Uncorrelated Pulses Research Articles

Simplifying tailored generation of complex structured femtosecond pulses with easily fabricated phase plates

This article presents a novel approach to targeted 4f pulse shaping using phase plates fabricated by single-point diamond turning (SPDT) machining. The manufacturing of the phase plates using SPDT is versatile, cost-effective, fast, robust, and applicable across a wide range of optical materials, spanning from visible to far-infrared spectra (e.g., PMMA, ZnSe). Manufactured profiles can be used for phase manipulation and pulse structuring, analogously to programable spatial light modulators (SLM). We demonstrate that the pulse waveforms can be reproduced with high fidelity by simple simulations based on calculating optical path differences induced by the phase plate for each wavelength and taking into account the finite focal spot. The simulated and reconstructed frequency-resolved optical gating spectrograms featured G errors between 1–2% and intensity errors between 0.02–0.06. Even for complex structured pulses with the rms value of the time-bandwidth product reaching 12, our method maintains high precision, in some cases even reaching lower G error compared to simpler waveforms. Finally, we also show that the phase plate can be used to attain a set of uncorrelated pulse waveforms by moving the plate relatively to the dispersed laser spectrum. Overall, this approach bypasses common limitations associated with pulse shaping using SLMs, such as pixelation, pixel cross-talk, and spectral or laser fluences constraints.

Strongly intermittent far scrape-off layer fluctuations in Alcator C-Mod plasmas close to the empirical discharge density limit

Intermittent plasma fluctuations in the boundary region of the Alcator C-Mod device were comprehensively investigated using data time-series from gas puff imaging and mirror Langmuir probe diagnostics. Fluctuations were sampled during stationary plasma conditions in ohmically heated, lower single null diverted configurations with scans in both line-averaged density and plasma current, with Greenwald density fractions up to 0.85. Utilizing a stochastic model, we describe the plasma fluctuations as a super-position of uncorrelated pulses, with large-amplitude events corresponding to blob-like filaments moving through the scrape-off layer (SOL). A deconvolution method is used to estimate the pulse arrival times and amplitudes. The analysis reveals a significant increase of pulse amplitudes and waiting times as the line-averaged density approaches the empirical discharge density limit. Broadened and flattened average radial profiles are thus accompanied by strongly intermittent and large-amplitude fluctuations. Although these filaments are arriving less frequently at high line-averaged densities, we show that there are significant increases in radial far-SOL particle and heat fluxes which will further enhance plasma–wall interactions. The stochastic model has been used as a framework for study of the scalings in the intermittency parameter, flux and mean amplitude and waiting times, and is being used to inform predictive capability for the effects of filamentary transport as a function of Greenwald fraction.

Reconstruction of intermittent time series as a superposition of pulses.

Fluctuations in a vast range of physical systems can be described as a superposition of uncorrelated pulses with a fixed shape, a process commonly referred to as a (generalized) shot noise or a filtered Poisson process. In this paper, we present a systematic study of a deconvolution method to estimate the arrival times and amplitudes of the pulses from realizations of such processes. The method shows that a time series can be reconstructed for various pulse amplitude and waiting time distributions. Despite a constraint on positive-definite amplitudes, it is shown that negative amplitudes may also be reconstructed by flipping the sign of the time series. The method performs well under moderate amounts of additive noise, both white noise and colored noise having the same correlation function as the process itself. The estimation of pulse shapes from the power spectrum is accurate except for excessively broad waiting time distributions. Although the method assumes constant pulse durations, it performs well under narrowly distributed pulse durations. The most important constraint on the reconstruction is information loss, which limits the method to intermittent processes. The ratio between the sampling time and the average waiting time between pulses must be about 1/20 or smaller for a well-sampled signal. Finally, given the system forcing, the average pulse function may be recovered. This recovery is only weakly constrained by the intermittency of the process.

