Showing papers on "Amplitude published in 1981"

An oscillation theory of handwriting

Abstract: Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape. Changing the slope at this zero crossing controls writing slant. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical source; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory.

Upstream hydromagnetic waves and their association with backstreaming ion populations: ISEE 1 and 2 observations

Abstract: Measurements from the Lepedea plasma instruments and the flux gate magnetometers on ISEE 1 and 2 are used to examine the nature of the hydromagnetic waves associated with the various classes of ions backstreaming from the earth's bow shock. The reflected ions, which are confined to a narrow energy and angular range, are accompanied by small amplitude (less than approximately 1/2 gamma peak to peak) left-handed waves at frequencies close to 1 Hz in the spacecraft frame. Diffuse backstreaming particles with a broad energy spectrum are associated with low frequency (approximately 30-s period), large amplitude (approximately 5 gamma peak to peak) waves. Intermediate particles are associated with a mixture of these two wave types. Often the waves associated with the diffuse beams steepen as if they were minishocks. The leading edge (trailing edge in the spacecraft frame) frequently appears to break up into a whistler mode wave packet. These discrete wave packets are right-hand polarized and have frequencies from below the proton gyrofrequency to well above it in the plasma frame and are blown back towards the earth by the solar wind.

Gravity wave initiation of equatorial spread F: A case study

Abstract: Jicamarca radar backscatter maps were made during four consecutive nights in March 1979. Two of these maps displayed single towering plumes extending to nearly 1000-km altitude. On a third night, discussed in detail here, six plumes were generated in clear association with a nearly sinusoidal oscillation of the height of the bottomside of the F layer. The vertical amplitude of the oscillation was several hundred kilometers, and the period about 100 minutes. The plumes were generated either when the bottomside of the F layer was at the highest altitude or in the descending phase of the motion. Families of curves are presented which correspond to the solution of the dispersion relation for gravity waves capable of initiating the observed bottomside oscillations via the spatial resonance mechanism. We conclude that the solutions thus derived are reasonable and present a criterion for how well matched the gravity wave phase velocity and plasma drift have to be to produce a given perturbation in the ionization density. This criterion indicates that although initiation by a gravity wave seems likely, the gravity wave interaction cannot yield the large displacements observed without further amplification by the Rayleigh-Taylor instability. Finally, we show that the preferential generation of plumes during the descending phase of the F layer height oscillation can be explained by a generalized Rayleigh-Taylor instability operating on the distorted ionosphere with the destabilizing effects of gravity, a zonal electric field, and a zonal neutral wind included.

An Experimental Investigation of Breaking Waves Produced by a Towed Hydrofoil

Abstract: This paper presents the results of experiments on breaking waves produced by towing a submerged, two-dimensional hydrofoil at constant depth and speed. The wave field consists of a breaker followed by a train of lower, non-breaking waves. The breaker has a small zone of turbulent water riding its forward slope; this zone is called the breaking region. Measurements were made of surface height profiles, the vertical distribution of mean horizontal velocity in the wake of the wave, and the vertical thickness of the wake. The results support the hypothesis that the breaking region imparts a shearing force along the forward slope equal to the component of its weight in that direction. The force produces a turbulent, momentum-deficient wake similar to the wake of a towed, two-dimensional body in an infinite fluid. The vertical thickness of the wake grows in proportion to the square root of distance behind the breaker. The momentum deficit is approximately equal to the maximum momentum flux of a Stokes wave with the same phase speed as the breaker. The surface profile measurements yield several results: the proper independent variables describing the wave are its speed and the slope of its forward face. The relation between breaking wavelength and speed follows the finite-amplitude Stokes wave equation. The amplitude and the vertical extent of the breaking region are both proportional to the phase speed squared; however, they are not functions of the slope of the forward face of the wave. The breaking region has a small oscillation in its length with a regular period of 4.4 the period of a wave with phase speed equal to the hydrofoil speed. The amplitude of the oscillation diminishes with time. It is believed that this oscillation is due to wave components produced when the foil is started from rest.

