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Ball lens reflections by direct solution of Maxwell`s equations

Description: Ball lenses are important for many applications. For example, ball lenses can be used to match the mode of a laser diode (LD) to a single mode fiber (SMF), essential for low-loss, high bit rate communication systems. Modeling the propagation of LD light through a ball lens presents a challenge due to the large angular divergence of the LD field (typically > 20{degrees} HWHM) and the subsequent significant effect of spherical aberration. Accurately calculating the reflected power is also difficult, but essential, since reflections as small as {minus}30 dB can destabilize the LID. A full-wave analysis of this system using, e.g., a finite-difference time-domain method is not practical because of the size of the ball lens, typically hundreds of wavelengths in diameter. Approximate scalar methods can give good results in some cases, but fail to calculate reflected power and miss polarization effects entirely. The authors` approach exploits the fact that the scattering of an arbitrary electromagnetic beam from a sphere is an exactly solvable problem. The scattering of a plane wave from a sphere is a classical problem which was solved by Mie in 1908. More recently, various workers have considered the scattering of a Gaussian beam from a sphere and its numerical implementation for other applications. To the authors knowledge, this is the first time this approach has been applied to a problem in optical design. They are able to calculate reflection and transmission accurately with modest computational effort.
Date: February 15, 1995
Creator: Ratowsky, R.P.; Deri, R.J. & Kallman, J.S.
Partner: UNT Libraries Government Documents Department

Group velocity and pulse lengthening of mismatched laser pulses in plasma channels

Description: Analytic solutions are presented to the non-paraxial wave equation describing an ultra-short, low-power, laser pulse propagating in aplasma channel. Expressions for the laser pulse centroid motion and laser group velocity are derived, valid for matched and mismatchedpropagation in a parabolic plasma channel, as well as in vacuum, for an arbitrary Laguerre-Gaussian laser mode. The group velocity of amismatched laser pulse, for which the laser spot size is strongly oscillating, is found to be independent of propagation distance andsignificantly less than that of a matched pulse. Laser pulse lengthening of a mismatched pulse owing to laser mode slippage isexamined and found to dominate over that due to dispersive pulse spreading for sufficiently long pulses. Analytic results are shown tobe in excellent agreement with numerical solutions of the full Maxwell equations coupled to the plasma response. Implications for plasmachannel diagnostics are discussed.
Date: July 7, 2011
Creator: Schroeder, Carl; Benedetti, Carlo; Esarey, Eric; van Tilborg, Jeroen & Leemans, Wim
Partner: UNT Libraries Government Documents Department

A perturbation expansion approach to solving the electromagnetic induction problem in three dimensions.

Description: We address the electromagnetic induction problem for fully 3D geologic media and present a solution to the governing Maxwell equations based on a power series expansion. The coefficients in the series are computed using the adjoint method assuming an underlying homogeneous reference model. These solutions are available analytically for point dipole source terms and lead to rapid calculation of the expansion coefficients. First order solutions are presented for a model study in petroleum geophysics composed of a multi-component induction sonde proximal to a fault within a compartmentalized hydrocarbon reservoir.
Date: October 1, 2003
Creator: Tobin, Harold (New Mexico Tech, Socorro, NM); Natek, Nancy H. & Weiss, Chester Joseph
Partner: UNT Libraries Government Documents Department

Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model

Description: The Pulse-Line Ion Accelerator (PLIA) is a promising approach to high-gradient acceleration of an ion beam at high line charge density [1, 2, 3, 4, 5, 6]. A recent note by R. J. Briggs [7] suggests that a ''sheath helix'' model of such a system can be solved numerically in the quasi-static limit. Such a model captures the correct macroscopic behavior from ''first principles'' without the need to time-advance the full Maxwell equations on a grid. This note describes numerical methods that may be used to effect such a solution, and their connection to the circuit model that was described in an earlier note by the author [8]. Fine detail of the fields in the vicinity of the helix wires is not obtained by this approach, but for purposes of beam dynamics simulation such detail is not generally needed.
Date: February 1, 2006
Creator: Friedman, A
Partner: UNT Libraries Government Documents Department

