Auroral Energy Flux and Joule Heating Derived From Global Maps of Field-Aligned Currents

We calculate auroral energy flux and Joule heating in the high-latitude ionosphere for 27 geomagnetically active days using two-dimensional maps of field-aligned currents determined by the Active Magnetosphere and Planetary Response Experiment. The energy input to the ionosphere due to Joule heating increases more rapidly with geomagnetic activity than that due to precipitating particles. The energy flux varies more smoothly with time than Joule heating, which is impulsive in nature on time scales from minutes to tens of minutes. These impulsive events correlate well with recoveries in the Sym-H index, with the maximum correlation when compared to Sym-H recoveries 70 min later. Because of prior studies that have associated transient recoveries of Sym-H with substorm expansions, the delay found here suggests that dissipation of energy in the ionosphere occurs during the substorm growth phase prior to the release of magnetic energy caused by diversion of tail currents.

Pseudononstationarity in the scaling exponents of finite-interval time series

The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently, a stationary stochastic process (time series) can yield anomalous time variation in the scaling exponents, suggestive of nonstationarity. The variance in the estimates of scaling exponents computed from an interval of N observations is known for finite variance processes to vary as approximately 1N as N-->infinity for certain statistical estimators; however, the convergence to this behavior will depend on the details of the process, and may be slow. We study the variation in the scaling of second-order moments of the time-series increments with N for a variety of synthetic and "real world" time series, and we find that in particular for heavy tailed processes, for realizable N , one is far from this approximately 1N limiting behavior. We propose a semiempirical estimate for the minimum N needed to make a meaningful estimate of the scaling exponents for model stochastic processes and compare these with some "real world" time series.

Diagnosis of magnetic structures and intermittency in space-plasma turbulence using the technique of surrogate data

Intermittency is usually identified in turbulent flows as non-Gaussian tails of the probability density functions (PDFs) of the turbulent field derivatives. Here we investigate the role of phase coherence among the Fourier modes in creating intermittency in magnetized space plasmas using the technique of surrogate data. We apply the technique to two examples: (i) synthetic data and (ii) magnetic field fluctuations recorded in the terrestrial magnetosheath by the Cluster spacecraft. We use a set of four series of data, one observed and three surrogate, and their PDFs and moments (q < or = 4) as discriminating statistics. We show that the technique allows for detecting coherent structures and estimating their scales. We show furthermore that the phases, but not the amplitudes, create the non-Gaussian tails of the PDFs. We show also that the surrogate data used cannot account for asymmetries of the PDFs of the observed data. This enables us to confirm a scenario of turbulent cascade of mirror structures proposed in previous publications, by showing the existence of an approximately constant energy flux in the inertial range.

Extracting the scaling exponents of a self-affine, non-Gaussian process from a finite-length time series

We address the generic problem of extracting the scaling exponents of a stationary, self-affine process realized by a time series of finite length, where information about the process is not known a priori. Estimating the scaling exponents relies upon estimating the moments, or more typically structure functions, of the probability density of the differenced time series. If the probability density is heavy tailed, outliers strongly influence the scaling behavior of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of these outliers. We test these ideas on a synthetically generated symmetric alpha -stable Lévy process and show that the Lévy exponent is recovered in up to the 6th order moment after only approximately 0.1-0.5% of the data are excluded. The scaling properties of the excluded outliers can then be tested to provide additional information about the system.