The nonlinear wave equation for higher harmonics in free-electron lasers

Abstract: The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and we use this picture to distinguish between the effects of high gain and Coulomb forces.

Particle motions in large-amplitude wave fields

Abstract: We calculate the trajectories of particles in two-dimensional model flows typifying atmospheric or oceanic eddy motions. Rather than restricting the flows to be weak (but solutions to the relevant dynamics), we have considered motions where the streamfunction is only a kinematic model resembling the actual flows but the amplitude can be large so that flow speeds can greatly exceed the phase speed. For steadily propagating disturbances, there is an equivalent one-dimensional Lagrangian motion problem and we have applied results from analyses of such to periodic channel waves and isolated circular eddies. We show that the mean Lagrangian drift rate in periodic channel waves is very sensitive to the initial position and may be either prograde or retrograde. Large volumes of the fluid may be “trapped” to translate along with the wave. The wave drift depends on the phase velocity relative to the Eulerian mean flow and peaks at about 1/3 of the transient Eulerian speed at geophysically relevant amplitu...

Wave-current interactions: an experimental and numerical study, part 2 - nonlinear waves

Abstract: The interaction between a regular wavetrain and a current possessing an arbitrary distribution of vorticity, in two dimensions, is considered for waves of finite amplitude. A numerical model is constructed, primarily for use in the finite depth regime, extending the work of Dalrymple (1973, 1977) and this is used to predict the wavelength and the particle velocities under the waves. These predictions agree very well with experimentally obtained data and the importance of the vorticity in the wave–current interaction is clarified. Amplitude and wavelength modulations are considered for finite amplitude waves on a slowly varying irrotational current; moderate agreement is found between theory and experiment.

Measurements of a saturated range in ocean wave spectra

Abstract: Wavestaff measurements made in the Gulf of Mexico and Waverider measurements from the Baltimore Canyon area have been used to study the form of ocean wave spectra at high frequencies. The observations are statistically consistent with the idea that the tail of the spectrum is in equilibrium with the local wind. Analysis showed that the spectral range between the mean wave frequency and about two and one half times that frequency is consistently proportional to the inverse of the fourth power of the frequency. At higher frequencies, the classical inverse fifth power law seems to hold. In the inverse fourth power range, the amplitude of the spectrum is also proportional to the wind friction velocity. These relationships should permit a reliable specification of this saturated range when only local wind observations are available. If the significant wave height and mean period are known, the amplitude of the tail of the spectrum can be predicted with somewhat greater accuracy. However, this relationship should be used with caution when the height and period statistics are influenced by swell.

Inertio‐gravity wave induced accelerations of mean flow having an imposed periodic component: Implications for tidal observations in the meteor region

Abstract: The semidiurnal harmonic exhibits great day-to-day variability in amplitude and phase. In addition, the variability appears to be substantially local and random, suggesting a connection with gravity wave activity. We suggest that a significant contribution to the observed semidiurnal harmonic at meteor heights might result from inertio-gravity wave induced accelerations of the mean flow. The rate of wave forcing of the mean wind is related to the Doppler-shifted phase velocity, so that during alternate phases of an imposed mean wind oscillation interactions with waves that accelerate the mean wind in opposite senses may be favored. Thus the imposed mean wind may modulate the mean-flow acceleration at the imposed frequency. In this view, the semidiurnal character of the acceleration is a manifestation of the modulation of the interaction process by the semidiurnal tide. The variability of the semidiurnal harmonic would then reflect the local variability of inertio-gravity wave fluctuations and also nonlinear feedback on the waves. Calculations with a simple time-dependent wave-mean-flow model indicate that a wave-induced component of the semidiurnal harmonic with amplitudes comparable to the semidiurnal tide itself is possible.

Power From Water Waves

Abstract: A review is presented of wave-energy devices and hydrodynamic properties of idealized equipment for extracting power from waves. The governing equations involve the fluid hydrodynamic theory applied to machines with zero forward speed which can absorb energy from the neighboring wave field. A mixture of waves of different amplitudes, periods, wavelengths, and directions with randomly distributed phases coexist at a given time a mathematical model of the sea surface assumes it to be an infinite superposition of wave trains of various amplitudes and frequencies. A theory was developed for the oscillation of two-dimensional energy-absorbing cylindrical sections which can be utilized for estimating hydrodynamic characteristics of fully three-dimensional ship hulls. Finally, three-dimensional wave-energy absorbers are represented by expressions in terms of the force amplitude, direction of motion, and the damping coefficient.

