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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

The composition, propagation and acceleration of energetic solar particles - A review of United States research 1979-1982

The present review has the objective to cover major developments in American research related to solar energetic particles, both observational and theoretical, taking into account the period from late 1978 to late 1982. It is pointed out that particular progress has been made in the area of solar energetic particle composition with respect to elemental, isotopic, and the distribution of charge states. This progress is primarily the result of improved instrumentation available at a time of higher solar activity. An important aspect of solar particle studies is to understand the propagation of particles from the vicinity of the sun through interplanetary space to wherever the observing instruments are located. Almost all mathematical models for the transport of solar cosmic rays are derived in some sense from the same general Boltzmann or Vlasov equations. Attention is also given to advances related to an understanding of coronal propagation, and acceleration and injection processes.

Mcguire, R. E.↗
NASA NTRS1983

Pedersen density drift instabilities

This paper describes the linear kinetic theory of electrostatic-drift instabilities driven by Pedersen and density-drift velocities. The model uses a uniform magnetic field B; a weak, uniform density gradient in the x direction; and a weak, uniform electric field in the y direction. Weak charged-neutral collisions are represented by the addition of BGK model terms to the Vlasov equation. The resulting local dispersion equation is used to study the properties of the associated instabilities at ka(i) greater than about 1 (where k is the wave number and a(i) is the ion gyroradius). Results show that the E x B gradient drift instability at ka(i) = about 1 may grow in the auroral ionosphere primarily in the vicinity of 200 km and only if the electron density is sufficiently small.

Gary, S. P.↗
NASA NTRS1984

Theory of high-harmonic rectangular gyrotron for TE(mn) modes

In this paper, the linearized relativistic Vlasov equation is solved and a dispersion relation is calculated for the interaction between a relativistic electron beam and the electromagnetic fields of a rectangular waveguide supporting TE(mn) modes. The dispersion relation is simplified to the special case of a frame of reference moving with the electrons and the resulting coupling coefficient epsilon(mn)super l is calculated for various TE(mn) modes. The dependence of epsilon(mn)super l on the parity of the harmonic number l and various mn modes of the waveguide are discussed.

Ferendeci, A. M.↗
NASA NTRS1986

Motion of an electron bunch through a plasma

In space research, pulse-modulated beams, or bunches, of energetic electrons have been used for tracing magnetic field lines and for remote sounding of magnetospheric electric fields. Doubts have been expressed regarding the possibility that an electron bunch would be able to travel through the plasma in space. However, experiments in the ionosphere have shown that, at least on some occasions, bunches of electrons with energies of a few keV have traveled over long distances with no apparent energy loss. The present study is concerned with the theoretical explanation for this phenomenon. The method employed in this study makes use of a direct numerical integration of the Vlasov equation. The results obtained provide the basis for a provisional conclusion concerning the stability of a moving electron bunch in the considered case. It appears that the system is mildly unstable.

Shoucri, M. M.↗
NASA NTRS1985

Linear analysis of an axially grooved rectangular gyrotron for harmonic operation

In an axially grooved rectangular waveguide the linearized Vlasov equation is solved to find the perturbed distribution function resulting from the electromagnetic forces on the electrons. The resulting beam current and the propagating electromagnetic waves of the cold tube are used in the inhomogeneous Maxwell's equation to derive the general dispersion equation. This equation is then transformed into the electron beam frame and the resulting linear growth rate of amplification is calculated. By maximizing the linear growth rate, the operational parameters of the gyrotron are then optimized.

Ferendeci, A. M.↗
NASA NTRS1985

Relationships among the harmonic coefficients of scan plane anisotropies

Frequently, a detector on a spinning spacecraft measures the flux of charged particles whose velocities lie in a plane containing the magnetic field. This flux may be Fourier analyzed as a function of the spacecraft roll angle. Relationships among the Fourier coefficients are derived using the adiabatic solution of the Vlasov equation. These relationships depend only on the fact that the lowest order (in gyroradius) of the distribution function is a function of the magnetic moment and that the first-order term is a function of the lowest order. These relationships may be used to separate the proton from the electron counts registered in Saturn's inner magnetosphere by the University of California's Cerenkov counter on Pioneer 11.

Northrop, T. G.↗
NASA NTRS1986

Missing matter in the vicinity of the sun

The Poisson and Vlasov equations are solved numerically for realistic Galaxy models which include multiple disk components, a Population II spheroid, and an unseen massive halo. The total amount of matter in the vicinity of the sun is determined by comparing the observed distributions of tracer stars, samples of F dwarfs, and K giants with the predictions of the Galaxy models. Results are obtained for a number of different assumed distributions of the unseen disk mass. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the sun is about 0.1 solar mass/cu pc; the corresponding column density is about 30 solar mass/sq pc. This so far unseen material must be in a disk with an exponential scale height of less than 0.7 kpc.

