[en] The octupole plug concept offers the attractive possibility of reducing the length of the plug and transition sections in tandem mirror reactors. In the Tandem Mirror Experiment Upgrade (TMX-U), we are designing an octupole plug-transition that will replace our current quadrupole plug-transition. The reduction in length is made possible by the more nearly circular plasma cross section throughout the plug and transition sections. The principal physics of the design is the magnetohydrodynamic (MHD) stabilization of the core plasma in the plug by a hot electron ring in the mantle region surrounding the core. This hot electron mantle is MHD stable because of the good curvature field lines provided by the octupole. The positive radial pressure gradient in the hot electron mantle in turn stabilizes the core's plasma. Each octupole set consists of six coils replacing the transition and plug sets in the existing TMX-U experiment. The central cell coils will remain unchanged. Five of the coils for each of the new sets will be fabricated, while one, the 6-T mirror coil, will be reused from TMX-U. This paper will elaborate on the design configuration of the magnets. In particular, the configuration provides for adequate neutral beam lines-of-sight, and access for 0.615 MW of electron-cyclotron resonant heating (ECRH) on each end