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Results for “VLASOV EQUATION”

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1965

The Vlasov equations

Vlasov equations studies and applications of statistical mechanics to plasma dynamics

VLASOV EQUATION↗
NASA NTRS1966

Numerical Studies of the Non-linear Vlasov Equation

The subject of this dissertation is the numerical integration of the initial-value problem for the non-linear Vlasov equation. The Vlasov equation is used to describe the dynamics of a "collisionless", one-dimensional, classical electron gas confined between two perfectly reflecting boundaries. Only the long-range Coulomb interactions of the electrons are considered; effects associated with the discrete structure are neglected. The numerical results obtained for non-linear Landau damping compare well with similar results obtained by Knorr. A general statement of the results on stable initial conditions is: As the degree of non-linearity of the initial conditions is increased, the deviation from linear Landau damping appears sooner and is more severe. In some cases damping was observed to cease. Curves showing the time dependence of the damping decrement are derived and compared with predictions of non-linear theories. New results obtained in this study include the observation that for strongly non-linear cases, the damping of the electric field causes an initially Maxwellian fo (v, O) to develop a peak in the neighborhood of the phase velocity; strong growth of the second harmonic is seen after fo (v, t) develops such a peak. Also new in this study is the interpretation of the development of a certain class of strongly unstable initial conditions as approaching an inhomogeneous equilibrium.

NUMERICAL INTEGRATION↗
NASA NTRS1974

Lagrangian formulation of the one-dimensional Vlasov equation

A new formulation of the one-dimensional Vlasov equation is derived which is analogous to the Kalman-transformed cold-plasma equations. The equations are shown to yield nonsecular, nonlinear approximations to a source or boundary-value problem. It is suggested that the formulation may have other applications in nonlinear plasma theory.

Lewak, G. J.↗
NASA NTRS1972

Vlasov equation eigenvalues and eigenvectors for Fourier-Hermite dispersion matrices of order greater than 1,000

The connection between the Van Kampen and Landau representations of the Vlasov equations has been extended to Fourier-Hermite expansions containing more than 1000 terms by taking advantage of the properties of tridiagonal matrices. These numerical results are regarded as conclusive indications of the nonuniformly convergent behavior of the approximation curve in the limit of an infinite number of terms and represent an extension of work begun by Grant (1967) and by Grant and Feix (1967).

Grant, F. C.↗
NASA NTRS2019

MMS Measurements of the Vlasov Equation: Probing the Electron Pressure Divergence Within Thin Current Sheets

We investigate the kinetic structure of electron-scale current sheets found in the vicinity of the magnetopause and embedded in the magnetosheath within the reconnection exhaust. A new technique for computing terms of the Vlasov equation using Magnetospheric Multiscale (MMS) measurements is presented and applied to study phase space density gradients and the kinetic origins of the electron pressure divergence found within these current sheets. Crescent-shaped structures in ∇(⟂2)f(e) give rise to bipolar and quadrupolar signatures in v · ∇f(e) measured near the maximum ∇ · P(e) inside the current layers. The current density perpendicular to the magnetic field is strong (J⟂ ∼2 μA/sq.m), and the thickness of the current layers ranges from 3 to 5 electron inertial lengths. The electron flows supporting the current layers mainly result from the combination of E × B and diamagnetic drifts. We find nonzero J · E′ within the current sheets even though they are observed apart from typical diffusion region signatures.

Shuster, J. R.↗