This report examines the problem of magnetic penetration of a conductive layer, including nonlinear ferromagnetic layers, excited by an electric current filament. The electric current filament is, for example, a nearby wire excited by a lightning strike. The internal electric field and external magnetic field are determined. Numerical results are compared to various analytical approximations to help understand the physics involved in the penetration.
The well-developed theory of Lorentz plasma that is dominated by electron–ion interactions is used to calculate the PETN arc characteristics. The spark-gap discharge current is a ramp with 10 to 25 ns rise time to peak and remaining constant subsequently. The approximate formulas for the arc channel conductivity, arc temperature, arc radius, and shock pressure from the arc are obtained from a system of nonlinear ordinary differential equations, which is the similarity solution of hydrodynamic equations similar to the Braginskii approximation. These arc parameters are given for the peak current ranging from 100 A to 1000 A and with different rise times. Representative cases are compared to the nonlinear ordinary differential equation code results. The shock pressures at the peak current are comparable to those from a typical commercial EBW bridgewire burst reported in the literature; the arc radius at the peak current is comparable to a typical bridgewire diameter of 0.0375 mm (e.g., RISI detonators, RP-1, and RP-80). The relevant Pop-Plot for low-density PETN is converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. This criterion is then used to determine the detonation thresholds, which are comparable with test data obtained by Tucker, et al.
We summarize the narrow slot algorithms, including the thick electrically small depth case, conductive gaskets, the deep general depth case, multiple fasteners along the length, and finally varying slot width.
Use of insensitive high explosives (IHEs) has significantly improved ammunition safety because of their remarkable insensitivity to violent cook-off, shock and impact. Triamino-trinitrobenzene (TATB) is the IHE used in many modern munitions. Previously, lightning simulations in different test configurations have shown that the required detonation threshold for standard density TATB at ambient and elevated temperatures (250 C) has a sufficient margin over the shock caused by an arc from the most severe lightning. In this paper, the Braginskii model with Lee-More channel conductivity prescription is used to demonstrate how electrical arcs from lightning could cause detonation in TATB. The steep rise and slow decay in typical lightning pulse are used in demonstrating that the shock pressure from an electrical arc, after reaching the peak, falls off faster than the inverse of the arc radius. For detonation to occur, two necessary detonation conditions must be met: the Pop-Plot criterion and minimum spot size requirement. The relevant Pop-Plot for TATB at 250 C was converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. The arc cross-section was required to meet the minimum detonation spot size reported in the literature. One caveat is that when the shock pressure exceeds the detonation pressure the Pop-Plot may not be applicable, and the minimum spot size requirement may be smaller.
We report a frequency-domain method based on transmission line theory that we name ATLOG-Analytic Transmission Line Over Ground-to model finite or infinite wires interacting with a conducting ground excited by an electromagnetic pulse. This method allows for the treatment of finite or infinite lossy, coated wires above a lossy ground, as well as resting on or buried beneath the ground. Comparisons with full-wave simulations strengthen the validity of the proposed method.
The growth of a cylindrical s park discharge channel in water and Lexan is studied using a series of one - dimensional simulations with the finite - element radiation - magnetohydrodynamics code ALEGRA. Computed solutions are analyzed in order to characterize the rate of growth and dynamics of the spark c hannels during the rising - current phase of the drive pulse. The current ramp rate is varied between 0.2 and 3.0 kA/ns, and values of the mechanical coupling coefficient K p are extracted for each case. The simulations predict spark channel expansion veloc ities primarily in the range of 2000 to 3500 m/s, channel pressures primarily in the range 10 - 40 GPa, and K p values primarily between 1.1 and 1.4. When Lexan is preheated, slightly larger expansion velocities and smaller K p values are predicted , but the o verall behavior is unchanged.
This paper details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG–Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reported method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.
This report examines bounds on the penetrant power through ports of entry into a conductive cavity. We first replace the cavity by a load and consider the maximum power transfer properties of an antenna or an aperture. We consider how limitations on the load quality factor place limits on received power. For general frequency ranges we model the backing region by means of a uniformly distributed matched load along a slot aperture and adjust its value for maximum power transfer. This result is derived in closed form using a transmission line model for the aperture. This result illustrates the reduction in received power for low frequencies with finitely conducting wall materials. At high frequencies it approaches the receiving cross section of a linear array having the slot length dimension. Next we examine a slot aperture in a conducting rectangular enclosure and determine how the cavity wall losses and resulting quality factor limit the penetrant power. Detailed simulations and experimental measurements are compared with each other and with the bounding results to assess the accuracy of the bounds. These comparisons also indicate limitations on the accuracy of the models due to perturbing influences in construction, such as bolted joints.
