unsolved problems are posed.

Vahala, G.↗
DOE OSTI2024

The fastVFP code for solution of the Vlasov–Fokker–Planck equation

Abstract We describe the fast VFP code for solution of the Vlasov–Fokker–Planck equation for non-local electron transport and the generation of magnetic field, especially for application to laser-produced plasmas. We describe the essential features of the code that make it fast and robust and suitable for inclusion as a transport package in a fluid simulation. We present a few sample results that demonstrate the abilities of the code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1976

A quasi-linear kinetic equation for cosmic rays in the interplanetary medium

A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.

Luhmann, J. G.↗