Papers by Vincenzo Carbone
STATISTICAL PROPERTIES OF SOLAR FLARES AND COMPARISON TO OTHER IMPULSIVE ENERGY RELEASE EVENTS
International Journal of Modern Physics B, 2009
ABSTRACT Impulsive energy release events are observed in many natural systems. Solar flares are c... more ABSTRACT Impulsive energy release events are observed in many natural systems. Solar flares are certainly among the most remarkable examples of such processes. In the last years the study of solar flare statistical properties has received considerable attention in the context of solar flare models based on different approaches, such as Self Organized Criticality (SOC) or magnetohydrodynamic (MHD) turbulence. In this talk the main statistical properties of solar flares will be presented and compared to those of other well known impulsive processes, such as earthquakes and soft γ-ray flashes occurring on neutron stars. It is shown that the these phenomena are characterized by different statistics that cannot be rescaled onto a single, universal curve and that this holds even for the same phenomenon, when observed in different periods or at different locations. Our results indicate apparent complexity of impulsive energy release processes, which neither follow a common behavior nor could be attributed to a universal physical mechanism.
Europhysics Letters (epl), 2005
The statistical properties of seismic time series, including both sequences of aftershocks, and p... more The statistical properties of seismic time series, including both sequences of aftershocks, and patterns of occurrence of mainshocks, are studied. In this case, the universality claimed by Bak et al. (Phys. Rev. Lett. 88 (2002) 178501) about the waiting times between earthquakes, has not been found. Looking for a different law, we show that the behavior of the surviving function P(τ) of inter-event times τ satisfy a simple relation, with two free parameter, which generalizes Omori's law also to catalogues of main earthquakes. Moreover we observe that the P(τ) calculated for all catalogues we investigate, collapse to a single curve when suitably scaled. This is an indication that the above relation expresses a unified scaling law for seismic events whatever their origin. On the base of this relation it results that the seismic event occurrence pattern within a given seismogenetic area, significantly departs from a Poissonian distribution.
Physical Review Letters, 2004
A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulen... more A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulence in coronal loops, is presented. The model is based on the use of the shell technique in the wave vector space applied to the set of reduced MHD equations. Numerical simulation showed that the energy injected is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions among these fluctuations give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. The statistical analysis performed on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics.
Europhysics Letters (epl), 2000
Intermittency in MHD turbulence has been analyzed using high resolution 2D numerical simulations.... more Intermittency in MHD turbulence has been analyzed using high resolution 2D numerical simulations. We show that the Probability Distribution Functions (PDFs) of the fluctuations of the Elsasser fields, magnetic field and velocity field depend on the scale at hand, that is they are self-affine. The departure of the PDFs from a Gaussian function can be described through the scaling behavior of a single parameter lambda_r^2 obtained by fitting the PDFs with a given curve stemming from the analysis of a multiplicative model by Castaing et al. (1990). The scaling behavior of the parameter lambda_r^2 can be used to extract informations about the intermittency. A comparison of intermittency properties in different MHD turbulent flows is also performed.
Astrophysical Journal, 2000
It was shown recently that current helicity, calculated using the photospheric magnetic Ðeld vect... more It was shown recently that current helicity, calculated using the photospheric magnetic Ðeld vector measurements, possesses a well-pronounced scaling behavior. The sign singularity of two-dimensional structures of current helicity, can be studied by introducing a signed measure and by h c \ B z AE ($ Â B) z , calculating the power-law exponent, the cancellation exponent i. The time variations of the cancellation exponent seem to be related to Ñare activity of an active region (AR). Periods of enhanced Ñaring are accompanied by a drop and subsequent rise of the cancellation exponent. Here we focus on the changes in the vortex structure of the photospheric magnetic Ðeld during the transition of an active region from low Ñaring to enhanced Ñaring state. We analyzed variations of the cancellation exponent, helicity imbalance, and total electric current in four Ñaring active regions and one quiet one. We show that the transition of an active region from a low Ñaring state to an enhanced one is always accompanied (in this study, the corresponding time interval is less than 2 hr) by the 30%È45% decrease of the cancellation exponent. In two active regions, a reliable 13%È22% decrease of the total electric current took place, and in three active regions the helicity imbalance changed. This, possibly, implies a reinforcement of the anticoriolis twist of the whole magnetic conÐguration. For comparison, the decrease of i in the quiet active region does not exceed 10%. This can be interpreted as a real preÑare reorganization of the vortex structure of the photospheric magnetic Ðeld : a combination of the exhausting of small-scale eddies along with the reinforcement of the total anticoriolis twist of the magnetic structure.
