Showing papers on "Amplitude published in 1988"

Laser wakefield acceleration and relativistic optical guiding

Abstract: An electron acceleration method is investigated which employs a short (τL ∼2πωω−1p ∼1 ps), high‐power (P≥1015 W), single frequency laser pulse to generate large amplitude (E≥1 GeV/m) plasma waves (wakefields). At sufficiently high laser powers [P≥17(ω/ωp )2 GW], relativistic optical guiding may be used to prevent the pulse from diffracting within the plasma.

Spectral wave attenuation by bottom friction: theory

Abstract: Based on the linearized form of the boundary layer equations and a simple eddy viscosity formulation of shear stress, the turbulent bottom boundary layer flow is obtained for a wave motion specified by its directional spectrum. Closure is obtained by requiring the solution to reduce, in the limit, to that of a simple harmonic wave. The resulting dissipation is obtained in spectral form with a single friction factor determined from knowledge of the bottom roughness and an equivalent monochromatic wave having the same root-mean-square near-bottom orbital velocity and excursion amplitude as the specified wave spectrum. The total spectral dissipation rate is obtained by integration and compared with the average dissipation obtained from a model considering the statistics of individual waves defined by their maximum orbital velocity and zero-crossing period. The agreement between the two different evaluations of total spectral dissipation supports the validity of the spectral dissipation model.

Resonance of a fluid-driven crack: Radiation properties and implications for the source of long-period events and harmonic tremor

Abstract: A dynamic source model is presented, in which a three-dimensional crack containing a viscous compressible fluid is excited into resonance by an impulsive pressure transient applied over a small area ΔS of the crack surface. The crack excitation depends critically on two dimensionless parameters called the crack stiffness, C = (b/μ)(L/d), and viscous damping loss, F = (12ηL)/(ρƒd2α), where b is the bulk modulus, η is the viscosity, ρƒ is the density of the fluid, μ is the rigidity, α is the compressional velocity of the solid, L is the crack length, and d is the crack thickness. The first parameter characterizes the ability of the crack to vibrate and shapes the spectral signature of the source, and the second quantifies the effect of fluid viscosity on the duration of resonance. Resonance is sustained by a very slow wave trapped in the fluid-filled crack. This guided wave, called the crack wave, is similar to the tube wave propagating in a fluid-filled borehole; it is inversely dispersive, showing a phase velocity that decreases with increasing wavelength, and its wave speed is always lower than the acoustic velocity of the fluid, decreasing rapidly as the crack stiffness increases. The source spectrum shows many sharp peaks characterizing the individual modes of vibration of the crack; the variation of spectral shape, both in the number and width of peaks, is surprisingly complex, reflecting the interference between the lateral and longitudinal modes of resonance, as well as nodes for these modes. The far-field spectrum is marked by narrow-band dominant and subdominant peaks that reflect the interaction of the various source modes. The frequency of the dominant spectral peak radiated by the source is independent of the radiation direction. The frequency, bandwidth, and spacing of the resonant peaks are strongly dependent on the crack stiffness, larger values of the stiffness factor shifting these peaks to lower frequencies and decreasing their bandwidth. The excitation of a particular mode depends on the position of the trigger and on the extent of the crack surface affected by the pressure transient. Fluid viscosity decreases the amplitudes of the main spectral peaks, smears out the finer structure of the spectrum, and greatly reduces the duration of the radiated signal. The energy loss by radiation is stronger for high frequencies, producing a seismic signature that is marked by a high-frequency content near the onset of the signal and dominated by a longer-period component of much longer duration in the signal coda. Such signature is in harmony with those displayed by long-period events observed on active volcanoes and in hydrofracture experiments. The very low velocity which is possible in a crack with high stiffness (C ≥ 100) also provides an attractive explanation for very long period tremor, such as type 2 tremor at Aso volcano, Japan, without the requirement of an unrealistically large magma container. The standing wave pattern set up on the crack surface by the sustained resonance in the fluid is observable in the near field of the crack, suggesting that the location and extent of the source may be estimated from the mapping of the pattern of nodes and antinodes seen in its vicinity. According to the model, the long-period event and harmonic tremor share the same source but differ in the boundary conditions for fluid flow and in the triggering mechanism setting up the resonance of the source, the former being viewed as the impulse response of the tremor generating system and the latter representing the excitation due to more complex forcing functions.

