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Showing papers on "Harmonics published in 1996"


Journal ArticleDOI
TL;DR: In this article, the authors present the present status of active filters based on state-of-the-art power electronics technology, and their future prospects and directions toward the 21st Century, including the personal views and expectations of the author.
Abstract: Attention has been paid to active filters for power conditioning which provide the following multifunctions: reactive power compensation; harmonic compensation; flicker/imbalance compensation; and voltage regulation. Active filters in a range of 50 kVA-60 MVA have been practically installed in Japan. In the near future, the term "active filters" will have a much wider meaning than it did in the 1970s. For instance, active filters intended for harmonic solutions are expanding their functions from harmonic compensation of nonlinear loads into harmonic isolation between utilities and consumers, and harmonic damping throughout power distribution systems. This paper presents the present status of active filters based on state-of-the-art power electronics technology, and their future prospects and directions toward the 21st Century, including the personal views and expectations of the author.

1,700 citations


Journal ArticleDOI
TL;DR: In this paper, a crack in a structural member introduces a local flexibility that affects its vibration response, and the crack will open and close in time depending on the rotation and vibration amplitude.

1,080 citations


Journal ArticleDOI
TL;DR: It is demonstrated that high-order harmonics generated by an atom in intense laser field form trains of ultrashort pulses corresponding to different trajectories of electrons that tunnel out of the atom and recombine.
Abstract: We demonstrate that high-order harmonics generated by an atom in intense laser field form trains of ultrashort pulses corresponding to different trajectories of electrons that tunnel out of the atom and recombine. Propagation in an atomic jet allows us to select one of these trajectories, leading to a train of pulses of extremely short duration.

494 citations


Journal ArticleDOI
TL;DR: In this article, the generation of harmonics by interaction of an ultrashort laser pulse with a step boundary of a plane overdense plasma layer is studied at intensities Iλ2=1017 −1019 W −2μm2 for normal and oblique incidence and different polarizations.
Abstract: The generation of harmonics by interaction of an ultrashort laser pulse with a step boundary of a plane overdense plasma layer is studied at intensities Iλ2=1017–1019 W cm−2 μm2 for normal and oblique incidence and different polarizations. Fully relativistic one‐dimensional particle‐in‐cell (PIC) simulations are performed with high spectral resolution. Harmonic emission increases with intensity and also when lowering the plasma density. The simulations reveal strong oscillations of the critical surface driven by the normal component of the laser field and by the ponderomotive force. It is shown that the generation of harmonics can be understood as reflection from the oscillating surface, taking full account of retardation. Describing the oscillations by one or more Fourier components with adjustable amplitudes, model spectra are obtained that well reproduce the PIC spectra. The model is based on relativistic cold plasma equations for oblique incidence. General selection rules concerning polarization of odd and even harmonics depending on incident polarization are derived.

493 citations


Journal ArticleDOI
Yves Surrel1
TL;DR: A method is proposed that permits the derivation of algorithms that satisfy both requirements of phase-stepping methods, up to any arbitrary order, based on a one-to-one correspondence between an algorithm and a polynomial.
Abstract: If the best phase measurements are to be achieved, phase-stepping methods need algorithms that are 112 insensitive to the harmonic content of the sampled waveform and 122 insensitive to phase-shift miscalibration. A method is proposed that permits the derivation of algorithms that satisfy both requirements, up to any arbitrary order. It is based on a one-to-one correspondence between an algorithm and a polynomial. Simple rules are given to permit the generation of the polynomial that corresponds to the algorithm having the prescribed properties. These rules deal with the location and multiplicity of the roots of the polynomial. As a consequence, it can be calculated from the expansion of the products of monomials involving the roots. Novel algorithms are proposed, e.g., a six-sample one to eliminate the effects of the second harmonic and a 10-sample one to eliminate the effects of harmonics up to the fourth order. Finally, the general form of a self-calibrating algorithm that is insensitive to harmonics up to an arbitrary order is given.

