SEARCH · Search NASA

Results for “dispersive equations”

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.

SourceResearch connectionFrom yearThrough year

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

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

NASA NTRS1977

Non-symmetric two-stream instability

A theoretical investigation is performed concerning the instability spectrum of quasi-electrostatic waves at shifted half-odd-integer values of the cyclotron frequency due to nonsymmetric counterstreaming electron beams. The beam velocities parallel and perpendicular to the static magnetic field are represented by double Dirac delta functions with no imposition of parameter limitations. Systematic consideration is given to the coupling between plasma modes and cyclotron modes as well as the coupling between cyclotron modes of the two beams that result in shifted half-odd-integer multiples of the cyclotron frequency. The general dispersion equation for quasi-electrostatic waves is analyzed, and plasma-cyclotron coupling in the nonsymmetric case is treated by deriving approximate analytical expressions for maximum growth rates and marginal stability. Exact numerical solutions in both frequency and wavenumber space are obtained and compared with the analytical expressions. Cyclotron-cyclotron coupling modes are treated in the same way, and the results for both types of coupling are compared. It is found that certain modes may be weakened or completely suppressed when the Bessel functions for specific plasma parameters vanish.

Cuperman, S.↗

NASA NTRS1979

Finite beta effects on the drift-cyclotron instability

The effects of finite plasma beta and strong plasma inhomogeneities on the microinstability resulting from the unstable coupling of ion-cyclotron oscillations and an ion drift wave are examined. A local electromagnetic, kinetic dispersion equation, which takes into account finite orbit modifications of both ions and electrons as well as the effects of strong inhomogeneities on the ions and permits the continuous tracking of the instability from the weak gradient regime to the strong gradient regime, is derived and solved numerically. Finite beta is shown to increase the frequency and reduce the growth rate of the instability, but not completely stabilize it due to electromagnetic effects. When plasma inhomogeneity is sufficiently strong, finite beta reduces the growth rate of the large k sub y band of a given harmonic more than the small k sub y band; however, the most unstable bands remain the same as in the case of zero beta. Implications of these results for the Tandem Mirror Experiment are discussed.

Gladd, N. T.↗

NASA NTRS1980

Interaction of ocean waves with a soft bottom

Soft muddy bottoms have significant effects on properties of water waves which propagate over them. The wave dispersion equation is modified and wave energy is dissipated by the coupling between the waves in water and those induced in the mud layer. These effects are theoretically determined by assuming a viscoelastic mud layer. A boundary-value problem is solved for the water-mud system with sinusoidal waves. The theoretical dissipation rates are compared favorably with field measurements.

Hsiao, S. V.↗

NASA NTRS1982

Wave excitation by inhomogeneous suprathermal electron beams

Wave excitation by an inhomogeneous suprathermal electron beam in a homogeneous magnetized plasma is studied. Not only is the beam density nonuniform, but the beam electrons possess a sheared bulk velocity. The general dispersion equation encompassing both electrostatic and electromagnetic effects is derived. Particular attention is given to the whistler mode. It is established that the density-gradient and velocity-shear effects are important for waves with frequencies close to the lower-hybrid resonance frequency.

Freund, H. P.↗

NASA NTRS1982

Electromagnetic cyclotron-loss-cone instability associated with weakly relativistic electrons

The amplification of fast extraordinary mode waves at frequencies very close to the electron cyclotron frequency, due to the presence of a population of energetic electrons with a loss-cone type distribution, is studied. Low-energy background electrons are included in the analysis. Two types of loss-cone distribution functions are considered, and it is found that the maximum growth rates for both distribution functions are of the same order of magnitude. When the thermal effects of the energetic electrons are included in the dispersion equation, the real frequencies of the waves are lower than those obtained by using the cold plasma approximation. This effect tends to enhance the growth rate. An idealized case including a parallel electric field such that the distribution function of the trapped energetic electrons is modified is also considered. It is assumed that the parallel electric field can remove the low-energy background electrons away from the source region of radiation. Both these effects increase the growth rate.

