Inter-ELM evolution of the edge current density profile on the ASDEX upgrade tokamak

The sudden decrease of plasma stored energy and subsequent power deposition on the first wall of a tokamak due to edge localised modes (ELMs) is potentially detrimental to the success of a future fusion reactor. Understanding and control of ELMs is critical for the longevity of these devices and also to maximise their performance. The commonly accepted picture of ELMs posits a critical pressure gradient and current density in the plasma edge, above which coupled magnetohy drodynamic peeling-ballooning modes become unstable. Much analysis has been presented in recent years on the spatial and temporal evolution of the edge pressure gradient. However, the edge current density has typically been overlooked due to the difficulties in measuring this quantity. In this thesis, a novel method of current density recovery is presented, using the equilibrium solver CLISTE to reconstruct a high resolution equilibrium utilising both external magnetic and internal edge kinetic data measured on the ASDEX Upgrade tokamak. The evolution of the edge current density relative to an ELM crash is presented, showing that a resistive delay in the buildup of the current density is unlikely. An uncertainty analysis shows that the edge current density can be determined with an accuracy consistent with that of the kinetic data used. A comparison with neoclassical theory demonstrates excellent agreement be- tween the current density determined by CLISTE and the calculated profiles. Three ELM mitigation regimes are investigated: Type-II ELMs, ELMs sup- pressed by external magnetic perturbations, and Nitrogen seeded ELMs. In the first two cases, the current density is found to decrease as mitigation on- sets, indicating a more ballooning-like plasma behaviour. In the latter case, the flux surface averaged current density can decrease while the local current density increases, providing a mechanism to suppress both the peeling and ballooning modes.

Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.