This equation can be used to compute the fraction of energy that falls within a specified non-dimensionalized radius “a,” or the non-dimensionalized radius that encloses a specified fraction of energy. The fraction of power in the main lobe for case n can be found by setting a equal to ao, the position of the first zero of Jn, giving: Note also that the integral in Equation 4 is equal to Sn(oo). Thus, the right side of Equation 32 can be substituted into Equation 4, and the result rearranged to give: Equation 35b shows that the peak beam intensity decreases with increasing beam taper. From Equation 1, it can be seen that the main lobe, whose width is proportional to the first zero of the n-th Bessel function, becomes wider. Combining Equations 1, 2b, and 35b yields: A "Good" Radiation Intensity Pattern Suddath [4] has combined the cases for n = 1 and n = 4 to yield a "good" energy intensity of the form:
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