485 citations


Journal ArticleDOI
TL;DR: In this article, a new model of shear velocity structure in the mantle is presented to fit data-sets of absolute and differential body-wave travel times, surface-wave phase velocities over a broad range of frequencies, and structure coefficients of modes of free oscillation.
Abstract: We present a new model of shear velocity structure in the mantle which is designed to fit data-sets of absolute and differential body-wave travel times, surface-wave phase velocities over a broad range of frequencies, and structure coefficients of modes of free oscillation. The model is parametrized laterally by spherical harmonics (truncated at degree 16) and by 30 natural cubic B-splines in radius. Our best model features large-amplitude structure (up to ±6% anomalies in shear velocity) in the topmost 400 km of the mantle and in the lowermost 500 km (up to ±2.5%) with most of the power in the low harmonics ( l

378 citations


Journal ArticleDOI
01 Mar 1996
TL;DR: In this paper, it is shown that in an inverter-motor system, the common mode voltages generated by a PWM inverter, which are attributed to PWM switching harmonics, couple through parasitic capacitances from stator windings to the rotor body and then returns through the motor bearings to the commonly grounded stator case as a closed loop circuit.
Abstract: The recent increase of bearing damage in induction machines driven by transistorized inverters has spurred activity on possible causes related to PWM inverters. This paper looks into a typical power conversion system from this perspective. It identifies the existence of the common mode voltages produced in all types of converters. A hypothesis is then proposed to explain the bearing current problem. In particular, it is shown that in an inverter-motor system the common mode voltages generated by a PWM inverter, which are attributed to PWM switching harmonics, couple through parasitic capacitances from stator windings to the rotor body and then returns through the motor bearings to the commonly grounded stator case as a closed loop circuit. The hypothesis is verified by experimental measurement of common mode coupling currents and true bearing currents in a specially modified induction motor. Solutions are then provided to suppress the bearing currents.

357 citations


Journal ArticleDOI
TL;DR: In this article, the authors propose definitions for power terms in alternating current systems that are practical and effective when voltage and/or currents are distorted or unbalanced, and also suggest definitions for measurable values that may be used to indicate the level of distortion and unbalance.
Abstract: Existing definitions for power terms in alternating current systems work well for single-phase and three-phase systems where both voltages and currents are sinusoidal with respect to time. This paper clarifies and proposes definitions for power terms that are practical and effective when voltage and/or currents are distorted and/or unbalanced. It also suggests definitions for measurable values that may be used to indicate the level of distortion and unbalance.

342 citations


Proceedings ArticleDOI
06 Oct 1996
TL;DR: In this article, a novel voltage modulation technique named unified PWM (pulse width modulation) for high performance voltage generation in a voltage-fed inverter is described, which has wide fitness to the general prospect for the loss minimization and the lowest current harmonic with full DC link voltage utilization.
Abstract: In this paper, a novel voltage modulation technique named unified PWM (pulse width modulation) for high performance voltage generation in a voltage-fed inverter is described. As increasing the interest in the high quality power conversion is, a simple PWM scheme that has the wide fitness to the general prospect for the loss minimization and the lowest current harmonic with full DC link voltage utilization is required. From the synthesis of the actual inverter action, a simple but useful concept for the 'effective time' is established. And, fully employing this concept, a new voltage modulation technique for various applications is presented with detailed explanation and actual test results. Implementing this facile strategy to actual fields will result in great reduction of calculation efforts and high applicability including the minimization of switching loss and current harmonics.

298 citations


Journal ArticleDOI
TL;DR: In this article, the authors present experimental and theoretical results on high-harmonic generation in noble gases using an 805 nm, 25 fs, titanium-doped sapphire laser.
Abstract: We present experimental and theoretical results on high-harmonic generation in noble gases using an 805 nm, 25 fs, titanium-doped sapphire laser. The harmonic energies observed are unexpectedly high when compared with experimental and theoretical results to date for longer excitation pulses. We observe that the efficiency of harmonic production is highest for shorter pulses. Furthermore, the wavelength of the harmonics can be tuned by adjusting the sign of the chirp of the excitation pulse, demonstrating a tunable, ultrashort-pulse, $l25\mathrm{fs}$ soft-x-ray source.

291 citations


Journal ArticleDOI
TL;DR: In this article, a generalized model of the PWM rectifier is presented using the Clarke notation in order to separate the positive and negative sequences of a PWM signal and an optimized regulation is presented for the latter case.
Abstract: This study concerns the modeling and control of a pulse-width-modulated (PWM) rectifier in the case of network variations. The aim is to limit and stabilize variations of DC output voltage and line currents in such circumstances. Network variations can result in costly damage to power converters and their loads but a power converter such as the PWM rectifier, using cascade digital control, offers many capabilities to stabilize the system with optimized control. A generalized model of the PWM rectifier is first presented using the Clarke notation in order to separate the positive and negative sequences. The model is also extended to the harmonics. The cases of harmonic disturbance and an unbalanced network are then analyzed and an optimized regulation is presented for the latter case, validating the generalized model. Experimental results are proposed. The line current compensation loop method coupled with identification of network parameters offers a good solution to stabilize the PWM rectifier in an unbalanced network.


