Sawtooth-like Waveform Research Articles

A harmonic study of electric field nonlinearity and field reversal in collisionless capacitive discharges driven by sawtooth-like waveforms

Understanding electron and ion heating phenomenon in capacitively coupled radio-frequency plasma discharges is vital for many plasma processing applications. In this article, using particle-in-cell simulation technique we investigate the collisionless argon discharge excited by temporally asymmetric sawtooth-like waveform. In particular, a systematic study of the electric field nonlinearity and field reversal phenomenon by varying the number of harmonics and its effect on electron and ion heating is performed. The simulation results predict higher harmonics generation and multiple field reversal regions formation with an increasing number of harmonics along with the local charge separation and significant displacement current outside sheath region. The field reversal strength is greater during the expanding phase of the sheath edge in comparison to its collapsing phase causing significant ion cooling. The observed behavior is associated with the electron fluid compression/rarefaction and electron inertia during expanding and collapsing phase respectively.

Plasma asymmetry and electron and ion energy distribution function in capacitive discharges excited by tailored waveforms

Using a particle-in-cell simulation technique, we investigate the plasma and ionization asymmetry, higher harmonics generation, and electron and ion energy distribution function (IEDF) in capacitive discharges excited by tailored waveforms. At a base frequency of 13.56 MHz, three different waveforms, namely sinusoidal, sawtooth, and square, are applied for a constant current density amplitude of 50 A m−2 and gas pressure of 5 mTorr. The simulation results show that the square waveform produces the highest plasma density in the discharge, whereas maximum asymmetry is observed for plasma excited by the sawtooth-like waveform. Both square and sawtooth waveforms generate multiple beams of high-energy electrons from near to the expanding phase of the sheath edge and high-frequency modulations up to 100 MHz on the instantaneous sheath position. The electron energy distribution function depicts three electron temperature and highly elevated tail-end electrons for the square waveform in comparison to the sinusoidal and sawtooth waveform. The IEDF is bimodal at both the powered and grounded electrodes with a large asymmetry and narrow-type distribution in the case of the sawtooth-like waveform. These results suggest that the choice of waveform is highly critical for achieving maximum asymmetry and plasma density simultaneously in capacitive discharges.

Signatures of Intermittency and Fine-scale Turbulence in the Very Local Interstellar Medium

Abstract This study presents the first Voyager 1 (V1) observation of magnetic turbulence intermittency and fine-scale structures associated with the propagation of a shock wave in the outer heliosheath. The intermittent event starts on DOY 178 in 2014 upstream of the shock wave that overtook V1 on DOY 237 at 140 au from the Sun. The distribution of magnetic field increments follows the q-Gaussian distribution with the index q ≈ 1.57 for the maximum variance component. Evidence is provided of fine-scale structures well below the Coulomb collisional scale. They undergo a turbulent cascade at scales less than 10−3 au. Observed magnetohydrodynamic fluctuations show signatures of irregular filamentary structures, sawtooth-like waveforms of mixed compressible/transverse nature, which evolve into shocklets and current sheets. Observational data challenges the interpretation of the interstellar plasma in the outer heliosheath as a featureless medium at scales below the collisional mean free path of about 1 au. These results are of importance for better understanding of turbulent processes in the outer heliosheath, including magnetic reconnection, shock-turbulence interaction, Galactic cosmic-ray transport, plasma wave generation, and radio emission.

Delta-Ramp Encoder for Amplitude Sampling and Its Interpretation as Time Encoding

The theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite-precision amplitude values. In this paper, we explore signal representation and recovery based on uniform amplitude sampling with assumed infinite precision timing information. The approach is based on the delta-ramp encoder which consists of applying a one-level level-crossing detector to the result of adding an appropriate sawtooth-like waveform to the input signal. The output samples are the time instants of these level crossings, thus representing a time-encoded version of the input signal. For theoretical purposes, this system can be equivalently analyzed by reversibly transforming through ramp addition a nonmonotonic input signal into a monotonic one which is then uniformly sampled in amplitude. The monotonic function is then represented by the times at which the signal crosses a predefined and equally-spaced set of amplitude values. We refer to this technique as amplitude sampling. The time sequence generated can be interpreted alternatively as nonuniform time sampling of the original source signal. We derive duality and frequency-domain properties for the functions involved in the transformation. Iterative algorithms are proposed and implemented for recovery of the original source signal. As indicated in the simulations, the proposed iterative amplitude-sampling algorithm achieves a faster convergence rate than frame-based reconstruction for nonuniform sampling. The performance can also be improved by appropriate choice of the parameters while maintaining the same sampling density.

