Weak electron beams in inhomogeneous plasma
Inhomogeneous plasma containing weak electron beam using Vlasov equation, noting wave-wave coupling effect
Baker, J. C.↗
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Verification of theory on weak turbulence relating to the sequence of diffuse plasma resonances in space.
An interpretation of the sequence of diffuse plasma resonances observed by space probes (Alouette 2 and ISIS-1 satellites) is developed in terms of wave-particle nonlinear interaction in a weakly turbulent plasma including the electrostatic electron cyclotron harmonic wave instability. The longest time duration of the center frequency of the diffuse plasma resonance is found to coincide with the most favorable condition for the electrostatic electron cyclotron harmonic wave instability which is obtained by solving the dispersion equation obtained for a linear approximation of the kinetic wave equation for the warm magnetoactive plasma. The electrostatic field due to the transmission of the intense rf pulse produces plasma turbulence involving nonlinear wave-wave interaction and temperature anisotropy which leads to instability. This instability supplies energy to the turbulence. The process can be thought of as a feedback system.
Oya, H.↗
Plasma waves in the dayside polar cusp. I - Magnetospheric observations.
General survey of the Ogo 5 plasma-wave measurements for the dayside polar-cusp encounters of Nov. 1, 1968, and detailed analysis of the observations at the low-altitude (r approximately 3 to 5 earth radii) cusp boundaries. The survey section contains an overall discussion of the ULF magnetic-field wave levels and the VLF electric-field amplitude ranges measured from perigee out to 9 earth radii on Nov. 1, 1968. These cusp-associated observations are compared with those made on Oct. 27 and Nov. 6, 1968, when Ogo 5 traversed the dayside magnetosphere without encountering the cusp. It is shown that at the November 1 low-altitude cusp boundaries intense wave levels were detected over a broad spectral region at the steep gradients in cusp plasma density and thermal energy. The results are interpreted in terms of drift instabilities for low-beta plasmas with hot ions, and associated wave-particle and wave-wave interactions are briefly discussed.
Scarf, F. L.↗
Wave-wave interactions due to scattering by electrons.
The kinetic wave equation which describes the nonlinear wave-particle interaction in a plasma is considered, and a method which uses the picture of quantized plasmons interacting with particles for the description of nonlinear wave-particle interactions is briefly described. In this method an assumption is made of the Markoffian character of the equation. It is shown that the Markoffian assumption can be justified at least for the case when the plasma is close to a stable stationary state. The diagram method developed by Nishikawa (1966) is used to derive an explicit expression for the kinetic equation. The application of the result to the case of interaction between an electron-wave and an ion-wave is discussed.
Nishikawa, K.↗
Lagrangian description of warm plasmas
Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.
Kim, H.↗
The energy balance of wind waves and the remote sensing problem
Measurements of wave growth indicate an energy balance of the wave spectrum governed primarily by input from the atmosphere, nonlinear transfer to shorter and longer waves, and advection. The pronounced spectral peak and sharp low frequency cut-off characteristic of fetch-limited spectra are explained as a self-stabilizing feature of the nonlinear wave-wave interactions. The momentum transferred from the atmosphere to the wind waves accounts for a large part of the wind drag. These findings are relevant for remote microwave sensing of the sea surface by backscatter and passive radiometry methods.
Hasselmann, K.↗
On the generation of the sequence of diffuse resonances observed on top side ionograms
Two different plasma wave instabilities have been invoked in earlier models for the generation of top side ionogram diffuse resonances. Arguments are presented that support the model based on the Harris instability, i.e., the instability resulting from a sounder-stimulated anisotropic electron velocity distribution. Two modifications to this model are also presented. First, it is only necessary for the instability mechanism to operate for a period of the order of milliseconds (rather than tens of milliseconds) in order to explain the observations. Second, the wave associated with the second harmonic of the electron cyclotron frequency, which enters into the nonlinear wave-wave interaction process included in the model, comes from the side bands of the transmitted sounder pulse rather than from the turbulent state of the plasma caused by the pulse. The second modification provides an explanation for the variation of the time duration observed among the members of the sequence of diffuse resonances.
Benson, R. F.↗
A new model for the high-frequency decametric radiation from Jupiter
It is generally accepted that the Jupiter decametric noise bursts occur at frequencies directly related to the electron gyrofrequencies in the Jupiter ionosphere, and it is frequently suggested that the radiation occurs at the gyrofrequency. The recent Pioneer 10 measurement of a 4-G-(R sub 5) cubed dipole moment provides some basis for a more detailed analysis of the local wave mode involved in the radiation. The direct measurement of a relatively small planetary dipole moment suggests that phenomena associated with local ionospheric wave modes having frequencies higher than local gyrofrequencies should be considered for at least some of the emissions. A possible explanation for certain intense high-frequency Jupiter noise bursts is discussed which is based on a wave-wave coupling mechanism that involves the radiation field and the (n + 1/2) gyrofrequency electrostatic modes.
Scarf, F. L.↗
Interaction between heavier ions and ring current protons
The interaction of thermal oxygen or helium ions and ring current protons may produce a wide variety of phenomena in the magnetosphere. These include the production of energetic oxygen ions or energetic helium ions, modification of the bulge region in the afternoon plasmasphere, heating of electrons in the upper ionosphere and production of stable auroral red arcs, precipitation of energetic protons, and precipitation of energetic alpha particles. Large-amplitude waves generated in the interaction may also lead to wave-wave coupling. The theory developed also suggests that heavier ions such as lithium artificially injected into the ring current to remove ring current protons may be heated substantially in the process. Computations of wave growth have been made for the first time by using measured ring current flux and anisotropies.