Journal ArticleDOI
04 Jun 1996
TL;DR: In this paper, the authors presented a new method of measurement of power system frequency, based on digital filtering and Prony's estimation method, which is more accurate than others, e.g., the measurement of angular velocity of the rotating voltage phasor.
Abstract: The main frequency is an important parameter of an electrical power system. The frequency can change over a small range due to generation-load mismatches. Some power system protection and control applications, e,g, frequency relay for load shedding, load-frequency controller, require accurate and fast estimation of the frequency. Most digital algorithms for measuring frequency have acceptable accuracy if voltage waveforms are not distorted. However, due to nonlinear devices, e,g, semiconductor rectifiers, electric arc furnaces, the voltage waveforms can include higher harmonics. The paper presents a new method of measurement of power system frequency, based on digital filtering and Prony's estimation method. Simulation results confirm, that the proposed method is more accurate than others, e,g, than the method based on the measurement of angular velocity of the rotating voltage phasor.

Journal ArticleDOI
TL;DR: Clusters containing about 10 atoms are produced in a high-pressure gas jet and are shown to be a unique nonlinear medium that yields higher appearance intensity for a given harmonic order, stronger nonlinear dependence of harmonic signal on laser intensity, higher-order harmonics, and reduced saturation of the harmonic signal at high laser intensity.
Abstract: We report the generation of short-wavelength, high-order harmonics of intense laser radiation from atom clusters. Clusters containing about 1${0}^{3}$ atoms are produced in a high-pressure gas jet. We show them to be a unique nonlinear medium. Compared with monomer gases they yield a higher appearance intensity for a given harmonic order, stronger nonlinear dependence of harmonic signal on laser intensity, higher-order harmonics, and reduced saturation of the harmonic signal at high laser intensity.

Journal ArticleDOI
TL;DR: In this paper, a linear adaptive neuron called Adaline is used for the estimation of harmonic components of a power system using a neural estimation algorithm that is adjusted to force the error between the actual and desired outputs to satisfy a stable difference error equation.
Abstract: The paper presents a new approach for the estimation of harmonic components of a power system using a linear adaptive neuron called Adaline. The learning parameters in the proposed neural estimation algorithm are adjusted to force the error between the actual and desired outputs to satisfy a stable difference error equation. The estimator tracks the Fourier coefficients of the signal data corrupted with noise and decaying DC components very accurately. Adaptive tracking of harmonic components of a power system can easily be done using this algorithm. Several numerical tests have been conducted for the adaptive estimation of harmonic components of power system signals mixed with noise and decaying DC components.

Journal ArticleDOI
TL;DR: In this paper, the authors describe nonlinear response in rock from resonance experiments and show that the resonant peak is observed to always shift downward (if indeed the peak shifts), indicating a net softening of the modulus with drive level.
Abstract: In a great variety of laboratory experiments over large intervals in stress, strain, and frequency, rocks display pronounced nonlinear elastic behavior. Here we describe nonlinear response in rock from resonance experiments. Two important features of nonlinear resonant behavior are a shift in resonant frequency away from the linear resonant frequency as the amplitude of the disturbance is increased and the harmonics in the time signal that accompany this shift. We have conducted Young's mode resonance experiments using bars of a variety of rock types (limestone, sandstone, marble, chalk) and of varying diameters and lengths. Typically, samples with resonant frequencies of approximately 0.5-1.5 kHz display resonant frequency shifts of 10% or more, over strain intervals of 10 -7 to 10 -6 and under a variety of saturation conditions and ambient pressure conditions. Correspondingly rich harmonic spectra measured from the time signal progressively develop with increasing drive level. In our experiments to date, the resonant peak is observed to always shift downward (if indeed the peak shifts), indicating a net softening of the modulus with drive level. This observation is in agreement with our pulse mode and static test observations, and those of other researchers. Resonant peak shift is not always observed, even at large drive levels ; however, harmonics are always observed even in the absence of peak shift when detected strain levels exceed 10 -7 or so. This is an unexpected result. Important implications for the classical perturbation model approach to resonance results from this work. Observations imply that stress-strain hysteresis and discrete memory may play an important role in dynamic measurements and should be included in modeling. This work also illustrates that measurement of linear modulus and Q must be undertaken with great caution when using resonance.