On vortex formation from a cylinder. part 1: the initial instability

Abstract: Vortex shedding from a circular cylinder is examined over a tenfold range of Reynolds number, 440 ≤ Re ≤ 5040. The shear layer separating from the cylinder shows, to varying degrees, an exponential variation of fluctuating kinetic energy with distance downstream of the cylinder. The characteristics of this unsteady shear layer are interpreted within the context of an absolute instability of the near wake. At the trailing-end of the cylinder, the fluctuation amplitude of the instability correlates well with previously measured values of mean base pressure. Moreover, this amplitude follows the visualized vortex formation length as Reynolds number varies. There is a drastic decrease in this near-wake fluctuation amplitude in the lower range of Reynolds number and a rapid increase at higher Reynolds number. These trends are addressed relative to the present, as well as previous, observations.

Time-domain response of a semi-circular canyon for incident SV, P, and Rayleigh waves calculated by the discrete wavenumber boundary element method

Abstract: The responses of a semi-circular canyon for incident SH, SV, P , and Rayleigh waves in a two-dimensional elastic half-space are investigated in time domain as well as in frequency domain. The author proposes the discrete wavenumber boundary element method, in which the direct boundary element method is used with the discrete wavenumber Green's function. This combination achieves both the efficiency in computation and the flexibility for boundary configurations. First, the validity of the method is confirmed by comparing its results with published ones in frequency domain. Then time histories of seismic motion along the surface in and around the canyon are studied for incident SH, SV, P , and Rayleigh waves with the shape of a Ricker wavelet. In all cases, the diffracted waves called the creeping waves can be seen propagating inside the canyon with P - or S -wave velocity. For SV -wave incidence, Rayleigh waves generated at the edges of the canyon carry a significant portion of energy outward, while for SH -wave incidence the direct and reflected waves play a major role. It should be noted that the amplitude fluctuation in frequency domain does not always mean that in time domain because different arrival time of wavelets results in the fluctuation in spectral amplitude even if each wavelet propagates with the same shape and amplitude.

A numerical model of the combined wave and current bottom boundary layer

Abstract: A numerical model of oscillatory rough-turbulent boundary layer flow, featuring closure via the turbulent energy equation, is used to examine the principal features of wave-current interaction above the seabed. Results are presented from case studies carried out with water depth of 10 m, bed roughness of 0.5 cm and wave period of 8 s. The steady surface current in the absence of waves is nominally 100 cm/s, and waves having near-bottom velocity amplitudes of 50, 100, and 150 cm/s are superimposed on this current at angles ϕ = 0, π/4, and π/2. Velocity, turbulent energy, shear stress, and eddy viscosity distributions are compared for the steady current alone, for waves alone, and for waves superimposed on the current, and the interaction in the wave-current boundary layer is examined. Cycle-averaged vertical profiles of horizontal velocity illustrate the extent to which the mean flow is retarded by wave-current interaction. For the general case in which the waves are superimposed at an arbitrary angle ϕ, the mean current veers to form an angle with the wave direction greater than that of the initial steady current. Finally, the enhancement of the bed shear stress and the increase in oscillatory boundary layer thickness associated with wave-current interaction are both quantified.

Dynamics of phase-locked semiconductor laser arrays

Abstract: Time‐dependent coupled mode theory is used to investigate the stability of phase‐locked semiconductor laser arrays. The output of individual array elements is dynamically unstable and exhibits large amplitude chaotic pulsations. The total output initially exhibits damped relaxation oscillations and then settles down to a quasi‐steady state characterized by small amplitude fluctuations. The theory predicts both the pulsation frequency and the phase lock‐in time of the array.

