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The phenomenon of quasi-periodic pulsations (QPPs) in solar and stellar flares has been known for over 50 years and significant progress has been made in this research area. It has become clear that QPPs are not rare—they are found in many flares and, therefore, robust flare models should reproduce their properties in a natural way. At least fifteen mechanisms/models have been developed to explain QPPs in solar flares, which mainly assume the presence of magnetohydrodynamic (MHD) oscillations in coronal structures (magnetic loops and current sheets) or quasi-periodic regimes of magnetic reconnection. We review the most important and interesting results on flare QPPs, with an emphasis on the results of recent years, and we present the predicted and prominent observational signatures of each of the fifteen mechanisms. However, it is not yet possible to draw an unambiguous conclusion as to the correct underlying QPP mechanism because of the qualitative, rather than quantitative, nature of most of the models and also due to insufficient observational information on the physical properties of the flare region, in particular the spatial structure of the QPP source. We also review QPPs in stellar flares, where progress is largely based on solar-stellar analogies, suggesting similarities in the physical processes in flare regions on the Sun and magnetoactive stars. The presence of QPPs with similar properties in solar and stellar flares is, in itself, a strong additional argument in favor of the likelihood of solar-stellar analogies. Hence, advancing our understanding of QPPs in solar flares provides an important additional channel of information about stellar flares. However, further work in both theory/simulations and in observations is needed.

Quasi-periodic, fast-mode propagating (QFP) wave trains in the corona have been studied intensively over the last decade, thanks to the full-disk, high spatio-temporal resolution, and wide-temperature coverage observations taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). In the AIA observations, the QFP wave trains are seen to consist of multiple coherent and concentric wavefronts emanating successively near the epicenter of the accompanying flares. They propagate outwardly either along or across coronal loops at fast-mode magnetosonic speeds from several hundred to more than 2000 km s −1 , and their periods are in the range of tens of seconds to several minutes. Based on the distinctly different properties of QFP wave trains, they might be divided into two distinct categories: narrow and broad ones. For most QFP wave trains, some of their periods are similar to those of the quasi-periodic pulsations (QPPs) in the accompanying flares, indicating that they are probably different manifestations of the same physical process. Currently, candidate generation mechanisms for QFP wave trains include two main categories: the pulsed energy excitation mechanism associated with magnetic reconnection and the dispersion-evolution mechanism related to the dispersive evolution of impulsively generated broadband perturbations. In addition, the generation of some QFP wave trains might be driven by the leakage of three- and five-minute oscillations from the lower atmosphere. As one of the discoveries of SDO, QFP wave trains provide a new tool for coronal seismology to probe the corona parameters, and they are also useful for diagnosing the generation of QPPs, flare processes including energy release, and particle acceleration. This review aims to summarize the main observational and theoretical results of spatially resolved QFP wave trains in extreme-ultraviolet observations and presents briefly a number of questions that deserve further investigation.

We analyse the phase shifts of standing, slow magnetohydrodynamic (MHD) waves in solar coronal loops using a linear MHD model taking into account the role of thermal conductivity, compressive viscosity, radiative losses, and heating–cooling misbalance. We estimate the phase shifts in time and space of density and temperature perturbations with respect to velocity perturbations and also calculate the phase difference between density and temperature perturbations. The overall significance of compressive viscosity is found to be negligible for most of the loops considered in the study. For loops with high background density and/or low background temperature, the role of radiative losses (with heating–cooling misbalance) is found to be more significant. Also, the effect of heating–cooling misbalance with a temperature- and density-dependent heating function is found to be more significant in the case of longer loop lengths ( L = 500  Mm). We derived a general expression for the polytropic index [ γ eff ] and found that under linear MHD the effect of compressive viscosity on the polytropic index is negligible. The radiative losses with constant heating lead to a monotonic increase of γ eff with increasing density, whereas the consideration of an assumed heating function [ H ( ρ , T ) ∝ ρ a T b , where a = − 0.5 and b = − 3 ] makes the γ eff peak at a certain loop density. We also explored the role of different heating functions by varying the free parameters a and b for a fixed loop of ρ 0 = 10 − 11  kg m −3 , T 0 = 6.3  MK, and loop length L = 180  Mm. We find that the consideration of different heating functions [ H ( ρ , T ) ] leads to a significant variation of the phase difference between density and temperature perturbations; however, the polytropic index remains close to a value of 1.66.