Journal ArticleDOI
01 May 1996
TL;DR: In this paper, an analytical model for cage induction motors with a static eccentric rotor is described, based on an airgap permeance approach including stator and rotor MMF harmonics.
Abstract: The paper describes an analytical model for cage induction motors with a static eccentric rotor. The method is based on an airgap permeance approach including stator and rotor MMF harmonics. The stator windings are resolved into harmonic conductor density distributions that allow different series/parallel winding connections to be accommodated in a straightforward manner. Sinusoidal and homopolar airgap field components are identified and the total airgap field distribution is used to determine the radial forces on the rotor. The model examines the principal harmonic interactions that influence the unbalanced magnetic pull.

Journal ArticleDOI
TL;DR: In this paper, the main properties of atomic photoelectron spectra are discussed via a numerical calculation, as they would be obtained by using a radiation pulse containing N+1 frequencies associated with a ''Dirac comb'' of N higher harmonics together with the laser which has been used to generate them.
Abstract: We discuss, via a numerical calculation, the main properties of atomic photoelectron spectra, as they would be obtained by using a radiation pulse containing N+1 frequencies associated with a ``Dirac comb'' of N higher harmonics together with the laser which has been used to generate them. We address more precisely the physically relevant situation in which the harmonics have much weaker intensities than the one of the laser. In such (N+1)-color photoionization processes, the atom can simultaneously absorb harmonic uv photons and exchange, i.e., absorb and/or emit, (via stimulated emission) laser ir photons. We have simulated the photoelectron spectra by numerically solving the time-dependent Schr\"odinger equation for a three-dimensional hydrogen atom in the presence of the radiation pulse. Our results show that, everything else being kept fixed, the magnitudes of the photoelectron peaks are strongly dependent on the difference of phase between successive harmonics. This strong dependence results from interference effects taking place between competing quantum paths leading to a given final state. An interesting feature is that these interferences involve transitions in the continuum states of the atom and do not depend on resonances in the discrete spectrum. Another interesting outcome of our study is to show that such effects should be observable with currently developed harmonic sources. \textcopyright{} 1996 The American Physical Society.

Journal ArticleDOI
TL;DR: In this paper, an orthogonal series expansion was proposed for phase recovery with the transport-of-intensity equation by use of a series expansion, which can be more easily adjusted for apertures of various shapes.
Abstract: In a previous paper [ J. Opt. Soc. Am. A12, 1932 ( 1995)] we presented a method for phase recovery with the transport-of-intensity equation by use of a series expansion. Here we develop a different method for the solution of this equation, which allows recovery of the phase in the case of nonuniform illumination. Though also based on the orthogonal series expansion, the new method does not require any separate boundary conditions and can be more easily adjusted for apertures of various shapes. The discussion is primarily for the case of a circular aperture and Zernike polynomials, but we also outline the solution for a rectangular aperture and Fourier harmonics. The latter example may have some substantial advantages, given the availability of the fast Fourier transform.

Journal ArticleDOI
TL;DR: In this paper, the optimal locations of a limited number of harmonic meters and the optimal dynamic estimates of harmonic source locations and their injections in unbalanced three-phase power systems are solved using Kalman filtering.
Abstract: In this paper, two problems have been addressed on harmonic sources identification: the optimal locations of a limited number of harmonic meters and the optimal dynamic estimates of harmonic source locations and their injections in unbalanced three-phase power systems. Kalman filtering is used to solve these problems. System error covariance analysis by the Kalman filter associated with a harmonic injection estimate determines the optimal arrangement of limited harmonic meters. Based on the optimally-arranged harmonic metering locations, the Kalman filter then yields the optimal dynamic estimates of harmonic injections with a few noisy harmonic measurements. The method is dynamic and has the capability of identifying, analyzing and tracking each harmonic injection at all buses in unbalanced three-phase power systems. Actual recorded harmonic measurements and simulated data in a power distribution system are provided to prove the efficiency of this approach.

