This thesis examines the structure and heating requirements of the outer atmospheres (the lower transition region, upper transition region and corona) of the five dwarfs χ¹ Ori (G0V), ϵ Eri (K2V), ξ Boo A (G8V), α Cen A (G2V) and α Cen B (K0V), and the sub-giant Procyon (F5 IV-V). Alternative fits to X-ray spectra of ten late-type dwarfs from ROSAT are made using the latest available versions of the radiative power loss codes of Raymond and Smith, Landini and Monsignori Fossi, and Mewe et al. Differences between these codes are found to arise from the choice of atomic physics and the number of transitions included. The resulting coronal temperatures and emission measures are found to follow correlations proposed by Montesinos and Jordan (1993). The lower transition region is modelled using observations made with the International Ultraviolet Explorer and up-to-date atomic data. Models of the upper transition region and corona are derived assuming a balance between the radiative and conductive losses. Wave pressure is included in these models for the first time. Recent observations with the Extreme Ultraviolet Explorer aid the choice of starting parameters. The calculations are carried out in plane parallel and spherically symmetric geometries. The models of the lower and upper transition region are then combined; the spherically symmetric models of the upper transition region fit more smoothly on to those of the lower transition region than do the plane parallel models. The new model of Procyon and new measurements of N_e resolve a previous discrepancy which led to suggestions that emission in the transition region is restricted in area. The heating requirements are examined. In the five dwarfs, but not in Procyon, the conductive fluxes at the base of the upper transition region are found to exceed the radiative energy losses for the layers immediately below. In Procyon, it is shown that acoustic wave heating is a viable mechanism for heating the lower transition region and corona, while the correlation of coronal properties with the dynamo Rossby number suggest that magnetic heating models are more likely for the five dwarfs.

Solutions of the magnetohydrodynamic (MHD) equations are very important for modelling laboratory, space and astrophysical plasmas, for example the solar and stellar coronae, as well as for modelling many of the dynamic processes that occur in these different plasma environments such as the fundamental process of magnetic reconnection. Our previous understanding of the behavior of plasmas and their associated dynamic processes has been developed through two-dimensional (2D) models. However, a more realistic model should be three-dimensional (3D), but finding 3D solutions of the MHD equations is, in general, a formidable task. Only very few analytical solutions are known and even calculating solutions with numerical methods is usually far from easy. In this thesis, 3D solutions which model magnetic reconnection and rigidly rotating magnetized coronae are presented. For magnetic reconnection, a 3D stationary MHD model is used. However, the complexity of the problem meant that so far no generic analytic solutions for reconnection in 3D exist and most work consists of numerical simulations. This has so far hampered progress in our understanding of magnetic reconnection. The model used here allows for analytic solutions at least up to a certain order of approximation and therefore gives some better insight in the significant differences between 2D and 3D reconnection. Three-dimensional numerical solutions are also obtained for this model. Rigidly rotating magnetized coronae, on the other hand, are modeled using a set of magnetohydrostatic (MHS) equations. A general theoretical framework for calculating 3D MHS solutions outside massive rigidly rotating central bodies is presented. Under certain assumptions, the MHS equations are reduced to a single linear partial differential equation referred to as the fundamental equation of the theory. As a first step, an illustrative case of a massive rigidly rotating magnetized cylinder is considered, which somehow allows for analytic solutions in a certain domain of validity. In general, the fundamental equation of the theory can only be solved numerically and hence numerical example solutions are presented. The theory is then extended to include a more realistic case of massive rigidly rotating spherical bodies. The resulting fundamental equation of the theory in this case is too complicated to allow for analytic solutions and hence only numerical solutions are obtained using similar numerical methods to the ones used in the cylindrical case.

I develop the first magnetospheric accretion model to take account of the observed complexity of T Tauri magnetic fields, and the influence of stellar coronae. It is now accepted that accretion onto classical T Tauri stars is controlled by the stellar magnetosphere, yet to date the majority of accretion models have assumed that the stellar magnetic field is dipolar. By considering a simple steady state accretion model with both dipolar and complex magnetic fields I find a correlation between mass accretion rate and stellar mass of the form M[dot above] proportional to M[asterisk subscript, alpha superscript], with my results consistent within observed scatter. For any particular stellar mass there can be several orders of magnitude difference in the mass accretion rate, with accretion filling factors of a few percent. I demonstrate that the field geometry has a significant effect in controlling the location and distribution of hot spots, formed on the stellar surface from the high velocity impact of accreting material. I find that hot spots are often at mid to low latitudes, in contrast to what is expected for accretion to dipolar fields, and that particularly for higher mass stars, accreting material is predominantly carried by open field lines. Material accreting onto stars with fields that have a realistic degree of complexity does so with a distribution of in-fall speeds. I have also modelled the rotational modulation of X-ray emission from T Tauri stars assuming that they have isothermal, magnetically confined coronae. By extrapolating from surface magnetograms I find that T Tauri coronae are compact and clumpy, such that rotational modulation arises from X-ray emitting regions being eclipsed as the star rotates. Emitting regions are close to the stellar surface and inhomogeneously distributed about the star. However some regions of the stellar surface, which contain wind bearing open field lines, are dark in X-rays. From simulated X-ray light curves, obtained using stellar parameters from the Chandra Orion Ultradeep Project, I calculate X-ray periods and make comparisons with optically determined rotation periods. I find that X-ray periods are typically equal to, or are half of, the optical periods. Further, I find that X-ray periods are dependent upon the stellar inclination, but that the ratio of X-ray to optical period is independent of stellar mass and radius. I also present some results that show that the largest flares detected on T Tauri stars may occur inside extended magnetic structures arising from the reconnection of open field lines within the disc. I am currently working to establish whether such large field line loops can remain closed for a long enough time to fill with plasma before being torn open by the differential rotation between the star and the disc. Finally I discuss the current limitations of the model and suggest future developments and new avenues of research.