Stochastic modeling of blob-like plasma filaments in the scrape-off layer: Theoretical foundation

A stochastic model for a superposition of uncorrelated pulses with a random distribution of amplitudes, sizes, and velocities is presented. The pulses are assumed to move radially with fixed shape and amplitudes decaying exponentially in time due to linear damping. The pulse velocities are taken to be time-independent but randomly distributed. The implications of a distribution of pulse amplitudes, sizes, and velocities are investigated. Closed-form expressions for the cumulants and probability density functions for the process are derived in the case of exponential pulses and a discrete uniform distribution of pulse velocities. The results describe many features of the boundary region of magnetically confined plasmas, such as high average particle densities, broad and flat radial profiles, and intermittent large-amplitude fluctuations. The stochastic model elucidates how these phenomena are related to the statistical properties of blob-like structures. In particular, the presence of fast pulses generally leads to flattened far scrape-off layer profiles and enhanced intermittency, which amplifies plasma–wall interactions.

Magnetized plasma pressure filaments: Analysis of chaotic and intermittent transport events driven by drift-Alfvén modes

The origin of intermittent fluctuations in an experiment involving several interacting electron plasma pressure filaments in close proximity, embedded in a large linear magnetized plasma device, is investigated. The probability density functions of the fluctuations on the inner and outer gradient of the filament bundle are non-Gaussian and the time series contain uncorrelated Lorentzian pulses that give the frequency power spectral densities an exponential shape. A cross-conditionally averaged spatial reconstruction of a temporal event reveals that the intermittent character is caused by radially and azimuthally propagating turbulent structures with transverse spatial scales on the order of the electron skin depth. These eruption events originate from interacting pressure gradient-driven drift-Alfvén instabilities on the outer gradient and edge of the filament bundle. The temporal Lorentzian shape of the intermittent structures and exponential spectra are suggestive of deterministic chaos in the underlying dynamics; this conclusion is supported by the complexity–entropy analysis (CH-plane) that shows the experimental time series are located in the chaotic regime.

Numerical turbulence simulations of intermittent fluctuations in the scrape-off layer of magnetized plasmas

Intermittent fluctuations in the boundary of magnetically confined plasmas are investigated by numerical turbulence simulations of a reduced fluid model describing the evolution of the plasma density and electric drift vorticity in the two-dimensional plane perpendicular to the magnetic field. Two different cases are considered: one describing resistive drift waves in the edge region and another including only the interchange instability due to unfavorable magnetic field curvature in the scrape-off layer. Analysis of long data time series obtained by single-point recordings is compared to predictions of a stochastic model describing the plasma fluctuations as a superposition of uncorrelated pulses. For both cases investigated, the radial particle density profile in the scrape-off layer is exponential with a radially constant scale length. The probability density function for the particle density fluctuations in the far scrape-off layer has an exponential tail. Radial motion of blob-like structures leads to large-amplitude bursts with an exponential distribution of peak amplitudes and the waiting times between them. The average burst shape is well described by a two-sided exponential function. The frequency power spectral density of the particle density is simply that of the average burst shape and is the same for all radial positions in the scrape-off layer. The fluctuation statistics obtained from the numerical simulations are in excellent agreement with recent experimental measurements on magnetically confined plasmas. The statistical framework defines a new validation metric for boundary turbulence simulations.

Intensity Estimation of Noise-Like Signal in Presence of Uncorrelated Pulse Interferences

The effective filtering of noisy signals is one of the topical and open problems of the processing of noisy signals characterized by the presence of pulse interferences. A robust approach to intensity estimation of noise-like signal in the presence of additive uncorrelated pulse interferences has been proposed. The presence of additive uncorrelated pulse interferences leads to an increase of dispersion of registered signal at separate sections with pulse interferences. The robustness of intensity estimation is achieved by reducing the influence of sections with pulse interferences. A variety of nonlinear filtering methods has been developed that are based on detecting the intensity using lower envelope: two-parameter recursive filter, dilation, limiting the derivative and order statistics. The numerical simulation was used to perform their comparison with the known most common methods. The numerical simulation confirmed the efficiency of the approach proposed for estimating the intensity of noise-like signal in the presence of additive uncorrelated pulse interferences. The developed techniques can be applied for signal processing in means of communications, measurement instrumentation, radio astronomy, and also for image processing.

