Localized Wave Pulses Research Articles

Nonlinear Landau resonance with localized wave pulses

AbstractWave‐particle resonant interaction is responsible for many important space plasma processes and can be formally described theoretically for two main regimes: particle scattering (quasilinear diffusion) by low‐intensity waves and particle trapping/phase bunching by sufficiently intense waves. There are important modifications of these regimes in inhomogeneous plasma systems. However, almost all theoretical results have been derived for harmonic waves and linear plasma modes. High‐resolution spacecraft measurements of spatially localized plasma waves in Earth's magnetosphere demonstrate electron acceleration attributed to the Landau resonance mechanism. In the classical mechanism, the magnitude of the electric potential determines the maximum energy gain of electrons. However, a less reported mechanism of electron acceleration becomes possible in inhomogeneous plasma and magnetic field. In this Commentary, we discuss how combination of wave localization and plasma inhomogeneity modifies the nonlinear Landau resonance. We underline the important property of this resonance: an electron energy gain depends on the gradient in wave potential and not just its magnitude. We also consider this modified resonance mechanism in context of generation of hot field‐aligned electron populations, particle transport, and energy transfer in the magnetosphere.

Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components

In this paper we use a unidirectional decomposition capable of furnishing localized wave pulses, with luminal and superluminal peak velocities, in exact form and totally free of backward components, which have been a chronic problem for such wave solutions. This decomposition is powerful enough for yielding not only ideal nondiffracting pulses but also their finite energy versions still in exact analytical closed form, avoiding the need for time-consuming numerical simulations. Another advantage of the present approach is that, since the backward spectral components are absent, the frequency spectra of the pulses do not need to possess ultrawidebands, as it is required by the usual localized wave (LW) solutions obtained by other methods. Finally, the present results bring the LW theory nearer to the real experimental possibilities of usual laboratories.

Tunable front interaction and localization of periodically forced waves.

In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We investigate wave pulses within the framework of coupled Ginzburg-Landau equations describing the traveling-wave amplitudes. We find that the introduction of resonant temporal forcing results in a tunable mechanism for stabilizing such wave pulses. In contrast to other localization mechanisms the temporal forcing can achieve localization by a repulsive as well as by an attractive interaction between the fronts. Systems for which the results are expected to be relevant include binary-mixture convection and electroconvection in nematic liquid crystals.

Broadband processing using localized waves in a shallow ocean environment

In this paper the MPS localized wave pulse is used as the basis for designing a broadband signal processor to discriminate between two point sources. The nonseparable nature of the MPS pulse requires a ‘‘best fit’’ approach to processor design. This approach illustrates the kinds of problems one would encounter when using localized waves in a processor. The processor design is described, then applied to simulated acoustic signals generated in a shallow ocean environment. The results show that the MPS-based processor can discriminate between the two sources at least as well as a more conventional broadband beamformer. No attempt is made to estimate the positions of the sources. [This work was performed under the auspices of the Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.]

Localized wave pulses in the Keyport experiment

Localized wave (LW) pulses were produced using a standard Navy array in the anechoic tank at NUWC Keyport. The LW pulses used were the MPS pulse first derived by Ziolkowski, and a new type of pulse based on a superposition of Gaussian beam modes. This new type is motivated by a desire to make a comparison of the MPS pulse with another broadband pulse built from solutions to the wave equation. The superposed Gaussian pulse can be described by parameters which are analogous to those describing the MPS pulse. The directivity patterns and the axial energy decay between the pulses are compared. The behavior of the pulses are found to be similar so that the superposed Gaussian could be another candidate in the class of low diffractive pulses known as localized waves.

Diffraction length of localized waves generated by dynamic apertures

A definition of the diffraction length characterizing the propagation of localized wave pulses launched from dynamic apertures is provided. Our inference of the diffraction range is based on an analysis of the spectral depletion of the spatial frequency components of the pulse as it propagates away from its source. We demonstrate the efficacy of our procedure by showing that it is capable of capturing some decay features of localized wave pulses that may be missed by other approaches.

Graphical simulation of superluminal acoustic localized wave pulses

This paper investigates, graphically, a simulation of the launching of recently obtained superluminal localized wave solutions of the homogeneous wave equation. These solutions represent focused interference patterns that travel with speed greater than c in the direction of propagation. Graphical simulation indicates that approximations to these solutions may be launched from a finite array of point sources, and the superluminal nature of the launched pulses is maintained in the near field of the array. >

The controlled nonlinear nonstationary evolution of localized wave pulses in dispersive media

The controlled rebuilding of localized intense electromagnetic pulses is described by means of exact solutions of the nonlinear Schrödinger equation. These solutions illustrate the essential dependence of dynamics of such pulses in a dispersive medium upon the details of the initial shape of the pulse; therefore the role of the periphery regions of the pulse may be very important. The threshold values of intensity, divided by the regions of subcritical and supercritical evolution regimes, are calculated for the different pulses. The gradual formation of the spikelike pulses and the electromagnetic shock waves in the supercritical regime and the limited time of such formation are analyzed.

Space-Time Solutions of the Linearized Coupled-Mode Equations

The linearized coupled-mode equations for parametric instability are solved exactly for various cases. The exact evolution of a localized wave-pulse in an unbounded interaction region is used to illustrate the relationship between damping rates, group velocities and instability. Criteria for absolute and convective instability follows in a natural way. The pulse-evolution in a finite interaction region is presented. It is shown that the boundaries create "kinks" in the pulse-profile travelling back and forth at the group velocities, and that the over-all effect of finiteness is to reduce the instability growth. The instability development from a time-constant point source, turned on at a given time, is studied. We find that in the case of parallel group velocities, the solution is stationary behind a front moving with the slowest group velocity. When the group velocities are anti-parallel, and the criterion for convective instability is satisfied, the amplitudes grow asymptotically towards a stationary solution which is explicitly given. Finally, it is demonstrated that a mismatch in frequency or wave number will produce frequency and wave number shifts, but does not otherwise change the growth of the instability.