Virtual dielectric waveguide mode description of a high-gain free-electron laser I: Theory

A set of mode-coupled excitation equations for the slowly-growing amplitudes of dielectric waveguide eigenmodes is derived as a description of the electromagnetic signal field of a high-gain free-electron laser, or FEL, including the effects of longitudinal space-charge. This approach of describing the field basis set has notable advantages for FEL analysis in providing an efficient characterization of eigenmodes, and in allowing a clear connection to free-space propagation of the input (seeding) and output radiation. The formulation describes the entire evolution of the radiation wave through the linear gain regime, prior to the onset of saturation, with arbitrary initial conditions. By virtue of the flexibility in the expansion basis, this technique can be used to find the direct coupling and amplification of a particular mode. A simple transformation converts the derived coupled differential excitation equations into a set of coupled algebraic equations and yields a matrix determinant equation for the FEL eigenmodes. A quadratic index medium is used as a model dielectric waveguide to obtain an expression for the predicted spot size of the dominant system eigenmode, in the approximation that it is a single gaussian mode.Comment: 14 page

Actors, Motivations and Outcomes in the Legislative Process: Policy Influence at Westminster

Legislatures in parliamentary systems are frequently seen as weak policy actors, and this is nowhere more true than of the British Westminster parliament. But real-world changes, and recent research, suggest that Westminster’s influence is significant and growing. This raises new questions about which non-government actors are influential, which we explore through analysing 4361 amendments proposed to 12 government bills. But assessing non-government amendment ‘success’ presents challenges, since many such proposals are clearly not sincere attempts at legislative change. We thus make two substantive contributions. First, we quantitatively assess the influence of different groups at Westminster, showing both non-government influence and cross-party working to be more extensive than traditionally assumed. Second, we link predictions about opposition and backbench parliamentarians’ motivations to the legislative amendment process, proposing a typology of motivations for such amendments, with wider application. Overall, we argue that understanding non-government parliamentarians’ diverse motivations shows that they ‘fail’ far less than commonly assumed

Does the executive dominate the Westminster legislative process?: Six reasons for doubt

The British Westminster parliament is frequently dismissed as a weak policy actor, in the face of dominant executive power. But through analysis of 4361 amendments to 12 government bills, and over 120 interviews, we suggest six reasons for doubting the orthodox view. These fall into three groups: overstating government success in making amendments, overstating non-government failure, and overlooking parliamentary influence before and after the formal passage of bills. We demonstrate that Westminster in fact has substantial influence in the policy process, not readily visible through commonly published data. Uncovering influence requires careful tracking of amendments, but also qualitative analysis of actors’ motivations and the power of ‘anticipated reactions’. Because Westminster is often seen as being at the weak end of a comparative spectrum of parliamentary influence, these results are important for demonstrating both the dynamics of British politics, and of parliamentary systems more broadly

A holonomy characterisation of Fefferman spaces

We prove that Fefferman spaces, associated to non--degenerate CR structures of hypersurface type, are characterised, up to local conformal isometry, by the existence of a parallel orthogonal complex structure on the standard tractor bundle. This condition can be equivalently expressed in terms of conformal holonomy. Extracting from this picture the essential consequences at the level of tensor bundles yields an improved, conformally invariant analogue of Sparling's characterisation of Fefferman spaces.Comment: AMSLaTeX, 15 page

Prolongations of Geometric Overdetermined Systems

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.Comment: 22 pages. In the second version, a comparison with the classical theory of prolongations was added. In this third version more details were added concerning our construction and especially the use of Kostant's computation of Lie algebra cohomolog

Sharp version of the Goldberg-Sachs theorem

We reexamine from first principles the classical Goldberg-Sachs theorem from General Relativity. We cast it into the form valid for complex metrics, as well as real metrics of any signature. We obtain the sharpest conditions on the derivatives of the curvature that are sufficient for the implication (integrability of a field of alpha planes)$\Rightarrow$(algebraic degeneracy of the Weyl tensor). With every integrable field of alpha planes we associate a natural connection, in terms of which these conditions have a very simple form.Comment: In this version we made a minor change in Remark 5.5 and simplified Section 6, starting at Theorem 6.

Local Unit Invariance, Back-Reacting Tractors and the Cosmological Constant Problem

When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.Comment: 20 pages, 2 figure

A classification of local Weyl invariants in D=8

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.Comment: LaTeX, 19 pages, typos corrected, one reference adde

Alien Registration- Gover, James D. (Houlton, Aroostook County)

https://digitalmaine.com/alien_docs/36186/thumbnail.jp

Simulation of Coherent Diffraction Radiation Generation by Pico-Second Electron Bunches in an Open Resonator

In this report we present new approach for calculation of processes of diffraction radiation generation, storage and decay in an open resonator based on generalized surface current method. The radiation characteristics calculated using the developed approach were compared with those calculated using Gaussian-Laguerre modes method. The comparison shows reasonable coincidence of the results that allows to use developed method for investigation of more complicated resonators