Journal of Geophysical Research, 2003
We analyzed intermittency in the solar wind, as observed on the ecliptic plane, looking at magnet... more We analyzed intermittency in the solar wind, as observed on the ecliptic plane, looking at magnetic field and velocity fluctuations between 0.3 and 1 AU, for both fast and slow wind and for compressive and directional fluctuations. Our analysis focused on the property that probability distribution functions of a fluctuating field affected by intermittency become more and more peaked at smaller and smaller scales. Since the peakedness of a distribution is measured by its flatness factor we studied the behavior of this parameter for different scales to estimate the degree of intermittency of our time series. We confirmed that both magnetic field and velocity fluctuations are rather intermittent and that compressive magnetic fluctuations are generally more intermittent than the corresponding velocity fluctuations. In addition, we observed that compressive fluctuations are always more intermittent than directional fluctuations and that while slow wind intermittency does not depend on the radial distance from the sun, fast wind intermittency of both magnetic field and velocity fluctuations clearly increases with the heliocentric distance.
Cancellation exponents and multifractal scaling laws in the solar wind magnetohydrodynamic turbulence
Annales Geophysicae, 1996
Some signed measures in turbulence are found to be sign-singular, that is their sign reverses con... more Some signed measures in turbulence are found to be sign-singular, that is their sign reverses continuously on arbitrary finer scales with a reduction of the cancellation between positive and negative contributions. The strength of the singularity is characterized by a scaling exponent , the cancellation exponent. In the present study by using some turbulent samples of the velocity field obtained from spacecraft measurements in the interplanetary medium, we show that sign-singularity is present everywhere in low-frequency turbulent samples. The cancellation exponent can be related to the characteristic scaling laws of turbulence. Differences in the values of , calculated in both high- and low-speed streams, allow us to outline some physical differences in the samples with different velocities.
Scale similarity of the velocity structure functions in fully developed magnetohydrodynamic turbulence
Physical Review E, 1994
Turbulence theory has been recently enriched by the concept of extended self-similarity introduce... more Turbulence theory has been recently enriched by the concept of extended self-similarity introduced by Benzi et al. [Phys. Rev. E 48, R29 (1993)] which showed that an extended scaling range, including both the inertial and the dissipative regions, can be observed when the usual qth-order velocity structure functions are plotted against the structure function of the third order. The same
Astrophysical Journal, 2008
Magnetic fluctuations in the solar wind are distributed according to Kolmogorov's power law $f^{-... more Magnetic fluctuations in the solar wind are distributed according to Kolmogorov's power law $f^{-5/3}$ below the ion cyclotron frequency $f_{ci}$. Above this frequency, the observed steeper power law is usually interpreted in two different ways: a dissipative range of the solar wind turbulence or another turbulent cascade, the nature of which is still an open question. Using the Cluster magnetic data we show that after the spectral break the intermittency increases toward higher frequencies, indicating the presence of non-linear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations raises. We show that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small scale inertial range. We conjecture that the time needed to establish this inertial range is shorter than the eddy-turnover time, and is related to dispersive effects. A simple phenomenological model, based on the compressible Hall MHD, predicts the magnetic spectrum $\sim k^{-7/3+2\alpha}$, which depends on the degree of plasma compression $\alpha$.
