Engineering topics

Nicholson, D. R.

Publications and source records attributed to Nicholson, D. R..

At least 19 records

NASA NTRS1992

A hybrid Zakharov particle simulation of ionospheric heating

A 1D hybrid simulation model incorporating one of the Zakharov equations for the high-frequency waves and a particle-in-cell simulation of the ions is described and applied to ionospheric heating using realistic parameters. Results from the hybrid simulation are compared with a Zakharov simulation that incorporates a phenomenological model of ion damping. Both the hybrid and Zakharov simulations predict the formation of solitonlike waves. The early time behavior of the two simulations is different due to the high noise level in the hybrid simulation, but the late time behavior is quite similar.

Clark, K. L.↗

NASA NTRS1990

Particle simulation of Langmuir turbulence during ionospheric heating

Ionospheric heating leads to strong Langmuir turbulence including modulational instability, soliton formation, and spatial collapse. The Zakharov model usually used to describe these effects contains a low-frequency ion-acoustic wave equation which cannot be rigorously justified in the ionosphere where the electron and ion temperatures are comparable. In the present work, the low-frequency physics is described by a many-ion computer simulation. While some differences are found, the results for the most part confirm the earlier, much less difficult, Zakharov calculations.

Clark, K. L.↗

NASA NTRS1989

Numerical test of weak turbulence theory

The analytic theory of weak Langmuir turbulence is well known, but very little has previously been done to compare its predictions with numerical solutions of the basic dynamical evolution equations. In this paper, numerical solutions of the statistical weak turbulence theory are compared with numerical solutions of the Zakharov model of Langmuir turbulence, and good agreement in certain regimes of very weak field strength is found.

Payne, G. L.↗

NASA NTRS1987

Stochasticity in numerical solutions of the nonlinear Schroedinger equation

The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.

Shen, Mei-Mei↗

NASA NTRS1987

Numerical comparison of strong Langmuir turbulence models

Two models of Langmuir turbulence, the nonlinear Schroedinger equation and the Zakharov equations, are solved numerically for an initial value problem in which the electric field evolves from an almost flat initial condition via the modulational instability and finally saturates into a set of solitons. The two models agree well with each other only when the initial dimensionless electric field has an amplitude less than unity. An analytic soliton gas model consisting of equal-amplitude, randomly spaced, zero-speed solitons is remarkably good at reproducing the time-averaged Fourier spectra in both cases.

Shen, Mei-Mei↗

NASA NTRS1986

Statistical approach to cubic Langmuir turbulence

Previous work on the cubic direct interaction approximation applied to the truncated (in Fourier space) cubically nonlinear Schroedinger equation model of Langmuir turbulence is extended to more modes. In the undriven, undamped case, excellent agreement between the statistical theory and a numerical ensemble of solutions of the dynamic equations is obtained. In the driven, damped case, satisfactory agreement is obtained provided the dynamic ensemble is limited to initial conditions in the basin of attraction.

Sun, G.-Z.↗

NASA NTRS1985

Statistical theory of cubic Langmuir turbulence

The cubic direct interaction approximation is applied to a truncated (in Fourier space) version of the cubically nonlinear Schroedinger equation model of Langmuir physics. The results are compared (in the three-mode case) to those for an ensemble of numerical solutions of the dynamical equations with 10,000 different sets of Gaussianly distributed initial conditions. In the undriven, undamped case, the statistical theory (but not the ensemble) evolves to a state of thermal equilibrium. In the driven, damped case, the statistical theory appears to evolve to a state close to that corresponding to one of the limit cycles of the dynamical equations.

Sun, G.-Z.↗

NASA NTRS1985

Statistical theory of cubic Langmuir turbulence

The cubic direct-interaction approximation is applied to the truncated cubically nonlinear Schroedinger equation. The statistical theory does a satisfactory job in several important respects.

Sun, G.-Z.↗

NASA NTRS1985

Statistical theories of Langmuir turbulence. II - Subsonic to sonic transition

The subsonic limit of the quadratic direct interaction approximation (DIA) applied to the Zakharov equations is compared with the cubic DIA applied to the nonlinear Schroedinger equation, which is the subsonic limit of the Zakharov equations. Comparisons with Monte Carlo simulations of a truncated system show that the first theory more accurately describes the regime of stationary turbulence, while the second theory more accurately describes the subsonic evolution of the modulational instability. The weak turbulence limits of the two theories describe the sonic and subsonic regimes, respectively. The addition of vertex corrections to the DIA leads to a hybrid weak turbulence theory that smoothly interpolates between the sonic and subsonic regimes.

Dubois, D. F.↗

NASA NTRS1984

Modulational instability and soliton formation during ionospheric heating

The most intense electric fields during ionospheric heating occur a fraction of a kilometer below the classical reflection point. At this location, the nonlinear evolution of Langmuir waves is studied within the context of the modified Zakharov equations. It is found that the modulational instability (oscillating two-stream instability) is more important than the three-wave parametric decay instability, leading to the rapid formation of solitons.

Payne, G. L.↗

NASA NTRS1984

Solitons versus parametric instabilities during ionospheric heating

Various effects associated with ionospheric heating are investigated by numerically solving the modified Zakharov (1972) equations. It is shown that, for typical ionospheric parameters, the modulational instability is more important than the parametric decay instability in the spatial region of strongest heater electric field. It is concluded that the modulational instability leads to the formation of solitons, as originally predicted by Petviashvili (1976).

Nicholson, D. R.↗

NASA NTRS1984

Parametric instabilities during electron cyclotron heating of tandem mirrors

Electron cyclotron resonance heating is one of the most commonly used methods of heating electrons in the plugs and in the thermal barriers of tandem mirrors. The intense coherent electromagnetic waves used for such heating are susceptible to parametric decay into other modes. Significant growth rates are found for the decay of either ordinary or extraordinary waves into two magnetized electron plasma waves. This and related effects may result in electron heating mechanisms rather different than those assumed in linear ray-tracing calculations. These results may help explain the unusual effects observed during heating of the Phaedrus tandem mirror device. In the general case, these instabilities may be strongly inhibited by density gradients.

Nicholson, D. R.↗

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 NTRS1983

Theory of radar detection of solitons during ionospheric heating

RF modifiers at some existing ionospheric-heating facilities are found to be sufficiently intense for the production of (collapsing) solitons. The detection of these solitons using Thomson radar is considered, and the problem of an electromagnetic wave scattering off a collection of collapsing solitons is treated. The cross section for the process is found to be relatively large, and an intense plasma-line backscatter is predicted. An explanation of the phenomenon of 'plasma-line overshoot' is suggested.

Sheerin, J. P.↗

NASA NTRS1983

Steady-state turbulence with a narrow inertial range

Coupled two-dimensional wave equations are solved on a computer to model Langmuir wave turbulence excited by a weak electron beam. The model includes wave growth due to beam-plasma interaction, and dissipation by Landau damping. The inertial range is limited to a relatively small number of modes such as could occur when the ratio of masses between the negative and positive ions is larger than in a hydrogen plasma, or when there is damping in long wavelength Langmuir waves. A steady state is found consisting of quasistable, collapsed wave packets. The effects of different beam parameters and the assumed narrow inertial range are considered. The results may be relevant to plasma turbulence observed in connection with type III solar bursts.

Weatherall, J. C.↗

NASA NTRS1983

Topics in strong Langmuir turbulence

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Nicholson, D. R.↗

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.↗