Fast and optimal solution to the Rankine-Hugoniot problem

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented

The inner edge of the plasma sheet and the diffuse aurora

Three dimensional measurements from the ISEE-1 low energy electron spectrometer are used to map the location of the inner edge of the plasma sheet and study the anisotropies in the electron distribution function associated with this boundary. Lower energy plasma sheet electrons have inner edges closer to the Earth than higher energies with the separations at different energies being larger near dawn and after dusk than at midnight. Lowest energy inner edges are frequently located adjacent to the plasmapause in the dawn hemisphere but are often separated from it in the dusk hemisphere by a gap of at least several Re. The energy dispersion is minimal in the afternoon quadrant where the inner edge is near the magnetopause and frequently oscillating on a time scale of minutes. The location of the inner edge is probably determined primarily by the motion of electrons in the existing electric and magnetic fields rather than by strong diffusion as has sometimes been supposed

Spectral analysis of magnetohydrodynamic fluctuations near interplanetary schocks

Evidence for two types of relatively large amplitude MHD waves upstream and downstream of quasi-parallel forward and reverse interplanetary shocks is presented. The first mode is an Alfven wave with frequencies (in the spacecraft frame) in the range of 0.025 to 0.07 Hz. This is a left-hand polarized mode and propagates within a few degrees of the ambient magnetic field. The second is a fast MHD mode with frequencies in the range of 0.025 to 0.17 Hz, right-hand polarization and propagating along the magnetic field. These waves are detected principally in association with quasi-parallel shock. The Alfven waves are found to have plasma rest frame frequencies in the range of 1.1 to 6.3 mHz with wavelengths in the order of 4.8 x 10 to the 8th power to 2.7 x 10 to the 9th power cm. Similarly, the fast MHD modes have rest frame frequencies in the range 1.6 to 26 mHz with typical wavelengths about 2.19 x 10 to the 8th power cm. The magnetic field power spectrum in the vicinity of these interplanetary shocks is much steeper than f to the -s/3 at high frequencies. The observed spectra have a high frequency dependence of f to the -2/5 to f to the -4

Large amplitude MHD waves upstream of the Jovian bow shock: Reinterpretation

Observations of large amplitude magnetohydrodynamic (MHD) waves upstream of the Jovian bow shock were previously interpreted as arising from a resonant electromagnetic ion beam instability. That interpretation was based on the conclusion that the observed fluctuations were predominantly right elliptically polarized in the solar wind rest frame. Because it was noted that the fluctuations are, in fact, left elliptically polarized, a reanalysis of the observations was necessary. Several mechanisms for producing left hand polarized MHD waves in the observed frequency range were investigated. Instabilities excited by protons appear unlikely to account for the observations. A resonant instability excited by relativistic electrons escaping from the Jovian magnetosphere is a likely source of free energy consistent with the observations. Evidence for the existence of such a population of electrons was found in both the Low Energy Charged Particle experiments and Cosmic Ray experiments on Voyager 2

The effect of parallel currents on auroral micropulsations

Field aligned currents play an important role in the global coupling between the magnetosphere and the ionosphere and in their relationship to the auroral phenomena. Moreover, there exists evidence that resonant oscillations are related to large-scale Birkeland currents. The spatial confinement of the field-aligned currents forms an inhomogeneous system susceptible to low-frequency oscillations, which can be excited due to periodic variations in the solar wind pressure or to the Kelvin-Helmholtz (KH) instability. In this paper we present a study of ultralow-frequency (ULF) oscillations in an inhomogeneous magnetic field formed by a large-scale current. We investigate the effects of the field-aligned currents on the generation of localized Alfven waves. The field oscillations are described by an eigenvalue wave equation which includes the effects of the field aligned currents and which produces a discrete spectrum of Alfven waves. These waves are observed mainly in three regions of the magnetosphere: in the magnetosheath, in the polar cusp, and in the plasmasphere. In the present study we limit our investigation to the auroral region