Surface consistent corrections

Abstract: Amplitudes of seismic reflections have been of interest since the first days of exploration seismology. Any change of amplitude or anomalous behavior may be significant, so it is important that the zones of interest be free from outside disturbances, such as those caused by the near‐surface layers. Surface consistent factors may be divided into source, receiver, offset, and subsurface components, and these may be divided further into amplitude and phase (or time shift) factors. Correction of trace amplitudes using multiplication by a scale factor is similar to correction of phase distortions by a static shift, and both corrections enhance seismic data. Displays of surface consistent components for time and amplitude corrections provide an additional diagnostic for the geophysicist.

Evidence for a traveling two‐day wave in the middle atmosphere

Abstract: Evidence is presented for the existence of a wave number 3, westward traveling 2-day oscillation in the temperature measurements made by the Nimbus 5 SCR and Nimbus 6 PMR instruments. The wave has largest amplitude in the mesosphere at low latitudes of the summer hemisphere and has a markedly asymmetrical meridional structure. It is suggested that the wave may be a free wave similar to the 5-day wave identified in Nimbus 5 SCR data by Rodgers (1976). The vertical structure shows little phase tilt and a slight indication of an increase in amplitude with height.

Superconducting transition of multiconnected Josephson network

Abstract: The response of superconducting Tc with multiconnected structure against a small ac magnetic field is studied in terms of complex susceptibility. It has been revealed that the fundamental susceptibility χ1′−iχ1″ is very sensitive to the amplitude h0 of the ac field; i.e., the superconducting transition width is appreciably broadened as h0 increases, but the onset temperature of the transition holds its value. In addition, χ1″ with respect to temperature has an asymmetric peak. We propose a phenomenological model on the assumption that the multiconnected network behaves like a single loop as a whole due to the coherent nature of the specimen. It has been revealed that the main features of observed characters are well reproduced by this model. Since our model predicts higher harmonics in susceptibility, the third harmonic response of the specimen against a small ac magnetic field is also studied. Measurements with respect to temperature are simultaneously performed for the amplitude of third harmonic suscep...

On the structure of turbulent flow over a progressive water wave: theory and experiment in a transformed, wave-following co-ordinate system

Abstract: An investigation of the turbulent flow structure over a progressive water wave, as well as the structure of the wave-induced flow field in a transformed wave-following frame, is reported. Experimental results are given for a free-stream velocity of 2·4 m s−1 over a 1 Hz mechanically generated deep-water wave. The velocity components were measured with a cross hot-film probe oscillating in a transformed wave-following frame. The amplitude and phase of the wave-induced velocity components are deduced by correlation to the generated water wave. The mean flow tends to follow the wave form so that the water wave should not be regarded as surface roughness. The mean velocity profile is basically log-linear and is similar to that over a smooth plate, because ripples riding on the waves do not produce sufficient roughness to interfere with the wind field. The wave-induced motion in the free stream is irrotational; but, in the boundary layer, it has strong shear behaviour related to the wave-associated Reynolds stress. The shear stress production as well as the energy production from the mean flow is concentrated near the interface. A phase jump of 180° in the wave-induced turbulent Reynolds stresses in the middle of the boundary layer was observed. The relationships between the induced turbulent Reynolds stresses and the induced velocities are of an eddy-viscosity type.

The plasma wave and quasi-static electric field instrument /PWI/ for dynamics Explorer-A

Abstract: It is explained that the Plasma Wave Instrument (PWI) on Dynamics Explorer-A measures both plasma wave phenomena and quasi-static electric fields. The quasi-static electric fields are measured parallel to the spin axis of the spacecraft in a range of 2 mV/m to 2 V/m and perpendicular to the spin axis 0.5 mV/m to 2 V/m at 16 samples/s. The ac electric field sensors include a 200-m tip-to-tip long wire antenna and a 0.6-m short electric antenna, both of which are perpendicular to the spin axis, and a 9-m tip-to-tip tubular antenna parallel to the spin axis. AC electric wave fields are measured over a frequency range of 1 Hz to 2 MHz and over an amplitude range of 0.03 microvolt/m to 100 mV/m.

