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.Comment: 12 pages, 4 figure

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.Comment: 12 pages, 3 figure

Convergence of statistical moments of particle density time series in scrape-off layer plasmas

Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a fixed shape, an exponential distribution of waiting times and amplitudes represents the radial motion of blob-like structures. With an analytic formulation of the process at hand, we derive expressions for the mean-squared error on estimators of sample mean and sample variance as a function of sample length, sampling frequency, and the parameters of the stochastic process. % Employing that the probability distribution function of a particularly relevant shot noise process is given by the gamma distribution, we derive estimators for sample skewness and kurtosis, and expressions for the mean-squared error on these estimators. Numerically generated synthetic time series are used to verify the proposed estimators, the sample length dependency of their mean-squared errors, and their performance. We find that estimators for sample skewness and kurtosis based on the gamma distribution are more precise and more accurate than common estimators based on the method of moments.Comment: 31 pages, 10 figure

The spectroscopic orbits and the geometrical configuration of the symbiotic binary AR Pavonis

We analyze optical and near infrared spectra of intermediate and high resolution of the eclipsing symbiotic system AR Pavonis. We have obtained the radial velocity curves for the red and the hot component from the M-giant absorption lines and from the wings of Halpha, H and He II4686 emission profiles, respectively. From the orbital elements we have derived the masses, Mgiant=2.5 and Mhot =1.0 solar masses, for the red giant and the hot component, respectively. We also present and discuss radial velocity patterns in the blue cF absorption spectrum as well as various emission lines. In particular, we confirm that the blue absorption lines are associated with the hot component. The radial velocity curve of the blue absorption system, however, does not track the hot companion's orbital motion in a straightforward way, and its departures from an expected circular orbit are particularly strong when the hot component is active. We suggest that the cF-type absorption system is formed in material streaming from the giant presumably in a region where the stream encounters an accretion disk or an extended envelope around the hot component. The broad emission wings originate from the inner accretion disk or the envelope around the hot star.We also suggest that the central absorption in H profiles is formed in a neutral portion of the cool giant's wind which is strongly concentrated towards the orbital plane. The nebula in AR Pav seems to be bounded by significant amount of neutral material in the orbital plane. The forbidden emission lines are probably formed in low density ionized regions extended in polar directions and/or the wind-wind interaction zone.Comment: 12 pages, 5 figures, accepted by A&

Stochastic modelling of intermittent scrape-off layer plasma fluctuations

Single-point measurements of fluctuations in the scrape-off layer of magnetized plasmas are generally found to be dominated by large-amplitude bursts which are associated with radial motion of blob-like structures. A stochastic model for these fluctuations is presented, with the plasma density given by a random sequence of bursts with a fixed wave form. Under very general conditions, this model predicts a parabolic relation between the skewness and kurtosis moments of the plasma fluctuations. In the case of exponentially distributed burst amplitudes and waiting times, the probability density function for the fluctuation amplitudes is shown to be a Gamma distribution with the scale parameter given by the average burst amplitude and the shape parameter given by the ratio of the burst duration and waiting times.Comment: 11 pages, 1 figur

Synchronization of Chaotic Systems by Common Random Forcing

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough intensity, to different trajectories which start from different initial conditions, leads eventually to the perfect synchronization of the trajectories. The largest Lyapunov exponent becomes negative due to the presence of the noise terms.Comment: 5 pages, uses aipproc.cls and aipproc.sty (included). Five double figures are provided as ten separate gif files. Version with (large) postscript figures included available from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

The ages of very cool hydrogen-rich white dwarfs

The evolution of white dwarfs is essentially a cooling process that depends primarily on the energy stored in their degenerate cores and on the transparency of their envelopes. In this paper we compute accurate cooling sequences for carbon-oxygen white dwarfs with hydrogen dominated atmospheres for the full range of masses of interest. For this purpose we use the most accurate available physical inputs for both the equation of state and opacities of the envelope and for the thermodynamic quantities of the degenerate core. We also investigate the role of the latent heat in the computed cooling sequences. We present separately cooling sequences in which the effects of phase separation of the carbon-oxygen binary mixture upon crystallization have been neglected, and the delay introduced in the cooling times when this mechanism is properly taken into account, in order to compare our results with other published cooling sequences which do not include a treatment of this phenomenon. We find that the cooling ages of very cool white dwarfs with pure hydrogen atmospheres have been systematically underestimated by roughly 1.5 Gyr at log(L/Lo)=-4.5 for an otherwise typical 0.6 Mo white dwarf, when phase separation is neglected. If phase separation of the binary mixture is included then the cooling ages are further increased by roughly 10%. Cooling tracks and cooling isochrones in several color-magnitude diagrams are presented as well.Comment: 8 Pages; ApJ, accepted for publicatio

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.Comment: 17 pages, 10 figure