Next generation plasma heating experiments in controlled thermonuclear fusion research using electron cyclotron waves require single-mode gyrotrons capable of delivering output powers at the 0.5-1.0 MW level with frequencies around 140 GHz. To lower the thermal loading of the cavity wall (ohmic losses) at such high output powers to manageable values and to reduce the problem of mode competition, a highly overmoded resonator operating in a rotating, asymmetric volume mode is required. Following the current experiment employing TE10,4 , KfK plans to use one of the modes TE22,n (n=4,5,6) as cavity working mode for a gyrotron oscillator which includes an internal quasi-optical mode converter to the fundamental Gaussian free-space beam mode. Results of Russian gyrotron experiments  indicate that these modes are promising candidates for 1 MW, CW operation. The present work compares the mode series TE22,n (n=4,5,6) as working modes for 140 GHz, 0.5-1 MW, CW gyrotrons, studies the influence of a misaligned electron beam in the cavity on the gyrotron operation and shows that the conversion of the operating mode to parasitic modes can be nearly avoided by introducing smooth, curved transition regions between the cylindrical central part of the resonator and its conical cutoff section and the nonlinear uptaper, respectively. Cavity and non-linearly tapered output waveguide are optimized as one single component.