A multigrid method for variable coefficient Maxwell's equations

Description: This paper presents a multigrid method for solving variable coefficient Maxwell's equations. The novelty in this method is the use of interpolation operators that do not produce multilevel commutativity complexes that lead to multilevel exactness. Rather, the effects of multilevel exactness are built into the level equations themselves--on the finest level using a discrete T-V formulation, and on the coarser grids through the Galerkin coarsening procedure of a T-V formulation. These built-in structures permit the levelwise use of an effective hybrid smoother on the curl-free near-nullspace components, and these structures permit the development of interpolation operators for handling the curl-free and divergence-free error components separately, with the resulting block diagonal interpolation operator not satisfying multilevel commutativity but having good approximation properties for both of these error components. Applying operator-dependent interpolation for each of these error components leads to an effective multigrid scheme for variable coefficient Maxwell's equations, where multilevel commutativity-based methods can degrade. Numerical results are presented to verify the effectiveness of this new scheme.
Date: May 13, 2004
Creator: Jones, J E & Lee, B
Partner: UNT Libraries Government Documents Department

Wakefield and the diffraction model due to a flat beam moving past a conducting wedge

Description: A collimator is often used to clean a beam of its excessive tail particles. If the beam intensity is high enough or if the beam is brought too close to the collimator, however, the wakefields generated by the beam-collimator interaction can cause additional beam tails to grow, thus defeating, or even worsening, the beam-tail cleaning process. The wakefield generated by a sheet beam moving past a conducting wedge has been obtained in closed form by Henke using the method of conformal mapping. This result is applied in the present work to obtain the wake force and the transverse kick received by a test charge moving with the beam. For the beam to be approximated as sheet beams, it is assumed to be flat and the collimator is assumed to have an infinite extent in the flat dimention. We derive an exact expression for the transverse wake force delivered to particles in the beam bunch. Implication of emittance growth as a beam passes closely by a collimator is discussed. We consider two idealized wedge geometries: In Section 2, when the wedge has the geometry as a disrupted beam pipe, and in Section 3, when it is like a semi-infinite screen. Unfortunately, we do not have solutions for more realistic collimator geometries such as when it is tapered to minimize the wakefield effects. However, our results should still serve as pessimistic limiting cases. An interesting opportunity is offered by our exact calculation of the wakefields: it can be used to confront the diffraction model used to estimate the high-frequency impedance of a cavity structure. It is shown that the field pattern, as well as the impedance, agrees with those obtained by the diffraction model in appropriate limits.
Date: July 1, 1995
Creator: Chao, A.W. & Henke, H.
Partner: UNT Libraries Government Documents Department

Approximate analytical description of the underdense short plasma lens

Description: The perturbative approach for describing the underdense plasma-ultrarelativistic electron bunch system is developed, using the ratio n{sup o}{sub b} as a small parameter (n{sub b}-bunch, n{sub o} plasma electron densities). Focusing of the electron bunch emerged in the first approximation of the perturbative procedure as a result of the plasma electrons redistribution. Focusing gradient and strength for ultrarelativistic, flat, uniform and short bunch are obtained and compared with the previous results.
Date: May 1, 1996
Creator: Amatuni, A.Ts.
Partner: UNT Libraries Government Documents Department

A brief review of dusty plasma effects in the solar system

Description: Dusty plasmas are commonly found in the solar system and in the rest of space. In this paper we briefly describe some of the more common dusty plasmas: the rings of Saturn, dust tails of comets, dust streams from Jupiter, and noctilucent clouds in the upper atmosphere. We also discuss some of the theoretical issues related to grain charging, dust particle dynamics, waves in dusty plasmas, and dusty plasma crystals.
Date: August 1, 1997
Creator: Winske, D.
Partner: UNT Libraries Government Documents Department

Iron free permanent magnet systems for charged particle beam optics

Description: The strength and astounding simplicity of certain permanent magnet materials allow a wide variety of simple, compact configurations of high field strength and quality multipole magnets. Here we analyze the important class of iron-free permanent magnet systems for charged particle beam optics. The theory of conventional segmented multipole magnets formed from uniformly magnetized block magnets placed in regular arrays about a circular magnet aperture is reviewed. Practical multipole configurations resulting are presented that are capable of high and intermediate aperture field strengths. A new class of elliptical aperture magnets is presented within a model with continuously varying magnetization angle. Segmented versions of these magnets promise practical high field dipole and quadrupole magnets with an increased range of applicability.
Date: September 3, 1995
Creator: Lund, S. M. & Halbach, K.
Partner: UNT Libraries Government Documents Department

Fast Solutions of Maxwell's Equation for High Resolution Electromagnetic Imaging of Transport Pathways

