An improved form of Bessel functions for efficiently and accurately simulating higher order modes in a cylindrical waveguide

We have found an improved form of a Bessel function for accurate and efficient numerical computation. This approximation is good for used in studying a higher order mode in a cylindrical system such as an overmoded waveguide or a fusion gyrotron cavity. The approximated solution is a fine tuned combination of a series expansion and an asymptotic form.