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if the tm currents are of the same phase and magnitude they don't cause radiation, when the currents are shifted in phase or magnitude you get common mode radiation,

it may not be the full story of the astroplane but i don't think we can ignore it and opt for a simple explanation.


as to the sigma, don't forget mr CEBIK said the sleeve could radiate in phase with the upper 1/2wave in a none aparent to most people co-linear manner,

the short leg of a j-pole radiates very little with close spaced conductors but causes some radiation with wider spacing = the lobsided pattern.