Implications of solar flare hard X-ray "knee" spectra observed by RHESSI

We analyse the RHESSI photon spectra of four flares that exhibit significant deviations from power laws - i.e. changes in the "local" Hard X-ray spectral index. These spectra are characterised by two regions of constant power law index connected by a region of changing spectral index - the "knee". We develop theoretical and numerical methods of describing such knees in terms of variable photon spectral indices and we study the results of their inversions for source mean thin target and collisional thick target injection electron spectra. We show that a particularly sharp knee can produce unphysical negative values in the electron spectra, and we derive inequalities that can be used to test for this without the need for an inversion to be performed. Such unphysical features would indicate that source model assumptions were being violated, particularly strongly for the collisional thick target model which assumes a specific form for electron energy loss. For all four flares considered here we find that the knees do not correspond to unphysical electron spectra. In the three flares that have downward knees we conclude that the knee can be explained in terms of transport effects through a region of non-uniform ionisation. In the other flare, which has an upward knee, we conclude that it is most likely a feature of the accelerated spectrum

The Specific Acceleration Rate in Loop-structured Solar Flares -- Implications for Electron Acceleration Models

We analyze electron flux maps based on RHESSI hard X-ray imaging spectroscopy data for a number of extended coronal loop flare events. For each event, we determine the variation of the characteristic loop length $L$ with electron energy $E$, and we fit this observed behavior with models that incorporate an extended acceleration region and an exterior "propagation" region, and which may include collisional modification of the accelerated electron spectrum inside the acceleration region. The models are characterized by two parameters: the plasma density $n$ in, and the longitudinal extent $L_0$ of, the acceleration region. Determination of the best-fit values of these parameters permits inference of the volume that encompasses the acceleration region and of the total number of particles within it. It is then straightforward to compute values for the emission filling factor and for the {\it specific acceleration rate} (electrons s$^{-1}$ per ambient electron above a chosen reference energy). For the 24 events studied, the range of inferred filling factors is consistent with a value of unity. The inferred mean value of the specific acceleration rate above $E_0=20$ keV is $\sim10^{-2}$ s$^{-1}$, with a 1$\sigma$ spread of about a half-order-of-magnitude above and below this value. We compare these values with the predictions of several models, including acceleration by large-scale, weak (sub-Dreicer) fields, by strong (super-Dreicer) electric fields in a reconnecting current sheet, and by stochastic acceleration processes

Solar hard X-ray imaging by means of Compressed Sensing and Finite Isotropic Wavelet Transform

This paper shows that compressed sensing realized by means of regularized deconvolution and the Finite Isotropic Wavelet Transform is effective and reliable in hard X-ray solar imaging. The method utilizes the Finite Isotropic Wavelet Transform with Meyer function as the mother wavelet. Further, compressed sensing is realized by optimizing a sparsity-promoting regularized objective function by means of the Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization parameter is selected by means of the Miller criterion. The method is applied against both synthetic data mimicking the Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The performances of the method are compared with the results provided by standard visibility-based reconstruction methods. The results show that the application of the sparsity constraint and the use of a continuous, isotropic framework for the wavelet transform provide a notable spatial accuracy and significantly reduce the ringing effects due to the instrument point spread functions

Vibration and buckling of open TWBs with local weakening

Free vibration and Ljapounov stability of compressed open thin-walled beams with a cross-section reduction are studied by a in-house finite differences numerical code, based on a refined direct beam model and allowing for investigating elastic stability of non-trivial equilibrium paths in a dynamic setting. The benchmark is a beam with doubly symmetric cross-section and non-zero warping rigidity, under free, semi-, and fully restrained warping at its ends. In all cases, the results of the direct model are compared to finite element and/or experimental ones. The reduction in the cross-section rigidity induces a weakening that may model a local damage; thus, the present investigation may be useful with an outlook to damage monitoring and identification

Fast spectral fitting of hard X-ray bremsstrahlung from truncated power-law electron spectra