Observations of Electron Vorticity in the Inner Plasmasheet and Its Relationship to Reconnection

Spatial derivatives of the electron moments can be estimated using data from the four Cluster spacecraft. Using spatial derivatives of the velocity we have computed the vorticity in the plasmasheet for several crossings. What we have found is that vorticity appears to be a common feature in the inner plasmasheet. We will show a number of examples. In at least some of the observations the vorticity is well correlated with the passage of Cluster through the ion diffusion region of known reconnection events. That most of the vorticity events observed are reconnection related cannot be dismissed and in fact observations of vorticity may provide a means to locate times when the Cluster spacecraft are magnetically connected to regions where reconnection is taking place. Understanding the role and source of the vorticity should advance our understanding of the dissipation of the turbulence associated with reconnection. In the course of the presentation we will also touch on the methods used to estimate the spatial derivatives as well as the limitations and assumptions involved

Observations of Electron Vorticity in the Inner Plasma Sheet

From a limited number of observations it appears that vorticity is a common feature in the inner plasma sheet. With the four Cluster spacecraft and the four PEACE instruments positioned in a tetrahedral configuration, for the first time it is possible to directly estimate the electron fluid vorticity in a space plasma. We show examples of electron fluid vorticity from multiple plasma sheet crossings. These include three time periods when Cluster passed through a reconnection ion diffusion region. Enhancements in vorticity are seen in association with each crossing of the ion diffusion region

Overview of methods used to evaluate the adequacy of nutrient intakes for individuals and populations

The objective of the present paper is to review the methods of measuring micronutrient intake adequacy for individuals and for populations in order to ascertain best practice. A systematic review was conducted to locate studies on the methodological aspects of measuring nutrient adequacy. The results showed that for individuals, qualitative methods (to find probability of adequacy) and quantitative methods (to find confidence of adequacy) have been proposed for micronutrients where there is enough data to set an average nutrient requirement (ANR). If micronutrients do not have ANR, an adequate intake (AI) is often defined and can be used to assess adequacy, provided the distribution of daily intake over a number of days is known. The probability of an individual's intake being excessive can also be compared with the upper level of safe intake and the confidence of this estimate determined in a similar way. At the population level, adequacy can be judged from the ANR using the probability approach or its short cut – the estimated average requirement cut-point method. If the micronutrient does not have an ANR, adequacy cannot be determined from the average intake and must be expressed differently. The upper level of safe intake can be used for populations in a similar way to that of individuals. All of the methodological studies reviewed were from the American continent and all used the methodology described in the Institute of Medicine publications. The present methodology should now be adapted for use in Europe

Reconstruction of a Broadband Spectrum of Alfvenic Fluctuations

Alfvenic fluctuations in the solar wind exhibit a high degree of velocities and magnetic field correlations consistent with Alfven waves propagating away and toward the Sun. Two remarkable properties of these fluctuations are the tendencies to have either positive or negative magnetic helicity (-1 less than or equal to sigma(sub m) less than or equal to +1) associated with either left- or right- topological handedness of the fluctuations and to have a constant magnetic field magnitude. This paper provides, for the first time, a theoretical framework for reconstructing both the magnetic and velocity field fluctuations with a divergence-free magnetic field, with any specified power spectral index and normalized magnetic- and cross-helicity spectrum field fluctuations for any plasma species. The spectrum is constructed in the Fourier domain by imposing two conditions-a divergence-free magnetic field and the preservation of the sense of magnetic helicity in both spaces-as well as using Parseval's theorem for the conservation of energy between configuration and Fourier spaces. Applications to the one-dimensional spatial Alfvenic propagation are presented. The theoretical construction is in agreement with typical time series and power spectra properties observed in the solar wind. The theoretical ideas presented in this spectral reconstruction provide a foundation for more realistic simulations of plasma waves, solar wind turbulence, and the propagation of energetic particles in such fluctuating fields