Description: A fast precondition technique has been developed which accelerates the finite difference solutions of the 3D Maxwell's equations for geophysical modeling. The technique splits the electric field into its curl free and divergence free projections, and allows for the construction of an inverse operator. Test examples show an order of magnitude speed up compared with a simple Jacobi preconditioner. Using this preconditioner a low frequency Neumann series expansion is developed and used to compute responses at multiple frequencies very efficiently. Simulations requiring responses at multiple frequencies, show that the Neumann series is faster than the preconditioned solution, which must compute solutions at each discrete frequency. A Neumann series expansion has also been developed in the high frequency limit along with spectral Lanczos methods in both the high and low frequency cases for simulating multiple frequency responses with maximum efficiency. The research described in this report was to have been carried out over a two-year period. Because of communication difficulties, the project was funded for first year only. Thus the contents of this report are incomplete with respect to the original project objectives.
Date: October 1, 1999
Partner: UNT Libraries Government Documents Department

Propagation of electromagnetic waves in a structured ionosphere

Description: The ionosphere is a birefringent medium which strongly affects the transmission of very high frequency (vhf) radio signals. These effects must be understood in detail if one wishes to look at the propagation of wide bandwidth coherent signals through the ionosphere. We develop a general perturbative solution of Maxwell`s equations for vhf signals propagating in the ionosphere, subject only to mild restrictions on the ionospheric structure. This solution can be extended to give the propagating field to any desired degree of precision. The case of a laminar ionosphere with harmonic waves is developed in greater detail, and we show how to calculate the ray path in this case. This solution is used to elucidate the effects of refraction on the phase of the signal, and we calculate the spatial- and frequency-coherence functions. The electric field for a laminar ionosphere without waves is analyzed to clarify the physical origins of the terms modifying the signal phase. We then calculate the solution in this case for the Appleton-Hartree model of the ionospheric dielectric function and express the result as a series in inverse powers of frequency. We conclude by calculating the ray path for a model ionosphere using the Appleton-Hartree dielectric function and a parabolic layer for the electron density.
Date: June 1, 1996
Creator: Murphy, T.
Partner: UNT Libraries Government Documents Department

Coherent spontaneous emission in high gain free-electron lasers.

Description: The authors investigate finite pulse effects in self-amplified spontaneous emission (SASE), especially the role of coherent spontaneous emission (CSE) in the start and the evolution of the free-electron laser (FEL) process. When the FEL interaction is negligible, they solve the one-dimensional Maxwell equation exactly and clarify the meaning of the slowly varying envelope approximation (SVEA). In the exponential gain regime, they solve the coupled Vlasov-Maxwell equations and extend the linear theory to a bunched beam with energy spread. A time-dependent, non-linear simulation algorithm is employed to study the CSE effect for a general beam distribution.
Date: April 14, 1999
Creator: muang, Z.
Partner: UNT Libraries Government Documents Department

A new type of massive spin-one boson: And its relation with Maxwell equations

Description: First, the author showed that in the (1, 0) {circle_plus} (0, 1) representation space there exist not one but two theories for charged particles. In the Weinberg construct, the boson and its antiboson carry same relative intrinsic parity, whereas in the author`s construct the relative intrinsic parities of the boson and its antiboson are opposite. These results originate from the commutativity of the operations of Charge conjugation and Parity in Weinberg`s theory, and from the anti-commutativity of the operations of Charge conjugation and Parity in the author`s theory. The author thus claims that he has constructed a first non-trivial quantum theory of fields for the Wigner-type particles. Second, the massless limit of both theories seems formally identical and suggests a fundamental modification of Maxwell equations. At its simplest level, the modification to Maxwell equations enters via additional boundary condition(s).
Date: October 1, 1995
Creator: Ahluwalia, D.V.
Partner: UNT Libraries Government Documents Department

Asymmetric perfectly matched layer for the absorption of waves

Description: The Perfectly Matched Layer (PML) has become a standard for comparison in the techniques that have been developed to close the system of Maxwell equations (more generally wave equations) when simulating an open system. The original Berenger PML formulation relies on a split version of Maxwell equations with numerical electric and magnetic conductivities. They present here an extension of this formulation which introduces counterparts of the electric and magnetic conductivities affecting the term which is spatially differentiated in the equations. they phase velocity along each direction is also multiplied by an additional coefficient. They show that, under certain constraints on the additional numerical coefficients, this ''medium'' does not generate any reflection at any angle and any frequency and is then a Perfectly Matched Layer. Technically it is a super-set of Berenger's PML to which it reduces for a specific set of parameters and like it, it is anisotropic. However, unlike the PML, it introduces some asymmetry in the absorption rate and is therefore labeled an APML for Asymmetric Perfectly Matched Layer. They present here the numerical considerations that have led them to introduce such a medium as well as its theory. Several finite-different numerical implementations are derived (in one, two and three dimensions) and the performance of the APML is contrasted with that of the PML in one and two dimensions. Using plane wave analysis, they show that the APML implementations lead to higher absorption rates than the considered PML implementations. Although they have considered in this paper the finite-different discretization of Maxwell-like equations only, the APML system of equations may be used with other discretization schemes, such as finite-elements, and may be applied to other equations, for applications beyond electromagnetics.
Date: February 10, 2002
Creator: Vay, Jean-Luc
Partner: UNT Libraries Government Documents Department

