Design,construction and characterization of the compact ultrafast terahertz free-electron laser undulator

A compact ultrafast terahertz (CUTE) free-electron laser (FEL) is being developed at the Raja Ramanna Centre for Advanced Technology (RRCAT), Indore. The undulator required for the CUTE-FEL has recently been developed. We have designed, built and characterized a variable gap, 5 cm period, 2.5 m long pure permanent magnet undulator in two identical segments. The tolerable error in the magnetic field was 1% in rms, and we have measured it to be 0.7%. The obtained rms phase shake is around 2°. To ensure that the trajectories do not have an exit error in position or angle, corrector coils have been designed. Shimming coils have been applied for both the undulator segments to reduce the amplitude of the betatron oscillations in the vertical trajectory. Details of novel corrector coils and soft iron shims are given and their performance is discussed.      

Asymptotic behavior of the pion electromagnetic form factors in Bethe-Salpeter model

Asymptotic behavior of the pion form factors has been discussed treating pion as a bound state of the elementary nucleon and antinucleon system. The matrix-element of the electromagnetic current is written in terms of the Bethe-Salpeter amplitude for the nucleon-antinucleon bound system. Using suitable approximations the Bethe-Salpeter equation for nucleon-antinucleon bound state with nucleons as Dirac spinors has been solved and the corresponding off-shell pion form factors are determined. The form factors are strongly interaction dependent. For coupling $\text{g}{}^2\text{16π}{}^2\text{=}\text{15}\text{4}$ the form factors vanish asymptotically like t^?1 and for $\text{14}\text{4}\text{<}\text{g}{}^2\text{16π}{}^2\text{<}\text{15}\text{4}$ the form factors still vanish but less rapidly than t^?1.     

Topical issue on Geometry, Integrability and Nonlinearity in Condensed Matter Physics

Recent developments in the study of nonlinear phenomena have led to the realization that a combination of the concepts of integrability, geometry and topology provides a new powerful framework for describing a great variety of physical systems. It was therefore felt that the compilation of a special issue comprising articles on the interdiseiplinary topic of Geometry, Integrability and Nonlinearity in Condensed Matter Physics, would indeed be timely. The enthusiastic response and support that we received from the active researchers in this subject, when we organized an International Conference on the above topic from July 15 to July 20, 2001, in Bansko, Bulgaria, provided a further motivation for undertaking this task. As the topic is interdisciplinary in nature, the articles in this volume contain new results on a wide range of subjects. These include among others, integrable equations and the interplay between geometry and nonlinearity, the role of optical solitons in communication. (and, possibly, computation), common nonlinear and geometrical aspects of condensed matter, field theory, and so on. The increasingly important role played by geometry and topology in diverse areas such as the quantum Hall effect, localization, deformation and elasticity, quasiparticle kinetics and dynamics, spin systems, membranes, is highlighted in some of the articles. There are papers in which essential links of nonlinearity to differential geometry are identified and many elegant mathematical methods are presented. Some other articles focus on how the mathematical tools of geometry and nonlinear analysis can be applied to solve certain physical problems. Given the vast range of titles, it was difficult to strictly divide the contributions into distinct categories. Except for the pedagogical introductory article by Rajaraman titled "CP _N Solitons in Quantum Hall Systems", which essentially "sets the stage" for the various themes covered, we have grouped the articles broadly under the following headings: Geometry, integrability and mathematical physics; Solitons: Interaction phenomena, nonlinear optics; Condensed matter physics; Soft condensed matter physics; Quantum phenomena. We gratefully acknowledge the support from Los Alamos National Lab, USA; Université de Cergy-Pontoise, France; The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy and the Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria, in putting this special volume together. We believe that the cross-fertilization and synergy of a host of ideas in seemingly disparate fields of physics would lead to the natural emergence of new paradigms, which in turn could pave the way for collaborative research to arrive at new solutions of complex nonlinear problems. It is our hope that this topical issue will be useful in providing an impetus for achieving this broad objective. Radha Balakrishnan, Chennai, India Rossen Dandoloff, Cergy-Pontoise, France Vladimir Gerdjikov, Sofia, Bulgaria Dimitar Pushkarov, Sofia, Bulgaria Avadh Saxena, Los Alamos, USA     

Equivariant Reduction to Torus of a Principal Bundle

Let M be an irreducible projective variety, over an algebraically closed field k of characteristic zero, equipped with an action of a connected algebraic group S over k. Let E _G be a principal G-bundle over M equipped with a lift of the action of S on M, where G is a connected reductive linear algebraic group. Assume that E _G admits a reduction of structure group to a maximal torus TG. We give a necessary and sufficient condition for the existence of a T-reduction of E _G which is left invariant by the action of S on E _G .     