Wong, H. K.↗

NASA NTRS1982

Collisionless electrostatic interchange instabilities

The linear Vlasov dispersion equation for electrostatic plasma instabilities driven by gravity and weak density gradients perpendicular to a uniform magnetic field is derived and solved numerically. Two interchange instabilities emerge: the well-known fluid mode at long wavelengths and a kinetic model at wavelengths short compared with the ion gyroradius. The properties of both instabilities are studied, as well as the effects of gravity on the universal and lower-hybrid density drift instabilities. The results show that the kinetic interchange generally has a larger growth rate than the fluid interchange instability, indicating that, whenever the latter is present in a collisionless plasma, the former may also be found.

Gray, S. P.↗

NASA NTRS1983

Density drift instabilities and weak collisions

A model is developed which describes the effects of weak collisions on the linear kinetic theory of electrostatic density drift instabilities. A dispersion equation valid at all frequencies and wave numbers is derived using the assumptions of a weak, uniform density gradient; a uniform magnetic field; and the BGK collision operator with a modification of the local approximation. The properties of the universal and collisional density drift instabilities at maximum growth rates are examined in detail. The thresholds of the instabilities are examined for an ionospheric model which includes ion-neutral, electron-neutral, and electron-ion collisions, and are compared with the threshold of the lower hybrid density drift instability. It is concluded that the k to the -5th short wavelength density power spectra observed above 280 km in the PLUMEX experiment are due to the effects of the universal density drift instability.

Gary, S. P.↗

NASA NTRS1982

Plasma waves produced by the xenon ion beam experiment on the Porcupine sounding rocket

The production of electrostatic ion cyclotron waves by a perpendicular ion beam in the F-region ionosphere is described. The ion beam experiment was part of the Porcupine program and produced electrostatic hydrogen cyclotron waves just above harmonics of the hydrogen cyclotron frequency. The plasma process may be thought of as a magnetized background ionosphere through which an unmagnetized beam is flowing. The dispersion equation for this hypothesis is constructed and solved. Preliminary solutions agree well with the observed plasma waves.

Kintner, P. M.↗

NASA NTRS1984

Velocities of guided ultrasonic waves in heterogeneous medium

Experimental and theoretical examinations were performed of the longitudinal velocity characteristics of waves in trilaminar and encapsulated waveguides. The study was confined to waveguides with core material that featured transverse wave velocities much worse than the longitudinal wave velocities. The velocities were obtained using a dispersion equation, with consideration given to both the core and encapsulant. Asymptotic velocities were also calculated for bending and twisting in trilaminar waveguides. Trials were run with bimetallic waveguides for comparison with the theoretical predictions. Good agreement was found between the predicted velocity of the propagation of the fundamental mode and the measured velocities. The method was calculated valid for modes above four, confirming that the data were contained in either the core or outer layer, and were unsensitive to the encapsulant.

Touratier, M.↗

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 NTRS1984

Electromagnetic ion beam instabilities

The linear theory of electromagnetic instabilities driven by an energetic ion beam streaming parallel to a magnetic field in a homogeneous Vlasov plasma is considered. Numerical solutions of the full dispersion equation are presented. At propagation parallel to the magnetic field, there are four distinct instabilities. A sufficiently energetic beam gives rise to two unstable modes with right-hand polarization, one resonant with the beam, the other nonresonant. A beam with sufficiently large T (perpendicular to B)/T (parallel to B) gives rise to the left-hand ion cyclotron anisotropy instability at relatively small beam velocities, and a sufficiently hot beam drives unstable a left-hand beam resonant mode. The parametric dependences of the growth rates for the three high beam velocity instabilities are presented here. In addition, some properties at oblique propagation are examined. It is demonstrated that, as the beam drift velocity is increased, relative maxima in growth rates can arise at harmonics of the ion cyclotron resonance for both right and left elliptically polarized modes.

Gary, S. P.↗

NASA NTRS1985

Perturbation-iteration theory for analyzing microwave striplines

A perturbation-iteration technique is presented for determining the propagation constant and characteristic impedance of an unshielded microstrip transmission line. The method converges to the correct solution with a few iterations at each frequency and is equivalent to a full wave analysis. The perturbation-iteration method gives a direct solution for the propagation constant without having to find the roots of a transcendental dispersion equation. The theory is presented in detail along with numerical results for the effective dielectric constant and characteristic impedance for a wide range of substrate dielectric constants, stripline dimensions, and frequencies.

