The exponential term is very sensitive to the relative values of and by reciprocity, . A illustrative plot of using varies ratio of is given below, The actual graph plotted is (sin(x))^3*e^{-4*a/cos(x)}*1/(cos(x))^2 where 1<a<2, in steps of 0.05.
It seems that the charge's orbit is only slightly larger than its size in order to give the radiation profile obtained experimentally.