Tunable narrow-band infrared emitters from hexagonal lattices

In this work, we present both the theoretical basis as well as supporting experimental measurements for development of a novel mid-infrared thermally stimulated narrow band emitter with a spectral bandwidth of less than 10%. To achieve this, we utilize a metallized-surface 2D photonic crystal of air voids in a silicon background with hexagonal structure symmetry. Our results are based on the generation of discrete surface plasmon (SP) modes in the thin metallized layer residing on the top surface. This yields a series of adequately spaced discrete peaks in the reflection spectrum, dominated by a single sharp feature corresponding to the lowest plasmon order, in an otherwise uniform highly reflective spectrum (>90%) over most of the IR spectrum. This, in turn, gives rise to a sharp absorption feature with a correspondingly narrow thermal emission peak in the emission spectrum. Transfer matrix calculations simulate well both the position and strengths of the absorption peaks. By altering the period of the surface photonic lattice, the SP peak and emissive band can be tuned to the desired wavelength. These devices promise a new class of tunable infrared emitters with high power in a narrow spectral bandwidth. Such narrow band sources are critical to achieving high efficiency gas sensors.     

A parametric study of pulsed Nd:YAG laser micro-drilling of gamma-titanium aluminide

In the present research, Nd:YAG laser micro-drilling of gamma-titanium aluminide, a new material which has performed well in laboratory tests as well as in different fields of engineering, is studied. The effect of different process parameters in the optimization of the process is investigated. The aspects considered are the hole circularity at exit and the hole taper of the drilled hole. Lamp current, pulse frequency, air pressure and thickness of the job are selected as independent process variables. The central composite design (CCD) technique based on response surface methodology (RSM) is employed to plan the experiments to achieve optimum responses with a reduced number of experiments.     

Exit time and invariant measure asymptotics for small noise constrained diffusions

Constrained diffusions, with diffusion matrix scaled by small ?>0, in a convex polyhedral cone G⊂R^k, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under conditions, an “exponential leveling” property that says that, as ?→0, the moments of functionals of exit location from B, corresponding to distinct initial conditions, coalesce asymptotically at an exponential rate, is established. It is shown that, with appropriate conditions, difference of moments of a typical exit time functional with a sub-logarithmic growth, for distinct initial conditions in suitable compact subsets of B, is asymptotically bounded. Furthermore, as initial conditions approach 0 at a rate ?² these moments are shown to asymptotically coalesce at an exponential rate.     

Approximation, integration and differentiation of time functions using a set of orthogonal hybrid functions (HF) and their application to solution of first order differential equations

Differential equations of different types and orders are of utmost importance for mathematical modeling of control system problems. State variable method uses the concept of expressing n number of first order differential equations in vector matrix form to model and analyze/synthesize control systems.The present work proposes a new set of orthogonal hybrid functions (HF) which evolved from synthesis of sample-and-hold functions (SHF) and triangular functions (TF). This HF set is used to approximate a time function in a piecewise linear manner with the mean integral square error (MISE) much less than block pulse function based approximation which always provides staircase solutions.The operational matrices for integration and differentiation in HF domain are also derived and employed for solving non-homogeneous and homogeneous differential equations of the first order as well as state equations. The results are compared with exact solutions, the 4th order Runge-Kutta method and its further improved versions proposed by Simos [6]. The presented HF domain theory is well supported by a few illustrations.     

Ballistic transmission through quasi-periodic shape barrier resonant tunneling structures

A theoretical model is proposed to study the ballistic electron transport for a quasi-periodic multibarrier structure where two different barrier shapes are arranged according to the Thue–Morse sequence. Important tunneling features are revealed form such arrangements. It is noted that the tunneling band spectrum could be fragmented by tailoring the shape of the barriers in the structure. Results for the transmission coefficients and the current densities are compared with the corresponding periodic and single shape barrier arrangements. The quasi-periodic structure consisting of the rectangular and triangular barrier shapes is suggested to be more suitable for the electronic and opto-electronic devices due to its high negative differential conducting effect.