The di ff usion through shells consisting of either a single conducting or double conducting layers are examined. Exterior drives resulting from Electromagn etic Radiation (EMR), Electromagnetic Pulse (EMP), nearby (indirect) lightning, and DC (low frequency) magnetic fi eldsareused. Boththeinterior fi eld and the induced voltage from a maximally oriented and sized single turn loop are estimated. It is shown that the loop voltage with the empty cavity bounds the case where the center region is excluded by a conducting object. The cases of interior magnetic and electric fi elds from an exterior magnetic drive and the interior electric fi eld from an exterior electric drive are both solved; the magnetic interior fi eldfromanexterior magnetic drive is the only case that results in a nonzero low frequency penetration. Intentionally Left Blank
This report presents analytic transmission line models for calculating the shielding effectiveness of two common calibration standard cables. The two cables have different canonical aperture types, which produce the same low frequency coupling but different responses at resonance. The dominant damping mechanism is produced by the current probe loads at the ends of the cables, which are characterized through adaptor measurements. The model predictions for the cables are compared with experimental measurements and good agreement between the results is demonstrated. This setup constitutes a nice repeatable geometry that nevertheless exhibits some of the challenges involved in modeling non-radio frequency geometries.
The voltage on a single-turn loop inside an enclosure characterizes the enclosure shielding effectiveness against a lightning insult. In this paper, the maximum induced voltage on a single-turn loop inside an enclosure from lightning coupling to a metal enclosure wall is expressed in terms of two multiplicative factors: (A) the normalized enclosure wall peak penetration ratio (i.e., ratio of the peak interior electric field multiplied by the sheet conductance to the exterior magnetic field) and (B) the DC voltage on an ideal optimum coupling loop assuming the ideal penetration ratio of one. As a result of the decomposition, the variation of the peak penetration ratio (A) for different coupling mechanisms is found to be small; the difference in the maximum voltage hence arises from the DC voltage on the optimum coupling loop (B). Maximum voltages on an optimum coupling loop inside a finite cylinder enclosure for direct attachment and a lightning line source at different distances from the enclosure are given in Table 3.
In this paper, fusing of a metallic conductor is studied by judiciously using the solution of the one-dimensional heat equation, resulting in an approximate method for determining the threshold fusing current. The action is defined as an integration of the square of the wire current over time. The burst action (the action required to completely vaporize the material) for an exploding wire is then used to estimate the typical wire gapping action (involving wire fusing), from which gapping time can be estimated for a gapping current greater than a factor of two over the fusing current. The test data are used to determine the gapped length as a function of gapping current and to show, for a limited range, that the gapped length is inversely proportional to gapping time. The gapping length can be used as a signature of the fault current level in microelectronic circuits.
In this paper, linear lightning diffusion into a Faraday cage is studied. The high-altitude Electromagnetic Pulse (HEMP) and nearby lightning are used as examples for a uniform field drive and the direct-strike lightning adjacent to the enclosure is used as a worst-case configuration of a line source excitation. The time-derivative of the magnetic field (HDOT) inside the enclosure for a uniform field drive with a decaying exponential waveform is analyzed and numerically determined. The physically relevant time-derivative of the magnetic field and voltage characterizations of an optimum coupling loop inside the enclosure for a decaying exponential waveform in a worst-case line source coupling configuration are numerically determined. First, the impulse and the unit step response peaks are shown to bound the decaying exponential peaks. Next, a simple fit function for a decaying exponential peak HDOT or a voltage bound for a single-turn loop inside the Faraday cage is constructed from peak responses of the unit step and impulse limiting cases. Excitations used are from (1) a uniform field drive of HEMP or nearby lightning and (2) a line source of direct-strike lightning. Comparisons of HDOT and voltage bounds of the fit function and actual numerical evaluations are given in Table 3.
Simple formulas are given for the interior voltages appearing across bolted joints from exterior lightning currents. External slot and bolt inductances as well as internal slot and bolt diffusion effects are included. Both linear and ferromagnetic wall materials are considered. A useful simplification of the slot current distribution into linear stripline and cylindrical parts (near the bolts) allows the nonlinear voltages to be estimated in closed form.
This report assembles models for the response of a wire interacting with a conducting ground to an electromagnetic pulse excitation. The cases of an infinite wire above the ground as well as resting on the ground and buried beneath the ground are treated. The focus is on the characteristics and propagation of the transmission line mode. Approximations are used to simplify the description and formulas are obtained for the current. The semi-infinite case, where the short circuit current can be nearly twice that of the infinite line, is also examined.