Infragravity energy in the surf zone

Abstract: Field measurements of onshore and longshore velocities in the surf zone have been obtained on Martinique Beach, Nova Scotia, for the purpose of investigating the dynamics of the infragravity band (0.0030.03 Hz) of the spectra. A total of 35 data runs were obtained during a 1-week period. Of particular interest is the response of the infragravity energy to the changing incident waves, which increased considerably in size during the latter haft of the week due to an approaching hurricane. It is shown theoretically, using equilibrium arguments, that the infragravity amplitude should vary approximately linearly with incident wave amplitude. This is supported from the field data if signifier wave height is used as a measure of incident amplitude. The incident band of spectra observed by instruments in the surf zone is limited by breaking. Thus the infragravity band appears to dominate these spectra during storms. The analysis is carried out in terms of a spectral transformation, the spectrum which would be observed at an offshore instrument if the shoreline amplitude spectrum were white with unit spectral energy density. For onshore velocity the transformation predicts the observed spectral structure in the infragravity band, showing that the structure did not represent any true frequency selection. The match of theory and data also implies that the onshore motions are free waves, forced near resonance. The longshore spectra are red and show no structure which would be associated with free waves. This is consistent with the theoretical prediction that many edge wave modes, including high modes, would be forced given the broad directional spread of the storm waves. It is noted that further field experiments would be simpler on the Pacific coast where the typical, narrow-band, incident swell should force only a few, low, edge wave modes, a more accommodating situation to observe and analyze. The term 'infragravity' has been used to indicate motions with time scales of about 30-300 s, usually associated with the surf zone. Munk [1949] was the first to observe infragravity energy by using a tsunami recorder, basically a stilling well which filtered out the higher frequency components of the spectrum. He called the phenomenon 'surf beat' to reflect the observed association of these low frequency motions with the beat in the incident waves. The term infragravity energy is perhaps preferable to indicate that it is the low frequency motion that is being referred to, not the simple beating of two, firstorder incident waves (which has no spectral representation at the beat frequency and does not necessarily provide the forcing at infragravity frequencies). Theoretical studies of infragravity dynamics have evolved along two lines. The earlier theories were two dimensional, with no longshore dependence [Munk, 1949; Tucker, 1950; Longuet-Higgins and Stewart, 1964; Suhayda, 1974]. Associated with incident groups (defined by Bowen and Guza [1978] as the amplitude modulation in the incoming wave train) is a second-order, forced correction to mean sea level, progressing shoreward with the group. This forced wave is then released as a seaward-propagating free wave when the incident waves break [Longuet. Higgins and Stewart, 1964]. The summation of the inward and outward propagating components should give a standing component to the wave pattern. This mechanism does not allow for longshore periodicity, and the response is limited since the interaction is not resonant. More recently, three -dimensional theories have been developed in which longshore modulation in the incident wave field is also considered. Gallagher [1971] was the first to discuss this case, showing that, under certain conditions, the incident wave groups could force edge waves. Longshore periodicity was thus introduced into the problem and, since the

The amplitude equation near the convective threshold: application to time-dependent heating experiments

Abstract: High-resolution measurements have been performed of the convective heat current as a function of time when a Rayleigh-Benard cell is swept through its threshold with a specified time-dependent heat input. The results are interpreted in terms of the amplitude equation which exactly describes the slow variations in space and time of hydrodynamic quantities near the threshold. A phenomenological forcing field is added to this equation, and its form and magnitude are fitted to the onset time of the convective heat current. A deterministic model in which the field is an adjustable constant yields a good fit to the data for both a step and a linear ramp in the heat input. An alternative stochastic model, in which the field is a Gaussian variable with zero mean and a white-noise spectrum, is adequate for the ramp experiments, but cannot fit the step data for any value of the mean-square field. The systematics of the field and onset time versus ramp rate are studied in both the deterministic and stochastic models, and attempts are made to interpret the field in terms of physical mechanisms. When the data for long times are analysed in terms of the amplitude equation, it is found that the state first excited at onset is not the roll pattern which is stable in steady state. Instead, the system goes first to an intermediate state, which we tentatively identify as a hexagonal configuration. The decay of this state is governed by a further adjustable field in the amplitude equation.