A shell model for anisotropic magnetohydrodynamic turbulence
Geophysical and Astrophysical Fluid Dynamics, 1990
In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describ... more In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B0, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers. We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 105 have been considered. Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B0 with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ''Alfvén effect''. A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range. Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation. The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.
Intermittency in fluid turbulence can be evidentiated through the analysis of Probability Distrib... more Intermittency in fluid turbulence can be evidentiated through the analysis of Probability Distribution Functions (PDF) of velocity fluctuations, which display a strong non-gaussian behavior at small scales. In this paper we investigate the occurrence of intermittency in plasma turbulence by studying the departure from the gaussian distribution of PDF for both velocity and magnetic fluctuations. We use data coming from two different experiments, namely in situ satellite observations of the inner solar wind and turbulent fluctuations in a magnetically confined fusion plasma. Moreover we investigate also time intermittency observed in a simplified shell model which mimics 3D MHD equations. We found that the departure from a gaussian distribution is the main characteristic of all cases. The scaling behaviour of PDFs are then investigated by using two different models built up in the past years, in order to capture the essence of intermittency in turbulence.
Evidences for extended self-similarity in hydromagnetic turbulence
Geophysical Research Letters, 1996
We investigate the occurrence of Extended Self-Similarity in the Solar Wind Magnetohydrodynamic (... more We investigate the occurrence of Extended Self-Similarity in the Solar Wind Magnetohydrodynamic (MHD) turbulence by using Helios 2 bulk velocity data recorded in the inner heliosphere at five different heliocentric distances. For each analysed time interval, we compute the sets of scaling exponents for the q-th order velocity structure functions and we show that these sets turn out to be to a good approximation the same whatever the different heliocentric distances. This result shows that a universal non gaussian probability distribution function, which depends on a unique parameter, describes the velocity differences in a MHD turbulent flow also outside the inertial range and in presence of intermittency. Moreover comparing the values of the obtained scaling exponents with those derived from the existing theoretical models of intermittency, we can infer that the most intermittent MHD structures should be two-dimensional current sheets.
Determination of anomalous exponents of structure functions in two-dimensional magnetohydrodynamic turbulence
Europhysics Letters (epl), 1998
... the drive for evaluating higher-order structure functions, for which accuracy issues become e... more ... the drive for evaluating higher-order structure functions, for which accuracy issues become essential, and large data sets must be handled. ... that when ρC ∼ 0, the z ± variables may presumably scale in identical ways (z+ ∼ z− ∼ z). The IK model leads to a linear scaling law ...
Annales Geophysicae, 1994
We analyze the scaling exponents of the velocity structure functions, obtained from the velocity ... more We analyze the scaling exponents of the velocity structure functions, obtained from the velocity fluctuations measured in the interplanetary space plasma. Using the expression for the energy transfer rate which seems the most relevant in describing the evolution of the pseudo-energy densities in the interplanetary medium, we introduce an energy cascade model derived from a simple fragmentation process, which takes into account the intermittency effect. In the absence and in the presence of the largescale magnetic field decorrelation effect the model reduces to the fluid and the hydromagnetic p-model, respectively. We show that the scaling exponents of the q-th power of the velocity structure functions, as obtained by the model in the absence of the decorrelation effect, furnishes the best-fit to the data analyzed from the Voyager 2 velocity field measurements at 8.5 AU. Our results allow us to hypothesize a new kind of scale-similarity for magnetohydrodynamic turbulence when the decorrelation effect is at work, related to the fourth-order velocity structure function.
Wavelet-based filtering of intermittent events from geomagnetic time-series
Planetary and Space Science, 2001
A four-years-long minute-mean geomagnetic time-series recorded in a middle-latitude observatory w... more A four-years-long minute-mean geomagnetic time-series recorded in a middle-latitude observatory was used to investigate the macroscopic dynamics of the magnetosphere???ionosphere complex system. Through probability density and structure function analyses it ...
