Weak electromagnetic missiles

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It is known that the energy flux of a transient electromagnetic wave can decrease with distance more slowly than the usual inverse-square law. Such cases are referred to as electromagnetic missiles. The rate of decrease depends on the frequency spectrum of the exciting current. For a class of excitations where the frequency spectrum behaves as ‖ω‖−1/2−ε , the rate of decrease has been stated to be z−2ε for 0≤ε≤1, implying that ε must be less than 1 in order for the decrease to be slower than z−2. It is shown that, in fact, the case ε=1 results in a dependence of z−2 ln z, i.e., an electromagnetic missile—albeit a weaker one than those previously discussed.