A novel single shot interferometry with a wide field of view by reference plates coated with various metals

A laser microscope with a wide field of view developed in our previous study allowed us to observe the whole surface of a cylinder in a very short time. In that study, resolution of the laser microscope in the depth direction was sacrificed to obtain a wide field of view. To overcome this shortcoming and achieve nano-level measurement of 3-dimensional profiles of various objects, we have introduced two-beam interferometry to the wide field of view laser microscope. To achieve a high contrast interference fringe pattern, a glass reference plate was coated with a thin Cr film or other pure metals. The interference fringe pattern was distorted from sinusoidal wave into a sawtooth-like waveform. The distortion of the interference fringe pattern appeared to correspond to the inclination of the specimen surface measured. This shows the possibility of realizing a novel single shot interferometry method capable of determining the surface profile from only one image of the interference fringe pattern without using the phase shift method. The type of distortion of intensity distribution was different for each metal. The mechanisms by which the intensity distribution of the interference fringes changed to sawtooth pattern are discussed from both a Fourier-transform analysis and an electromagnetic approach.

Hue shifts produced by temporal asymmetries in chromatic signals depend on the alignment of the first and second harmonics.

When M- or L-cone-isolating sawtooth waveforms flicker at frequencies between 4 and 13.3 Hz, there is a mean hue shift in the direction of the shallower sawtooth slope. Here, we investigate how this shift depends on the alignment of the first and second harmonics of sawtooth-like waveforms. Below 4 Hz, observers can follow hue variations caused by both harmonics, and reliably match reddish and greenish excursions. At higher frequencies, however, the hue variations appear as chromatic flicker superimposed on a steady light, the mean hue of which varies with second-harmonic alignment. Observers can match this mean hue against a variable-duty-cycle rectangular waveform and, separately, set the alignment at which the mean hue flips between reddish and greenish. The maximum hue shifts were approximately frequency independent and occurred when the peaks or troughs of the first and second harmonics roughly aligned at the visual input-consistent with the hue shift's being caused by an early instantaneous nonlinearity that saturates larger hue excursions. These predictions, however, ignore phase delays introduced within the chromatic pathway between its input and the nonlinearity that produces the hue shifts. If the nonlinearity follows the substantial filtering implied by the chromatic temporal contrast-sensitivity function, phase delays will alter the alignment of the first and second harmonics such that at the nonlinearity, the waveforms that produce the maximum hue shifts might well be those with the largest differences in rising and falling slopes-consistent with the hue shift's being caused by a central nonlinearity that limits the rate of hue change.

The Climatology of Australian Aerosol

Abstract. Airborne particles or aerosols have long been recognised for their major contribution to uncertainty in climate change. In addition, aerosol amounts must be known for accurate atmospheric correction of remotely sensed images, and are required to accurately gauge the available solar resource. However, despite great advances in surface networks and satellite retrievals over recent years, long-term continental-scale aerosol data sets are lacking. Here we present an aerosol assessment over Australia based on combined sun photometer measurements from the Bureau of Meteorology Radiation Network and CSIRO/AeroSpan. The measurements are continental in coverage, comprising 22 stations, and generally decadal in timescale, totalling 207 station-years. Monthly climatologies are given at all stations. Spectral decomposition shows that the time series can be represented as a weighted sum of sinusoids with periods of 12, 6 and 4 months, corresponding to the annual cycle and its second and third harmonics. Their relative amplitudes and phase relationships lead to sawtooth-like waveforms sharply rising to an austral spring peak, with a slower decline often including a secondary peak during the summer. The amplitude and phase of these periodic components show significant regional change across the continent. Fits based on this harmonic analysis are used to separate the periodic and episodic components of the aerosol time series. An exploratory classification of the aerosol types is undertaken based on (a) the relative periodic amplitudes of the Ångström exponent and aerosol optical depth, (b) the relative amplitudes of the 6- and 4-month harmonic components of the aerosol optical depth, and (c) the ratio of episodic to periodic variation in aerosol optical depth. It is shown that Australian aerosol can be broadly grouped into three classes: tropical, arid and temperate. Statistically significant decadal trends are found at 4 of the 22 stations. Despite the apparently small associated declining trends in mid-visible aerosol optical depth of between 0.001 and 0.002 per year, these trends are much larger than those projected to occur due to declining emissions of anthropogenic aerosols from the Northern Hemisphere. There is remarkable long-range coherence in the aerosol cycle across the continent, suggesting broadly similar source characteristics, including a possible role for intercontinental transport of biomass burning aerosol.

