Time harmonic scar statistics in two dimensional cavities

Warne, Larry K.; Jorgenson, Roy E.; Kotulski, Joseph D.; Lee, K.S.H.

doi:10.1109/aps.2007.4396247

Cited by 5 publications

(5 citation statements)

References 9 publications

(11 reference statements)

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“…More details on these scar constructions can be found in Warne et al (2006). The generalized formalism used in this article is needed to treat cavities with concave walls containing interior foci, which were briefly summarized in Warne et al (2007) (scalar axisymmetric 3D results were also presented in Warne et al [2008]); a paper is being prepared on the treatment of the stadium cavity using these methods.…”

Section: Introductionmentioning

confidence: 99%

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

et al. 2011

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This article examines the localization of time harmonic high-frequency modal fields in two-dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This article examines the enhancements for these unstable orbits when the opposing mirrors are convex, constructing the high-frequency field in the scar region using elliptic cylinder coordinates in combination with a random reflection phase from the outer chaotic region. The enhancements when the cavity is symmetric as well as asymmetric about the orbit are examined.

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Section: Introductionmentioning

confidence: 99%

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

et al. 2011

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“…(34) which is the quantity used in equation (26). The directivity gain  is 164 for a resonant antenna and is 15 for a short antenna.…”

Section: Capacitive Antennamentioning

confidence: 99%

“…The normalization is assumed to be the same throughout the cavity (homogeneity). Cavities can exhibit deviations from this simple density (the modal spacings can also deviate) due to periodic ray trajectories [21], [24], [25], [26], as well as proximity to the source (of course in low quality factor situations we would also expect field inhomogeneity).…”

Section: Modal Statistics In High Q Cavitymentioning

confidence: 99%

Electromagnetic field limits set by the V-Curve.

Warne

Jorgenson

Hudson

2014

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When emitters of electromagnetic energy are operated in the vicinity of sensitive components, the electric field at the component location must be kept below a certain level in order to prevent the component from being damaged, or in the case of electro-explosive devices, initiating. The V-Curve is a convenient way to set the electric field limit because it requires minimal information about the problem configuration. In this report we will discuss the basis for the V-Curve. We also consider deviations from the original V-Curve resulting from inductive versus capacitive antennas, increases in directivity gain for long antennas, decreases in input impedance when operating in a bounded region, and mismatches dictated by transmission line losses. In addition, we consider mitigating effects resulting from limited antenna sizes.

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“…In particular, the localization of the eigenfunctions about unstable periodic orbits, known as scarring, is investigated. The approach used by Antonsen [1], on convex mirror geometries in two dimensions, is generalized [2], [3], [4] by introducing the curved ray path formalism, used previously by Vaynshteyn [5] on stable orbits. This combined approach was used recently to investigate scars in two-dimensional geometry [6], [7].…”

Section: Introductionmentioning

confidence: 99%

“…This combined approach was used recently to investigate scars in two-dimensional geometry [6], [7]. This report explores both the scalar (acoustic) [8], [9] and vector (electromagnetic) problems in three-dimensional axisymmetric geometry, first with convex walls, and second with concave walls supporting interior foci. The mirror boundaries at the ends of the orbit each have two equal radii of curvature in this axisymmetric geometry, which is the other distinct limit from the two-dimensional case, where one of the radii becomes infinite.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

Warne¹,

Jorgenson²

2014

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This report examines the localization of high frequency electromagnetic fields in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated first but the approximations required to treat the vector field components are also examined. Particular attention is focused on the normalization through the electromagnetic energy theorem. Both projections of the field along the scarred orbit as well as point statistics are examined. Statistical comparisons are made with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric case forms the opposite extreme (where the two mirror radii at each end of the ray orbit are equal) from the two-dimensional solution examined previously (where one mirror radius is vastly different from the other). The enhancement of the field on the orbit axis can be larger here than in the two-dimensional case.

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Time harmonic scar statistics in two dimensional cavities

Cited by 5 publications

References 9 publications

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

Electromagnetic field limits set by the V-Curve.

Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

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