235 research outputs found
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
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
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
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
Smooth metric measure spaces, quasi-Einstein metrics, and tractors
We introduce the tractor formalism from conformal geometry to the study of
smooth metric measure spaces. In particular, this gives rise to a
correspondence between quasi-Einstein metrics and parallel sections of certain
tractor bundles. We use this formulation to give a sharp upper bound on the
dimension of the vector space of quasi-Einstein metrics, providing a different
perspective on some recent results of He, Petersen and Wylie.Comment: 33 pages; final versio
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
Current Exchanges for Reducible Higher Spin Multiplets and Gauge Fixing
We compute the current exchanges between triplets of higher spin fields which
describe reducible representations of the Poincare group. Through this
computation we can extract the propagator of the reducible higher spin fields
which compose the triplet. We show how to decompose the triplet fields into
irreducible HS fields which obey Fronsdal equations, and how to compute the
current-current interaction for the cubic couplings which appear in
ArXiv:0708.1399 [hep-th] using the decomposition into irreducible modes. We
compare this result with the same computation using a gauge fixed (Feynman)
version of the triplet Lagrangian which allows us to write very simple HS
propagators for the triplet fields.Comment: 26 pages, 1 table; v3 some clarifications and references added, typos
corrected. Published versio
Holographic Description of Gravitational Anomalies
The holographic duality can be extended to include quantum theories with
broken coordinate invariance leading to the appearance of the gravitational
anomalies. On the gravity side one adds the gravitational Chern-Simons term to
the bulk action which gauge invariance is only up to the boundary terms. We
analyze in detail how the gravitational anomalies originate from the modified
Einstein equations in the bulk. As a side observation we find that the
gravitational Chern-Simons functional has interesting conformal properties. It
is invariant under conformal transformations. Moreover, its metric variation
produces conformal tensor which is a generalization of the Cotton tensor to
dimension . We calculate the modification of the holographic
stress-energy tensor that is due to the Chern-Simons term and use the bulk
Einstein equations to find its divergence and thus reproduce the gravitational
anomaly. Explicit calculation of the anomaly is carried out in dimensions
and . The result of the holographic calculation is compared with that of
the descent method and agreement is found. The gravitational Chern-Simons term
originates by Kaluza-Klein mechanism from a one-loop modification of M-theory
action. This modification is discussed in the context of the gravitational
anomaly in six-dimensional theory. The agreement with earlier
conjectured anomaly is found.Comment: 24 pages, Latex; presentation re-structured, new references adde
Equivalence of the coupled‐mode and Floquet‐Bloch formalisms in periodic optical waveguides
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