Fourier transform mechanical spectroscopy of viscoelastic materials with transient structure

Abstract: A new technique is presented to measure the frequency dependent complex modulus simultaneously at several frequencies instead of consecutively as in a frequency sweep. For this purpose, the strain in a dynamical mechanical experiment is prescribed as a superposition of several different modes (three in our case). The resulting stress is decomposed into sinusoidal components, each of them characterized by their frequency, amplitude, and phase shift with respect to the corresponding strain component. Phase shift and amplitude are expressible in a frequency dependent complex modulus. A single experiment gives, therefore, values for the complex modulus at a set of prescribed frequencies. The method was demonstrated on three stable viscoelastic fluids and was applied to determine the instant of sol-gel transition (gel point) of a crosslinking polymer.

Weak nonlinear electromagnetic waves and low-frequency magnetic-field generation in electron-positron-ion plasmas

Abstract: The weakly nonlinear localization of obliquely modulated high-frequency electromagnetic waves in an electron-positron-ion plasma is considered. It is shown that the amplitude of the wave turns out to be a strongly dependent function of the angle between the slow modulations and the fast spatial variations and that the possibility appears of spontaneous generation of low-frequency magnetic fields. These magnetic fields are also functions of this angle and of the high-frequency wave polarization. The analysis of colinear modulation in electron-positron plasmas shows that some restriction must be made regarding the validity of previous calculations.

Wave-breaking amplitude of relativistic oscillations in a thermal plasma.

Abstract: The maximum amplitude of relativistic plasma oscillations (${\ensuremath{\upsilon}}_{\mathrm{ph}}$ near $c$) is obtained with a combined one-dimensional waterbag and warm-fluid model. The waterbag description is used to obtain expressions for the pressure and internal energy as functions of the proper density. A relativistic Euler's equation that is valid for arbitrarily large amplitudes and an analytic expression for the wave-breaking amplitude in the limit ${\ensuremath{\upsilon}}_{\mathrm{ph}}\ensuremath{\cong}c$ are obtained. Even a small amount of thermal energy can significantly reduce the maximum plasma-wave amplitude relative to the cold wave-breaking value. The significance of the results for recent accelerator schemes is discussed.

Observations of 20-Day Period Meridional Current Oscillations in the Upper Ocean along the Pacific Equator

Abstract: Prominent oscillations of the meridional current, with a mean period of approximately 20 days, have been observed in the upper ocean over several years from May 1979 to October 1985 using moored current measurements along the Pacific equator at 95°, 110°, 124°,140°W and 152°W, as well as off (but near) the equator at 110° and 140°W. The fluctuations are relatively narrowband (±0.005 cpd) in frequency. A 95% statistically significant peak in power spectra of meridional current occurred at 110°, 124° and 140°W, but not at 95° and 152°W where the spectral peaks were smaller. The dominant wave period decreased by about 4% from 110° to 140°W. Maximum amplitude was measured at 124°W; the amplitude above 80 m was maximum at the equator and decreased poleward from the equator. At 15 m the annual averaged root-mean-square amplitude was about 20.5 cm s−1, and individual peak-to-trough values reached 150 cm s−1. The wave amplitude decreased with depth and the wave was essentially confined to the upper 80 m....

Small-scale structure in the lithosphere and asthenosphere deduced from arrival time and amplitude fluctuations at NORSAR

