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The paper develops a Model Predictive Controller for constrained control of spacecraft attitude with reaction wheel actuators. The controller exploits a special formulation of the cost with the reference governor like term, a low complexity addition of integral action to guarantee offset-free tracking of attitude set points, and an online optimization algorithm for the solution of the Quadratic Programming problem which is tailored to run in fixed-point arithmetic. Simulations on a nonlinear spacecraft model demonstrate that the MPC controller achieves good tracking performance while satisfying reaction wheel torque constraints. The controller also has low computational complexity and is suitable for implementation in spacecrafts with fixed-point processors.

We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope (DRE), whose stationary points correspond to the solutions of the original (possibly nonsmooth) problem. By proving the equivalence between the Douglas-Rachford splitting method and a scaled gradient method applied to the DRE, results from smooth unconstrained optimization are employed to analyze convergence properties of DRS, to tune the method and to derive an accelerated version of it.

A three-dimensional (3D) reconstruction of the 2007, May 20 partial-halo Coronal Mass Ejection (CME) has been made using STEREO/EUVI and STEREO/COR1 coronagraphic images. The trajectory and kinematics of the erupting filament have been derived from EUVI image pairs with the "tie-pointing" triangulation technique, while the polarization ratio technique has been applied to COR1 data to determine the average position and depth of the CME front along the line of sight. These 3D geometrical information have been combined for the first time with spectroscopic measurements of the OVI $\lambda\lambda$1031.91, 1037.61 \AA\ line profiles made with the Ultraviolet Coronagraph Spectrometer (UVCS) on board SOHO. Comparison between the prominence trajectory extrapolated at the altitude of UVCS observations and the core transit time measured from UVCS data made possible a firm identification of the CME core observed in white light and UV with the prominence plasma expelled during the CME. Results on the 3D structure of the CME front have been used to calculate synthetic spectral profiles of the OVI $\lambda\lambda1031.91$ \AA\ line expected along the UVCS slit, in an attempt to reproduce the measured line widths. Observed line widths can be reproduced within the uncertainties only in the peripheral part of the CME front; at the front center, where the distance of the emitting plasma from the plane of the sky is greater, synthetic widths turn out to be $\sim 25$% lower than the measured ones. This provides strong evidence of line broadening due to plasma heating mechanisms in addition to bulk expansion of the emitting volume.

In this work UV and white light (WL) coronagraphic data are combined to derive the full set of plasma physical parameters along the front of a shock driven by a Coronal Mass Ejection. Pre-shock plasma density, shock compression ratio, speed and inclination angle are estimated from WL data, while pre-shock plasma temperature and outflow velocity are derived from UV data. The Rankine-Hugoniot (RH) equations for the general case of an oblique shock are then applied at three points along the front located between $2.2-2.6$ R$_\odot$ at the shock nose and at the two flanks. Stronger field deflection (by $\sim 46^\circ$), plasma compression (factor $\sim 2.7$) and heating (factor $\sim 12$) occur at the nose, while heating at the flanks is more moderate (factor $1.5-3.0$). Starting from a pre-shock corona where protons and electrons have about the same temperature ($T_p \sim T_e \sim 1.5 \cdot 10^6$ K), temperature increases derived with RH equations could better represent the protons heating (by dissipation across the shock), while the temperature increase implied by adiabatic compression (factor $\sim 2$ at the nose, $\sim 1.2-1.5$ at the flanks) could be more representative of electrons heating: the transit of the shock causes a decoupling between electron and proton temperatures. Derived magnetic field vector rotations imply a draping of field lines around the expanding flux rope. The shock turns out to be super-critical (sub-critical) at the nose (at the flanks), where derived post-shock plasma parameters can be very well approximated with those derived by assuming a parallel (perpendicular) shock., Comment: 29 pages, 7 figures, accepted for publication on ApJ

This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the second one combines the global efficiency estimates of the corresponding first-order methods, while achieving fast asymptotic convergence rates. Furthermore, they are computationally attractive since each Newton iteration requires the approximate solution of a linear system of usually small dimension.

Placed at L4, Sun Chaser is a mission concept that will follow (or chase) high-energy processes around the west limb, combining solar remote sensing & in situ observations, and overseeing the entire solar radiation hemisphere. Sun Chaser’s remote sensing is essential for ~90% of current physics-based and empirical solar energetic particle (SEP) event forecasting techniques. Without Sun Chaser, there cannot be a basis for SEP event all-clear forecasting. It establishes and maintains a space weather (SWx) radiation safe zone that supports all near-term human missions to the Moon and Mars. Sun Chaser latitude in-situ coverage also provides a unique opportunity for solar wind-, interplanetary- and interstellar-dust science. In combination with existing and planned observatories at L1 and L5, the three locations provide 240° longitude coverage of resolving photospheric magnetic field structure and safe Earth-directed CME viewing. A ~14°-inclination of both L4 and L5 out of the ecliptic guarantees continuous viewing of both solar poles and continuous in-situ presence on both sides of the heliographic equator, with >3.6° elevation. Extended observations in both longitude and latitude will revolutionize global solar wind modeling and immediate validation, and enables the development of local helioseismology, with potential for long-term solar activity forecasting.

