Cyclotron resonance masers (CRMs) are important devices for the generation of high power electromagnetic radiation in the millimetre and sub-millimetre region of the electromagnetic spectrum. In these devices, an electromagnetic wave is amplified by its interaction with a beam of relativistic electrons gyrating in a magnetostatic field. This thesis presents the results of novel theoretical investigations into the physical processes which occur in a CRM amplifier. The basis of these investigations was a system of universally scaled evolution equations which describe the linear and nonlinear evolution of the CRM interaction. These equations involve a minimum number of free parameters and allow a general analysis of the interaction. By considering various limits of the free parameters, the physical processes which occur in the steady-state limit were identified and studied using numerical analysis and an extensive linear analysis based on the method of collective variables. Neglecting the recoil of the electrons, it was shown that the universally scaled evolution equations could be written as a set of Hamilton's equations. The behaviour of this Hamiltonian system was investigated via a phase space analysis for some specific cases of the free parameters. In addition, it was shown that it is possible to approximately describe the evolution of the electromagnetic field up to saturation in a CRM amplifier by an analytically solveable Landau-Ginzburg equation. Including slippage effects, it was shown that for electron beams with relativistic axial velocities, in addition to the steady-state evolution of the electromagnetic field, superradiant field evolution could also occur. Superradiant phenomena were studied using an heuristic dissipative model, an extensive linear analysis and a nonlinear numerical analysis. The existence of weak superradiance, involving short electron pulses and low radiation intensities, and strong superradiance, involving long electron pulses and high intensity spikes of radiation, was demonstrated.

No description available.

No description available.

We compute the two-loop contributions to the free energy in the null compacti¯cation of perturbative string theory at ¯nite temperature. The cases of bosonic, Type II and heterotic strings are all treated. The calculation exploits an explicit reductive parametrization of the moduli space of in¯nite-momentum frame string worldsheets in terms of branched cover instantons. Various arithmetic and physical properties of the instanton sums are described. Applications to symmetric product orbifold conformal ¯eld theories and to the matrix string theory conjecture are investigated by analyzing the correspondence be- tween the two-loop thermal partition function of DLCQ strings in °at space and the integrated two-point correlator of twist ¯elds in a symmetric product orbifold con- formal ¯eld theory at one-loop order. This is carried out by deriving combinatorial expressions for generic twist ¯eld correlation functions in permutation orbifolds us- ing the covering surface method, by deriving the one-loop modi¯cation of the twist ¯eld interaction vertex, and by relating the two-loop ¯nite temperature DLCQ string theory to the theory of Prym varieties for genus two covers of an elliptic curve. The case of bosonic Z2 orbifolds is worked out explicitly and precise agreement between both amplitudes is found. We use these techniques to derive explicit expressions for Z2 orbifold spin twist ¯eld correlation functions in the Type II and heterotic string theories.

Theories which have a dimensional coupling constant are generally considered non-renormalisable unless the loop diagrams are free of ultra-violet divergences. In this work we investigate two theories in higher dimensions which have (positive) dimensionful coupling constants; Yang-Mills theory and gravity. We calculate the ultra-violet infinities associated with the one-loop four-point on-shell amplitudes using two methods which are more efficient than a Feynman diagram approach, these are the Cutkosky cutting technique and the Bern-Kosower string based rules. Dimensional regularisation is used to regulate the integrals and so the infinities only appear in even dimensions (at one-loop). Different particle types are considered circulating within the loop and the counterterms necessary to render these theories one-loop finite are determined for different dimensions. For the Yang-Mills case, we calculate the infinities associated with one-loop amplitudes with external gluons and consider scalars, fermions and gluons within the loop. These are determined for six, eight and ten dimensions and we find that supersymmetric combinations within the loop do, in general, simplify the counterterm structure and for six dimensions the counterterm vanishes. For gravity in six dimensions we consider one-loop amplitudes with combinations of external gravitons and two-forms and extract the infinities of these. We find that again in six dimensions and counterterm for supersymmetric matter within the loop is zero. In eight dimensions we investigate one-loop amplitudes with external gravitons and determine the counterterm structure for various particles within the loop. Supersymmetry does simplify the counterterm structure, but they do not vanish. We have also included more one-loop amplitudes than are necessary to determine the counterterms in order to provide a database for others.

No description available.

No description available.

No description available.

No description available.

No description available.