Takayasu Tanaka

Possible Excitation of High-Frequency Waves by a Large Amplitude Low-Frequency Wave in a Plasma

It is well known that when a high-frequency wave (h.£. wave) is present with large amplitude a certain low-frequency wave (Lf. wave) becomes unstable as a result of the parametric interaction.!) Little is known, however, about the reversed problem, namely. whether a h.f. wave becomes unstable due to the presence of a large amplitude 1.£. wave. The purpose of this note is to point out two possible mechanisms which lead to this type of instability. The first mechanism is the emission of a h.£. wave accompanied by absorption of a Lf. wave. Obviously, such a process is inhibited in a transparent medium because of the frequency matching condition. However, if the electron thermal motion is taken into account, the above process becomes possible since the Doppler shifted frequency of the h.£. wave may become comparable to that of the 1.£. wave. Consider, for instance, the case in which a large amplitude ion acoustic wave with wave-number q is present. Then the nonlinear Landau damping of the electron plasma wave with wave-number k can be written in the form 2}

On a Simple One-Dimensional Model of Rough Film Surfaces on a Substrate

A simple one-dimensional model of rough film surfaces on a substrate, in which unit square “atoms” are put at ramdom on a line “substrate” subdivided into unit cells is studied statistically. One of the fractal dimension of asperity of the film surfaces, the average surface length of clusters as a function of its given bottom length, is rigorously obtained. The calculated value of this fractal dimension for the above-mentioned model is approximately equal to \(b/(b+\sqrt{\pi\bar{n}})\) and is smaller than 1.00 for a large average thickness \bar n and a bottom length b . But this result disagrees with the result, 1.05, obtained by Nakamura by means of computer simulation [Phys. Rev. B 40 (1989) 2549]. But, assuming that the deposits are nonuniform and composed of an ensemble of deposits with various average thicknesses, the fractal dimension of the simulation can well be explained.

Direct Excitation of a High Frequency Wave by a Low Frequency Wave in a Plasma

A new mechanism is presented of an excitation of a high frequency wave by a low frequency wave in a plasma. This mechanism works when the low frequency wave varies in time in a manner deviated from a usual periodic motion with a constant amplitude. The conversion rate is usually not large but the conversion is done without time delay after the variation of the low frequency wave. The Manley Rowe relation in the usual sense does not hold in this mechanism. This mechanism can excite also waves with same or lower frequencies.

General Relations among Voltages and Currents in Nonlinear Elements. I

In nonlinear capacitors, inductors and resistors, general equations holding among the voltages and currents at different frequencies are derived. These are obtained only on the assumption that the characteristics for the nonlinear elements are single-valued. The well-known Manley-Rowe relation is the lowest order and simplest ones among these equations. But, even then, the relations are more extensive, in the sense that the number of the voltage generators may be arbitrary.

One-Dimensional Nonlinear Lattices with Exactly Solvable Steady Motion

A simple systematic method is presented to seek for models of one-dimensional nonlinear lattices, which admit exactly solvable steady motion. Each atom is assumed to interact with its nearest neighbors. Some examples are given, focusing attension on the cases where steady motions are described by elliptic functions.

A Method for Nonlinear Plasma Wave Kinetics

A new method is presented to investigate the nonlinear wave kinetics in a plasma. While most previous theories assume that the wave-amplitudes and other average quantities vary very little within the duration time τ of the wave-wave interaction, the present theory is valid under much less restrictive condition that their variation is small in the oscillation periods of the waves under consideration. The method consists in a systematic use of the interaction representation; the unique point of the present method lies in the introduction of many time variables in order to describe phenomena with many physical quantities in a simple manner. The method is applied to the investigation of quasi-linear and weakly turbulent evolution of the system. Several new features, including the amplitude oscillation discussed in a previous report, are derived for the case where the characteristic timescale of the wave amplitude is short compared with τ.

Manley-Rowe Relations in Energy Transports among Plasma Waves

Starting from a kind of general kinetic equations for the electric potentials of waves, the Manley-Rowe relations in the nonlinear energy transport phenomena among waves in plasmas are rigorously studied. It is found that, contrary to our anticipation, the relations do not rigorously hold in general due to the presence of the wave-particle interaction process of virtual wave and instead new relations hold, which are modified in the form that also the frequency shifts of waves due to the nonlinear process are concerned. But, only for special cases, including the case of wave-wave interaction only, the relations reduce to the traditional Manley-Rowe relation. Also a new kind of general relations are found on the nonlinear frequency shifts of waves. They are of similar forms to the modified Manley-Rowe relations and complement them.

Natures of Steady Motions in One-Dimensional Nonlinear Lattices

General natures of steady motions in one-dimensional nonlinear lattices are studied. Each constituting atom is then assumed to interact only with its nearest neighbors. One of the conclusions is that the Toda lattice is very special in the sense that the degree of freedom of steady wave in it is less restrictive than those of other nonlinear lattices.

Nonlinear Inter-Particle Potentials Sustaining Exact Steady Motions in One-Dimensional Lattices

A method is presented to get a sustaining nonlinear inter-particle potential for an arbitrarily given steady motion in a one-dimensional nonlinear lattice. Here each particle is simply assumed to interact only with its nearest neighbors. This scheme is carried with an extensive use of formal series expansions and manipulations. In the latter half of this paper, this method is applied to some simple cases.

Double Resonance Parametric Excitation Due to Zero and Finite Wavenumber Pumps

We study parametric instabilities in plasmas driven by both a dipole-field and a finite-wavenumber pumps with high frequencies, their difference being chosen close to a low frequency resonance. General dispersion relations are derived by a general scheme. They are applied to a special case of the pumps of a Langmuir wave and a transparent dipole field. The analysis is limited to the extreme region that ω P e k 2 λ D e 2 ≫ y , γ, ω P i k λ D e , where k is the given wavenumber of the excited low frequency wave, y the growth rate and γ the linear damping rate of the excited Langmuir wave. A lowering of the pump energy is found for the dipole field when γ≫ω P i k λ D e , or for one pump when the other pump is near the usual decay instability threshold. The excitations take place most easily in one-dimensional configurations.