The design studies of a relatively higher-order mode, TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10,4</sub> , gyrotron have been presented for reduced beam interception, ohmic loss, and dimensional tolerance issues. The tapered RF interaction cavity and the nonlinear taper (NLT) designed using axial mode profile calculations were optimized with time-dependent, multimode theory with tapered magnetic field profile. 3-D particle-in-cell (PIC) simulation predicted the desired device temporal growth with ~40% efficiency and the percentage of agreement with the analytical values is presented. Device behavior under practical tolerances has also been studied confirming the rated device performance. Further, its interaction structure design has been checked from thermal considerations without any additional cooling fins. Furthermore, Denisov type quasi optical mode (QOM) launcher along with a sapphire disk window has been designed using in-house developed algorithm and coupled-mode theory-based code. The designed profile provides >98% Gaussian content on the launcher cut.