Astrophysical Journal, 2001
The waiting time distribution for solar flares has been considered. Using Geostationary Operation... more The waiting time distribution for solar flares has been considered. Using Geostationary Operational Environmental Satellite X-ray data, we show that a local Poisson hypothesis for solar flares is not consistent with observations, while the observed distribution is well reproduced by a Lévy function, which displays asymptotically a power-law tail. The origin of the observed waiting time distribution is then attributed to the fact that the physical process underlying solar flares is statistically self-similar in time and is characterized by a certain amount of "memory."
Journal of Geophysical Research, 1995
Using statistical homogeneity, magnetic field fluctuations in the solar wind during Alfvenic peri... more Using statistical homogeneity, magnetic field fluctuations in the solar wind during Alfvenic periods are analyzed in terms of the two independent polarizations allowed for each wave vector k. It is shown that the energy spectra of the two polarizations can be related both to the correlation tensor and to the variance matrix, which is generally used to characterize the anisotropy of the turbulence. Assuming simple anisotropic power law models, the parameters defining the spectra of the two polarizations are determined by fitting eigenvalues of the variance matrix on the corresponding eigenvalues evaluated by Bavassano et al. (1982) for Helios 2 data. Then the corresponding form of the correlation tensor is obtained. In particular, we found that the spectrum of polarization (1) fluctuations (corresponding, in a weak turbulence theory approach, to the Alfven mode) is steeper than the polarization (2) spectrum (corresponding to the magnetosonic modes). While the former spectrum is dominated by wave vectors parallel to B0, the latter is strongly flattened on the plane containing the radial and the mean magnetic field B0 directions. A discussion of these results in connection with other observational and theoretical issues is outlined.
Geophysical Research Letters, 1999
Intermittency is a well-established feature of interplanetary MHD fluctuations and, we show the e... more Intermittency is a well-established feature of interplanetary MHD fluctuations and, we show the effect of intermittency on the radial evolution of solar wind velocity and magnetic field fluctuations anisotropy. On one hand we confirm results obtained by previous investigations which showed that magnetic fluctuation anisotropy increases with distance and, on the other hand, we prove that much of this trend is due to intermittency. Once intermittency has been reduced, thanks to a technique based on wavelet transform for the identification of the intermittent events, the radial trend vanishes. Similar analysis performed on velocity fluctuations, showed that intermittency although altering the anisotropy, does not markedly change its radial trend.
Identifying intermittency events in the solar wind
Planetary and Space Science, 2001
Many complex physical systems in Nature are characterized by intermittency. For these systems, en... more Many complex physical systems in Nature are characterized by intermittency. For these systems, energy at a given scale is not evenly distributed in space and any variable affected by intermittency alternates strong activity to quiescence. Within interplanetary space context, solar wind parameters are highly intermittent. Although the influence of this phenomenon on the scaling of solar wind fluctuations has been evaluated using existing intermittency models, it has never been possible to single out intermittent structures within a given time series until new methods, based on the use of wavelets, have been recently adopted. This new approach to the study of intermittency allows to begin a characterization of those events contributing to solar wind intermittency. Our first results on a single case study of magnetic field intermittency showed that this event was located at the border between two adjacent interplanetary regions mainly characterized by different total pressure and bulk velocity, possibly the border between two adjacent flux-tubes.
Planetary and Space Science, 2011
The occurrence of a nonlinear turbulent energy cascade in solar wind plasma has been recently est... more The occurrence of a nonlinear turbulent energy cascade in solar wind plasma has been recently established through the observation of an exact law from spacecraft measurements. The main results obtained in the fast, polar wind measured by Ulysses spacecraft are reviewed here. In particular, the turbulent cascade is seen as the mean to provide the energy necessary for the local heating in the non-adiabatic expansion of the solar wind. The importance of the density fluctuations in enhancing the turbulent energy transport is also evidenced. The ecliptic wind data measured by Ulysses are studied here in the same framework. This has been done by separating fast and slow streams, in order to avoid mixing of different physical conditions. The results further support the need for separate analysis of the two types of wind.
Uploads
Papers by Vincenzo Carbone