Abstract: We analyze the pattern of phase and amplitude variations of seismic waves across the NORSAR array on a statistical basis in order to determine the statistical distribution of heterogeneities under NORSAR. Important observables that have been analyzed in the past are the phase (or travel time) and log amplitude variances and the transverse coherence functions (TCFs) of phase and amplitude fluctuations. We propose and develop the theory and methods of using other observables to reduce the degree of nouniqueness and increase the spatial resolution of the analysis. Most important are the angular coherence functions (ACFs), which characterize quantitatively the change in the pattern of fluctuations across the array from one incoming angle (or beam) to another and which have a different sensitivity to the depth distribution of heterogeneities than the TCFs. A combination of the ACFs and TCFs allows estimation of the power spectra of the P wave speed variations under the array as a function of depth. We use data for phase fluctuations from 104 incident beams and amplitude fluctuations from 185 beams with 2-Hz center frequency at NORSAR to calculate the three ACFs and three TCFs (of phase, log amplitude, and their cross coherence). The measured rms travel time fluctuation is 0.135 s, and the rms log amplitude fluctuation is 0.41. The half-coherence widths of the ACFs are 3° for log amplitude and 9° for phase. The half-coherence widths of the TCFs are 18 km for phase and less than the minimum separation between the elements of the array for log amplitude. In order to account for these features of the data, we adopt a two-overlapping-layer model for lithospheric and asthenospheric heterogeneities underneath NORSAR, with spectra that are band-limited between the wavelengths of 5.5 and 110 km. Our best model has an upper layer with a flat power spectrum extending from the surface to about 200 km, and a lower layer with a K−4 power spectrum extending from 15 to 250 km. The latter spectrum corresponds to an exponential correlation function with scale larger than the observation aperture (110 km). The rms P wave speed variations the in the range 1–4%. The small scale heterogeneities may be attributed to clustered cracks or intrusions; the larger-scale wavespeed heterogeneities are temperature or compositional heterogeneities that may be related to chemical differentiation, or dynamical processes in the boundary layer of mantle convection.

Large‐Scale waveform inversions of surface waves for lateral heterogeneity: 2. Application to surface waves in Europe and the Mediterranean

Abstract: Linear surface wave scattering theory is used to reconstruct the lateral heterogeneity under Europe and the Mediterranean using surface wave data recorded with the Network of Autonomously Recording Seismographs (NARS). The waveform inversion of the phase and the amplitude of the direct surface wave leads to a variance reduction of approximately 40% and results in phase velocity maps in the period ranges 30–40 s, 40–60 s and 60–100 s. A resolution analysis is performed in order to establish the lateral resolution of these inversions. Using the phase velocity perturbations of the three period bands, a two-layer model for the S velocity under Europe and the Mediterranean is constructed. The S′ velocity perturbations in the deepest layer (100–200 km) are much more pronounced than in the top layer (0–100 km), which confirms that the low-velocity zone exhibits pronounced lateral variations. In both layers the S velocity is low under the western Mediterranean, while the S velocity is high under the Scandinavian shield. In the deepest layer a high S velocity region extends from Greece under the Adriatic to northern Italy. Several interesting smaller features, such as the Massif Central, are reconstructed. One of the spectacular features of the reconstructed models is a sharp transition in the layer between 100 and 200 km near the Tornquist-Tesseyre zone. This would indicate that there is a sharp transition at depth between Central Europe and the East European platform. The waveform inversion of the surface wave coda leads to good waveform fits, but the reconstructed models are chaotic. This is due both to a lack of sufficient data for a good imaging of the surface wave energy on the heterogeneities and to an appreciable noise component in the surface wave coda.

The turbulent layer in the water at an air—water interface

Abstract: The velocity fields beneath an air—water interface have been determined in a laboratory facility for the cases of wind-generated waves, with wind speeds ranging from 1.5 to 13.1 m/s, and of wind-ruffled mechanically generated waves of about 22 mm amplitude and 1 Hz frequency, with wind speeds ranging from 1.7 to 6.2 m/s. The velocity was measured in a fixed frame of reference with a two-component, laser-Doppler anemometer. It was possible to determine the lengthscales and evaluate the behaviour of the mean, wave-related and turbulent components of the flows. The waves affect the mean flows, even though the profiles remain essentially logarithmic and the wave field conforms generally with the results of linear theory. In the wind-wave cases the turbulent quantities behave similarly to those in flows over flat plates. They have different trends in the mechanical-wave cases, suggesting a coupling between waves and turbulence. Finally, measured values of the mean wave-induced shear stress were negative, leading to an energy transfer from the waves to the mean flow.

