Theory of the infinite cylindrical antenna including the feedpoint singularity in antenna current

The us ual id e~,li zed model for a cy lindrical antenna consists of a n extrcm ely thin-walled t llbe of infini te co ndu ctivi ty w it h an infin itesima lly narrow circLlmfe rcnti a l gap.Phy ~i ca ll .\•,one expects the an te nn a current at the feedpoint of such a mod el to be infi ni te.H owevc r, t he sin gula rity in feedpoin t curre nt is not detcctcd by cit hcr itcrativ c or Fouri cr sc ri cs solutions of t hc intcgral cqu ation for a ntenn a cul't'cnt.Thcsc solut io ns arc co ntinuous on JzJ50 h, whcrc h is the half-l ength of t he a ntc nna.They a rc a lso in good agrcc mc nt with cach othcr a nd with experimental data.From a forma l poin t of v icw this amo un ts to say in~ that thc convcntional solu t ion s o f t hc in tcg ra l cquat ion ar e solu t ions on most, but not a li , of the rangc JzJ50h.Ins idc a small rcg ion , IzJ50z" the con cc t solution to th c intcgral equat ion is p eculiar to t hc id cali zed ge nerator.Low-o rd er itcrative and Fou ricr sc ri cs solu t ions ignorc thesc pccu liariti es and producc a s mooth cll1' re nt d istri bulion which ca n bc u scd in predi ct ing t he behav ior of practical st ructurcs .This p ape r is co ncc rn ccl with a dctail ed study of t hc t hco rctical CUl'I'ent nCIll' t he rccdpo int of t he idealized model a nd the d cvclopmcut of a dcfin ition of z •.