where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

Foreword. Preface. 1 Introduction. 1.1 The Text Organization. References. 2 Measurement Principles Pertaining to Anechoic Chamber Design. 2.1 Introduction. 2.2 Measurement of Electromagnetic Fields. 2.2.1 Introduction. 2.2.2 Antennas. 2.2.3 Radiated Emissions. 2.2.4 Radiated Susceptibility. 2.2.5 Military Electromagnetic Compatibility. 2.2.6 Antenna System Isolation. 2.2.7 Radar Cross Section. 2.3 Free-Space Test Requirements. 2.3.1 Introduction. 2.3.2 Phase. 2.3.3 Amplitude. 2.3.4 Polarization. 2.3.5 The Friis Transmission Formula. 2.4 Supporting Measurement Concepts. 2.4.1 Introduction. 2.4.2 Coordinate Systems and Device Positioners. 2.4.3 Decibels. 2.4.4 Effects of Reflected Energy. 2.4.5 Effects of Antenna Coupling. 2.5 Outdoor Measurement Facilities. 2.5.1 Introduction. 2.5.2 Electromagnetic Design Considerations and Criteria. 2.5.3 Elevated Outdoor Antenna Range. 2.5.4 Ground Reflection Antenna Range. 2.5.5 Open-Area Test Sites (OATS). References. 3 Electromagnetic Absorbing Materials. 3.1 Introduction. 3.2 Microwave Absorbing Materials. 3.2.1 Pyramidal Absorber. 3.2.2 Wedge Absorber. 3.2.3 Convoluted Microwave Absorber. 3.2.4 Multilayer Dielectric Absorber. 3.2.5 Hybrid Dielectric Absorber. 3.2.6 Walkway Absorber. 3.3 Low-Frequency Absorbing Material. 3.3.1 Introduction. 3.3.2 Ferrite Absorbers. 3.3.3 Hybrid Absorbers. 3.4 Absorber Modeling. 3.5 Absorber Testing. References. 4 The Chamber Enclosure. 4.1 Introduction. 4.2 Electromagnetic Interference. 4.3 Controlling the Environment. 4.4 Electromagnetic Shielding. 4.4.1 Introduction. 4.4.2 The Welded Shield. 4.4.3 The Clamped Seam or Prefabricated Shield. 4.4.4 The Single-Shield Systems. 4.5 Penetrations. 4.6 Performance Verification. 4.7 Shielded Enclosure Grounding. 4.8 Fire Protection. References. 5 Anechoic Chamber Design Techniques. 5.1 Introduction. 5.2 Practical Design Procedures. 5.2.1 Introduction. 5.2.2 Quick Estimate of Chamber Performance. 5.2.3 Detailed Ray-Tracing Design Procedure. 5.3 Computer Modeling. 5.3.1 Introduction. 5.3.2 Ray Tracing. 5.3.3 Finite-Difference Time-Domain Model. 5.4 Other Techniques. 5.5 Antennas Used In Anechoic Chambers. 5.5.1 Introduction. 5.5.2 Rectangular Chamber Antennas. 5.5.3 Antennas for Tapered Chambers. 5.5.4 EMI Chambers. References. 6 The Rectangular Chamber. 6.1 Introduction. 6.2 Antenna Testing. 6.2.1 Introduction. 6.2.2 Design Considerations. 6.2.3 Design Example. 6.2.4 Acceptance Test Procedures. 6.3 Radar Cross-Section Testing. 6.3.1 Design Considerations. 6.3.2 Design Example. 6.3.3 Acceptance Test Procedures. 6.4 Near-Field Testing. 6.4.1 Introduction. 6.4.2 Chamber Design Considerations. 6.4.3 Design Example. 6.4.4 Acceptance Test Procedure. 6.5 Electromagnetic Compatibility Testing. 6.5.1 Introduction. 6.5.2 Chamber Design Considerations. 6.5.3 Design Examples. 6.5.4 Acceptance Test Procedures. 6.6 Immunity Testing. 6.6.1 Introduction. 6.6.2 Mode-Stirred Test Facility. 6.7 EM System Compatibility Testing. 6.7.1 Design Considerations. 6.7.2 Acceptance Testing. References. 7 The Compact Range Chamber. 7.1 Introduction. 7.2 Antenna Testing. 7.2.1 Prime Focus Compact Range. 7.2.2 Dual Reflector Compact Range. 7.2.3 Shaped Reflector Compact Range. 7.2.4 Compact Antenna Range Absorber Layout. 7.2.5 Acceptance Testing of the Compact Antenna Anechoic Chamber. 7.3 Compact RCS Ranges. 7.3.1 Introduction. 7.3.2 Design Example. 7.3.3 Acceptance Testing. References. 8 Incorporating Geometry in Anechoic Chamber Design. 8.1 Introduction. 8.2 The Tapered Chamber. 8.2.1 Introduction. 8.2.2 Antenna Testing. 8.2.3 Radar Cross-Section Measurements. 8.3 The Double Horn Chamber. 8.3.1 Introduction. 8.3.2 Antenna Testing. 8.3.3 Emissions and Immunity Testing. 8.4 The Missile Hardware-in-the-Loop Chamber. 8.4.1 Introduction. 8.4.2 Design Considerations. 8.4.3 Design Example. 8.4.4 Acceptance Test Procedures. 8.5 Consolidated Facilities. 8.5.1 Introduction. 8.5.2 Design Considerations. 8.5.3 Design Examples. 8.5.4 Acceptance Test Procedures. 8.6 The TEM Cell. 8.6.1 Introduction. 8.6.2 TEM Principles of Operation. 8.6.3 Typical Performance. References. 9 Test Procedures. 9.1 Introduction. 9.2 Absorber Testing. 9.2.1 Introduction. 9.2.2 Testing of Microwave Absorber. 9.2.3 Low-Frequency Testing. 9.2.4 Compact Range Reflector Testing. 9.2.5 Fire-Retardant Testing. 9.3 Microwave Anechoic Chamber Test Procedures. 9.3.1 Introduction. 9.3.2 Free-Space VSWR Method. 9.3.3 Pattern Comparison Method. 9.3.4 X-Y Scanner Method. 9.3.5 RCS Chamber Evaluation. 9.4 EMC Chamber Acceptance Test Procedures. 9.4.1 Introduction. 9.4.2 Volumetric Site Attenuation. 9.4.3 Field Uniformity. 9.5 Shielding Effectiveness. References. 10 Examples of Indoor Electromagnetic Test Facilities. 10.1 Introduction. 10.2 Antenna Testing. 10.2.1 Introduction. 10.2.2 Rectangular Test Chamber. 10.2.3 Tapered Anechoic Chamber. 10.2.4 Compact Range Test Chamber. 10.2.5 Near-Field Test Chamber. 10.3 Radar Cross-Section Testing. 10.3.1 Introduction. 10.3.2 Compact Range Radar Cross-Section Facilities. 10.4 EMC Test Chambers. 10.4.1 Introduction. 10.4.2 Emission Test Chambers. 10.5 Electromagnetic System Compatibility Testing. 10.5.1 Introduction. 10.5.2 Aircraft Systems. 10.5.3 Spacecraft Test Facilities. References. Appendix A: Procedure for Determining the Area of Specular Absorber Treatment. A.1 Introduction. A.2 Fresnel Zone Analysis. Appendix B :Test Region Amplitude Taper. B.1 Introduction. B.2 Antenna Data. Appendix C: Design/Specification Checklists. C.1 Introduction. C.2 The Rectangular Chamber. C.2.1 Introduction. C.2.2 Antenna Testing. C.2.3 RCS Testing. C.2.4 Near-Field Testing. C.2.5 EMI Testing. C.2.6 Isolation Testing. C.2.7 Impedance Testing. C.3 Compact Range. C.3.1 Introduction. C.3.2 Antenna/Radome Testing. C.3.3 RCS Testing. C.4 Shaped Chambers. C.4.1 Introduction C.4.2 Tapered Chamber. C.4.3 Double Horn Chamber. C.4.4 Hardware-in-the-Loop Testing. C.5 Shielding Design Checklist. C.5.1 Introduction. C.5.2 Checklist for Prefabricated Shielding. C.5.3 Checklist for Welded Enclosures. C.5.4 Checklist for Architectural Shielding. C.5.5 Conventional Construction. C.5.6 Fire Protection. References. Glossary. Selected Bibliography. Index. About the Author.

