arXiv subjects

Audun Theodorsen

Publications and source records attributed to Audun Theodorsen.

14 recordsLinked to original sources

arXiv2026

Deviations from spectral Dirac comb due to semiperiodic pulses

In the frequency power spectral density, periodic oscillations appear as a Dirac comb at integer multiples of the frequency of the period. In weakly nonlinear systems or systems close to the primary instability threshold, the periodicity may be perturbed, resulting in deviations from the Dirac comb. We review and discuss a stochastic model of such semiperiodic fluctuations, while also providing several new results which widen the applicability of the model. The fluctuations are described as a superposition of pulses with a fixed shape. Closed form expressions are derived for the frequency power spectral density in the case of periodic pulse arrivals and a random distribution of pulse amplitudes. In general, the spectrum is a Dirac comb located at multiples of the inverse periodicity time and modulated by the pulse spectrum. Deviations from strict periodicity in the arrivals are considered in two ways: either as a random offset to each periodic arrival (jitter) or as independently distributed waiting times between arrivals (renewal). In this contribution, we show that both ways of including deviations from periodicity remove the Dirac comb with remarkable efficiency, leaving mainly the spectrum of the pulse function. Where the jitter process modulates the mass of the higher harmonics, the renewal process leads to spectral broadening. We clarify the effects of random pulse amplitudes on the frequency power spectrum and demonstrate the applicability of normally distributed waiting times to modeling. Contrary to the previous literature, we argue that negative waiting times do not pose problems for the theory, broadening the applicability of the normal approximation. Randomness in the pulse arrival times is investigated by numerical realizations of the process, and the model is used to describe time series of kinetic energy of fluctuating motions in two-dimensional thermal convection.

nlin.CD↗

arXiv2024

On the distribution of the the near-solar bound dust grains detected with Parker Solar Probe

Parker Solar Probe (PSP) counts dust impacts in the near-solar region, but modelling effort is needed to understand the dust population's properties. We aim to constrain the dust cloud's properties based on the flux observed by PSP. We develop a forward-model for the bound dust detection rates using the formalism of 6D phase space distribution of the dust. We apply the model to the location table of different PSP's solar encounter groups. We explain some of the near-perihelion features observed in the data as well as the broader characteristic of the dust flux between 0.15 AU and 0.5 AU. We compare the measurements of PSP to the measurements of Solar Orbiter (SolO) near 1 AU to expose the differences between the two spacecraft. We found that the dust flux observed by PSP between 0.15 AU and 0.5 AU in post-perihelia can be explained by dust on bound orbits and is consistent with a broad range of orbital parameters, including dust on circular orbits. However, the dust number density as a function of the heliocentric distance and the scaling of detection efficiency with the relative speed are important to explain the observed flux variation. The data suggest that the slope of differential mass distribution $δ$ is between 0.14 and 0.49. The near-perihelion observations, however, show the flux maxima, which are inconsistent with the circular dust model, and additional effects may play a role. We found indication that the sunward side of PSP is less sensitive to the dust impacts, compared to the other PSP's surfaces. Conclusions. We show that the dust flux on PSP can be explained by non-circular bound dust and the detection capabilities of PSP. The scaling of flux with the impact speed is especially important, and shallower than previously assumed.

astro-ph.EP↗

arXiv2024

Radiative forcing by super-volcano eruptions

We investigate the climatic effects of volcanic eruptions spanning from Mt.\ Pinatubo-sized events to super-volcanoes. The study is based on ensemble simulations in the Community Earth System Model Version 2 (CESM2) climate model using the Whole Atmosphere Community Climate Model Version 6 (WACCM6) atmosphere model. Our analysis focuses on the impact of different \ce{SO2}-amount injections on stratospheric aerosol optical depth (AOD), effective radiative forcing (RF), and global temperature anomalies. Unlike the traditional linear models used for smaller eruptions, our results reveal a non-linear relationship between RF and AOD for larger eruptions. We also uncover a notable time-dependent decrease in aerosol forcing efficiency across all eruption magnitudes during the first post-eruption year. In addition, the study reveals that larger as compared to medium-sized eruption events produce a delayed and sharper peak in AOD, and a longer-lasting temperature response while the time evolution of RF remains similar between the two eruption types. When including the results of previous studies, we find that relating \ce{SO2} to any other parameter is inconsistent across models compared to the relationships between AOD, RF, and temperature anomaly. Thus, we expect the largest uncertainty in model codes to relate to the chemistry and physics of \ce{SO2} evolution. Finally, we find that the peak RF approaches a limiting value, and that the peak temperature response follows linearly, effectively bounding the temperature anomaly to at most (\sim\SI{-12}{\kelvin}).

physics.ao-ph↗

arXiv2023

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. 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.

physics.plasm-ph↗

arXiv2023

Reconstruction of intermittent data 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 contribution, we present a systematic study of a novel deconvolution method to estimate the arrival times and amplitudes of the pulses from realizations of such processes. The method shows that 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.