L2 amplitude density method for multichannel inelastic and rearrangement collisions

Abstract: A new method for quantum mechanical calculations of cross sections for molecular energy transfer and chemical reactions is presented, and it is applied to inelastic and reactive collisions of I, H, and D with H2. The method involves the expansion in a square‐integrable basis set of the amplitude density due to the difference between the true interaction potential and a distortion potential and the solution of a large set of coupled equations for the basis function coefficients. The transition probabilities, which correspond to integrals over the amplitude density, are related straightforwardly to these coefficients.

Trapping of Low-Level Internal Gravity Waves

Abstract: The characteristics of internal gravity waves propagating on a layer of high stratification near the ground with a deeper, weakly stratified layer above are examined with the aid of a nonhydrostatic numerical model. Simulations are performed of a density current propagating into an environment with a typically observed thermodynamic structure and with no shear. These simulations indicate that the amplitude of the disturbance that forms ahead of the density current is limited considerably by the upward propagation of energy in the upper layer. To explain the large amplitude of observed gravity waves there must exist some additional mechanism, besides the weak stratification in the upper layer, to trap energy at low levels. A thorough examination of several observed gravity wave events suggested three commonly occurring mechanisms. The first mechanism, explored in a previous paper, occurs when winds in the upper layer oppose the wave motion. This reduces the Scorer parameter l2 = N2/(U − c)2 − U″/(...

Large amplitude quasi-stationary MHD modes in JET

Abstract: Oscillating MHD modes in JET are often observed to slow down as they grow and generally stop rotating (lock) when the amplitude exceeds a critical value, then continue to grow to large amplitudes (r/Bθ ~ 1%). The mode can grow early in the current rise or after perturbations, such as a pellet injection or a large sawtooth collapse, and maintain a large amplitude throughout the remainder of the discharge. Such large amplitude quasistationary MHD modes can apparently have profound effects on the plasma, including stopping central ion plasma rotation, reducing the amplitude and changing the shape of sawteeth, flattening the temperature profile around resonant q surfaces and reducing the stored energy. Perhaps most important, large amplitude locked modes are precursors to most disruptions. Some large amplitude modes can be avoided by proper programming of the q evolution. The apparent reasons for the mode locking in a particular location are discussed and a comparison with theory is made.

Rapid movements with reversals in direction. II: Control of movement amplitude and inertial load

Abstract: Transformations of the underlying movement control of rapid sequential (reversal) responses were examined as the movement amplitude (Experiment 1) and moment of inertia (Experiment 2) were altered, with constant movement time. Increases in amplitude and inertia were both met by sharply increased joint torques with a constant temporal structure, suggesting that the alterations may have been governed by a single gain parameter. The durations of various EMG bursts were essentially constant across changes in inertia, supporting a model in which the output of a fixed temporal representation is amplified to alter joint torques. The EMG amplitudes increased greatly with both amplitude and load. However, the fact that the EMG durations increased systematically with increases in distance provided difficulties for this model of amplitude control. The data suggest an economy in motor control in simple agravitational movements, whereby relatively simple transformations of an underlying representation can accomodate large changes in movement amplitude and moment of inertia.

On frequency estimation

Abstract: SUMMARY t This paper discusses a least-squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series. It is shown that the usual asymptotics on estimation of frequency, amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective. Computational issues are discussed and some illustrations are provided. Bolt & Brillinger (1979) make use of these asymptotic results. We consider a time series model of the form X, = a cos {wt + (f>) + e,, where e, is a stationary noise sequence, and one is interested in estimating the amplitude, frequency and phase of the harmonic component. The asymptotic theory of the least-squares estimates of these parameters has a long history. Whittle (1951,1953) obtained some of the earliest results. More recent results are by Hasan (1982), Hannan (1973) and Walker (1971), who formalize and extend Whittle's results. In these works it is shown that the asymptotic variance of the frequency estimate is of order n~3 and that the asymptotic variances of the other two components are of the more usual order n~\ These results extend when there are several harmonic components. The rate for the estimate of w seems almost unbelievably good, and our work was motivated by a desire to see how reliable the asymptotic theory is. In brief, we find that the product of the amplitude and the sample size, n, must be quite large in order for the asymptotic theory to be meaningful. If this product is not large, the frequency estimate is much more variable than indicated by the asymptotic theory and the amplitude estimate is severely biased. In applications in which the amplitude is small, giving rise to a small peak in the periodogram, these results suggest that naive application of the asymptotic theory to gauge resolution can be quite misleading. Section 2 of this paper is devoted to a review and examination of the asymptotic theory. We are also concerned with computational issues arising from the least-squares problem. This problem is nonlinear in the parameters, so that some sort of iterative search must be employed. Typically, search methods start from an initial guess and then proceed by a sequence of modified Newton-Raphson steps. For this nonlinear least-squares problem, it turns out that there are many local minima with a separation in frequency about n~l which makes the stationary point to which the iterative scheme converges extremely sensitive to the starting values, and this problem gets worse as the sample size increases. Furthermore, it follows from the results of § 2 that the estimate of the amplitude is very biased unless the frequency is resolved with order o(n~') so that failure to converge to the global minimum may give a very poor estimate of amplitude. The problem becomes

