arXiv subjects

O. E. Garcia

Publications and source records attributed to O. E. Garcia.

At least 19 recordsLinked to original sources

arXiv2025

Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations

Long-range correlations manifested as power spectral density scaling $1/f^β$ for frequency $f$ and a range of exponents $β$ are investigated for a superposition of uncorrelated pulses with distributed durations $τ$. Closed-form expressions for the frequency power spectral density are derived for a one-sided exponential pulse function and several variants of bounded and unbounded power-law distributions of pulse durations ${P_τ(τ)\sim1/τ^α}$ with abrupt and smooth cutoffs. The asymptotic scaling relation $β=3-α$ is demonstrated for $1<α<3$ in the limit of an infinitely broad distribution $P_τ(τ)$. Logarithmic corrections to the frequency scaling are exposed at the boundaries of the long-range dependence regime, $β=0$ and $β=2$. Analytically demonstrated finite-size effects associated with distribution truncations are shown to reduce the frequency ranges of scale invariance by several decades. The regimes of validity of the $β=3-α$ relation are clarified.

cond-mat.stat-mech↗

arXiv2025

Time delay velocity estimation from a superposition of localized and uncorrelated pulses

This study investigates a novel method for estimating two-dimensional velocities using coarse-grained imaging data, which is particularly relevant for applications in plasma diagnostics. The method utilizes measurements from three non-collinear points and is derived from a stochastic model that describes the propagation of uncorrelated pulses through two-dimensional space. We demonstrate that the method provides exact time delay estimates when applied to a superposition of Gaussian structures and remains accurate for various other pulse functions. Through extensive numerical simulations, we evaluate the method's performance under variations in signal duration, pulse overlap, spatial and temporal resolution, and the presence of additive noise. Additionally, we investigate the impact of temporal pulse evolution due to linear damping and explore the so-called barberpole effect, which occurs with elongated and tilted structures. Although the method is susceptible to the barberpole effect, we analytically demonstrate that this effect does not occur when the elongated structures propagate parallel to one of their axes, and we establish bounds for the associated errors. We propose a series of safeguards to anticipate the applicability of the velocity estimation method, considering factors such as signal length, number of pulses, temporal and spatial resolution, signal-to-noise ratio, and pulse size. However, these safeguards do not ensure applicability in cases involving the barberpole effect or correlations between amplitudes and velocities. Overall, our findings provide a comprehensive and robust framework for accurate two-dimensional velocity estimation, enhancing the capabilities of fusion plasma diagnostics and potentially benefiting other fields requiring precise motion analysis.

physics.plasm-ph↗

arXiv2025

Blob velocities and sizes in the Alcator C-Mod scrape-off layer for ohmic and high confinement mode plasmas

An improved time delay estimation method is used to calculate the velocity of cross-field blob motion in the scrape-off layer of Alcator C-Mod for an ohmic and two high confinement (H-mode) plasmas; an edge localized mode free and an enhanced D-alpha H-mode. The gas puff imaging data analysis results are interpreted in the framework of a stochastic model that describes the fluctuations as a super-position of uncorrelated blob-like structures. In all confinement modes investigated, the scrape-off layer is dominated by large amplitude, blob-like filaments moving radially outwards with velocities in the range from 400 to 1000 m/s. Blobs in high confinement mode plasmas have similar velocities and sizes as in ohmic plasma, which is consistent with the close similarity of conditionally averaged burst shapes and frequency spectra for the confinement modes investigated.

physics.plasm-ph↗

arXiv2024

Stochastic modeling of blob-like plasma filaments in the scrape-off layer: Time-dependent velocities and pulse stagnation

A stochastic model for a super-position of uncorrelated pulses with a random distribution of and correlations between amplitudes and velocities is analyzed. The pulses are assumed to move radially with fixed shape and amplitudes decreasing exponentially in time due to linear damping. The pulse velocities are taken to be time-dependent with a power law dependence on the instantaneous amplitudes, as suggested by blob velocity scaling theories. In accordance with experimental measurements, the pulse function is assumed to be exponential and the amplitudes are taken to be exponentially distributed. As a consequence of linear damping and time-dependent velocities, it is demonstrated that the pulses stagnate during their radial motion. This makes the average pulse waiting time increase radially outwards in the scrape-off layer of magnetically confined plasmas. In the case that pulse velocities are proportional to their amplitudes, the mean value of the process decreases exponentially with radial coordinate, similar to the case when all pulses have the same, time-independent velocity. The profile e-folding length is then given by the product of the average pulse velocity and the parallel transit time. Moreover, both the average pulse amplitude and the average velocity are the same at all radial positions due to stagnation of slow and small-amplitude pulses. In general, an increasing average pulse velocity results in a flattened radial profile of the mean value of the process as well as a higher relative fluctuation level, strongly enhancing plasma-surface interactions.