In this work we study the kinematics of three small-scale (0.01 R$_\odot$) blobs of chromospheric plasma falling back to the Sun after the huge eruptive event of June 7, 2011. From a study of 3-D trajectories of blobs made with the Solar TErrestrial RElations Observatory (STEREO) data, we demonstrate the existence of a significant drag force acting on the blobs and calculate two drag coefficients, in the radial and tangential directions. The resulting drag coefficients $C_D$ are between 0 and 5, comparable in the two directions, making the drag force only a factor of 0.45-0.75 smaller than the gravitational force. To obtain a correct determination of electron densities in the blobs, we also demonstrate how, by combining measurements of total and polarized brightness, the H$\alpha$ contribution to the white-light emission observed by the COR1 telescopes can be estimated. This component is significant for chromospheric plasma, being between 95 and 98 % of the total white-light emission. Moreover, we demonstrate that the COR1 data can be employed even to estimate the H$\alpha$ polarized component, which turns out to be in the order of a few percent of H$\alpha$ total emission from the blobs. If the drag forces acting on small-scale blobs reported here are similar to those that play a role during the CME propagation, our results suggest that the magnetic drag should be considered even in the CME initiation modelling.

We studied the radiative muon decay $\mu^+ \to e^+\nu\bar{\nu}\gamma$ by using for the first time an almost fully polarized muon source. We identified a large sample (~13000) of these decays in a total sample of 1.8x10^14 positive muon decays collected in the MEG experiment in the years 2009--2010 and measured the branching ratio B($\mu^+ \to e^+\nu\bar{\nu}\gamma$) = (6.03+-0.14(stat.)+-0.53(sys.))x10^-8 for E_e > 45 MeV and E_{\gamma} > 40 MeV, consistent with the Standard Model prediction. The precise measurement of this decay mode provides a basic tool for the timing calibration, a normalization channel, and a strong quality check of the complete MEG experiment in the search for $\mu^+ \to e^+\gamma$ process., Comment: 8 pages, 7 figures. Added an introduction to NLO calculation which was recently calculated. Published version

High spatial- and temporal-resolution images of coronal hole regions show a dynamical environment where mass flows and jets are frequently observed. These jets are believed to be important for the coronal heating and the acceleration of the fast solar wind. We studied the dynamics of two jets seen in a polar coronal hole with a combination of imaging from EIS and XRT onboard Hinode. We observed drift motions related to the evolution and formation of these small-scale jets, which we tried to model as well. We found observational evidence that supports the idea that polar jets are very likely produced by multiple small-scale reconnections occurring at different times in different locations. These eject plasma blobs that flow up and down with a motion very similar to a simple ballistic motion. The associated drift speed of the first jet is estimated to be $\approx$ 27 km s$^{-1}$. The average outward speed of the first jet is $\approx 171$ km s$^{-1}$, well below the escape speed, hence if simple ballistic motion is considered, the plasma will not escape the Sun. The second jet was observed in the south polar coronal hole with three XRT filters, namely, C$_{-}$poly, Al$_{-}$poly, and Al$_{-}$mesh filters. We observed that the second jet drifted at all altitudes along the jet with the same drift speed of $\simeq$ 7 km s$^{-1}$. The enhancement in the light curves of low-temperature EIS lines in the later phase of the jet lifetime and the shape of the jet's stack plots suggests that the jet material is falls back, and most likely cools down. To support this conclusion, the observed drifts were interpreted within a scenario where reconnection progressively shifts along a magnetic structure, leading to the sequential appearance of jets of about the same size and physical characteristics. On this basis, we also propose a simple qualitative model that mimics the observations., Comment: Accepted Astronomy and Astrophysics

Off-limb observations of the solar corona after Coronal Mass Ejections (CMEs) often show strong, compact, and persistent UV sources behind the eruption. They are primarily observed by the SOHO/UVCS instrument in the "hot" Fe XVIII {\lambda}974 {\AA} line and are usually interpreted as a signature of plasma heating due to magnetic reconnection in the post-CME Current Sheet (CS). Nevertheless, the physical process itself and the altitude of the main energy release are currently not fully understood. In this work, we studied the evolution of plasma heating after the CME of 2004 July 28 by comparing UV spectra acquired by UVCS with soft X-ray (SXR) and hard X-ray (HXR)images of the post-flare loops taken by GOES/SXI and RHESSI. The X-ray data show a long-lasting extended source that is rising upwards, toward the high-temperature source detected by UVCS. UVCS data show the presence of significant non-thermal broadening in the CS (signature of turbulent motions) and a strong density gradient across the CS region. The thermal energy released in the HXR source is on the order of about 10^32 erg, a factor about 2-5 larger than the energy required to explain the high-temperature plasma sampled by UVCS. Nevertheless, the very different time evolutions of SXR and HXR sources compared to the UV emission suggest that reconnection occurring above the post-eruption arcades are not directly responsible for the high-temperature plasma sampled higher up by UVCS. We conclude that an additional plasma heating mechanism (such as turbulent reconnection) in the CS is likely required.