An Enhanced Iterative Clipping and Filtering Method Using Time-Domain Kernel Matrix for PAPR Reduction in OFDM Systems

Iterative clipping and filtering (ICF) is a straight-forward method for reducing the peak-to-average power ratio (PAPR) of signals in orthogonal frequency-division multiplexing (OFDM) system. Recently, convex optimization has been used to find the optimal filter coefficients that minimize the error vector magnitude (EVM) and meet the PAPR constraint. However, high-computation complexity may be incurred when solving the convex optimization problem. Therefore, we develop an efficient PAPR reduction method that uses the time-domain kernel matrix to generate the PAPR-reduction signal. Besides, we relax the assumption that the clipping noise is a series of uncorrelated parabolic pulses and apply the proposed method to more general cases. Based on the instantaneous observation of clipping noise, the proposed method constructs a simple time-domain kernel matrix and employs the curve fitting approach to optimize the corresponding scaling factors. The simulation results show that the proposed method can achieve very close performance to that using convex optimization in terms of both the PAPR reduction and EVM while the computational cost is reduced greatly. In addition, due to the decrease of iteration numbers and computational complexity, the proposed method is more efficient than some existing clipping and filtering methods.

Experimental generation and analysis of chaos-modulated pulses for pulsed chaos lidar applications based on gain-switched semiconductor lasers subject to optical feedback.

We experimentally generate and analyze chaos-modulated pulses for pulsed chaos lidar applications based on gain-switched semiconductor lasers subject to optical feedback. While conventional pulsed lidars emit repetitive short pulses without specificity making them vulnerable to interference and range ambiguity, chaos lidars possess the advantages of having no range ambiguity and being immune to interference and jamming, which are benefits of the aperiodic and uncorrelated waveforms we use. Compared to the cw chaos lidars originally proposed, the pulsed chaos lidars can have significantly higher peak power under the class-1 eye-safe regulation that is essential for long-range low-reflectivity target detection. We investigate the temporal, spectral, and cross-correlation characteristics of the modulated pulses obtained with different feedback strengths and modulation currents. Induced by the transient response and evolving with the delayed feedback, modulated pulses exhibiting periodic oscillations and complex dynamics such as chaos are observed. Under a weakly damped condition with large modulation current and moderate feedback strength, we successfully generate uncorrelated chaos-modulated pulses suitable for the pulsed chaos lidar applications. With the current configuration, for cross-correlations comparable to the benchmark of 0.19 set by the cross-correlation of the intensity fluctuation on the sole gain-switched pulses without feedback, uncorrelated waveforms with durations up to 218 ns in a 500 ns modulated pulse can be effectively utilized.

Intermittent electron density and temperature fluctuations and associated fluxes in the Alcator C-Mod scrape-off layer

The Alcator C-Mod mirror Langmuir probe system has been used to sample data time series of fluctuating plasma parameters in the outboard mid-plane far scrape-off layer. We present a statistical analysis of one second long time series of electron density, temperature, radial electric drift velocity and the corresponding particle and electron heat fluxes. These are sampled during stationary plasma conditions in an ohmically heated, lower single null diverted discharge. The electron density and temperature are strongly correlated and feature fluctuation statistics similar to the ion saturation current. Both electron density and temperature time series are dominated by intermittent, large-amplitude burst with an exponential distribution of both burst amplitudes and waiting times between them. The characteristic time scale of the large-amplitude bursts is approximately 15 . Large-amplitude velocity fluctuations feature a slightly faster characteristic time scale and appear at a faster rate than electron density and temperature fluctuations. Describing these time series as a superposition of uncorrelated exponential pulses, we find that probability distribution functions, power spectral densities as well as auto-correlation functions of the data time series agree well with predictions from the stochastic model. The electron particle and heat fluxes present large-amplitude fluctuations. For this low-density plasma, the radial electron heat flux is dominated by convection, that is, correlations of fluctuations in the electron density and radial velocity. Hot and dense blobs contribute only a minute fraction of the total fluctuation driven heat flux.

