RF power generation

This paper reviews the main types of r.f. power amplifiers which are, or may be, used for particle accelerators. It covers solid-state devices, tetrodes, inductive output tubes, klystrons, magnetrons, and gyrotrons with power outputs greater than 10 kW c.w. or 100 kW pulsed at frequencies from 50 MHz to 30 GHz. Factors affecting the satisfactory operation of amplifiers include cooling, matching and protection circuits are discussed. The paper concludes with a summary of the state of the art for the different technologies.Comment: 35 pages, contribution to the CAS - CERN Accelerator School: Specialised Course on RF for Accelerators; 8 - 17 Jun 2010, Ebeltoft, Denmar

Inter-ethnic Issues in Lorraine Hansberry\u27s The Sign in Sidney Brustein\u27s Window by Steven R. Carter

When Lorraine Hansberry\u27s second produced play, The Sign in Sidney Brustein\u27s Window, opened on Broadway in 1964, some white critics expressed surprise that her protagonist was Jewish rather than black and some blacks were disappointed or even outraged by this, feeling that she was deserting the cause and trying too hard to win acclaim as a universal writer.[1] Others from both groups, of course, warmly defended her

Recent developments in Vorton Theory

This article provides a concise overview of recent theoretical results concerning the theory of vortons, which are defined to be (centrifugally supported) equilibrium configurations of (current carrying) cosmic string loops. Following a presentation of the results of work on the dynamical evolution of small circular string loops, whose minimum energy states are the simplest examples of vortons, recent order of magnitude estimates of the cosmological density of vortons produced in various kinds of theoretical scenario are briefly summarised.Comment: 6 pages Latex. Contribution to 1996 Cosmology Meeting, Peyresq, Franc

Kink oscillations in magnetic tubes with twisted annulus

Aims.We study kink waves in a magnetic flux tube modelled as a straight core surrounded by a magnetically twisted annulus, both embedded in a straight ambient external field, and derive the dispersion relation for this configuration. Methods.The existence and behaviour of the kink modes are examined with specific attention to the effect that the addition of magnetic twist has on phase speeds and periods. Analytic expansions to the short and long wavelength approximations are also considered. Results.The magnetic twist is found to introduce of an infinite set of body modes into solutions of the dispersion relation not present in the untwisted case. Moreover, for the kink modes, the width of interval of this infinite set, generally found to occupy phase speeds around the annulus' longitudinal Alfvén speed, increases for longer wavelengths. Two surface modes are also present in the solution, one at each surface: the internal and the external edges of the annulus. The magnetic twist is found to increase or decrease the phase speeds of these surface modes that are depending on the ratio of internal and external Alfvén speeds in the flux tube. Conclusions.The magnetic twist of the annulus region of a flux tube is found to have a marked effect on the phase speeds of occurring modes. A straight annulus layer increased (or decreased) the periods of the surface modes for a tube modelled as a density (magnetic) enhancement. The addition of twist reduces the periods of the modes in both cases

Renormalisation of gravitational self interaction for wiggly strings

It is shown that for any elastic string model with energy density $U$ and tension $T$, the divergent contribution from gravitational self interaction can be allowed for by an action renormalisation proportional to $(U-T)^2$. This formula is applied to the important special case of a bare model of the transonic type (characterised by a constant value of the product $UT$) that represents the macroscopically averaged effect of shortwavelength wiggles on an underlying microscopic model of the Nambu-Goto type (characterised by $U=T$).Comment: 11 pages, Latex; original 8 page version extended to include estimates of relevant orders of magnitude. To be published in Physical Review,

Symplectic structure for elastic and chiral conducting cosmic string models

This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman and others in the context of field theory. After recalling the basic principles of this procedure, we construct the conserved bilinear symplectic current for generic elastic string models. These models describe current carrying cosmic strings evolving in an arbitrary curved background spacetime. Particular attention is paid to the special case of the chiral string for which the worldsheet current is null. Different formulations of the chiral string action are discussed in detail, and as a result the integrability property of the chiral string is clarified.Comment: 18 page

Cosmic Vortons and Particle Physics Constraints

We investigate the cosmological consequences of particle physics theories that admit stable loops of superconducting cosmic string - {\it vortons}. General symmetry breaking schemes are considered, in which strings are formed at one energy scale and subsequently become superconducting in a secondary phase transition at what may be a considerably lower energy scale. We estimate the abundances of the ensuing vortons, and thereby derive constraints on the relevant particle physics models from cosmological observations. These constraints significantly restrict the category of admissible Grand Unified theories, but are quite compatible with recently proposed effects whereby superconducting strings may have been formed close to the electroweak phase transition.Comment: 33 pages, 2 figures, RevTe

Poly-essential and general Hyperelastic World (brane) models

This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient type describable as hyperelastic, for which a complete set of equations of motion is provided just by the energy-momentum conservation law. Particular cases include those of a perfect fluid in quintessential backgrounds of various kinds, as well as models of the elastic solid kind that has been proposed to account for cosmic acceleration. It is shown how an appropriately generalised Hadamard operator can be used to construct a symplectic structure that controles the evolution of small perturbations, and that provides a characteristic equation governing the propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds. The special case of a poly-essential model - the k-essential analogue of an ordinary polytropic fluid - is examined and shown to be well behaved (like the fluid) only if the pressure to density ratio $w$ is positive.Comment: 16 pages Latex, Contrib. to 10th Peyresq Pysics Meeting, June 2005: Micro and Macro Structures of Spacetim

Convergence analysis of Crank-Nicolson and Rannacher time-marching

This paper presents a convergence analysis of Crank-Nicolson and Rannacher time-marching methods which are often used in finite difference discretisations of the Black-Scholes equations. Particular attention is paid to the important role of Rannacher's startup procedure, in which one or more initial timesteps use Backward Euler timestepping, to achieve second order convergence for approximations of the first and second derivatives. Numerical results confirm the sharpness of the error analysis which is based on asymptotic analysis of the behaviour of the Fourier transform. The relevance to Black-Scholes applications is discussed in detail, with numerical results supporting recommendations on how to maximise the accuracy for a given computational cost