The MEG (Mu to Electron Gamma) experiment has been running at the Paul Scherrer Institut (PSI), Switzerland since 2008 to search for the decay \meg\ by using one of the most intense continuous $\mu^+$ beams in the world. This paper presents the MEG components: the positron spectrometer, including a thin target, a superconducting magnet, a set of drift chambers for measuring the muon decay vertex and the positron momentum, a timing counter for measuring the positron time, and a liquid xenon detector for measuring the photon energy, position and time. The trigger system, the read-out electronics and the data acquisition system are also presented in detail. The paper is completed with a description of the equipment and techniques developed for the calibration in time and energy and the simulation of the whole apparatus., Comment: 59 pages, 90 figures

The analysis of a combined data set, totaling 3.6 \times 10^14 stopped muons on target, in the search for the lepton flavour violating decay mu^+ -> e^+ gamma is presented. The data collected by the MEG experiment at the Paul Scherrer Institut show no excess of events compared to background expectations and yield a new upper limit on the branching ratio of this decay of 5.7 \times 10^-13 (90% confidence level). This represents a four times more stringent limit than the previous world best limit set by MEG., Comment: 5 pages, 3 figures, a version accepted in Phys. Rev. Lett

White-light coronagraphic images of Coronal Mass Ejections (CMEs) observed by SOHO/LASCO C2 have been used to estimate the density jump along the whole front of two CME-driven shocks. The two events are different in that the first one was a "radio-loud" fast CME, while the second one was a "radio quiet" slow CME. From the compression ratios inferred along the shock fronts, we estimated the Alfv\'en Mach numbers for the general case of an oblique shock. It turns out that the "radio-loud" CME shock is initially super-critical around the shock center, while later on the whole shock becomes sub-critical. On the contrary, the shock associated with the "radio-quiet" CME is sub-critical at all times. This suggests that CME-driven shocks could be efficient particle accelerators at the shock nose only at the initiation phases of the event, if and when the shock is super-critical, while at later times they lose their energy and the capability to accelerate high energetic particles., Comment: 7 pages, 5 figures. In press on the "Journal of Advanced Research", Cairo University Press

Shocks driven by Coronal Mass Ejections (CMEs) are primary agents of space weather. They can accelerate particles to high energies and can compress the magnetosphere thus setting in motion geomagnetic storms. For many years, these shocks were studied only in-situ when they crossed over spacecraft or remotely through their radio emission spectra. Neither of these two methods provides information on the spatial structure of the shock nor on its relationship to its driver, the CME. In the last decade, we have been able to not only image shocks with coronagraphs but also measure their properties remotely through the use of spectroscopic and image analysis methods. Thanks to instrumentation on STEREO and SOHO we can now image shocks (and waves) from the low corona, through the inner heliosphere, to Earth. Here, we review the progress made in imaging and analyzing CME-driven shocks and show that joint coronagraphic and spectrscopic observations are our best means to understand shock physics close to the Sun., Comment: 6 pages, 3 figures

Between February 24-25, 2009, the EIS spectrometer onboard the Hinode spacecraft performed special "sit & stare" observations above the South polar coronal hole continuously over more than 22 hours. Spectra were acquired with the 1" slit placed off-limb covering altitudes up to 0.48 R$_\odot$ ($3.34\times 10^2$ Mm) above the Sun surface, in order to study with EIS the non-thermal spectral line broadenings. Spectral lines such as Fe {\sc xii} $\lambda$186.88, Fe {\sc xii} $\lambda$193.51, Fe {\sc xii} $\lambda$195.12 and Fe {\sc xiii} $\lambda$202.04 are observed with good statistics up to high altitudes and they have been analyzed in this study. Results show that the FWHM of Fe {\sc xii} $\lambda$195.12 line increases up to $\simeq 0.14$ R$_\odot$, then decreases higher up. EIS stray light has been estimated and removed. Derived electron density and non-thermal velocity profiles have been used to estimate the total energy flux transported by Alfv\'en waves off-limb in polar coronal hole up to $\simeq 0.4$ R$_\odot$. The computed Alfv\'en wave energy flux density $f_w$ progressively decays with altitude from $f_w \simeq 1.2 \cdot 10^6$ erg cm$^{-2}$ s$^{-1}$ at 0.03 R$_\odot$ down to $f_w \simeq 8.5 \cdot 10^3$ erg cm$^{-2}$ s$^{-1}$ at 0.4 R$_\odot$, with an average energy decay rate $\Delta f_w / \Delta h \simeq -4.5 \cdot 10^{-5}$ erg cm$^{-3}$ s$^{-1}$. Hence, this result suggests energy deposition by Alfv\'en waves in a polar coronal hole, thus providing a significant source for coronal heating., Comment: Physical units of the Alfv\'en wave Energy Decay Rate $\Delta f_w / \Delta h$ revised with respect to the published version. Scientific results and conclusions unchanged