physics.plasm-ph↗

arXiv2024

A three-point velocity estimation method for turbulent flows in two spatial dimensions

Time delay and velocity estimation has been a widely studied subject in the context of signal processing, with applications in many different fields of physics. The velocity of fluctuation structures is typically estimated as the distance between two measurement points divided by the time lag that maximizes the cross-correlation function between the measured signals. In this contribution, we demonstrate that this technique is not suitable in two spatial dimensions unless the velocity is aligned with the separation between the measurement points. We present an improved method to accurately estimate both components of the velocity vector relying on three non-aligned measurement points. The cross-correlation based three-point time delay method is shown to give exact results for the velocity components in the case of a super-position of uncorrelated Gaussian pulses. The new technique is tested on synthetic data generated from realizations of such processes for which the underlying velocity components are known. The results are compared with and found vastly superior to those obtained using the standard two-point technique. Finally, we demonstrate the applicability of the three-point method on gas puff imaging data of strongly intermittent plasma fluctuations at the boundary of the Alcator C-Mod tokamak.

physics.plasm-ph↗

arXiv2024

Stochastic modelling of blob-like plasma filaments in the scrape-off layer: Continuous velocity distributions

A stochastic model for a superposition of uncorrelated pulses with a random distribution of amplitudes, sizes, and velocities is analyzed. The pulses are assumed to move radially with fixed shape and amplitudes decreasing exponentially in time due to linear damping. The pulse velocities are taken to be time-independent but randomly distributed. The implications of a broad distribution of pulse amplitudes and velocities, as well as correlations between these, are investigated. Fast and large-amplitude pulses lead to broad and flat average radial profiles with order unity relative fluctuations in the scrape-off layer. For theoretically predicted blob velocity scaling relations, the stochastic model reveals average radial profiles similar to the case of a degenerate distribution of pulse velocities but with more intermittent fluctuations. The average profile e-folding length is given by the product of the average pulse velocity and the linear damping time due to losses along magnetic field lines. The model describes numerous common features from experimental measurements and underlines the role of large-amplitude fluctuations for plasma-wall interactions in magnetically confined fusion plasmas.

physics.plasm-ph↗

arXiv2023

Apparent universality of $1/f$ spectra as an artifact of finite-size effects

Power spectral density scaling with frequency $f$ as $1/f^β$ and $β\approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics of complex phenomena. Here, we show that for a superposition of uncorrelated pulses with a power-law distribution of duration times the estimated scaling exponents $\barβ$ depend on the system size. We derive a parametrized, closed-form expression for the power spectral density, and demonstrate that for $β\in [0,2]$ the estimated scaling exponents have a bias towards $\barβ=1$. For $β=0$ and $β=2$ the explicit logarithmic corrections to frequency scaling are derived. The bias is particularly strong when the scale invariance spans less than four decades in frequency. Since this is the case for the majority of empirical data, the boundedness of systems well described by the superposition of uncorrelated pulses may contribute to overemphasizing the universality of $1/f$.

physics.data-an↗

arXiv2023

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

A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. 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 and correlations between pulse sizes, velocities and amplitudes are investigated. Expressions for the lowest order statistical moments, probability density functions and correlation functions for the process are derived for the case of exponential pulses and a discrete uniform distribution of pulse velocities. The results describe many features of high average particle densities, broad and flat average radial profiles, and large-amplitude, intermittent fluctuations at the boundary region of magnetically confined plasmas. The stochastic model elucidates how these phenomena are related to the statistics of blob-like structures.

physics.plasm-ph↗

arXiv2020

Comparison between mirror Langmuir probe and gas puff imaging measurements of intermittent fluctuations in the Alcator C-Mod scrape-off layer

