Norman M. Kroll

Quantum electrodynamical corrections to the fine structure of helium

Order α6mc2 corrections to the fine structure splitting of the deepest triplet P state (23P0,1,2) of the He4 atom have been investigated. The investigation is based on the covariant Bethe-Salpeter equation including external potential to take account of the nuclear Coulomb field. All order α6mc2 corrections which arise from Feynman diagrams involving the exchange of one, two, and three photons, as well as radiative corrections to the electron magnetic moment have been found. The results are presented in a form suitable for computerized numerical evaluation.

Free-electron lasers with variable parameter wigglers

A general discussion of the free-electron lasers (FELs) with variable parameter wigglers is presented with a view towards their potential for the production of high power optical radiation at reasonable efficiency. The theoretical analysis is based upon a one-dimensional relativistic Hamiltonian formulation and is developed in a manner to take advantage of the analogy between the FEL process and radio frequency accelerators. Three promising operational modes are identified and analyzed. The first may be thought of as an electron decelerator and is thought to have the most promise for single-pass devices. Both oscillator and amplifier configurations are studied. The second is based upon adiabatic trapping and detrapping, intended to reduce the spread in electron energy typically induced by the FEL process. The third is based upon the method of phase area displacement. It has the advantage of wide gain bandwidth and small induced energy spread, and is thought to have the most promise for storage ring applications. Generally speaking, it is found that high peak power is intrinsic to these modes of operation. Potential problems from parasitic oscillations analogous to the stimulated Raman effect are analyzed, and some others arising from transverse inhomogeneity are identified.

Excitation of Hypersonic Vibrations by Means of Photoelastic Coupling of High‐Intensity Light Waves to Elastic Waves

A theory of the excitation of elastic waves arising from photoelastic coupling with light is presented. It is similar in character to the theory of optical parametric amplification in spatially extended media. Special attention is given to the self‐excited transient case. A novel form for the space—time development of the instability appears for the case in which the spatial dimensions of the interaction region are large compared to the distance traveled by an elastic wave during the illumination time. The predicted effects should be readily observable with existing giant pulse lasers.

Photonic band structure and defects in one and two dimensions

We present an experimental and numerical study of electromagnetic wave propagation in one-dimensional (1D) and two-dimensional (2D) systems composed of periodic arrays of dielectric scatterers. We demonstrate that there are regions of frequency for which the waves are exponentially attenuated for all propagation directions. These regions correspond to band gaps in the calculated band structure, and such systems are termed photonic band-gap (PBG) structures. Removal of a single scatterer from a PBG structure produces a highly localized defect mode, for which the energy density decays exponentially away from the defect origin. Energy-density measurements of defect modes are presented. The experiments were conducted at 6–20 GHz, but we suggest that they may be scaled to infrared frequencies. Analytic and numerical solutions for the band structure and the defect states in 1D structures are derived. Applications of 2D PBG structures are briefly discussed.

Direct calculation of permeability and permittivity for a left-handed metamaterial

Recently, an electromagnetic metamaterial was fabricated and demonstrated to exhibit a “left-handed” (LH) propagation band at microwave frequencies. A LH metamaterial is one characterized by material constants—the permeability and permittivity—which are simultaneously negative, a situation never observed in naturally occurring materials or composites. While the presence of the propagation band was shown to be an inherent demonstration of left handedness, actual numerical values for the material constants were not obtained. In the present work, using appropriate averages to define the macroscopic fields, we extract quantitative values for the effective permeability and permittivity from finite-difference simulations using three different approaches.

Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity

We demonstrate, by both microwave experiments and numerical simulation, that a two‐dimensional lattice of metal cylinders can form a complete photonic band‐gap (PBG) structure. The band structure exhibits a single broad PBG extending from zero frequency to a threshold frequency, above which all modes may propagate in some direction. A single cylinder removed from the lattice produces a defect mode localized about the defect site, with an energy density attenuation rate of 30 dB per lattice constant. The frequency dependence of the transmission through a finite thickness of this structure is also calculated in good agreement with the measurements. We suggest that the defect mode resonant cavity when formed by appropriate low loss metals may be advantageous for use in PBG high energy accelerator structures that we are evaluating.

Theory of the transverse gradient wiggler

We develop analytical models for the operation of gain-expanded transverse gradient wigglers in the low, medium, and high optical intensity regimes. The first two are Raman regimes in which the optical wave and transverse betatron oscillations grow simultaneously. They differ from one another only in the nature of the saturation mechanism. The third or high intensity regime is a trapped particle regime physically very similar to the regime of high extraction variable parameter wigglers.

An RF cavity for the B-factory

The authors describe the proposed design for the 476 MHz accelerating cavity for the Stanford linear Accelerator Center/Lawrence Berkeley Laboratory/Lawrence Livermore National Laboratory B-factory. Use of conventional construction in copper means that careful consideration has to be paid to the problem of cooling. The need for a high shunt impedance for the accelerating mode dictated the use of a reentrant shape. This maximized the impedance of the fundamental mode with respect to the troublesome longitudinal and deflecting higher order modes, when compared to open or bell-shaped designs. A specialized damping scheme was employed to reduce the higher-order mode impedances while sacrificing as little of the fundamental mode power as possible. This was required to suppress the growth of coupled bunch beam instabilities and minimize the workload of the feedback system needed to control them. A window design capable of handling the high power was also required.<<ETX>>

Left-Handed Metamaterials

The response of a material to electromagnetic radiation can be entirely characterized by the material parameters: the electrical permittivity, or e, and the magnetic permeability, or μ. The range of possible values for the material parameters, as dictated by fundamental considerations such as causality or thermodynamics, extends beyond that found in naturally occurring materials. We thus seek to extend the material parameter space by creating electromagnetic metamaterials—ordered composite materials that display electromagnetic properties beyond those found in naturally occurring materials. Recently, we have demonstrated a metamaterial made of a repeated lattice of conducting, nonmagnetic elements that exhibits an effective μ and an effective e, both of which are simultaneously negative over a band of frequencies [1]. Such a medium has been termed Left-Handed [2], as the electric field (E), magnetic intensity (H) and propagation vector (k) are related by a left-hand rule. We introduce the reader to the expected properties predicted by Maxwell’s equations for Left-Handed media, and describe our recent numerical and experimental work in developing and analyzing this new metamaterial.

Studies of a metal photonic bandgap cavity

We describe work on a metal photonic bandgap (PBG) cavity for potential use in high gradient, high Q accelerator structures. The configuration we discuss is a square periodic array of metal cylinders, with one cylinder removed from the center. The unit is bounded on top and bottom by conducting plates, and terminated on the periphery by microwave absorber. Numerical simulations suggest that the metal PBG cavity should have only one high Q resonant mode with monopole symmetry. Experimental measurements confirm the existence of the predicted mode, but also reveal higher order, low Q, resonances. We examine the origin of these resonances, and suggest possible methods of removing them, to eventually produce a structure with no significant higher order modes.