The size and weight of a high power microwave (HPM) source can make a difference in strategic use. The compactness of the virtual cathode oscillator (vircator) is undoubtedly the most significant advantage of this device. Civil industry and agriculture can use it to treat objects, food, and soils for disinfestation and disinfection. Vircators could also generate electromagnetic pulses (EMPs) to force the arrest of vehicles and drones; EMPs could inhibit or activate improvised explosive devices (IEDs). The coaxial type vircator is a highly compact device. Due to its symmetric geometry, coaxial vircator is typically designed to work with a TM 01 mode. Still, when radiated into space, this mode gives maximum RF energy away from the antenna axis, a situation not desired. Instead, the TE 11 is convenient in applications involving precise antenna pointing since this mode gives a maximum RF energy precisely aligned to the antenna axis. By studying Mathieu functions applied to elliptical waveguides, we improve the performances of a TE 11 mode coaxial vircator using an elliptic drift tube (EDT). This is a completely innovative solution to reduce the mode competition inside the coaxial vircator. The rms and peak output power efficiency of the EDT coaxial vircator were measured on the TE 11 mode, obtaining the values of 6.1% and 10%, respectively, with a peak power of 450 MW in a highly compact device.