Statistical properties of the scrape-off layer (SOL) plasma fluctuations are studied in ohmically heated plasmas in the Alcator C-Mod tokamak. For the first time, plasma fluctuations as well as parameters that describe the fluctuations are compared across measurements from a mirror Langmuir probe (MLP) and from gas-puff imaging (GPI) that sample the same plasma discharge. This comparison is complemented by an analysis of line emission time-series data, synthesized from the MLP electron density and temperature measurements. The fluctuations observed by the MLP and GPI typically display relative fluctuation amplitudes of order unity together with positively skewed and flattened probability density functions. Such data time series are well described by an established stochastic framework which model the data as a superposition of uncorrelated, two-sided exponential pulses. The most important parameter of the process is the intermittency parameter, γ = τd / τw where τd denotes the duration time of a single pulse and τw gives the average waiting time between consecutive pulses. Here we show, using a new deconvolution method, that these parameters can be consistently estimated from different statistics of the data. We also show that the statistical properties of the data sampled by the MLP and GPI diagnostic are very similar. Finally, a comparison of the GPI signal to the synthetic line-emission time series suggests that the measured emission intensity can not be explained solely by a simplified model which neglects neutral particle dynamics.

physics.plasm-ph↗

arXiv2020

Intermittent fluctuations due to Lorentzian pulses in turbulent thermal convection

Turbulent motions due to flux-driven thermal convection is investigated by numerical simulations and stochastic modelling. Tilting of convection cells leads to the formation of sheared flows and quasi-periodic relaxation oscillations for the energy integrals far from the threshold for linear instability. The probability density function for the temperature and radial velocity fluctuations in the fluid layer changes from a normal distribution at the onset of turbulence to a distribution with an exponential tail for large fluctuation amplitudes for strongly driven systems. The frequency power spectral density has an exponential shape, which is a signature of deterministic chaos. By use of a novel deconvolution method, this is shown to result from the presence of Lorentzian pulses in the underlying time series, demonstrating that exponential frequency spectra can persist in also in turbulent flow regimes.

physics.flu-dyn↗

arXiv2018

Universality of Poisson-driven plasma fluctuations in the Alcator C-Mod scrape-off layer

Large-amplitude, intermittent fluctuations are ubiquitous in the boundary region of magnetically confined plasmas and lead to detrimental plasma-wall interactions in the next-generation, high duty cycle fusion power experiments. Using gas puff imaging data time series from the scrape-off layer in the Alcator C-Mod device, it is here demonstrated that the large-amplitude fluctuations can be described as a super-position of pulses with fixed shape and constant duration. By applying a new deconvolution algorithm on the data time series with a two-sided exponential pulse function, the arrival times and amplitudes of the pulses can be estimated and the measurement time series can be reconstructed with high accuracy. The pulse amplitudes are shown to follow an exponential distribution. The waiting times between pulses are uncorrelated, their distribution has an exponential tail, and the number of arrivals is a linear function of time. This demonstrates that pulse arrivals follow a homogeneous Poisson process. Identical statistical properties apply to both ohmic and high confinement mode plasmas, clearly demonstrating universality of the fluctuation statistics in the boundary region of Alcator C-Mod.

physics.plasm-ph↗

arXiv2018

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.

physics.plasm-ph↗

arXiv2018

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 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 to 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.

physics.plasm-ph↗

arXiv2018

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 wave forms 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 self-similar for all these confinement modes. These results are 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.

physics.plasm-ph↗

arXiv2017

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 intermittent 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 model also describes the rate of threshold level crossings, which provide novel predictions of plasma--wall interactions due to transient transport events.

physics.plasm-ph↗

arXiv2017

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.

physics.plasm-ph↗

arXiv2016

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 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 for 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 to estimate the basic properties of fluctuations from measurement data and describe the diversity of frequency spectra reported from measurements in magnetized plasmas.

physics.plasm-ph↗

arXiv2016

Amplitude and size scaling for interchange motions of plasma filaments

The interchange dynamics and velocity scaling of blob-like plasma filaments are investigated using a two-field reduced fluid model. For incompressible flows due to buoyancy the maximum velocity is proportional to the square root of the relative amplitude and the square root of its cross-field size. For compressible flows in a non-uniform magnetic field this square root scaling only holds for ratios of amplitudes to cross-field sizes above a certain threshold value. For small amplitudes and large sizes, the maximum velocity is proportional to the filament amplitude. The acceleration is proportional to the amplitude and independent of the cross-field size in all regimes. This is demonstrated by means of numerical simulations and explained by the energy integrals satisfied by the model.

physics.plasm-ph↗