Observation of a long-time tail in Brownian motion

Abstract: By photon correlation dynamic laser light scattering the authors have measured the time dependence of the mean-square displacement ( Delta x2(t)) of spherical particles (radius approximately 1.7 mu m) in Brownian motion. Clear evidence was found for the existence of a t1/2 term in ( Delta x2(t)) which corresponds to the expected t-3/2 'long-time tail' in the particle velocity autocorrelation function. The experimentally determined amplitude of the t1/2 term was about 74+or-3% of the value predicted theoretically. Despite detailed consideration of possible systematic errors the authors were unable to explain the magnitude of this disagreement.

Interpretation of magnetic anomalies due to dikes; the complex gradient method

Abstract: A method to interpret the magnetic anomaly due to a dipping dike using the resultant of the horizontal and vertical gradients of the anomaly is suggested. The resultant of both the gradients is a vector quantity and is defined as the “complex gradient.” A few characteristic points defined on the amplitude and phase plots of the complex gradient are used to solve for the parameters of the dike. For a dike uniformly magnetized in the earth’s magnetic field, the amplitude plot is independent of θF, the index parameter, which depends upon the strike and dip of the dike and the magnetic inclination of the area. The phase plot of the complex gradient is an antisymmetric curve with an offset value equal to -θF. For a dike whose half‐width is greater than its depth of burial, two maxima at equal distances on either side of a minimum value appear on the amplitude plot. For a dike whose half‐width is equal to or less than its depth of burial, the amplitude plot is a bell‐shaped symmetric curve with its maximum appe...

A semi-analytic solution for nonlinear standing waves in deep water

Abstract: A method of time-dependent conformal mapping is introduced to simplify the power-series solution procedure for time- and space-periodic standing waves in deep water. A solution has been found to 25th order in the wave amplitude. The values of certain coefficients are determined by the requirement that secular terms must be suppressed. Because the series for the wave profile is not always uniformly convergent, Pade approximants are used for summation. For very high waves, the slope of the surface has at least two relative maxima. The singularity structure of the solution is also discussed.

Focusing of two-dimensional waves

Abstract: Two different methods are presented for efficient computation of two-dimensional wave fields in focal regions. Both methods are valid for arbitrarily large relative apertures. One method is based on the impulse-response integral and the other on the angular-spectrum representation. The latter method is used to analyze the discrepancy between applying the Kirchhoff or the Debye assumption to obtain an approximation for the field in the aperture. Two cases of idealized incident waves are analyzed in detail. First, we treat the case of a perfect incident wave, i.e., a wave that, in the limit of an infinitely large aperture, would produce a δ-function field distribution on the focal line if account were taken of evanescent waves. Second, the incident wave is taken to be the field radiated by a point source and subsequently focused by a lens that delays the phase of the incoming wave in a perfect manner without influencing its amplitude. The latter wave has the same phase distribution over the aperture as the perfect wave, but a different amplitude distribution.

A numerical study of the generation of an azimuthal current in a plasma cylinder using a transverse rotating magnetic field

Abstract: The generation of a steady azimuthal current in a cylindrical plasma column using a rotating magnetic field is numerically investigated. The mixed initial-boundary-value problem is solved using a finite difference method. It is shown that substantial azimuthal current can be driven provided that the amplitude of the rotating magnetic field is greater than a certain threshold value which depends on the plasma resistivity.

The amplitude and phase response of a seismic vibrator

Abstract: The amplitude and phase response of a simple model is compared with the performance of a real vibrator working in the field. The field results show a characteristic phase response which confirms that the real drive force applied to the baseplate and its load impedance is faithfully represented by the acceleration of the reaction mass. It follows that all the parameters necessary to calculate the load impedance and the true power dissipated in the earth can be measured at the output of the vibrator. It also follows that the current method of baseplate phase compensation should be reconsidered.

