DOE OSTI2010
The report explains radio frequency (RF) coupling to unconventional dipole antennas. Normal dipoles have thin equal length arms that operate at maximum efficiency around resonance frequencies. In some applications like high-explosive (HE) safety analysis, structures similar to dipoles with ''fat'' unequal length arms must be evaluated for indirect-lightning effects. An example is shown where a metal drum-shaped container with HE forms one arm and the detonator cable acts as the other. Even if the HE is in a facility converted into a ''Faraday cage'', a lightning strike to the facility could still produce electric fields inside. The detonator cable concentrates the electric field and carries the energy into the detonator, potentially creating a hazard. This electromagnetic (EM) field coupling of lightning energy is the indirect effect of a lightning strike. In practice, ''Faraday cages'' are formed by the rebar of the concrete facilities. The individual rebar rods in the roof, walls and floor are normally electrically connected because of the construction technique of using metal wire to tie the pieces together. There are two additional requirements for a good cage. (1) The roof-wall joint and the wall-floor joint must be electrically attached. (2) All metallic penetrations into the facility must also be electrically connected to the rebar. In this report, it is assumed that these conditions have been met, and there is no arcing in the facility structure. Many types of detonators have metal ''cups'' that contain the explosives and thin electrical initiating wires, called bridge wires mounted between two pins. The pins are connected to the detonator cable. The area of concern is between the pins supporting the bridge wire and the metal cup forming the outside of the detonator. Detonator cables usually have two wires, and in this example, both wires generated the same voltage at the detonator bridge wire. This is called the common-mode voltage. The explosive component inside a detonator is relatively sensitive, and any electrical arc is a concern. In a safety analysis, the pin-to-cup voltage, i.e., detonator voltage, must be calculated to decide if an arc will form. If the electric field is known, the voltage between any two points is simply the integral of the field along a line between the points. Eq. 1.1. For simplicity, it is assumed that the electric field and dipole elements are aligned. Calculating the induced detonator voltage is more complex because of the field concentration caused by metal components. If the detonator cup is not electrically connected to the metal HE container, the portion of the voltage generated by the dipole at the detonator will divide between the container-to-cup and cup-to-pin gaps. The gap voltages are determined by their capacitances. As a simplification, it will be assumed the cup is electrically attached, short circuited, to the HE container. The electrical field in the pin-to-cup area is determined by the field near the dipole, the length of the dipole, the shape of the arms, and the orientation of the arms. Given the characteristics of a lightning strike and the inductance of the facility, the electric fields in the ''Faraday cage'' can be calculated. The important parameters for determining the voltage in an empty facility are the inductance of the rebars and the rate of change of the current, Eq. 1.3. The internal electric fields are directly related to the facility voltages, however, the electric fields in the pin-to-cup space is much higher than the facility fields because the antenna will concentrate the fields covered by the arms. Because the lightning current rise-time is different for every strike, the maximum electric field and the induced detonator voltage should be described by probability distributions. For pedantic purposes, the peak field in the simulations will be simply set to 1 V/m. Lightning induced detonator voltages can be calculated by scaling up with the facility fields. Any metal object around the explosives, such as a work stand, will also distort the electric fields. A computer simulation of the electric fields in a facility with a work stand and HE container is shown. In this configuration, the work stand is grounded, and the intensity of field around the HE (denoted in dark blue) is reduced relative to the rest of the work bay (denoted lighter blue). The area above work stand posts has much higher fields indicated by red. The fields on top of the container are also affected. Without an understanding of how the electric fields are distributed near the detonator cable and container, it is not possible to calculate the induced detonator voltage. The average lightning current has rise- and fall-times of 3 us and 50 us respectively, and this translates to a wavelength that is long when compared with the length of the HE container or detonator cable.