Journal ArticleDOI
TL;DR: A new implementation scheme based on real-time solution of nonlinear harmonic elimination equations using a digital signal processor DSP56001 is reported, which shows that optimal pulse patterns having 15 switching angles in each quarter fundamental period can be determined within 2.15 ms.
Abstract: Pulse-width modulation of DC/AC power converters (PWM) based on the elimination of low-order harmonics necessitates solving systems of nonlinear equations. Conventional implementations of this technique based on storing off-line calculated solutions have the common problem that the system flexibility is very limited, especially for applications that require both amplitude and frequency control. A new implementation scheme based on real-time solution of nonlinear harmonic elimination equations using a digital signal processor DSP56001 is reported in this paper. With this digital signal processor (DSP), optimal pulse patterns having 15 switching angles in each quarter fundamental period can be determined within 2.15 ms. Details of the system hardware and software are described. New theoretical results concerning the solvability of harmonic elimination equations are also presented.

Journal ArticleDOI
TL;DR: It is found that the harmonics exhibit good fringe visibility and high spatial coherence, though the coherence is somewhat degraded at high intensity because of the production of free electrons through optical field ionization during the harmonic generation.
Abstract: We have executed a series of Young's two-slit experiments to measure the spatial coherence of soft x rays produced by high order harmonic generation in helium within the 270 to 480 \AA{} wavelength range. We find that the harmonics exhibit good fringe visibility and high spatial coherence, though the coherence is somewhat degraded at high intensity because of the production of free electrons through optical field ionization during the harmonic generation.

Journal ArticleDOI
TL;DR: The results of the calculations, including propagation for both the intensity and polarization properties of harmonics as a function of laser ellipticity, compare very well with recent experimental observations.
Abstract: We generalize a recently formulated theory of high-order harmonic generation by low-frequency laser fields [Anne L'Huillier et al., Phys. Rev. A 48, R3433 (1993)] to the case of an elliptically polarized light. Our theoretical description includes both the single-atom response and propagation. Phase matching significantly modifies the results obtained in the single-atom response. The results of our calculations, including propagation for both the intensity and polarization properties of harmonics as a function of laser ellipticity, compare very well with recent experimental observations.

Journal ArticleDOI
01 May 1996
TL;DR: A new access control method called SMART (Structural Vibration Minimized Acceleration Trajectory) has been developed for hard disk drives that suppressed the high harmonics of the actuator acceleration are suppressed in comparison with conventional control.
Abstract: A new access control method called SMART (Structural Vibration Minimized Acceleration Trajectory) has been developed for hard disk drives. The access formula is derived from a minimum-jerk cost function. The closed loop of access mode is based on velocity control and the target velocity to keep minimum-jerk is easily calculated as a function of position by a DSP controller. With SMART control the high harmonics of the actuator acceleration are suppressed in comparison with conventional control. Residual vibration after the access operation and spacing fluctuation of the head slider are both greatly decreased.

Proceedings ArticleDOI
M.S. Elmore1
03 Mar 1996
TL;DR: In high power factor AC-to-DC applications, boost power converters operating on the boundary of continuous mode and discontinuous mode switch with variable frequency and draw high peak input currents.
Abstract: In high power factor AC-to-DC applications, boost power converters operating on the boundary of continuous mode and discontinuous mode switch with variable frequency and draw high peak input currents. A method is presented to parallel two or more of these power converters to reduce the high peak input currents. Each power converter continues to operate on the boundary of continuous mode and discontinuous mode and maintains the benefits of zero-voltage switching.

Journal ArticleDOI
TL;DR: In this paper, the power quality of a lowvoltage grid with two wind turbines is investigated and the spectrum of the power is determined so that the presence of periodic power components can be investigated.
Abstract: The power quality of a low-voltage grid with two wind turbines is investigated. Slow voltage variations as well as transients and harmonics are measured and analysed. Furthermore, the spectrum of the power is determined so that the presence of periodic power components can be investigated. Although periodic power fluctuations reaching 10% of the rated power are registered, voltage variations are lower than the prescribed IEC flicker limit at steady-state operation. As the turbines are put on-line, the voltage level is lowered by 3%, which exceeds the flicker limit. The risk for flicker increases if the X/R ratio of the grid is low and if turbines which have a tendency to produce large periodic power fluctuations are used.