Effect of gas properties on the dynamics of the electrical slope asymmetry effect in capacitive plasmas: comparison of Ar, H2 and CF4

Tailored voltage excitation waveforms provide an efficient control of the ion energy (through the electrical asymmetry effect) in capacitive plasmas by varying the ‘amplitude’ asymmetry of the waveform. In this work, the effect of a ‘slope’ asymmetry of the waveform is investigated by using sawtooth-like waveforms, through which the sheath dynamic can be manipulated. A remarkably different discharge dynamic is found for Ar, H2, and CF4 gases, which is explained by the different dominant electron heating mechanisms and plasma chemistries. In comparison to Argon we find that the electrical asymmetry can even be reversed by using an electronegative gas such as CF4. Phase resolved optical emission spectroscopy measurements, probing the spatiotemporal distribution of the excitation rate show excellent agreement with the results of particle-in-cell simulations, confirming the high degree of correlation between the excitation rates with the dominant heating mechanisms in the various gases. It is shown that, depending on the gas used, sawtooth-like voltage waveforms may cause a strong asymmetry.

Ion flux asymmetry in radiofrequency capacitively-coupled plasmas excited by sawtooth-like waveforms

Using particle-in-cell simulations, we predict that it is possible to obtain a significant difference between the ion flux to the powered electrode and that to the grounded electrode—with about 50% higher ion flux on one electrode—in a geometrically symmetric, radiofrequency capacitively-coupled plasma reactor by applying a non-sinusoidal, ‘Tailored’ voltage waveform. This sawtooth-like waveform presents different rising and falling slopes over one cycle. We show that this effect is due to differing plasma sheath motion in front of each electrode, which induces a higher ionization rate in front of the electrode which has the fastest positive rising voltage. Together with the higher ion flux comes a lower voltage drop across the sheath, and therefore a reduced maximum ion bombardment energy; a result in contrast to typical process control mechanisms.

Adjusting gap plasmon transmission and intensity in metal-insulator-metal waveguide

A device capable of adjusting gap plasmon (GP) transmission and intensity is proposed. The structure consists of two metallic films: one is etched with a nanoslit, and the other below is movable. Between them is a horizontal air channel. Numerical simulations show that the GP sources can produce alternatively in ports A and B when the film below is moved together with a groove in the center; thus, a sawtooth-like waveform is observed, which is different from the sine-like case without a groove and can be explained well by Fourier series. In addition, with the optimized length of film below, the source intensity can be further enhanced for Fabry–Perot resonance producing in both channels A and B.

Enhancement of temporal periodicity cues in cochlear implants: Effects on prosodic perception and vowel identification

Standard continuous interleaved sampling processing, and a modified processing strategy designed to enhance temporal cues to voice pitch, were compared on tests of intonation perception, and vowel perception, both in implant users and in acoustic simulations. In standard processing, 400 Hz low-pass envelopes modulated either pulse trains (implant users) or noise carriers (simulations). In the modified strategy, slow-rate envelope modulations, which convey dynamic spectral variation crucial for speech understanding, were extracted by low-pass filtering (32 Hz). In addition, during voiced speech, higher-rate temporal modulation in each channel was provided by 100% amplitude-modulation by a sawtooth-like wave form whose periodicity followed the fundamental frequency (F0) of the input. Channel levels were determined by the product of the lower- and higher-rate modulation components. Both in acoustic simulations and in implant users, the ability to use intonation information to identify sentences as question or statement was significantly better with modified processing. However, while there was no difference in vowel recognition in the acoustic simulation, implant users performed worse with modified processing both in vowel recognition and in formant frequency discrimination. It appears that, while enhancing pitch perception, modified processing harmed the transmission of spectral information.