Geometric jphases in self-induced transparency

Description: We consider the geometric phases arising in the lossless propagation of light pulses through a medium composed of near resonant two-level atoms. A reformulation of the coupled Maxwell-Schroedinger equations allows us to construct conservation laws in a general context. There exist periodic solutions of these equations which lead to the possibility of cyclical evolution of the state vector and the appearance of a geometric phase. We first show that if the ground state is the initial state of the system, then it acquires a geometric phase after the passage of the soliton pulses of McCall and Hahn. More generally if the initial state is a superposition of the two levels, continuous pulse trains can propagate without appreciable loss. We also find in this case that the state vector develops a geometric phase provided the parameters take on the particular values required for cyclical evolution. In both cases we exhibit the geometric character of the calculated phases by showing that they equal half the solid angle subtended by a closed curve traced by the Bloch, vector on the Bloch sphere. We verify a recent assertion of Anandan and Aharonov that the energy uncertainty in the state is directly related to the speed at which the tip of the Bloch vector moves along the curve on the Bloch sphere (or in more general terms the energy uncertainty is related to the speed in the projective Hilbert space).
Date: May 1, 1991
Creator: Sen, T. & Milovich, J.
Partner: UNT Libraries Government Documents Department

EMPHASIS/Nevada CABANA user Guide. Version 2.0.

Description: The CABle ANAlysis (CABANA) portion of the EMPHASIS{trademark} suite is designed specifically for the simulation of cable system-generated electromagnetic pulse (SGEMP). The code can be used to evaluate the response of a specific cable design to threat or to compare and minimize the relative response of difference designs. This document provides user-specific information to facilitate the application of the code to cables of interest. It solves the electrical portion of a cable SGEMP simulation. It takes specific results from the deterministic radiation-transport code CEPTRE as sources and computes the resulting electrical response to an arbitrary cable load. The cable geometry itself is also arbitrary and is limited only by the patience of the user in meshing and by the available computing resources for the solution. The CABANA simulation involves solution of the quasi-static Maxwell equations using finite-element method (FEM) techniques.
Date: September 1, 2011
Creator: Turner, C. David; Powell, Jennifer L. & Bohnhoff, William J.
Partner: UNT Libraries Government Documents Department

Maxwell Equation for the Coupled Spin-Charge Wave Propagation

Description: We show that the dissipationless spin current in the ground state of the Rashba model gives rise to a reactive coupling between the spin and charge propagation, which is formally identical to the coupling between the electric and the magnetic fields in the 2 + 1 dimensional Maxwell equation. This analogy leads to a remarkable prediction that a density packet can spontaneously split into two counter propagation packets, each carrying the opposite spins. In a certain parameter regime, the coupled spin and charge wave propagates like a transverse 'photon'. We propose both optical and purely electronic experiments to detect this effect.
Date: January 15, 2010
Creator: Bernevig, B.Andrei; Yu, Xiaowei; Zhang, Shou-Cheng & /Stanford U., Phys. Dept.
Partner: UNT Libraries Government Documents Department

Coupling impedance of a periodic array of diaphragms

Description: A method is presented for calculating the high-frequency longitudinal and transverse coupling impedances in a periodic array of diaphragms in a circular perfectly conducting pipe. The method is based on Weinstein`s theory of diffraction of a plane electromagnetic wave on a stack of halfplanes. Using Weinstein`s solution, it is shown that the problem of finding the beam field in the pipe reduces to an effective boundary condition at the radius of the diaphragms that couples the longitudinal electric field with the azimuthal magnetic one. Solving Maxwell`s equations with this boundary condition leads to simple formulae for Z(long) and Z(tr). A good agreement with a numerical solution of the problem found by other authors is demonstrated.
Date: June 1, 1995
Creator: Stupakov, G.V.
Partner: UNT Libraries Government Documents Department