Electromagnetic field solutions for infinite and finite cables for conducting half-space models- both frequency - and time-domain
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Electromagnetic field solutions for infinite and finite cables for conducting half-space models- both frequency - and time-domain

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      Introduction The fields of an infinite line source in the presence of a conducting half-space have been examined by Wait and Spies (1971). In any real communication link using a current-carrying cable for the transmitting antenna, the cable is of finite length. Here we examine the fields of a finite length cable carrying a constant current in the presence of a homogeneous conducting half-space. The constant current assumption is valid at sufficiently low frequencies when an insulated cable is grounded at the end points (Wait, 1952; Sunde, 1968). Here we examine both surface and buried cables since both downlink and uplink communication links are of interest. Also, we examine both frequency and time solutions since either CW or pulsed communications may be used. Finally, it is necessary to include both magnetic and electric field solutions since reception could be with either loops or dipoles. Since the finite cable solution is more complicated than both the infinite line source and the short dipole solutions, we explore under what conditions a cable appears to be either infinitely long or very short. Some special cases, such as- the low frequency limit, permit analytical solutions which exhibit the dependence on various parameters, such as cable length, quite clearly. Frequency Domain Subsurface Fields The geometry of a line source of length 2[l] located on a conducting half-space with the observer in the half-space is shown in Figure 1. 
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