We study the phase shifts of propagating slow magnetoacoustic waves in solar coronal loops invoking the effects of thermal conductivity, compressive viscosity, radiative losses, and heating–cooling imbalance. We derive the general dispersion relation and solve it to determine the phase shifts of density and temperature perturbations relative to the velocity and their dependence on the equilibrium parameters of the plasma such as the background density [ ρ 0 ] and temperature [ T 0 ]. We estimate the phase difference [ Δ ϕ ] between density and temperature perturbations and its dependence on ρ 0 and T 0 . The role of radiative losses, along with the heating–cooling imbalance for an assumed specific heating function [ H ( ρ , T ) ∝ ρ − 0.5 T − 3 ], in the estimation of the phase shifts is found to be significant for the high-density and low-temperature loops. Heating–cooling imbalance can significantly increase the phase difference ( Δ ϕ ≈ 140 ∘ ) for the low-temperature loops compared to the constant-heating case ( Δ ϕ ≈ 30 ∘ ). We derive a general expression for the polytropic index [ ] using the linear MHD model. We find that in the presence of thermal conduction alone, remains close to its classical value 5 / 3 for all the considered ρ 0 and T 0 observed in typical coronal loops. We find that the inclusion of radiative losses (with or without heating–cooling imbalance) cannot explain the observed polytropic index under the considered heating and cooling models. To make the expected match the observed value of 1.1 ± 0.02 in typical coronal loops, the thermal conductivity needs to be enhanced by an order of magnitude compared to the classical value. However, this conclusion is based on the presented model and needs to be confirmed further by considering more realistic radiative functions. We also explore the role of different heating functions for typical coronal parameters and find that although the remains close to 5 / 3 , but the phase difference is highly dependent on the form of the heating function.

Magnetohydrodynamic (MHD) oscillatory processes in different plasma systems, such as the corona of the Sun and the Earth’s magnetosphere, show interesting similarities and differences, which so far received little attention and remain under-exploited. The successful commissioning within the past ten years of THEMIS, Hinode, STEREO and SDO spacecraft, in combination with matured analysis of data from earlier spacecraft (Wind, SOHO, ACE, Cluster, TRACE and RHESSI) makes it very timely to survey the breadth of observations giving evidence for MHD oscillatory processes in solar and space plasmas, and state-of-the-art theoretical modelling. The paper reviews several important topics, such as Alfvénic resonances and mode conversion; MHD waveguides, such as the magnetotail, coronal loops, coronal streamers; mechanisms for periodicities produced in energy releases during substorms and solar flares, possibility of Alfvénic resonators along open field lines; possible drivers of MHD waves; diagnostics of plasmas with MHD waves; interaction of MHD waves with partly-ionised boundaries (ionosphere and chromosphere). The review is mainly oriented to specialists in magnetospheric physics and solar physics, but not familiar with specifics of the adjacent research fields.

This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD) processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 10 32 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence), local enhancement of electric current in the corona (formation of a current sheet), and rapid dissipation of electric current (magnetic reconnection) that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely), while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.

This review examines recent theoretical developments in our understanding of turbulence in cold, non-magnetically active, planetesimal-forming regions of protoplanetary disks that we refer to throughout as \"Ohmic zones.\" We give a brief background introduction to the subject of disk turbulence followed by a terse pedagogical review of the phenomenology of hydrodynamic turbulence. The equations governing the dynamics of cold astrophysical disks are given and basic flow states are described. We discuss the Solberg-Høiland conditions required for stability, and the three recently identified turbulence-generating mechanisms that are possibly active in protoplanetary disk Ohmic zones: (i) the vertical shear instability, (ii) the convective overstability, and (iii) the zombie vortex instability. We summarize the properties of these processes, identify their limitations, and discuss where and under what conditions these processes are active in protoplanetary disk Ohmic zones.