Measurements of plasma wave spectra in Jupiter's magnetosphere

Abstract: Compressed plots of E field averages for all of the 16-channel spectrum analyzer data from the Voyager 1 and 2 magnetosphere traversals are presented to provide an overall framework for the discussion. The importance of considering peaks as well as averages is illustrated by using 16-channel measurements from the first inbound and last outbound bow shock for Voyager 2. Selected wideband measurements from the waveform receivers are presented to demonstrate how many important wave bursts are variable in times less than or comparable to the 4-s scan period of the 16-channel analyzer.

Body wave amplitude patterns and upper mantle attenuation variations across North America

Abstract: Summary. A broad band amplitude study of P- and SH-waves from deep South American events recorded at WWSSN stations in the United States provides constraints on upper mantle variations in attenuation. The events were selected to minimize contamination due to source complexity, radiation pattern, and source structure. The prevalent feature in the short- and longperiod bands is that the SH amplitudes show the same regional variations as the P amplitudes, with the regional variations of short periods being similar, but enhanced relative to the variations at long periods. The amplitudes show some systematic regional difference between the East Coast and Rocky Mountain provinces, and both short and long periods are enhanced at the Gulf Coast and midwestern stations, probably due to thick sedimentary bed receiver structure. Since detailed receiver structures for individual stations are poorly known, we used the working hypothesis that the regional amplitude patterns are caused by lateral variations in upper mantle attenuation. Both a constant Q and a frequency-dependent attenuation operator were considered, with the relative amplitudes and waveforms in short- and long-period bands used to estimate the acceptable range of At* in the constant Q model, or the acceptable range of the parameter r, , which describes the high-frequency roll-off of the absorption band in the frequency-dependent model. Time domain modelling indicates that the short-period P and SH amplitudes and waveforms in the 1-10s period range do not unambiguously demand frequency-dependent attenuation, allowing for the uncertainty in source frequency content and long-period absorption band amplitude. The short-period P amplitudes can be fit with a range in At; = 0.5 s or a range in r, from 0.001 to 0.25s, with either single parameter variation consistent with the general short-period SH amplitude behaviour. A technique for determining the absolute value of t* and possible r, values appropriate for the 5-20s band was applied to selected data. A value of t* = 0.8 s and small 7, were found for travel paths from the deep events to North America, and lower t* or large r,, values were found for paths to southern African stations. Longperiod amplitude variations cannot be explained by frequency-dependent

Amplitude variations of electron cyclotron harmonic waves

Abstract: Electron cyclotron harmonic (ECH) instabilities just outside the plasmapause and at frequencies near the cold upper hybrid frequency are a common feature of the Earth's magnetosphere. These waves which have virtually no magnetic component, are believed to have an important role in the generation of weak diffuse aurora1,2. They are able to interact strongly with electrons in the hundred eV to several keV energy range which can result in pitch angle scattering and precipitation on magnetic field lines which map down into the auroral zone. On the dayside magnetosphere these waves can exhibit large amplitude variations of 30–40 dB and can also exist at steady amplitudes on time scales of the order of tens of seconds. Here we seek an explanation for the sporadic nature of such instabilities by performing linear stability calculations and extending the technique used in the accompanying paper3.

Transient nonlinear pitch angle scattering of energetic electrons by coherent VLF wave packets in the magnetosphere

Abstract: Adiabatic theory is used in studying the transient nonlinear pitch angle scattering experienced by energetic electrons under the influence of coherent VLF wave packets in the magnetosphere. Finite wave packets of both fixed and variable frequency are considered, as are wide ranges of L shell, wave amplitude, and wave frequency. The results indicate that large mean pitch angle changes can be induced in the portion of the energetic population that undergoes a nonlinear cyclotron resonance interaction with the wave packet.

ac Stark splitting in intense stochastic driving fields with Gaussian statistics and non-Lorentzian line shape

Abstract: Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.