Three-wave Decay Processes Research Articles

Formation of low-frequency harmonics on the surface of liquid hydrogen and helium in a turbulent regime

The formation of harmonics at frequencies below a monochromatic pump frequency in a system of capillary-gravity waves on surfaces of liquid hydrogen and superfluid helium in a turbulent regime is studied experimentally. By choosing the spectral characteristics of the exciting force and the resolution in the spectrum of the surface oscillations, it is possible to create conditions for low-frequency wave generation by changing the boundaries of the experimental cell. For certain monochromatic pump frequencies, low-frequency harmonics are observed on liquid hydrogen surfaces only in a rectangular cell. Energy transfer to the low-frequency subharmonics, as well as to high-frequency harmonics, is caused by three-wave decay processes. An inverse cascade develops on superfluid helium surfaces in a cylindrical cell as a result of three-wave decay processes, with about 90% of the energy concentrated in the inverse cascade.

Observation of the modulation instability and spin wave solitons in ferromagnetic films under the conditions of coexistence of four-wave and three-wave parametric processes

Nonlinear phenomena that arise during the propagation of spin waves in thin ferromagnetic films under conditions of the simultaneous existence of three-wave and four-wave parametric processes have been investigated. Investigations have been performed for single-frequency and double-frequency regimes of excitation of intense spin waves. The spontaneous modulation instability of the monochromatic running spin wave has been revealed for the first time at frequencies at which three-wave decay processes are allowed. The pronounced generation of a periodic sequence of bright spin wave solitons has been observed under excitation of two monochromatic spin waves at the same frequencies.

Proton heating by parallel Alfvén wave cascade

In a recent series of papers, the present authors developed a kinetic theory for low-frequency turbulence propagating parallel to the ambient magnetic field. Making use of this theory, it was shown that low-frequency Alfvénic turbulence may cascade to ion-cyclotron frequency range and beyond by nonlinear three-wave decay processes. The significance of such a finding is that it may lead to the proton heating by cyclotron resonance. However, the actual proton heating process was not demonstrated. The present paper complements the previous works by including the proton heating in the discussion. It is found that the left-hand circularly polarized Alfvén-cyclotron turbulence leads to a moderate heating of the protons in the perpendicular direction and cooling in the parallel direction. It is also found that ion-acoustic turbulence is generated by the decay instability process. Finally, the heating rate is shown to increase in inverse proportion to the time scale of the wave source.

Parallel cascade of Alfvén waves

A heuristic semi-classical kinetic theory of turbulence in magnetized plasmas was formulated in the 1960s, but the statistical mechanical formulation of the same problem, which is necessary for a quantitative analysis, has not been accomplished. Recently, the present authors formulated the statistical mechanical kinetic turbulence theory in a formal manner (P H Yoon 2007 Phys. Plasmas 14 10230, P H Yoon and T-M Fang 2007 Phys. Plasmas 14 102303). In this paper, the parallel cascade of Alfvén waves via the three-wave decay process is numerically investigated on the basis of the results outlined in the above references. It is shown that the cascade of low-frequency Alfvén waves to high-frequency ion-cyclotron and magnetosonic waves takes place mediated by ion-sound turbulence. The Alfvén wave cascade is important, for instance, in the solar wind acceleration and coronal heating problem, since the low-frequency, long-wavelength Alfvén waves must first undergo cascade to high-frequency, short-wavelength modes in order for cyclotron resonant absorption to take place. The cyclotron resonance is believed to be important for charged-particle acceleration in the aforementioned applications. The present analysis may be important in such a context.

Dynamics of Langmuir wave decay in two dimensions

The present paper reports on the first two-dimensional (2D) self-consistent solution of weak turbulence equations describing the evolution of electron-beam-plasma interaction in which quasilinear as well as nonlinear three-wave decay processes are taken into account. It is found that the 2D Langmuir wave decay processes lead to the formation of a quasicircular ring spectrum in wave number space. It is also seen that the 2D ring-spectrum of Langmuir turbulence leads to a tendency to isotropic heating of the electrons. These findings contain some important ramifications. First, in the literature, isotropization of energetic electrons, detected in the solar wind for instance, is usually attributed to pitch-angle scattering. The present finding constitutes an alternative mechanism, whose efficiency for other parametric regimes has to be investigated. Second, when projected onto the one-dimensional (1D) space, the 2D ring spectrum may give a false impression of Langmuir waves inverse cascading to longer wavelength regime, when in reality, the wavelength of the turbulence does not change at all but only the wave propagation angle changes. Although the present analysis excludes the induced scattering, which is another process potentially responsible for the inverse cascade, the present finding at least calls for an investigation into the relative efficacy of the inverse-cascading process in 1D vs 2D.

Two-dimensional particle-in-cell simulations of plasma cavitation and bursty Brillouin backscattering for nonrelativistic laser intensities

Two-dimensional particle-in-cell simulations of laser-plasma interaction using a plane-wave geometry show strong bursty stimulated Brillouin backscattering, rapid filamentation, and subsequent plasma cavitation. It is shown that the cavitation is not induced by self-focusing. The electromagnetic fields below the plasma frequency that are excited are related to transient soliton-like structures. At the origin of these solitons is a three-wave decay process exciting new modes in the plasma. The cavitation is responsible for a strong local reduction of the reflectivity and goes along with an efficient but transient heating of the electrons. Once heating ceases, transmission starts to increase. Local as well as global average reflectivities attain a very low value due to strong plasma density variations brought about by the cavitation process. On the one hand, the simulations confirm the existence of a new mechanism of cavity and soliton formation in nonrelativistic laser-plasma interaction in two dimensions, which was shown to exist in one-dimensional simulations [S. Weber, C. Riconda, and V. T. Tikhonchuk, Phys. Rev. Lett. 94, 055005 (2005)]. On the other hand, new aspects are introduced inherently related to the additional degree of freedom.