In the present paper, we describe a 2.5D (two-and-a-half-dimensional) magnetohydrodynamic (MHD) simulation that provides a detailed picture of the evolution of cool jets triggered by initial vertical velocity perturbations in the solar chromosphere. We implement random multiple velocity, Vy, pulses of amplitude 20–50 km s−1 between 1 Mm and 1.5 Mm in the Sun’s atmosphere below its transition region (TR). These pulses also consist of different switch-off periods between 50 s and 300 s. The applied vertical velocity pulses create a series of magnetoacoustic shocks steepening above the TR. These shocks interact with each other in the inner corona, leading to complex localized velocity fields. The upward propagation of such perturbations creates low-pressure regions behind them, which propel a variety of cool jets and plasma flows in the localized corona. The localized complex velocity fields generate transverse oscillations in some of these jets during their evolution. We study the transverse oscillations of a representative cool jet J1, which moves up to the height of 6.2 Mm above the TR from its origin point. During its evolution, the plasma flows make the spine of jet J1 radially inhomogeneous, which is visible in the density and Alfvén speed smoothly varying across the jet. The highly dense J1, which is triggered along the significantly curved magnetic field lines, supports the propagating transverse wave of period of approximately 195 s with a phase speed of about 125 km s−1. In the distance–time map of density, it is manifested as a transverse kink wave. However, the careful investigation of the distance–time maps of the x- and z-components of velocity reveals that these transverse waves are actually of mixed Alfvénic modes. The transverse wave shows evidence of damping in the jet. We conclude that the cross-field structuring of the density and characteristic Alfvén speed within J1 causes the onset of the resonant conversion and leakage of the wave energy outward to dissipate these transverse oscillations via resonant absorption. The wave energy flux is estimated as approximately of 1.0 × 106 ergs cm−2 s−1. This energy, if it dissipates through the resonant absorption into the corona where the jet is propagated, is sufficient energy for the localized coronal heating.

The plasmasphere and plasma sheet are physically distinct but dynamically connected through global magnetospheric processes. Using a multifluid magnetohydrodynamic model including solar wind, ionospheric, and plasmaspheric H+ and O+ components, coupled with ring current and polar wind models, we simulate the 8 September 2017 storm. The modeled plasmaspheric density closely matches RBSP observations on the dayside. Plasmaspheric‐origin H+ contributes significantly to plasma sheet mass density throughout the storm and becomes a major pressure source during the early main phase, accounting for up to 60% of the total pressure in localized regions. This pressure dominance occurs when pre‐existing plasmaspheric ions, accumulated in the dawnside plasma sheet due to asymmetric erosion, are energized by storm‐time processes. As the plasmasphere becomes depleted and refilling lags behind convection, this contribution diminishes. These results reveal a previously underappreciated role of plasmaspheric‐origin ions in pressure dynamics and provide new insight into storm‐time mass and energy transport.

We investigate the transverse coronal-loop oscillations induced by the eruption of a prominence-carrying flux rope on 7 December 2012. The flux rope, originating from NOAA Active Region (AR) 11621, was observed in extreme-ultraviolet (EUV) wavelengths by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) spacecraft and in the H α line center by the ground-based telescope at the Big Bear Solar Observatory (BBSO). The early evolution of the flux rope is divided into two steps: a slow-rise phase at a speed of ≈ 230 km s −1 and a fast-rise phase at a speed of ≈ 706 km s −1 . The eruption generates a C5.8 flare and the onset of the fast rise is consistent with the hard X-ray (HXR) peak time of the flare. The embedded prominence has a lower speed of ≈ 452 km s −1 . The eruption is significantly inclined from the local solar normal by ≈ 60 ∘ , suggesting a typical non-radial eruption. During the early eruption of the flux rope, the nearby coronal loops are disturbed and experience independent kink-mode oscillations in the horizontal and vertical directions. The oscillation in the horizontal direction has an initial amplitude of ≈ 3.1 Mm, a period of ≈ 294 seconds, and a damping time of ≈ 645 seconds. It is most striking in 171 Å and lasts for three to four cycles. The oscillations in the vertical directions are observed mainly in 171, 193, and 211 Å. The initial amplitudes are in the range of 3.4 – 5.2 Mm, with an average value of 4.5 Mm. The periods are between 407 seconds and 441 seconds, with an average value of 423 seconds. The oscillations are damping and last for nearly four cycles. The damping times are in the range of 570 – 1012 seconds, with an average value of 741 seconds. Assuming a semi-circular shape of the vertically oscillating loops, we calculate the loop lengths according to their heights. Using the observed periods, we carry out coronal seismology and estimate the internal Alfvén speeds (988 – 1145 km s −1 ) and the magnetic-field strengths (12 – 43 G) of the oscillating loops.