Bispectra of internal waves in shallow seas

Densely sampled thermistor chain data have been obtained from several shallow-water acoustics experiments in the Yellow Sea, East China Sea and South China Sea. The data are analyzed to study bispectra of the internal waves observed in this paper. The magnitudes, real and imaginary parts of the bispectra are presented. It is found that strong quadratic interactions occur within the power spectral peak, and also between the peak and its first three harmonics. The real and imaginary parts of the bispectra represent the contributions to the vertical and horizontal asymmetry (skewness and asymmetry) of the internal wave elevations from each frequency pair, respectively. The nonzero asymmetry values indicate the sawtoothlike waveforms. Bispectral analysis is thus a useful means for investigating nonlinear properties of shallow-water internal waves. [Work supported by NSFC.]

Effect of Linewidth Enhancement Factor on Doppler Beat Waveform Obtained from a Self-Mixing Laser Diode

The asymmetry and fringe inclination of the sawtooth-like waveform observed in the self-mixing signal obtained from a semiconductor laser with optical feedback enable the direction discrimination of line-of-sight motion of external target surfaces. We investigated the effects of linewidth enhancement factor and feedback strength on the asymmetry and the direction of fringe inclination of the signal by numerical simulations. For the first time, we show that direction of the fringe inclination is determined not only by the direction of the target motion but also by the value of the linewidth enhancement factor.

Kinematic analysis of cat hindlimb stepping.

1. The purpose of this study is to analyze the kinematics of stepping from the point of view of limb control by attempting to dissociate the various neuronal and mechanical factors that shape actual movements observed experimentally. The cat hindlimb, like the primate arm, is a multijointed mechanical system with redundant degrees of freedom. We contend that a number of issues studied in the context of arm movement control, such as end point control and trajectory planning, may also be applicable to limb movement in locomotion. 2. We recorded and analyzed the kinematics of cat hindlimb movement in unrestrained over-ground locomotion at various speeds and with a variety of surface conditions. We found we could represent limb movement in the step cycle simply and concisely by the trajectories of the limb segment orientation angles. Each trajectory conformed to a monophasic sawtoothlike waveform, and the relative timing between segments was largely invariant in the range of movements studied. This contrasts with the representation using relative joint angles, as in Philippson's scheme, which exhibits a monophasic waveform at the hip but biphasic waveforms at the knee and ankle. 3. To investigate how whole limb kinematics, i.e., changes in the length and orientation of the whole limb, relates to that of the limb segments, we reconstructed limb movement from segment trajectories, assuming as a first approximation that they were indeed sawtooth wave forms. The result strongly suggested that the relative timing of segment movements played an important role in regulating limb length during the swing phase of the step cycle. A strong correlation between segment relative timing and changes in limb length was also observed experimentally. 4. A comparison between reconstructed and actual limb movement revealed two major differences. In contrast with the actual movement, which exhibited at least two extension phases and limb shortening during the stance phase, the reconstructed movement had only a single extension phase and no limb shortening. The discrepancies were fully accountable, however, by the limb-ground interaction in stance, indicating that the features present in the actual movement resulted from the limb-ground interaction rather than from any elaborated control by the nervous system. 5. A second difference between reconstructed and actual movements was evident in an apparent jerkiness of the former and a difference in the hindpaw paths during the swing phase. These differences could be accounted for by including the consequences of limb inertia and finite muscle power, namely a gradual rather than instant change in velocity. Using a bell-shaped velocity profile for the segment movements, we were able to accurately reconstruct limb kinematics during the swing phase. 6. We conclude from this analysis that the overall features of limb kinematics in stepping may be controlled by regulating a small set of parameters related to the orientation angles of the limb segments. Specifically, the position of the endpoint, the hindpaw in this case, may be determined by the relative timing and amplitudes of segment trajectories. The point-by-point details of the observed limb kinematics may be largely attributed to limb mechanics and the interaction of the limb with its environment. Thus the neural control may be simpler than the kinematics suggests.