<p><b>Context:</b> Hard X-ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs.</p> <p><b>Aims:</b> We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading especially at energies below the low-energy cutoff, and consider how to improve fitting procedures.</p> <p><b>Methods:</b> We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the non-relativistic Bethe-Heitler case.</p> <p><b>Results:</b> We show that below the low-energy cutoff Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results, but that our analytical forms are a good match; and that above a low-energy cutoff, the Kramers and non-relativistic Bethe-Heitler results match reasonably well with results for up to energies around 100 keV.</p> <p><b>Conclusions:</b> Analytical forms of the non-relativistic Bethe-Heitler photon spectra from general power-law electron spectra are good match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations.</p&gt

Properties of the Acceleration Regions in Several Loop-structured Solar Flares

Using {\em RHESSI} hard X-ray imaging spectroscopy observations, we analyze electron flux maps for a number of extended coronal loop flares. For each event, we fit a collisional model with an extended acceleration region to the observed variation of loop length with electron energy $E$, resulting in estimates of the plasma density in, and longitudinal extent of, the acceleration region. These quantities in turn allow inference of the number of particles within the acceleration region and hence the filling factor $f$ -- the ratio of the emitting volume to the volume that encompasses the emitting region(s). We obtain values of $f$ that lie mostly between 0.1 and 1.0; the (geometric) mean value is $f = 0.20 \times \div 3.9$, somewhat less than, but nevertheless consistent with, unity. Further, coupling information on the number of particles in the acceleration region with information on the total rate of acceleration of particles above a certain reference energy (obtained from spatially-integrated hard X-ray data) also allows inference of the specific acceleration rate (electron s$^{-1}$ per ambient electron above the chosen reference energy). We obtain a (geometric) mean value of the specific acceleration rate $\eta(20$ keV) $= (6.0 \times / \div 3.4) \times 10^{-3}$ electrons s$^{-1}$ per ambient electron; this value has implications both for the global electrodynamics associated with replenishment of the acceleration region and for the nature of the particle acceleration process

Inverse diffraction for the Atmospheric Imaging Assembly in the Solar Dynamics Observatory

The Atmospheric Imaging Assembly in the Solar Dynamics Observatory provides full Sun images every 1 seconds in each of 7 Extreme Ultraviolet passbands. However, for a significant amount of these images, saturation affects their most intense core, preventing scientists from a full exploitation of their physical meaning. In this paper we describe a mathematical and automatic procedure for the recovery of information in the primary saturation region based on a correlation/inversion analysis of the diffraction pattern associated to the telescope observations. Further, we suggest an interpolation-based method for determining the image background that allows the recovery of information also in the region of secondary saturation (blooming)

A self-learning algorithm for biased molecular dynamics

A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias potential in terms of a patchwork of one-dimensional, locally valid collective coordinates. These collective coordinates are obtained from trajectory analyses so that they adapt to any new features encountered during the simulation. We show how this methodology can be used to enhance sampling in real chemical systems citing examples both from the physics of clusters and from the biological sciences.Comment: 6 pages, 5 figures + 9 pages of supplementary informatio

Energy saving in typical architecture: The flow energy in traditional solutions in a sustainable perspective

Quick urbanization increment causes a few difficult problems, such as social assessment, more energy demands, and pollution increase. A positive factor for a city is the concentration of energy requests. On the other hand, urbanization trend is going to fragmentation of settlements, with a consequent expansion of the energy distribution networks but also an increase of the energy wasted. Each building needs some of the total energy distributed in the city. Energy needs can be grouped into four essential parameters: construction, heating, electricity, and water. How were these four parameters satisfied in the XIX century, before the industrial revolution? In those days' energy requirement wasn't so high and could be supplied with basic energy production technology. The knowledge of appropriate building technology (project), the use of (energy saving) materials, with a low and punctual heating system (fireplace, stove) or passive refreshment all intervened in this process. These requirements were achieved in each country using building plans studied to face different weather conditions with different architectural typology and with human effort and time (work-energy). This paper analyses an energy balance in a single typical building in the center of Italy, describing the energy flow that will show the logical and technical solution for "energy-saving". Old buildings (before the introduction of "building-plant") were always designed and built with an energy-saving concern. This article wants to propose the study of a typical building in which are used only low-energy systems to meet all the comfort requirements, to demonstrate that it is not necessary to use high-energy technology. This is how architecture urbanization studies and implementation can be used to reduce high-energy production needs. © 2019 Author(s)