Bahcall, John N.↗
NASA NTRS1987

Dark matter in the galactic disk

Observational data on the distributions of tracer stars, F dwarfs and K giants were used as input to obtain self-consistent solutions for the Poisson and Vlasov equations to set bounds on the amount of missing matter in the solar neighborhood. The numerical computations were carried out using Galaxy models which feature multiple disk components and an unseen massive halo. The star data included the mass components and velocity dispersions. Consideration of various possible distributions of the unseen matter leads to the conjecture that half of the disk material in the solar neighborhood has yet to be observed. Techniques for determining if brown dwarfs are a significant component of the missing mass are discussed, as are improved models which would use limited numbers of tracer stars to set further constraints on the amount and distribution of the missing mass.

Bahcall, John N.↗
NASA NTRS1988

Nonlinear evolution of longitudinal plasma waves

Long-time nonlinear behavior of single-mode longitudinal plasma waves is studied on the basis of the Vlasov equation with Fokker-Planck collision terms. The resonant layer, trapped island, collisional sublayers, and X-point neighborhoods are analyzed. A nonlinear evolution equation is obtained and the wave-generated current is also evaluated.

Pao, Young-Ping↗
NASA NTRS1990

Kinetic equilibria of plasma shear layers

The analysis of plasma beam and shear problems in magnetic fields is usually based on a hydromagnetic fluid model. In a low-density collisionless plasma, however, the kinetic effects of the plasma, such as finite Larmor radius effects, are not yet clearly understood. In this paper, the kinetic equilibria of plasma shears in a uniform and fixed magnetic field, with full ion motion, are discussed by solving the Vlasov equation with a given electric field and drift velocity. In this model, the ion density profile through the plasma shear layer is quite different from the one predicted by a hydromagnetic model. As a result of a complicated ion gyromotion through the shear layer, single- and double-humped ion density profiles are obtained. The dependence on the temperature and the strength of the shear will be discussed. The results show a significant difference between positive and negative shears.

Cai, D.↗
NASA NTRS1990

Equilibrium structure of the plasma sheet boundary layer-lobe interface

Observations are presented which show that plasma parameters vary on a scale length smaller than the ion gyroradius at the interface between the plasma sheet boundary layer and the lobe. The Vlasov equation is used to investigate the properties of such a boundary layer. The existence, at the interface, of a density gradient whose scale length is smaller than the ion gyroradius implies that an electrostatic potential is established in order to maintain quasi-neutrality. Strongly sheared (scale lengths smaller than the ion gyroradius) perpendicular and parallel (to the ambient magnetic field) electron flows develop whose peak velocities are on the order of the electron thermal speed and which carry a net current. The free energy of the sheared flows can give rise to a broadband spectrum of electrostatic instabilities starting near the electron plasma frequency and extending below the lower hybrid frequency.

Romero, H.↗
NASA NTRS1992

A comparison of two plasma models

The time dependent behavior of a plasma which surrounds a highly biased conducting sphere is considered. This plasma is treated as either a cold two component fluid or as a warm plasma whose time development can be found by solving the Vlasov equation. Both models demonstrate oscillatory behavior, but the electric fields predicted by the models are quantitatively quite different in regions close to the surface of the sphere and very similar otherwise. A broadening of the electron distribution function with time is observed indicating local heating of the plasma near the surface of the sphere.

Cottam, Russell↗
NASA NTRS1992

The scaling of relativistic double-year widths - Poisson-Vlasov solutions and particle-in-cell simulations

The study of relativistic plasma double layers is described through the solution of the one-dimensional, unmagnetized, steady-state Poisson-Vlasov equations and by means of one-dimensional, unmagnetized, particle-in-cell simulations. The thickness vs potential-drop scaling law is extended to relativistic potential drops and relativistic plasma temperatures. The transition in the scaling law for 'strong' double layers suggested by analytical two-beam models by Carlqvist (1982) is confirmed, and causality problems of standard double-layer simulation techniques applied to relativistic plasma systems are discussed.

Sulkanen, Martin E.↗
NASA NTRS1992

Birkeland currents in an anisotropic, magnetostatic plasma

The paper derives an expression for the parallel current density for a plasma characterized by negligible bulk flow (magnetostatic velocity and a two-component (anisotropic) pressure tensor by expanding the equilibrium Vlasov equation for each species in the adiabatic parameter until such point as a nonvanishing moment j-parallel = integral d-cubed vv-parallel f is identified. The result is a nonlocal one: it relates j-parallel at one point s along a field line to j-parallel at another (reference) point s0 plus an integral function of the pressure and magnetic field between them. The equation derived by Vasyliunas (1970) is generalized and extended to a plasma in which the pressure tensor is comprised of two separate elements, P-perpendicular and P-parallel. This equation follows when P-perpendicular is set equal to P-parallel and s and s0 are taken to be at the ionosphere and the equator. These results are compared to others in the literature.