Intermittent fluctuations in the Alcator C-Mod scrape-off layer for ohmic and high confinement mode plasmas

Plasma fluctuations in the scrape-off layer of the Alcator C-Mod tokamak in ohmic and high confinement modes have been analyzed using gas puff imaging data. In all cases investigated, the time series of emission from a single spatially resolved view into the gas puff are dominated by large-amplitude bursts, attributed to blob-like filament structures moving radially outwards and poloidally. There is a remarkable similarity of the fluctuation statistics in ohmic plasmas and in edge localized mode-free and enhanced D-alpha high confinement mode plasmas. Conditionally averaged waveforms have a two-sided exponential shape with comparable temporal scales and asymmetry, while the burst amplitudes and the waiting times between them are exponentially distributed. The probability density functions and the frequency power spectral densities are similar for all these confinement modes. These results provide strong evidence in support of a stochastic model describing the plasma fluctuations in the scrape-off layer as a super-position of uncorrelated exponential pulses. Predictions of this model are in excellent agreement with experimental measurements in both ohmic and high confinement mode plasmas. The stochastic model thus provides a valuable tool for predicting fluctuation-induced plasma–wall interactions in magnetically confined fusion plasmas.

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.

Level crossings and excess times due to a superposition of uncorrelated exponential pulses.

A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a superposition of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency parameter. Expressions for excess time statistics, that is, the rate of level crossings above a given threshold and the average time spent above the threshold, are derived from the joint distribution of the process and its derivative. Limits of both high and low intermittency are investigated and compared to previously known results. In the case of a strongly intermittent process, the distribution of times spent above threshold is obtained analytically. This expression is verified numerically, and the distribution of times above threshold is explored for other intermittency regimes. The numerical simulations compare favorably to known results for the distribution of times above the mean threshold for an Ornstein-Uhlenbeck process. This contribution generalizes the excess time statistics for the stochastic model, which find applications in a wide diversity of natural and technological systems.

Intermittent fluctuations due to uncorrelated Lorentzian pulses

Fluctuations due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes and duration times are considered. These are demonstrated to be strongly intermittent in the limit of weak pulse overlap, resulting in large skewness and flatness moments. The characteristic function and the lowest order moments are derived, revealing a parabolic relationship between the skewness and flatness moments. Numerical integration reveals the probability density functions in the case of exponential and Laplace distributed pulse amplitudes. This stochastic model describes the intermittent fluctuations and probability densities with exponential tails commonly observed in turbulent fluids and magnetized plasmas.

Skewed Lorentzian pulses and exponential frequency power spectra

Frequency power spectra due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes are considered. For pulses with a constant duration, there is an exponential frequency spectrum which is independent of the degree of pulse overlap and the pulse amplitude distribution. The spectrum is furthermore shown to be unaffected by skewness of the Lorentzian pulses and even a random distribution of the pulse asymmetry parameter and its correlation with the pulse amplitude. This stochastic model provides new insight into the ubiquitous exponential spectra in fluids and magnetized plasmas exhibiting deterministic chaos, where non-linear advection processes lead to amplitude dependent steepening of smooth pulses.

Relationship between frequency power spectra and intermittent, large-amplitude bursts in the Alcator C-Mod scrape-off layer

Fluctuations in the boundary region of the Alcator C-Mod tokamak have been analyzed using gas puff imaging data from a set of Ohmically heated plasma density scan experiments. It is found that the relative fluctuation amplitudes are modest and close to normally distributed at the separatrix but become increasingly larger and skewed towards the main chamber wall. The frequency power spectra are nevertheless similar for all radial positions and line-averaged densities. Predictions of a stochastic model, describing the plasma fluctuations as a super-position of uncorrelated pulses, are shown to be in excellent agreement with the measurements. This implies that the pulse duration is the same, while the degree of pulse overlap decreases radially outwards in the scrape-off layer. The universal frequency power spectral density is thus determined by the shape and duration of the large-amplitude bursts associated with blob-like structures. The model also describes the rate of threshold level crossings, for which the exponential tails underline the intermittency of the fluctuations in the far scarpe-off layer.

