Temporal and Spatial Development of the EM Field in a Shielding Enclosure with Aperture after Transient Interference Caused by a Subnanosecond High-Energy EM Plane Wave Pulse

A proper assessment of the shielding effectiveness of an enclosure with aperture under subnanosecond transient interference requires a better understanding of the coupling and development mechanisms of the EM field induced inside the enclosure. In this paper, the results of a numerical study of the temporal and spatial development of the electromagnetic (EM) field in a shielding enclosure with aperture after transient interference caused by a subnanosecond high-energy EM plane wave pulse are presented. The interference pulse had Gaussian distribution of the electric and magnetic fields with amplitudes of 106 V/m and 2.68·103 A/m, respectively. The maximum pulse power density was 2.68 GW/m2. The novelty of this study was 2D and 3D images, which visualized the temporal and spatial build-up of electric and magnetic fields in the shielding enclosure within 90 ns after the transient interference. This is 58 times longer than the time needed by any EM wave to travel the distance between the front and rear walls of the enclosure. The presented images, showing the EM field morphology over a relatively long period of time, were crucial for understanding the EM field build-up process inside the shielding enclosure with aperture. They revealed the existence of two unknown phases of the EM field build-up in the enclosure with aperture. We call these two phases the wave phase and the interference phase. In the wave phase, the EM field is generated in the form of so-called primary and secondary wave pulses, traveling towards the enclosure rear wall. In the interference phase, the EM field has the form of temporally and spatially varying pulse-like interference (size-limited) patterns of the associated electric and magnetic fields. The EM field induced in the enclosure is long-lasting compared to the interference pulse duration. The amplitudes of the electric and magnetic fields decreased about threefold in 5 ns and 30-fold in 90 ns, thus exhibiting a severe EM hazard for much longer than the external interference duration. For a long period of time, the highest EM field amplitudes would change their locations in the enclosure, which makes it difficult to assess the shielding effectiveness on the basis of classical definitions. The existence of the long-lasting temporally and spatially varying EM field induced in the enclosure with aperture by the subnanosecond transient interference, visualized in detail in this paper, confirms that a new definition and measurement methods of shielding effectiveness under transient conditions are needed. The obtained results provide a source of data that can be useful when working on the introduction of time-domain parameters to evaluate the transient shielding effectiveness in the case of the ultrashort EM interference.

Analytical representation for amplitudes and differential cross section of pp elastic scattering at 13 TeV

With analytical representation for the pp scattering amplitudes introduced and tested at lower energies, a description of high precision is given of the $$d\sigma /dt$$ d σ / d t data at $$\sqrt{s}= 13$$ s = 13 TeV for all values of the momentum transfer, with explicit identification of the real and imaginary parts. In both t and b coordinates the amplitudes have terms identified as of non-perturbative and perturbative nature, with distinction of their influences in forward and large |t| ranges and in central and peripheral regions respectively. In the forward range, the role of the Coulomb-nuclear interference phase is investigated. The energy dependence of the parameters of the amplitudes are reviewed and updated, revealing a possible emergence of a peculiar behavior of elastic and inelastic profiles in b-space for central collisions, which seems to be enhanced quickly at higher energies. Some other models are also briefly discussed in comparison, including the above mentioned behavior in b-space.

Potential interference immunity of coherent reception of quadruple phase-manipulated radio signal in the presence of coherent harmonic interference

Introduction: The known methods for calculating the interference immunity of radio signal reception in the presence of, for example, harmonic interference, often lead to significantly different numerical values. Each calculation technique of this type has its own algorithm for the resulting formula output, and these conclusions are based on a different level of “engineering rigor”. Purpose: To develop, оn the basis of linear transformation of coordinates, a correct method for calculating the error probability in the correlating reception of a four-fold phase-manipulated radio signal in the presence of coherent harmonic interference. Methods: Four-dimensional probability density of a vector of output voltages of the demodulator correlators in a four-fold integral was represented by a product of one-dimensional probability densities in the space of eigenvectors of the covariance matrix, in which two probability densities are Dirac delta functions. The quadruple integral is brought to double, with new integration limits defined from the plane equations bounding the integration region in this space. Results: Formulas were derived for accurate calculation of average probabilities of symbol and bit errors in coherent reception of a four-fold phase-manipulated radio signal in the presence of coherent harmonic interference. The derived exact formulas were used to plot the dependencies of the average probabilities of symbol and bit errors on the signal-to-noise ratio for the given interference-to-noise ratio and the given interference phase shift relative to the signal phase. It has been studied how the energy ratios of the signal and interference, as well as the interference phase shift, affect the probabilities of symbol and bit errors. It was found that the influence of a non-energy parameter equivalently leads to a change in the energy ratios. Practical relevance: The results of the research can be used in assessing the communication efficiency under interference. The developed technique will allow you to accurately determine the energy characteristics of a radio channel providing the required quality for the reception of transmitted messages in presence of harmonic interference.

Measurement of step surface contour based on variable sampling phase shift interference phase extraction algorithm based on selective sampling

Variable frequency phase shift interferometry is widely applied in optical precision measurement, with the accuracy of phase extraction’s direct impact on that of phase shift interferometry. In the variable-frequency phase-shift interferometry, the commonly used phase-shifting devices are prone to phase shift errors, because the ordinary equal-step phase extraction algorithm, which can be merely used to measure simple and smooth surface, influences the accuracy of phase extraction resulting in measuring error, and causes inefficiency led by the long time the iterative process lasts for when applied in complex stepped surfaces measurement. As a sort of step-by-step phase-shifting phase extraction algorithm based on selective sampling is used to measure the step surface contour, the interference image is firstly sampled at equal intervals to reduce the iterative calculation, and in view of the fact that the phase calibration of the test system is not required in this algorithm, the measured phase is given by using the alternating iterative method despite the unknown phase and unknown phase shift amount. The phase extraction accuracy and iteration time among traditional iterative algorithm, four-step phase shift algorithm and the variable phase shift phase interpolation algorithm based on selective sampling are compared in the simulation and experiment. It is shown that the variable frequency phase shifting interference phase extraction algorithm based on selective sampling has shorter operation time, less error and higher accuracy than traditional iterative algorithm in measuring complex step surface.