Kretch, B. E.↗

NASA NTRS1985

Whistler damping at oblique propagation - Laminar shock precursors

This paper addresses the collisionless damping of whistlers observed as precursors standing upstream of oblique, low-Mach number terrestrial bow shocks. The linear theory of electromagnetic waves in a homogeneous Vlasov plasma with Maxwellian distribution functions and a magnetic field is considered. Numerical solutions of the full dispersion equation are presented for whistlers propagating at an arbitrary angle with respect to the magnetic field. It is demonstrated that electron Landau damping attenuates oblique whistlers and that the parameter which determines this damping is beta-e. In a well-defined range of parameters, this theory provides damping lengths which are the same order of magnitude as those observed. Thus electron Landau damping is a plausible process in the dissipation of upstream whistlers. Nonlinear plasma processes which may contribute to precursor damping are also discussed, and criteria for distinguishing among these are described.

Gary, S. P.↗

NASA NTRS1985

Electromagnetic ion beam instabilities - Hot beams at interplanetary shocks

This paper considers Vlasov instabilities driven by a very hot ion beam streaming parallel to a magnetic field. The linear theory of electromagnetic instabilities driven by such a beam in a homogeneous, collisionless, nonrelativistic plasma is used. Numerical solutions of the full linear dispersion equation for bi-Maxwellian distribution functions are presented. If the thermal speed of the beam is greater than its drift speed, the two dominant modes are the right-hand and left-hand resonant ion beam instabilities. The parametric dependencies of the threshold drift speeds and growth rates for both modes are presented. In particular, the thresholds are shown to be sensitive functions of the beam temperature anisotropies. Arguments are presented that these two modes are driven by the suprathermal ion component at interplanetary shocks, and that the growth of these modes is sufficient to account for the amplitudes of MHD-like waves observed at such shocks.

Gary, S. P.↗

NASA NTRS1985

Coupling of newborn ions to the solar wind by electromagnetic instabilities and their interaction with the bow shock

The process by which the solar wind assimilates newly ionized atoms is important for understanding the presence of planetary or interstellar helium in the solar wind, the dynamics of the Active Magnetospheric Particle Tracer Explorers (AMPTE) lithium releases in front of the earth's bow shock, and the formation of cometary tails. In this paper is examined how newborn ions can be coupled to the solar wind in the direction parallel to the magnetic field by means of electromagnetic instabilities driven by the distribution of newborn ions. The linear properties of three instabilities are analyzed and compared with numerical solutions of the linear dispersion equation, while their nonlinear behavior is followed by means of computer simulation to obtain the characteristic time for the pickup process. With a primary emphasis on the AMPTE lithiuim releases, various degrees of realism are introduced into the calculations to model the upstream conditions and the intersection of the lithium with the bow shock. It is shown that a time-dependent shock model is needed to correctly reproduce the amount of lithium which is transmitted through the shock and that the resulting lithium ion distribution is still likely to be subject to the same type of instabilities in the magnetosheath. Applications of these results to comets, in particular the artificial comet expected to be generated by the AMPTE barium release in the magnetosheath, is also briefly discussed.

Winske, D.↗

NASA NTRS1985

The whistler mode in a Vlasov plasma

In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation. To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions. For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate. The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory.

Tokar, R. L.↗

NASA NTRS1985

Pulsar magnetospheres in binary systems

The criterion for stability of a tangential discontinuity interface in a magnetized, perfectly conducting inviscid plasma is investigated by deriving the dispersion equation including the effects of both gravitational and centrifugal acceleration. The results are applied to neutron star magnetospheres in X-ray binaries. The Kelvin-Helmholtz instability appears to be important in determining whether MHD waves of large amplitude generated by instability may intermix the plasma effectively, resulting in accretion onto the whole star as suggested by Arons and Lea and leading to no X-ray pulsar behavior.

Ershkovich, A. I.↗

NASA NTRS1985

Electromagnetic electron temperature anisotropy instabilities

This paper considers electromagnetic Vlasov instabilities driven by electron temperature anisotropies in a homogeneous, nonrelativistic magnetized plasma. Numerical solutions of the full linear dispersion equation for bi-Maxwellian distribution functions and instabilities propagating parallel to the magnetic field are presented. Parametric dependences of the maximum growth rates of the electron fire hose and whistler anisotropy instabilities are given.

Gary, S. P.↗