Simultaneous inversion of regional wave spectra for attenuation and seismic moment in Scandinavia

Abstract: Frequency-dependent regional wave attenuation is estimated for continental paths to the NORESS array in Norway. Regional Lg and Pn spectra from 186 events at ranges between 200 and 1400 km and local magnitudes between 1.1 and 4.8 are inverted for both seismic moment and apparent attenuation. The Lg spectra were inverted between 1 and 7 Hz, and the Pn spectra were inverted between 1 and 15 Hz. The method uses both the spectral and spatial decay of observed signal amplitudes to separate source and path contributions. The assumptions include the geometric spreading rate and the source spectrum to be uniquely defined by its long-period level. Most events considered have local magnitudes less than 3.0, so the source corner frequencies are near or beyond the upper limit of the inverted bandwidth. The Q results, particularly for Lg, are therefore not very sensitive to the details of our source parameterization. The inversion parameters are source moment (for each event), a constant relating corner frequency and moment for the entire data set, and two parameters describing a power law frequency dependence of Q in the region. For fixed source and spreading assumptions the inversion defines clear trade-offs among model parameters. These trade-offs are resolved by adding the constraint that the separately derived source parameters for Lg and Pn are consistent. The “preferred” estimates for the apparent attenuation are QLg(f) = 560f0.26 and QPn(f) = 325f0.48. These Q values correspond to assumed geometric spreading rates of r−0.5 for Lg and r−1.3 for Pn. For fixed Lg spreading, the Pn spreading rate is constrained by requiring that the relative Lg amplitude for earthquakes and explosions of the same moment be consistent with well-supported results from previous empirical studies. The relationship between the inverted seismic moment values and local magnitude is generally consistent with values from near-field studies. Since magnitude does not enter the inversion, this result lends considerable support to the derived Q models. Whatever the physical interpretation of the results, they certainly provide an accurate parameterization of observed amplitude spectra in this region. This is valuable for representing wave propagation in the region, and it provides important data for assessing the event monitoring capabilities of small regional networks.

Long Internal Waves of Large Amplitude

Abstract: The results of an analytical investigation of the propagation of a strongly nonlinear, long internal gravity wave in a two-fluid system are presented. The governing equation is derived and shown to possess a steady-state solitary wavelike solution. The theory is tested experimentally by comparing measured and theoretical shapes of solitary waves.

Structure of nonlinear traveling-wave states in finite geometries.

Abstract: Numerical simulation of coupled amplitude equations is used to investigate the effect of the wave propagation on the one-dimensional spatial structure of nonlinear wave states in finite geometries. The work is motivated by experiments on oscillatory convection in binary fluid convection. Predictions of confined states, temporally modulated confined states, and other dynamic states are discussed and compared with experiment.

