We study kink waves and oscillations in a thin expanding magnetic tube in the presence of flow. The tube consists of a core region and a thin transitional region at the tube boundary. In this region the plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using the multiscale expansions we derive the system of two equations describing the kink oscillations. When there is no transitional layer the oscillations are described by the first of these two equations. We use this equation to study the effect of plasma density variation with time on kink oscillations of an expanding tube with a sharp boundary. We assume that the characteristic time of the density variation is much greater than the characteristic time of kink oscillations. Then we use the Wentzel-Kramer-Brillouin (WKB) method to derive the expression for the adiabatic invariant, which is the quantity that is conserved when the plasma density varies. The general theoretical results are applied to the kink oscillations of coronal magnetic loops. We consider an expanding loop with the half-circle shape and assume that the plasma temperature inside a loop decays exponentially with time. We numerically calculated the dependences of the fundamental mode frequency, the ratio of frequencies of the first overtone and fundamental mode, and the oscillation amplitude on time. We obtained that the oscillation frequency and amplitude increase and the frequency ratio decreases due to cooling. The amplitude increase is stronger for loops with a greater expansion factor. This effect is also more pronounced for higher loops. However, it is fairly moderate even for loops that are quite high.

Energy consumption of households is not evenly distributed. To satisfy peak demand, additional CO 2 intensive generators are turned on when demand peaks. To avoid peak demand from dwellings, the RED WoLF (Rethink Electricity Distribution Without Load Following) hybrid storage system is proposed, consisting of batteries, storage heaters and a water cylinder. This aims at avoiding the use of these peak generators and integrating a higher share of renewables on the Power Grid. This system is planned to be tested in 100 houses distributed in 6 pilot sites in Great Britain, Ireland and France, which are currently undergoing construction or refurbishment. This study presents the theoretical model of the controlling algorithm, which enables the uptake of Grid electricity only when CO 2 intensity is below a dynamically computed threshold. The algorithm is tested in computer simulations over the four seasons with varying size of batteries and photovoltaic arrays. Results show how RED WoLF algorithm satisfies households demands while, at the same time, successfully avoiding domestic peak demand, with a significant drop of CO 2 emissions. This is achieved by both increasing photovoltaic self-consumption and uptake of low carbon Grid energy. For example, with a 7 kWh battery and a 4 kW photovoltaic array, CO 2 emissions drop by 30% to almost 100%, depending on the season, relative to the same house without the RED WoLF system. The system has the potential to shift residential demand from peak power/peak times to low value electricity at a time of low demand.

Ever since their detection two decades ago, standing kink oscillations in coronal loops have been extensively studied both observationally and theoretically. Almost all driven coronal loop oscillations (e.g., by flares) are observed to damp through time often with Gaussian or exponential profiles. Intriguingly, however, it has been shown theoretically that the amplitudes of some oscillations could be modified from Gaussian or exponential profiles if cooling is present in the coronal loop systems. Indeed, in some cases the oscillation amplitude can even increase through time. In this article, we analyse a flare-driven coronal loop oscillation observed by the Solar Dynamics Observatory's Atmospheric Imaging Assembly (SDO/AIA) in order to investigate whether models of cooling can explain the amplitude profile of the oscillation and whether hints of cooling can be found in the intensity evolution of several SDO/AIA filters. During the oscillation of this loop system, the kink mode amplitude appears to differ from a typical Gaussian or exponential profile with some hints being present that the amplitude increases. The application of cooling coronal loop modelling allowed us to estimate the density ratio between the loop and the background plasma, with a ratio of between 2.05-2.35 being returned. Overall, our results indicate that consideration of the thermal evolution of coronal loop systems can allow us to better describe oscillations in these structures and return more accurate estimates of the physical properties of the loops (e.g., density, scale height, magnetic field strength).

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We have considered resonant damping of kink oscillations of cooling and expanding coronal magnetic loops. We derived an evolutionary equation describing the dependence of the oscillation amplitude on time. When there is no resonant damping, this equation reduces to the condition of conservation of a previously derived adiabatic invariant. We used the evolutionary equation describing the amplitude to study the competition between damping due to resonant absorption and amplification due to cooling. Our main aim is to investigate the effect of loop expansion on this process. We show that the loop expansion acts in favour of amplification. We found that, when there is no resonant damping, the larger the loop expansion the faster the amplitude growths. When the oscillation amplitude decays due to resonant damping, the loop expansion reduces the damping rate. For some values of parameters the loop expansion can fully counterbalance the amplitude decay and turn the amplitude evolution into amplification.

We study the resonant damping of kink oscillations of thin expanding magnetic flux tubes. The tube consists of a core region and a thin transitional region at the tube boundary. The resonance occurs in this transitional layer where the oscillation frequency coincides with the local Alfvén frequency. Our investigation is based on the system of equations that we previously derived. This system is not closed because it contains the jumps of the magnetic pressure perturbation and plasma displacement across the transitional layer. We calculate these jumps and thus close the system. We then use it to determine the decrements of oscillation eigenmodes. We introduce the notion of homogeneous stratification. In accordance with this condition the ratio of densities in the tube core and outside the tube does not vary along the tube, while the density in the transitional layer can be factorised and written as a product of two function, one depending on the variable along the tube and the other on the magnetic flux function. Our main result is that, under the condition of homogeneous stratification, the ratio of the decrement to the oscillation frequency is independent of a particular form of the density variation along the tube. This ratio is also the same for all oscillation eigenmodes.

Propagating kink waves have been observed in many magnetic waveguides in the solar atmosphere, like coronal magnetic loops, spicules, and fine structures of prominences. There are also observational evidences that these waves are damped. At present resonant absorption is considered as the most likely candidate for explaining this damping. First the attenuation of propagating kink waves due to resonant absorption was studied using the simplest model with a straight magnetic tube and the density only varying in the radial direction. Later a more advanced model with the density also varying along the tube was used. It was shown that the variation of the wave amplitude along the tube is determined by the combined effect of resonant damping and the longitudinal density variation. In our article we extend the analysis of resonant damping of propagating kink waves to take into account the magnetic loop expansion. We also consider non-stationary magnetic tubes to model, for example, cooling coronal loops. In particular, we found that cooling enhances the wave amplitude and the loop expansion makes this effect more pronounced.

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