Brice, N.↗
Nonlinear stability of solar type 3 radio bursts. 1: Theory
A theory of the excitation of solar type 3 bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one dimension. In this case, the oscillating two stream instability (OTSI) is the dominant nonlinear instability, and is stablized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 A.U. and beyond.
Smith, R. A.↗
Symmetry and selection rules for wave-wave interactions
Selection rules for nonlinear three-wave interactions are derived on the basis of the symmetry of the background medium and the waves themselves. The process described bypasses the formal derivation of the coupling coefficient itself. The primary concern is with the effect of the polarization of the waves on the selection rules. Although consideration is limited to three-wave interactions, the method is easily generalized to more waves. Results are derived for these examples: three waves with parallel propagation vectors in an unmagnetized medium, and three waves propagating parallel, and then perpendicular, to a static magnetic field.
Harker, K. J.↗
VLF wave-wave interaction experiments in the magnetosphere
VLF wave-wave interaction experiments were carried out by injecting various forms of VLF pulses into the magnetosphere from a 21.2 km dipole antenna at Siple, Antarctica. The injected signals propagate along a geomagnetic field line and often interact strongly with energetic electrons trapped in the radiation belts near the equator. Signals may be amplified and trigger emissions. These signals may then interact with one another through these energetic electrons. This report is divided into three parts. In the first part, simulations of VLF pulses propagating in the magnetosphere are carried out. In the second part, it is found for the first time that a 10 ms gap in a triggering wave can induce emission, which may then interact with the post-gap signals. In the third part, sideband triggering is reported for the first time.
Chang, D. C. D.↗
Dynamics of severe storms through the study of thermospheric-tropospheric coupling
Atmospheric acoustic-gravity waves associated with severe local thunderstorms, tornadoes, and hurricanes can be studied through the coupling between the thermosphere and the troposphere. Reverse group ray tracing computations of acoustic-gravity waves, observed by an ionospheric Doppler sounder array, show that the wave sources are in the neighborhood of storm systems and the waves are excited prior to the storms. It is suggested that the overshooting and ensuing collapse of convective turrets may be responsible for generating the acoustic-gravity waves observed. The results of this study also show that the study of wave-wave resonant interactions may be a potential tool for investigating the dynamical behavior of severe storm systems using ionospheric observations of atmospheric acoustic-gravity waves associated with severe storms.
Hung, R. J.↗
Siple station experiments on wave-particle interactions in the magnetosphere
Natural and controlled whistler-mode signals have been used to study nonlinear mechanisms of wave growth and wave-wave interactions (WWI) in the magnetosphere; three general classes of WWI (triggering, suppression, and entrainment) are identified and interpreted in terms of a model based on cyclotron resonance interaction. This model is also used to estimate the wave field intensity associated with different types of WWI. A new type of triggered emission, the band-limited impulse (BLI) is interpreted in terms of the switching of phase-bunched currents. In addition, an experiment to find a threshold for the excitation of the coherent wave instability is discussed, and observed VLF wave-induced transient bursts of X-rays, light and E-region ionization enhancements are considered with regard to a step function wave interacting with all resonant electrons in a given energy range.
Helliwell, R. A.↗
Nonlinear stability of solar type III radio bursts. I - Theory
A theory of the excitation of solar type III bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one-dimension. In that case the oscillating two-stream instability (OTSI) is the dominant nonlinear instability. OTSI is stabilized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 AU and beyond.
Smith, R. A.↗
Mechanisms of wave transformation in finite-depth water
Mechanisms of wave transformation in finite-depth water are investigated. The linear mechanisms examined are percolation, bottom motion, shoaling, and refraction. The nonlinear mechanisms examined are wave-wave interaction and bottom friction. New exact computations of the nonlinear transfer for finite-depth waves are presented for some directional wave spectra. These mechanisms are found to explain satisfactorily wave decay observations obtained at several sites with different bottom sediment properties. The decay rates at these sites are found to be dominated by different mechanisms which are determined by the bottom conditions. As an example, detailed calculations are presented for data obtained at the Jonswap site.
Shemdin, O. H.↗
The damping of ocean surface waves by a monomolecular film measured by wave staffs and microwave radars
Open ocean and wave tank experiments were carried out with the aim of studying the damping of capillary and gravity waves by a monomolecular film. These films of biogenic origin influence air-sea interaction processes and thereby affect the use of remote sensing techniques in oceanography. Measurement was carried out by wave staffs, by a coherent X band microwave scatterometer mounted on a sea-based platform, and by an incoherent K band microwave scatterometer carried by an aircraft under moderate wind conditions. A wave attenuation of about 40-60% is observed in the frequency range between 3.2 and 16 Hz. Tank experiments show that a direct influence of oleyl alcohol surface films on wave damping is confined to frequencies equal to or greater than 2 Hz; a further indirect effect of films on the damping of ocean waves in the frequency range between 0.12 and 0.7 Hz (by modifying the wind input and wave-wave interaction mechanisms) is also indicated
Huehnerfuss, H.↗
Numerical simulation of stratospheric sudden warmings with a primitive equation spectral model
A 26-level primitive equation spherical harmonic spectral model allowing for wave-wave and wave-zonal flow interactions is presented for the study of stratospheric sudden warmings. The warmings are simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere. In the case involving both wave-wave and wave-zonal flow interactions, this was manifested by the split in the initial polar vortex into a quasi-wave number 2 pattern. In the cases at 60 deg N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. The linear cases exhibit warmings which are more shallow and more intense at 30 km than the nonlinear cases.
Lordi, N. J.↗