To obtain meaningful diagnostic measurements of hot solar plasmas requires that we must extract the greatest amount of physical information from remotely sensed data whilst differentiating between its information and noise content. The inference of 'reliable' plasma structure models from the data relies heavily upon the inferential 'inversion' method used. Such inversion methods allows us to infer the likely form of the underlying physical source model from the data and theoretical estimates of the emission processes taking place. It is widely known that such 'inverse problems' can give rise to highly ambiguous (non-unique) solutions when errors are present in the observed data. Clearly, an understanding of such inverse approaches and the propagation of errors in data, and in the emission rates involved, through to the final solution is paramount in obtaining useful diagnostic measurements. The work presented here addresses inversion formalisms and their application in the face of typical data and emission model uncertainties. This thesis presents results in a field of study where the uncertainties associated with remote sensing and inverse methodology can run amok if not carefully treated: the inference of the electron density and temperature distribution of the highly inhomogeneous plasmas of the upper solar atmosphere. In Chapter 1 a brief description is given of the solar atmosphere and why it is best to observe its hotter regions from space. We continue, in Chapter 2, by presenting the necessary theoretical and numerical tools required to understand inverse problems and to make reliable estimates of the underlying plasma structure using such inverse techniques. Chapter 3 digresses from the main theme to introduce an important data analysis tool which is used extensively in the later chapters of this thesis; the Genetic Algorithm (GA). The flexibility of the GA method is clearly demonstrated therein. As an example we discuss the Gaussian fitting GA (Ga-GA) and its application to the decomposition of real and synthetic emission line spectra.In Chapter 4 we discuss the ill-posed inference of plasma diagnostic distributions from emission line intensities and ratios. These distributions are widely known as the Differential Emission Measure functions, or DEMs for short. In Section 4.1 we demonstrate that there is a formal relationship between the 'spectroscopic mean values' of ng, Te obtained using line ratios and their respective DEM functions xi(Te) and zeta(ne) with an extension to mu(ne,Te) (the general bivarate DEM function) where mean values of ne and Tg are simultaneously defined. Following this, in Section 4.2, we develop an entirely novel GA based technique (the Ratio Inversion Technique; RIT), by which we are able to ascertain these diagnostic distributions to a higher degree of uniqueness than methods used previously. In particular, the RIT proves to be quite insensitive to the theoretical uncertainties in the atomic emission models used; which posed a major difficulty in the intensity inversions of previous authors. In Chapter 5 we present another GA based method (SELECTOR) to overcome the serious numerical instability of inferred DEM functions when noise is present in the observed emission line intensities. We show that the impact of this data noise on the poorly conditioned DEM inversions is dramatically reduced by isolating a subset of emission lines (in the wavelength range of the CDS and SUMER instruments of the ESA/NASA Solar and Heliospheric Observatory - SOHO - satellite) that improve the conditioning of the DEM inverse problems. Chapter 6 draws together the points raised and conclusions reached in the preceding chapters and briefly discusses possible improvements, extensions and future applications of the methods introduced. This study is considered to be both valuable and timely given the increased usage of inverse diagnostics from the high quality data acquired by instruments onboard the aforementioned SOHO satellite.
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