Journal ArticleDOI
K. Srinivasan1
01 Apr 1996
TL;DR: In this paper, the authors proposed an approach to quantifying the distortion caused by a single customer, when there are many customers in the network, by isolating the contributions to waveform distortion from a customer side and the supply side.
Abstract: In this paper, we propose an approach to quantifying the distortion caused by a single customer, when there are many customers in the network. We have described a method for isolating the contributions to waveform distortion from a customer side and the supply side. The voltage and current measurements at a single point are sufficient. This approach will be useful in arriving at equitable ways of settling customer complaints, sharing the cost of waveform distortion through rate structures, penalties, etc. The principle is illustrated using six example loads. The method proposed can be implemented in any power quality measurement device, which monitors the voltage as well as the current harmonics simultaneously.

Proceedings ArticleDOI
06 Oct 1996
TL;DR: It is shown that whilst the rotor position-dependent signals are robust to changes in load, interference harmonics arising from slot saturation and rotor slot harmonics cause problems for rotor position tracking.
Abstract: This paper describes a new method of obtaining a rotor position signal from a cage induction machine operating without a mechanical sensor. The method is based on introducing a circumferential variation in the resistance of a high-resistance outer-section cage of an induction-machine rotor. Simulation results using a linear "double-cage" machine equivalent show that the method is feasible and provides incremental rotor position tracking with good dynamics. The paper describes an implementation of the method for a 30 kW double-cage machine having variable-gauge copper wire in the outer slots. It is shown that, while the rotor position-dependent signals are robust to changes in load, interference harmonics arising from slot saturation and rotor slot harmonics cause problems for rotor position tracking. These problems are discussed in relation to the present method and that of designed asymmetries in general.

Journal ArticleDOI
06 Oct 1996
TL;DR: In this article, a hybrid parallel active filter (HPAF) system intended for high-power applications-up to 100 MW nonlinear loads-to meet IEEE 519 recommended harmonic standards is presented.
Abstract: This paper presents a new control scheme for a hybrid parallel active filter (HPAF) system intended for high-power applications-up to 100 MW nonlinear loads-to meet IEEE 519 recommended harmonic standards. The active filter inverter is realized with small-rated (1%-2% of the load rating) square-wave inverters operating at the dominant harmonic frequencies. The proposed system achieves harmonic isolation at desired dominant harmonic frequencies, such as the fifth and seventh, even in the presence of supply voltage harmonic distortions. A novel method of active filter inverter DC-bus control, as proposed here, achieves power balancing by exchanging energy at the fundamental frequency and at the dominant harmonic frequency (such as the fifth). The proposed square-wave inverter-based HPAF system provides improved filtering characteristics as compared to the conventional passive filter and is expected to be cost effective for high-power nonlinear loads compared to the conventional passive filter or other active filtering solutions. The concept of harmonic isolation at dominant harmonic frequencies by square-wave inverters with the proposed control scheme is validated by simulation results.

Journal ArticleDOI
TL;DR: Relativistic harmonic generation by the scattering of very-high-intensity laser light from fast free electrons is investigated theoretically and it is found, among other results, that at laser intensities higher than, say ${10}^{18}$ W/${\mathrm{cm}}^{2}$, the low-order harmonics are suppressed while the higher-order harmonicics are enhanced.
Abstract: Relativistic harmonic generation by the scattering of very-high-intensity laser light from fast free electrons is investigated theoretically. A general solution for the trajectory of an electron, moving initially with an arbitrary velocity in a light pulse of arbitrary intensity and polarization, is presented. This solution generalizes the classical analysis of Eberly [Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1969), Vol. 7] and that of Sarachik and Schappert [Phys. Rev. D 1, 2738 (1970)] for the trajectory of an electron initially at rest. The result is then applied to the case of effective harmonic generation in a monochromatic, circularly polarized field under three different initial conditions for the electron, namely, (a) electron initially at rest, (b) electron initially moving in the direction of light propagation (and opposite to it), and (c) electron initially crossing the radiation beam at right angles. Angular distributions of the harmonics generated by the scattering process are presented in terms of the power scattering cross section in each case. Effects of increasing the light intensity and/or the initial electron speed and/or direction on the angular distributions are discussed. It is found, among other results, that at laser intensities higher than, say ${10}^{18}$ W/${\mathrm{cm}}^{2}$, the low-order harmonics are suppressed while the higher-order harmonics are enhanced. \textcopyright{} 1996 The American Physical Society.