Nonlinear electromagnetic susceptibilities of unmagnetized plasmas

Fully electromagnetic nonlinear susceptibilities of unmagnetized plasmas are analyzed in detail. Concrete expressions of the second-order nonlinear susceptibility are found in various forms in the literature, usually in connection with the discussions of various three-wave decay processes, but the third-order susceptibilities are rarely discussed. The second-order susceptibility is pertinent to nonlinear wave-wave interactions (i.e., the decay/coalescence), whereas the third-order susceptibilities affect nonlinear wave-particle interactions (i.e., the induced scattering). In the present article useful approximate analytical expressions of these nonlinear susceptibilities that can be readily utilized in various situations are derived

The outer scale of solar-wind turbulence from GALILEO coronal-sounding data

Radio sounding experiments on of the solar plasma were carried out by the GALILEO spacecraft using S-band (2295 MHz) signals in 1995–1996 a period of minimum solar activity. Equatorial regions at heliocentric distances of 7–80 solar radii were studied. The frequency of the received signal was detected by three ground stations. By carrying out continuous observations of unprecedented duration and processing the data using spectral and correlation methods, we have obtained reliable information on large-scale inhomogeneities of the solar-wind density for the first time. The outer turbulence scale increases with heliocentric distance, the dependence being close to linear. We estimate the outer turbulence scale and analyze its dependence on distance from the Sun and local plasma parameters for a model in which the outer scale is formed due to competition between the linear amplification of Alfven waves in the irregular, moving solar-wind plasma and the nonlinear transfer of turbulent energy to higher frequencies. A comparison of predictions for various specific cases of this model with the observational data suggests that the main nonlinear processes responsible for the formation of the inertial range of the spectrum on the investigated scales are three-wave decay processes involving Alfven and magnetoacoustic waves.

The decay instability of Langmuir waves in the non-neutral electron plasma column

The behaviour of large amplitude Langmuir waves is experimentally observed in a non-neutral electron plasma column with a cylindrical boundary. It is found that a Langmuir wave whose amplitude is above a threshold decays into lower frequency Langmuir waves. Since the dispersion relation is different from that of the unbounded neutral plasma, which is theoretically considered, the three-wave decay process of Langmuir waves becomes possible. In these processes, sidebands due to a large amplitude Langmuir wave satisfy the energy and momentum conservation relation. The threshold of this decay instability depends on the plasma temperature and becomes lower as the temperature becomes higher.

Driven random-phase three-wave interactions: Cycles, bursts, and stochasticity

Steadily driven, undriven, and stochastically driven three-wave decay processes involving groups of random-phase waves are investigated analytically and numerically. Steadily driven systems in which one product wave is suppressed exhibit neutrally stable Lotka–Volterra cycles, as for the true two-component case, whereas three-component systems are stable below a critical driver strength and unstable beyond that point. Initially unstable, but undriven, systems produce bursts of product waves, after which the parent waves fall to a final level that is an exponentially decreasing function of their initial level. Three-component systems where the product waves have near-equal dissipation rates are an exception to the latter behavior; in such systems the final parent-wave level is almost independent of the initial one. Stochastic driving gives rise to bursts of product waves in a cycle of fluctuating period, whereas a low-level noise source tends to stabilize the system.

Nonlinear behavior and turbulence spectra of drift waves and Rossby waves

Spectrum cascade in drift wave turbulence in a magnetized plasma as well as Rossby wave turbulence in an atmospheric pressure system are studied based on a three-wave decay process derivable from the model equation applicable to both cases. The decay in the three-way interaction occurs to smaller and larger values of ‖k‖. In a region of large wavenumbers this leads to the dual cascade; the energy spectrum cascades to smaller ‖k‖ and the enstrophy spectrum to larger ‖k‖, similar to the case of two-dimensional Navier–Stokes turbulence. In a small wavenumber region a resonant three-wave decay process dominates the cascade process, and an anisotropic spectrum develops. As a consequence of the cascade, zonal flows in the direction perpendicular to the direction of inhomogeneity appear which presents a potential implication for the particle confinement in a turbulent plasma.

Parametric decay of non-ducted whistler-mode signal

It is shown that a whistler-mode signal propagating obliquely to the external magnetic field can parametrically decay into a daughter wave and an ion cyclotron wave. A dispersion relation involving a three-wave decay process is derived. Application of our results in space plasma is pointed out.

Experimental Observation of Wave-Wave Coupling in a Beam-Plasma System

Abstract : The interaction between unstable waves has been investigated in a beam-plasma system under conditions such that nonlinear wave-particle interactions are negligible. At small wave amplitudes the results can be interpreted in terms of a simple three-wave decay process; at large amplitudes the situation is dominated by multiple wave coupling that leads to generation of satellite waves. (Author)