Electron density in the quiet solar coronal transition region from SoHO/SUMER measurements of S VI line radiance and opacity

Context: The sharp temperature and density gradients in the coronal transition region are a challenge for models and observations. Aims: We set out to get linearly- and quadratically-weighted average electron densities in the region emitting the S VI lines, using the observed opacity and the emission measure of these lines. Methods: We analyze SoHO/SUMER spectroscopic observations of the S VI lines, using the center-to-limb variations and radiance ratios to derive the opacity. We also use the Emission Measure derived from radiance at disk center. Results: We get an opacity at S VI line center of the order of 0.05. The resulting average electron density is 2.4 10^16 m^-3 at T = 2 10^5 K. This value is higher than the values obtained from radiance measurements. Conversely, taking a classical value for the density leads to a too high value of the thickness of the emitting layer. Conclusions: The pressure derived from the Emission Measure method compares well with previous determinations and implies a low opacity of 5 10^-3 to 10^-2. The fact that a direct derivation leads to a much higher opacity remains unexplained, despite tentative modeling of observational biases. Further measurements need to be done, and more realistic models of the transition region need to be used.Comment: 11 pages, 9 figure

Influence of the definition of dissipative events on their statistics

A convenient and widely used way to study the turbulent plasma in the solar corona is to do statistics of properties of events (or structures), associated with flares, that can be found in observations or in numerical simulations. Numerous papers have followed such a methodology, using different definitions of an event, but the reasons behind the choice of a particular definition (and not another one) is very rarely discussed. We give here a comprehensive set of possible event definitions starting from a one-dimensional data set such as a time-series of energy dissipation. Each definition is then applied to a time-series of energy dissipation issued from simulations of a shell-model of magnetohydrodynamic turbulence as defined in Giuliani and Carbone (1998), or from a new model of coupled shell-models designed to represent a magnetic loop in the solar corona. We obtain distributions of the peak dissipation power, total energy, duration and waiting-time associated to each definition. These distributions are then investigated and compared, and the influence of the definition of an event on statistics is discussed. In particular, power-law distributions are more likely to appear when using a threshold. The sensitivity of the distributions to the definition of an event seems also to be weaker for events found in a highly intermittent time series. Some implications on statistical results obtained from observations are discussed.Comment: 8 pages, 13 figures. Submitted to Astronomy&Astrophysic

Intermittent turbulent dynamo at very low and high magnetic Prandtl numbers

Context: Direct numerical simulations have shown that the dynamo is efficient even at low Prandtl numbers, i.e., the critical magnetic Reynolds number Rm_c necessary for the dynamo to be efficient becomes smaller than the hydrodynamic Reynolds number Re when Re -> infinity. Aims: We test the conjecture (Iskakov et al. 2007) that Rm_c actually tends to a finite value when Re -> infinity, and we study the behavior of the dynamo growth factor \gamma\ at very low and high magnetic Prandtl numbers. Methods: We use local and nonlocal shell-models of magnetohydrodynamic (MHD) turbulence with parameters covering a much wider range of Reynolds numbers than direct numerical simulations, but of astrophysical relevance. Results: We confirm that Rm_c tends to a finite value when Re -> infinity. The limit for Rm -> infinity of the dynamo growth factor \gamma\ in the kinematic regime behaves like Re^\beta, and, similarly, the limit for Re -> infinity of \gamma\ behaves like Rm^{\beta'}, with \beta=\beta'=0.4. Conclusion: Comparison with a phenomenology based on an intermittent small-scale turbulent dynamo, together with the differences between the growth rates in the different local and nonlocal models, indicate a weak contribution of nonlocal terms to the dynamo effect.Comment: 5 pages, 6 figure