Broadening of interfacial solitary waves

Abstract: Progressing interfacial gravity waves are considered for two fluids of differing densities confined in a channel of finite vertical extent and infinite horizontal extent. An integrodifferential equation for the unknown shape of the interface is derived. This equation is discretized and the resulting algebraic equations are solved using Newton’s method. It is found that, for a range of heights and densities of the two fluids, the system supports a branch of solitary waves. Progression along the branch produces a broadening of the wave. With increased broadening both the amplitude and the wave speed approach limiting values. The results are in good agreement with analytical studies and indicate the existence of internal surges.

Finite amplitude convection and magnetic field generation in a rotating spherical shell

Abstract: Finite amplitude solutions for convection in a rotating spherical fluid shell with a radius ratio of η=0.4 are obtained numerically by the Galerkin method. The case of the azimuthal wavenumber m=2 is emphasized, but solutions with m=4 are also considered. The pronounced distinction between different modes at low Prandtl numbers found in a preceding linear analysis (Zhang and Busse, 1987) is also found with respect to nonlinear properties. Only the positive-ω-mode exhibits subcritical finite amplitude convection. The stability of the stationary drifting solutions with respect to hydrodynamic disturbances is analyzed and regions of stability are presented. A major part of the paper is concerned with the growth of magnetic disturbances. The critical magnetic Prandtl number for the onset of dynamo action has been determined as function of the Rayleigh and Taylor numbers for the Prandtl numbers P=0.1 and P=1.0. Stationary and oscillatory dynamos with both, dipolar and quadrupolar, symmetries are close...

VLF wave stimulation experiments in the magnetosphere from Siple Station, Antarctica

Abstract: The Earth's magnetosphere is host to remarkable very low frequency (VLF) electromagnetic signals of natural origin. One of these, called a whistler, originates in lightning. Others, such as hiss and chorus, originate within the plasma itself. They are important for at least three reasons. First, they reveal the properties of the plasma through which they travel and thus can be used as remote sensing tools. Second, their high intensity and narrow bandwidths indicate the presence of a previously unknown kind of wave particle interaction that converts the kinetic energy of charged particles to coherent electromagnetic radiation. This process is called the coherent wave instability (CWI). Third, energetic charged particles are precipitated into the ionosphere through resonant scattering by these same waves, causing enhanced thermal ionization, X rays, light, and heat. To better understand and use the CWI, controlled VLF signals have been injected into the magnetosphere from Siple Station, Antarctica and received on satellites and near the conjugate point in Quebec, Canada. In addition to reproducing many puzzling natural phenomena, these experiments have provided critical new data on the CWI, laying a foundation for various theories and computer simulations. Key findings are as follows: 1) Coherent VLF signals often exhibit exponential temporal growth (∼30 dB) and saturation at levels estimated to be of order 5 pT. 2) Temporal growth requires that the input signal exceed a threshold that varies widely with time. The probable cause of the growth threshold is in situ background noise that reduces the efficiency of phase bunching by a coherent input signal whose intensity is comparable to the noise level within the frequency band of the interaction (∼100 hz). 3) Narrowband triggered emissions can be entrained by Siple frequency ramps of different slope but of much lower (−20 dB) amplitude. The mechanism of entrainment is not yet understood. 4) For two equal amplitude input waves spaced 20 Hz apart, the temporal growth of each component is almost totally suppressed. For larger spacings, 40–100 Hz, the lower frequency is more suppressed than the upper. For 10 < Δƒ < 100 Hz, unsymmetrical sidebands at integer multiples (up to seventh order) of Δƒ are created, along with subharmonics. The integer sidebands are attributed to emission growth triggered by one beat and suppressed by the next. Taken together, the spectrum of the stimulated sidebands and sub-harmonics is thus more noise-like than the transmitted spectrum. 5) Simulated hiss shows coalescence of selected noise wavelets into longer and stronger chorus-like emissions, suggesting that chorus and hiss originate in the same mechanism. Future objectives of a VLF wave injection facility include (1) new experiments on the physics of wave growth and wave-induced particle scattering and precipitation, (2) testing of the predictions of theories of VLF wave-particle interaction, (3) development of new techniques for remote sensing and control of space plasmas using VLF techniques, and (4) improvements in the design and operation of VLF communication and navigation systems.