Birmingham, Thomas J.↗
NASA NTRS1997

Generalized Kinetic Description of Steady-State Collisionless Plasmas

We present a general solution to the collisionless Boltzmann (Vlasov) equation for a free-flowing plasma along a magnetic field line using Liouville's theorem, allowing for an arbitrary potential structure including non-monotonicities. The constraints of the existing collisionless kinetic transport models are explored, and the need for a more general approach to the problem of self- consistent potential energy calculations is described. Then a technique that handles an arbitrary potential energy distribution along the field line is presented and discussed. For precipitation of magnetospherically trapped hot plasma, this model yields moment calculations that vary by up to a factor of two for various potential energy structures with the same total potential drop. The differences are much greater for the high-latitude outflow scenario, giving order of magnitude variations depending on the shape of the potential energy distribution.

Khazanov, G. V.↗
NASA NTRS2006

Pickup Ion Phase Space Distributions at Titan in a Three Dimensional Exosphere

The composition and structure of neutral exospheres imbedded in moving plasmas can be determined by measurements of the velocity distributions of their pickup ion progeny. In turn, the velocity distributions are dependent on the spatial structure of the neutral source gases. Since Titan's neutral exosphere extends into the Saturn's magnetosphere (or solar wind) and well above its ionopause, it serves as a good place to analyze such characteristics. They are analyzed using pickup ion measurements made by the Cassini Plasma Spectrometer (CAPS) at Titan [e.g., Hartle et al., 2006] and an ion kinetic model. An early version of the model [Hartle and Sittler, 2007] is an expression describing the phase space density of pickup ions, which is derived from the Vlasov equation with an ion source that explicitly accounts for the velocity and spatial variation of the exosphere source gases. The current version used here includes exosphere source gases in three dimensions. A fundamental parameter of the phase space densities is the ratio of the gyroradius to the neutral scale height alpha, = r(sub g)/H. Titan's exosphere structure yields pickup ions whose phase space distributions are beam-like when alpha >> 1 and fluid-like when alpha << 1. Downstream from the source peak, the light pickup ions, with alpha << 1, are easily observed because their phase space densities are almost uniform over the orbit phases. On the other hand, the phase space distributions of the heavier ions, with alpha >> 1, peak over narrow velocity and spatial ranges. This beam-like nature makes it considerably more difficult to observe heavy ions because their downstream positions and viewing directions are narrowly constrained. Examples of these extremes will be discussed.

Hartle, Richard↗
NASA NTRS2009

Lunar Neutral Exposphere Properties from Pickup Ion Analysis

Composition and structure of neutral constituents in the lunar exosphere can be determined through measurements of phase space distributions of pickup ions borne from the exosphere [1]. An essential point made in an early study [ 1 ] and inferred by recent pickup ion measurements [2, 3] is that much lower neutral exosphere densities can be derived from ion mass spectrometer measurements of pickup ions than can be determined by conventional neutral mass spectrometers or remote sensing instruments. One approach for deriving properties of neutral exospheric source gasses is to first compare observed ion spectra with pickup ion model phase space distributions. Neutral exosphere properties are then inferred by adjusting exosphere model parameters to obtain the best fit between the resulting model pickup ion distributions and the observed ion spectra. Adopting this path, we obtain ion distributions from a new general pickup ion model, an extension of a simpler analytic description obtained from the Vlasov equation with an ion source [4]. In turn, the ion source is formed from a three-dimensional exospheric density distribution, which can range from the classical Chamberlain type distribution to one with variable exobase temperatures and nonthermal constituents as well as those empirically derived. The initial stage of this approach uses the Moon's known neutral He and Na exospheres to deriv e He+ and Na+ pickup ion exospheres, including their phase space distributions, densities and fluxes. The neutral exospheres used are those based on existing models and remote sensing studies. As mentioned, future ion measurements can be used to constrain the pickup ion model and subsequently improve the neutral exosphere descriptions. The pickup ion model is also used to estimate the exosphere sources of recently observed pickup ions on KAGUYA [3]. Future missions carrying ion spectrometers (e.g., ARTEMIS) will be able to study the lunar neutral exosphere with great sensitivity, yielding the necessary ion velocity spectra needed to further analysis of parent neutral exosphere properties.

Hartle, R. E.↗
NASA NTRS2011

Pickup Ion Distributions from Three Dimensional Neutral Exospheres

Pickup ions formed from ionized neutral exospheres in flowing plasmas have phase space distributions that reflect their source's spatial distributions. Phase space distributions of the ions are derived from the Vlasov equation with a delta function source using three.dimensional neutral exospheres. The ExB drift produced by plasma motion picks up the ions while the effects of magnetic field draping, mass loading, wave particle scattering, and Coulomb collisions near a planetary body are ignored. Previously, one.dimensional exospheres were treated, resulting in closed form pickup ion distributions that explicitly depend on the ratio rg/H, where rg is the ion gyroradius and H is the neutral scale height at the exobase. In general, the pickup ion distributions, based on three.dimensional neutral exospheres, cannot be written in closed form, but can be computed numerically. They continue to reflect their source's spatial distributions in an implicit way. These ion distributions and their moments are applied to several bodies, including He(+) and Na(+) at the Moon, H(+2) and CH(+4) at Titan, and H+ at Venus. The best places to use these distributions are upstream of the Moon's surface, the ionopause of Titan, and the bow shock of Venus.

Hartle, R. E.↗