Shell-models of RMHD turbulence and the heating of solar coronal loops

A simplified non-linear numerical model for the development of incompressible magnetohydrodynamics (MHD) in the presence of a strong magnetic field B0 and stratification, nicknamed Shell-Atm, is presented. In planes orthogonal to the mean field, the non-linear incompressible dynamics is replaced by 2D shell-models for the complex variables u and b, allowing one to reach large Reynolds numbers while at the same time carrying out sufficiently long time integrations to obtain a good statistics at moderate computational cost. The shell-models of different planes are coupled by Alfven waves propagating along B0. The model may be applied to open or closed magnetic field configurations where the axial field dominates and the plasma pressure is low; here we apply it to the specific case of a magnetic loop of the solar corona heated via turbulence driven by photospheric motions, and we use statistics for its analysis. The Alfven waves interact non-linearly and form turbulent spectra in the directions perpendicular and, via propagation, also parallel to the mean field. A heating function is obtained, and is shown to be intermittent; the average heating is consistent with values required for sustaining a hot corona, and is proportional to the aspect ratio of the loop to the power -1.5; characteristic properties of heating events are distributed as power-laws. Cross-correlations show a delay of dissipation compared to energy content.Comment: 12 pages, 16 figures, accepted for publication in Ap

Drying air-induced disturbances in multi-layer coating systems

A range of new experimental techniques is developed to quantify drying-air induced disturbances on low viscosity single and multi-layer coating systems. Experiments on prototype slide-bead coating systems show that the surface disturbances take the form of a wavelike pattern and quantify precisely how its amplitude increases rapidly with wet thickness and decreases with viscosity. Heat transfer measurements show that the redistribution of water to form an additional lower viscosity carrier layer while increasing the solids concentration of the upper layer or layers enables the maximum drying rate, for which drying-air induced surface disturbances are acceptably small, to be increased with significant commercial benefits

Shell Models of Magnetohydrodynamic Turbulence

Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models. In this review we set up a general mathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decaying MHD turbulence, dynamo action, Alfven waves and the Hall effect.Comment: published in Physics Report

On the ultraviolet signatures of small scale heating in coronal loops

Studying the statistical properties of solar ultraviolet emission lines could provide information about the nature of small scale coronal heating. We expand on previous work to investigate these properties. We study whether the predicted statistical distribution of ion emission line intensities produced by a specified heating function is affected by the isoelectronic sequence to which the ion belongs, as well as the characteristic temperature at which it was formed. Particular emphasis is placed on the strong resonance lines belonging to the lithium isoelectronic sequence. Predictions for emission lines observed by existing space-based UV spectrometers are given. The effects on the statistics of a line when observed with a wide-band imaging instrument rather than a spectrometer are also investigated. We use a hydrodynamic model to simulate the UV emission of a loop system heated by nanoflares on small, spatially unresolved scales. We select lines emitted at similar temperatures but belonging to different isoelectronic groups: Fe IX and Ne VIII, Fe XII and Mg X, Fe XVII, Fe XIX and Fe XXIV. Our simulations confirm previous results that almost all lines have an intensity distribution that follows a power-law, in a similar way to the heating function. However, only the high temperature lines best preserve the heating function's power law index (Fe XIX being the best ion in the case presented here). The Li isoelectronic lines have different statistical properties with respect to the lines from other sequences, due to the extended high temperature tail of their contribution functions. However, this is not the case for Fe XXIV which may be used as a diagnostic of the coronal heating function. We also show that the power-law index of the heating function is effectively preserved when a line is observed by a wide-band imaging instrument rather than a spectromenter

On the von Karman-Howarth equations for Hall MHD flows

The von Karman-Howarth equations are derived for three-dimensional (3D) Hall magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic turbulence. From these equations, we derive exact scaling laws for the third-order correlation tensors. We show how these relations are compatible with previous heuristic and numerical results. These multi-scale laws provide a relevant tool to investigate the non-linear nature of the high frequency magnetic field fluctuations in the solar wind or, more generally, in any plasma where the Hall effect is important.Comment: 11 page