A simple way of solving transient thin‐wire problems

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Abstract
A simple way of calculating the transient response of a thin wire is presented. The method is based on (i) the asymptotic antenna theory for thin wires and (ii) an expansion of the induced current in terms of the so‐called natural modes. An explicit series representation of the transient induced current in terms of the resonances of the wire is obtained and this representation is used to numerically evaluate the wire current using a desk calculator. A comparison is made between the results obtained using the asymptotic theory presented here and those obtained from a numerical solution of a space‐time integral equation. Good agreement between the results is found except for early times. The method points to a fast way of estimating the transient induced currents on more complicated structures such as a wire model of an aircraft.

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