Aims. With strong evidence of fast and slow magnetoacoustic modes arising in the solar atmosphere there is scope for improved determinations of coronal parameters through coronal seismology. Of particular interest is the ratio P 1 /2P 2 between the period P 1 of the fundamental mode and the period P 2 of its first harmonic; in an homogeneous medium this ratio is one, but in a more complex configuration it is shifted to lower values. Methods. We consider analytically the effects on the different magnetohydrodynamic modes of structuring and stratification, pointing out that transverse or longitudinal structuring or gravitational stratification modifies the ratio P 1 /2P 2 . Results. The deviations caused by gravity and structure are studied for the fast and slow modes. Structure along the loop is found to be the dominant effect. Conclusions. The departure of P 1 /2P 2 from unity can be used as a seismological tool in the corona. We apply our technique to the observations by Verwichte et al. (2004), deducing the density scale height in a coronal loop.

Context. In transverse coronal loop oscillations, two periodicities have been measured simultaneously and are interpreted as the fundamental kink mode (with period P 1 ) and the first harmonic (with period P 2 ). Deviations of the period ratio P 1 /2P 2 from unity provide information about the extent of longitudinal structuring within the loop. Aims. Here we develop an analytical approximation that describes the shift in P 1 /2P 2 in terms of the ratio L/Λ c of the length 2L of a coronal loop and the density scale height Λ c . Methods. We study the MHD wave equations in a low β plasma using the thin tube approximation. Disturbances are described by a differential equation which may be solved for various equilibrium density profiles, obtaining dispersion relations in terms of Bessel functions. These dispersion relations may be used to obtain analytical approximations to the periods P 1 and P 2 . We also present a variational approach to determining the period ratio and show how the WKB method may be used. Results. Analytical approximations to the period ratio P 1 /2P 2 are used to shed light on the magnitude of longitudinal structuring in a loop, leading to a determination of the density scale height. We apply our formula to the observations in Verwichte et al. (2004) and Van Doorsselaere et al. (2007), obtaining the coronal density scale height. Conclusions. Our simple formula and approximate approaches highlight a useful analytical tool for coronal seismology. We demonstrate that P 1 /2P 2 is linked to the density scale height, with no need for estimates of other external parameters. Given the accuracy of current observations, our formula provides a convenient means of determining density scale heights.

The aim of this paper is two-fold: to increase the number of examples of observed longitudinal oscillations in coronal loops and to find evidence of the small temporal and spatial scales of these loop oscillations. Increasing the number of observed longitudinal oscillations allows for improvement in the statistics of the measured parameters, providing more accurate values for numerical and theoretical models. Furthermore, the small temporal and spatial scales of these loop oscillations could give indication of a driving force, symptomatic of coupling with the global p-modes. We found evidence that individual loop strands of wide coronal loop footpoints oscillate independently for short time periods. These strands have a diameter of the order of a few Mm, and the timescales on which the oscillations exist are typically less than an hour. We suggest that this is indicative of the oscillating strands being driven by the leakage of the global 5 min p-modes up into the corona, as simulated by The intensity oscillations travel outwards with a propagation speed of order v = 99.7 ± 3.9 km s −1 and they are of small amplitude, with variations of approximately 3.7 ± 0.2% of the background intensity. These disturbances are only detected for short distances, around 8.3 ± 0.6 Mm along the loops, and the main period of oscillation is around 300 s. A second peak of period was found at around 200 s, however no correlation with the presence of a sunspot was observed within this study. Using these measured parameters we have estimated the energy flux to be of order 313 ± 26 erg cm −2 s −1 .

The diffusion of innovation curve has become common parlance when considering the adoption of technology-enhanced learning in higher education. Innovators, early adopters, early majority, late majority and laggards indicate the different rates of technology adoption. This study explored the views and experiences of staff at one research-led institution within one of four colleges, to determine whether there were differences between the characteristics and digital academic practices of teachers, based on their self-identification as one of the five types in a questionnaire. Subsequently, two focus groups allowed comparisons between early adopters and early majority. The questionnaire found differences in terms of using a VLE to foster deep thinking through discussion, teachers’ digital practices and attributes, previous engagement with developmental TEL opportunities, perceived level of support from management, and perceived usefulness of CPD events. Focus groups revealed qualitative differences in terms of the amount of time participants invested in learning new technologies, sources of TEL support, preference for different types of academic development, and how they engaged with exemplars in their own or other disciplines. In addition to recommendations for different types of academic development for different groups, the study highlighted the importance of early adopters in leading digital practice. Institutions need to recognise and support the unique contribution made by early adopters. They contribute to the resilience, agility and digital capabilities of an institution in responding to rapid changes, such as the Covid19 pandemic, in terms of supporting and leading other staff, and prompting the institution to expand its digital education infrastructure.

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