physics.data-an↗

arXiv2022

Modelling Solar Orbiter Dust Detection Rates in Inner Heliosphere as a Poisson Process

Solar Orbiter provides dust detection capability in inner heliosphere, but estimating physical properties of detected dust from the collected data is far from straightforward. First, a physical model for dust collection considering a Poisson process is formulated. Second, it is shown that dust on hyperbolic orbits is responsible for the majority of dust detections with Solar Orbiter's Radio and Plasma Waves (SolO/RPW). Third, the model for dust counts is fitted to SolO/RPW data and parameters of the dust are inferred, namely: radial velocity, hyperbolic meteoroids predominance, and solar radiation pressure to gravity ratio as well as uncertainties of these. Non-parametric model fitting is used to get the difference between inbound and outbound detection rate and dust radial velocity is thus estimated. A hierarchical Bayesian model is formulated and applied to available SolO/RPW data. The model uses the methodology of Integrated Nested Laplace Approximation, estimating parameters of dust and their uncertainties. SolO/RPW dust observations can be modelled as a Poisson process in a Bayesian framework and observations up to this date are consistent with the hyperbolic dust model with an additional background component. Analysis suggests a radial velocity of the hyperbolic component around $(63 \pm 7) \mathrm{km/s}$ with the predominance of hyperbolic dust about $(78 \pm 4) \%$. The results are consistent with hyperbolic meteoroids originating between $0.02 \mathrm{AU}$ and $0.1 \mathrm{AU}$ and showing substantial deceleration, which implies effective solar radiation pressure to gravity ratio $\gtrsim 0.5$. The flux of hyperbolic component at $1 \mathrm{AU}$ is found to be $(1.1 \pm 0.2) \times 10^{-4} \mathrm{m^{-2}s^{-1}}$ and the flux of background component at $1 \mathrm{AU}$ is found to be $(5.4 \pm 1.5) \times 10^{-5} \mathrm{m^{-2}s^{-1}}$.

physics.space-ph↗

arXiv2021

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 are compared to predictions of a stochastic model describing the plasma fluctuations as a super-position 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.

physics.plasm-ph↗

arXiv2019

Scaling of shot noise processes

In this contribution, we investigate the scaling of the distribution of the shot noise process, its power spectral density and its time above threshold.

cond-mat.stat-mech↗

arXiv2018

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 difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the probability density function. In this contribution, the effect of changing the amplitude distribution on the moments, probability density function and characteristic function of the process is investigated and a parameter estimation method using the empirical distribution function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations in the boundary region of magnetized plasmas.

physics.plasm-ph↗

arXiv2018

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 15μs. 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 approximately 6% of the total fluctuation driven heat flux.

physics.plasm-ph↗

arXiv2017

Level crossings and excess times due to a super-position of uncorrelated exponential pulses

A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position 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 results 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.

physics.plasm-ph↗

arXiv2017

Statistical properties of a filtered Poisson process with additive random noise: Distributions, correlations and moment estimation

Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model pa- rameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the parameters, but are unable to separate the noise types. The auto-correlation function and the power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type.

physics.data-an↗

arXiv2016

Level crossings, excess times and transient plasma-wall interactions in fusion plasmas

Based on a stochastic model for intermittent fluctuations in the boundary region of magnetically confined plasmas, an expression for the level crossing rate is derived from the joint distribution of the process and its derivative. From this the average time spent by the process above a certain threshold level is obtained. This provides novel predictions of plasma-wall interactions due to transient transport events associated with radial motion of blob-like structures in the scrape-off layer.

physics.plasm-ph↗

arXiv2016

Fluctuation statistics in the scrape-off layer of Alcator C-Mod

We study long time series of the ion saturation current and floating potential, sampled by Langmuir probes dwelled in the outboard mid-plane scrape off layer and embedded in the lower divertor baffle of Alcator C-Mod. A series of ohmically heated L-mode plasma discharges is investigated with line-averaged plasma density ranging from n_e/n_G = 0.15 to 0.42, where n_G is the Greenwald density. All ion saturation current time series that are sampled in the far scrape-off layer are characterized by large-amplitude burst events. Coefficients of skewness and excess kurtosis of the time series obey a quadratic relationship and their histograms coincide partially upon proper normalization. Histograms of the ion saturation current time series are found to agree well with a prediction of a stochastic model for the particle density fluctuations in scrape-off layer plasmas. The distribution of the waiting times between successive large-amplitude burst events and of the burst amplitudes are approximately described by exponential distributions. The average waiting time and burst amplitude are found to vary weakly with the line-averaged plasma density. Conditional averaging reveals that the radial blob velocity, estimated from floating potential measurements, increases with the normalized burst amplitude in the outboard mid-plane scrape-off layer. For low density discharges, the conditionally averaged waveform of the floating potential associated with large amplitude bursts at the divertor probes has a dipolar shape. In detached divertor conditions the average waveform is random, indicating electrical disconnection of blobs from the sheaths at the divertor targets.

physics.plasm-ph↗