Electromagnetic Anechoic Chambers: A Fundamental Design and Specification Guide [Book Review]

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Computing Spectra without Solving Eigenvalue Problems

We consider the Neumann boundary value problem for the operator L = − div A grad + V on a Lipschitz domain Ω and, more generally, on manifolds with and without boundary. The eigenfunctions of L are often localized, as a result of disorder of the potential V , the matrix of coefficients A, irregularities of the boundary, or all of the above. In earlier work, two of us introduced the function u solving Lu = 1, and showed numerically that it strongly reflects this localization. In this paper, we deepen the connection between the eigenfunctions and this landscape function u by proving that its reciprocal 1/u acts as an effective potential. The effective potential governs the exponential decay of the eigenfunctions of the system and delivers information on the distribution of eigenvalues near the bottom of the spectrum.

https://hal.archives-ouvertes.fr/hal-02360595/document

Localization of eigenfunctions via an effective potential

Stimulated adiabatic passage utilizes radiation pulses to efficiently and selectively transfer population between quantum states, via an intermediate state that is normally decaying. In this Letter, we propose the analog of stimulated adiabatic passage in an acoustic system. It is realized with cavities that correlate through adiabatically time-varying couplings, where the cavities and time-varying couplings mimic discrete states and radiation pulses, respectively. With appropriate arrangements of coupling actions, an acoustic wave can be efficiently transferred from the initial excited cavity to the target cavity in the forward direction, immune to the intermediate dark cavity. On the other hand, for the backward propagation, the acoustic energy is perfectly localized in the intermediate dark cavity and completely dissipated. We analytically, numerically, and experimentally demonstrate such unidirectional sound localization and unveil the essential role of zero-eigenvalue eigenstates in the adiabatic passage process.

One-Way Localized Adiabatic Passage in an Acoustic System.

A recent theoretical breakthrough has brought a new tool, called the localization landscape, for predicting the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the subregions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way for controlling and engineering eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible.

Aimé Labbé

Papers

One Single Static Measurement Predicts Wave Localization in Complex Structures