Kyoji Nishikawa

Parametric Excitation of Coupled Waves I. General Formulation

The coupling of two waves due to the presence of a third wave with large amplitude is studied. On the basis of simple model equations, the conditions for excitation of the first two waves are discussed for the following three cases: i) \(\omega_{1}+\omega_{2}{\risingdotseq}\omega_{0}\) and ω 1 , ω 2 are large compared with their frequency shift, ii) \(\omega_{1}{\ll}\omega_{2}{\lesssim}\omega_{0}\) and iii) \(\omega_{1}{\ll}\omega_{0}{\lesssim}\omega_{2}\), where ω 1 , ω 2 are the unperturbed frequencies of the two waves under consideration and ω 0 is the frequency of the incident large amplitude wave. In the first two cases, the excited wave is found oscillatory, while in the third it is found non-oscillatory. The threshold power of the incident wave for the onset of excitation, the frequency shift at the threshold and the growth rate above threshold are calculated in each case.

PARAMETRIC EXCITATION OF COUPLED WAVES. II. PARAMETRIC PLASMON--PHOTON INTERACTION.

The general theory of the parametric excitation of coupled waves developed in the preceding paper is applied to the parametric interaction of the electrostatic waves in a plasma with radiation whose frequency is close to the electron plasma frequency. On the basis of the hydrodynamic equations, the coupled equations for the electron plasma wave and ion acoustic wave are derived. The effect of the Landau damping is also considered phenomenologically. Using the coupled wave equations, the expressions for the threshold radiation intensity, the frequency shift at the threshold and the growth rate above threshold are obtained. In particular, the dependence of these quantities on the wave-length of the electrostatic waves is discussed in detail. The results are compared with experiment of Stern and Tzoar.

Analysis of fast-ion velocity distributions in laser plasmas with a truncated Maxwellian velocity distribution of hot electrons

Fast‐ion production in laser plasmas with a truncated Maxwellian velocity distribution of hot electrons is investigated by using a new numerical method, namely the systematic Newton’s iteration method which has been applied to nonlinear equations. The analysis of the temporal evolution of coronal plasma expansion discloses that the ion‐front velocity approaches a constant value within thirty ion plasma oscillation periods, when the high‐energy tail is truncated. In such a case, the maximum ion velocity is found to be proportional to the maximum energy of hot electrons. Consequently, the ion velocity distributions are steepened and truncated. Furthermore, it is found that the energy partition of the absorbed laser energy to fast ions is appreciably reduced when the maximum electron energy is below a few times the hot‐electron temperature.

Relaxation of Relativistic Electron Beam in a Plasma with Random Density Inhomogeneities

The relaxation of kinetically unstable relativistic electron beam in plasma with random density inhomogeneities is studied. Their effect is treated as angular diffusion of resonantly excited Langmuir waves in the wavenumber space. Formulas effective for obtaining the beam energy deposition rate and the Langmuir-wave fluctuation spectrum are presented. The result shows a strong reduction of the energy relaxation rate due to diffusion of Langmuir waves from linearly unstable region to the region where they are damped by the beam itself. The model attributing the formation of random density inhomogeneities to the modulational instability of the Langmuir condensate produced by the beam plasma interaction is used to estimate self-consistently the level of inhomogeneities.

Self-Modulation of High-Frequency Electric Field and Formation of Plasma Cavities

Self-modulation of the oscillating electric field is observed when its frequency is near the electron plasma frequency. The localized field due to the self-modulation is found to make depressions in the plasma density, and to move in unison with the density dip with approximately the ion-acoustic speed. The maximum amplitudes of the high-frequency field and the density dip are linearly proportional to each other, but the former shows a phase jump at the bottom of the density dip. All these features are qualitatively explained by the results of the recent theory of coupled electron-plasma and ion-acoustic solitary waves. The self-modulation occurs in the overdense region, the parametric decay instability is observed in the underdense region.