Auto-correlation function and frequency spectrum due to a super-position of uncorrelated exponential pulses

The auto-correlation function and the frequency power spectral density due to a super-position of uncorrelated exponential pulses are considered. These are shown to be independent of the degree of pulse overlap and thereby the intermittency of the stochastic process. For constant pulse duration and a one-sided exponential pulse shape, the power spectral density has a Lorentzian shape which is flat for low frequencies and a power law at high frequencies. The algebraic tail is demonstrated to result from the discontinuity in the pulse function. For a strongly asymmetric two-sided exponential pulse shape, the frequency spectrum is a broken power law with two scaling regions. In the case of a symmetric pulse shape, the power spectral density is the square of a Lorentzian function. The steep algebraic tail at high frequencies in these cases is demonstrated to follow from the discontinuity in the derivative of the pulse function. A random distribution of pulse durations is shown to result in apparently longer correlation times but has no influence on the asymptotic power law tail of the frequency spectrum. The effect of additional random noise is also discussed, leading to a flat spectrum for high frequencies. The probability density function for the fluctuations is shown to be independent of the distribution of pulse durations. The predictions of this model describe the variety of auto-correlation functions and power spectral densities reported from experimental measurements in the scrape-off layer of magnetically confined plasmas.

Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses

A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For a constant pulse duration, this is shown to result in an exponential power spectral density for the stationary process. A random distribution of pulse durations modifies the frequency spectrum, and several examples are shown to result in power law spectra. The distribution of pulse durations does not influence the characteristic function and thus neither the moments nor the probability density function of the random variable. It is demonstrated that the fluctuations are intrinsically intermittent through a large excess kurtosis moment in the limit of weak pulse overlap. These results allow for estimation of the basic properties of fluctuations from measurement data and describe the diversity of frequency spectra reported from measurements in magnetized plasmas.

Stochastic modelling of intermittent fluctuations in the scrape-off layer: Correlations, distributions, level crossings, and moment estimation

A stochastic model is presented for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas. The fluctuations in the plasma density are modeled by a super-position of uncorrelated pulses with fixed shape and duration, describing radial motion of blob-like structures. In the case of an exponential pulse shape and exponentially distributed pulse amplitudes, predictions are given for the lowest order moments, probability density function, auto-correlation function, level crossings, and average times for periods spent above and below a given threshold level. Also, the mean squared errors on estimators of sample mean and variance for realizations of the process by finite time series are obtained. These results are discussed in the context of single-point measurements of fluctuations in the scrape-off layer, broad density profiles, and implications for plasma–wall interactions due to the transient transport events in fusion grade plasmas. The results may also have wide applications for modelling fluctuations in other magnetized plasmas such as basic laboratory experiments and ionospheric irregularities.

Associative Enhancement of Time Correlated Response to Heterogeneous Stimuli in a Neuromorphic Nanowire Device

In spite of the strong interest in brain‐like or neuromorphic computation, relatively few devices have emerged whose neuromorphic behavior is embedded in the hardware itself and not reliant on external programming of synaptic weights. Here, a neuromorphic device is described based on a TiO2 nanowire that exhibits an associative memory response to the time correlation between voltage and optical stimuli. Memristive characteristics are also observed with current–voltage sweeps showing hysteresis loops and continuum resistance levels. The nanowire device responds to heterogeneous voltage and optical pulse stimuli with spike‐like neuromorphic outputs. Moreover, uncorrelated pulses produce a weak response, consistent with the interaction of coincident pulses with adsorbed and bulk oxygen in the surface depletion region, leading to a nonlinear enhancement in conductance. The strength of this learned enhancement depends on both the time correlation and the number of pulse stimuli, consistent with spike timing dependent plasticity. The nanowire devices presented have neural synapse‐like properties that could serve as a building block for neuromorphic computation.