Engineering topics

Hansen, P. J.

Publications and source records attributed to Hansen, P. J..

9 records

NASA NTRS1994

Parallel inhomogeneity and the Alfven resonance. 1: Open field lines

In light of a recent demonstration of the general nonexistence of a singularity at the Alfven resonance in cold, ideal, linearized magnetohydrodynamics, we examine the effect of a small density gradient parallel to uniform, open ambient magnetic field lines. To lowest order, energy deposition is quantitatively unaffected but occurs continuously over a thickened layer. This effect is illustrated in a numerical analysis of a plasma sheet boundary layer model with perfectly absorbing boundary conditions. Consequences of the results are discussed, both for the open field line approximation and for the ensuing closed field line analysis.

Hansen, P. J.↗

NASA NTRS1993

On the Prediction of the Number of Solitons Excited by an Arbitrary Potential: An Observation from Inverse Scattering

A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.

Hansen, P. J.↗

NASA NTRS1992

Validity of the field line resonance expansion

The field line resonance expansion is studied with a magnetohydrodynamic (MHD) model applicable to earth's magnetotail. Using a Frobenius series solution, this expansion is found to be inconsistent. The inconsistency is seen by evaluating the terms in the model equations that the expansion neglects as small. Their effect is to provide a solution more singular than that determined by the expansion procedure. A tentative alternative expansion procedure, retaining these neglected terms approximately, yields a nonsingular solution, suggesting that resonant mode conversion rather than field line resonance is the appropriate phenomenon.

Hansen, P. J.↗

NASA NTRS1990

Resonant Alfven wave heating of the plasma sheet boundary layer

The exchange of energy between the plasma mantle and the plasma sheet boundary layer (PSBL) is examined with a one-dimensional magnetotail model. The energy exchange occurs via Poynting flux generated by the localized mode conversion of a surface wave to an Alfven wave. This Poynting flux propagates through the lobe and into the PSBL where it is absorbed by two processes. The first arises from a gradient in the plasma beta causing a smooth absorption of Poynting flux. The second process results from the localized mode conversion of the decaying surface wave to an Alfven wave, causing a localized absorption of energy. A numerical solution of the linearized ideal MHD equations is obtained by assuming an adiabatic equation of state.

Harrold, B. G.↗

NASA NTRS1986

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

Kaup, D. J.↗

NASA NTRS1985

The Toda lattice as a forced integrable system

The analytic properties of the Jost functions for the inverse scattering transform associated with the forced Toda lattice are shown to determine the time evolution of this particular boundary value problem. It is suggested that inverse scattering methods may be used generally to analyze forced integrable systems. Thus an extension of the applicability of the inverse scattering transform is indicated.

Hansen, P. J.↗

NASA NTRS1983

Weak cubic Langmuir turbulence

The cubically nonlinear Schroedinger equation model of Langmuir turbulence is solved in the weak turbulence limit. Steady-state power-law solutions for the energy spectra are found in arbitrary dimensionality. In one spatial dimension, the theory incorrectly predicts that no spectrum evolves in time. In three spatial dimensions, numerical solutions are obtained for the undriven, undamped, initial value problem and for the driven, damped, initial value problem.

Hansen, P. J.↗

NASA NTRS1982

Solitons and ionospheric modification

The possibility of Langmuir soliton formation and collapse during ionospheric modification is investigated. Parameters characterizing former facilities, existing facilities, and planned facilities are considered, using a combination of analytical and numerical techniques. At a spatial location corresponding to the exact classical reflection point of the modifier wave, the Langmuir wave evolution is found to be dominated by modulational instability followed by soliton formation and three-dimensional collapse. The earth's magnetic field is found to affect the shape of the collapsing soliton. These results provide an alternative explanation for some recent observations.

Sheerin, J. P.↗

NASA NTRS1982

Solitons and ionospheric heating

It is noted that for parameters characterizing the Platteville ionospheric heating facility, the Langmuir wave evolution at the exact reflection point of the heater wave involves an oscillating two-stream instability followed by a collisionally damped three-dimensional soliton collapse. The result gives an alternative explanation for certain experimental observations.

Weatherall, J. C.↗