Parametric instabilities with finite wavelength pump

The general problem of parametric instabilities driven by a finite wavelength pump is investigated. For the particular case of a Langmuir wave pump, it is shown that resonant decay instabilities (forward or backward scattering in the one‐dimensional case), with thresholds which vanish in the colisionless limit, can occur only for pump wavenumber k0 greater than the critical value [(m/M)1/2/γ]kD, where m and M are the electron and the ion mass, respectively, and γ is the specific heat ratio. For smaller wavenumbers, there is always a nonzero threshold, the instability being of modulation character at long wavelengths and almost pure growing for short wavelengths. Frequency locking for small k0 and wavenumber locking for large k0 are demonstrated. The results are generalized to the case where the coupled waves satisfy arbitrary dispersion relations and simple physical interpretations of the instabilities are given.

On the Theory of Trapped Particle Instability. I. General Formulation and Analysis for Weak Coupling Limit

A general formulation is developed to investigate the stability of a collisionless, one-dimensional plasma which sustains a large-amplitude, monochromatic electron plasma wave. A nonlinear dispersion relation is derived which governs the stability of a small-amplitude test wave. It is shown that untrapped electrons can produce a significant modification to the Kruer-Dawson-Sudan dispersion relation which was derived by considering only the effect of trapped electrons on the test wave. As an application a weak-coupling limit is considered. It is shown that in this limit waves can grow in the distinct wavenumber regions given by \(|\varDelta k|{=}\sqrt{2n+1}k_{B}(n{=}0,1,2,\cdots)\), and | Δ k |≪ k B where Δ k is the difference of the wavenumbers of the test wave and the original large-amplitude wave and k B the bounce frequency divided by the phase velocity of the large-amplitude wave. Various characteristics of the growing waves are obtained.

Theory of double resonance parametric excitation in plasmas

Parametric instabilities in a plasma driven by a long wavelength electric field with two “pump” frequencies ω1 and ω2 which lie near the resonant frequency for Langmuir oscillations, their difference Δ = ω1 − ω2 being chosen close to a low frequency resonance, linear or nonlinear, at Ω − i Γ are studied. A general dispersion relation in terms of linear susceptibilities, χ, is derived by retaining, on a selective basis, terms of fourth order in the pump amplitudes. Illustrative calculations are carried out using resonant fluid approximations for the χ. The most interesting cases occur when Δ = Ω or Δ = 2Ω. A lowering of the net power threshold for instability is found in both cases, when the linear damping rate of the electronic wave is large compared with Ω. In addition, a coupling between the “decay” and “oscillating two‐stream” instabilities occurs when Δ = Ω, the threshold for exciting the latter with the ω2 pump being arbitrarily small when the ω1 pump amplitude is near the usual decay instability thr...

Trapped‐Ion Instabilities in Ion‐Acoustic Wave

Growth of two types of sideband waves has been observed experimentally when a relatively large‐amplitude ion‐acoustic wave propagates in a collisionless plasma having the electron‐to‐ion temperature ratio Te/Ti≈20. The observed frequency spectrum and growth rate, as well as the frequency and amplitude ranges of the large‐amplitude wave for which the sideband wave growth is observed are in good agreement with the theory of trapped particle instabilities. The sidebands extract the energy from the large‐amplitude wave and cause it to be heavily damped.

Anomalous Transport Due to Electromagnetic Fluctuations across a Magnetic Field

A general theory is presented for the transport fluxes across a magnetic field due to electromagnetic fluctuations. The transport coefficients are expressed in terms of the spectral functions or the correlation functions of the fluctuations under the assumption that the scale length of the inhomogeneity is large as compared with the ion Larmor radius. As a simple application of the formulas obtained, we investigate the finite-β effects on the diffusion and the heat fluxes of electrons due to the drift wave turbulence neglecting the effect of the magnetic shear. We find that these fluxes are reduced by the finite-β effect.