As the generated wavelength shortens, overmoded slow wave structures (SWSs) with large diameters are employed in O-type Cerenkov high power microwave (HPM) generators to achieve high power capacity. However, reported experimental results suggest that overmoded slow wave HPM generators working at millimeter wavelength output much lower power than those working at X-band do, despite the fact that the value of D/lambda (here, D is the average diameter of SWSs and lambda is the generated wavelength) of the former is much larger than that of the latter. In order to understand this, the characteristics of the power capacity of the TM0n modes in overmoded SWSs are numerically investigated. Our analysis reveals the following facts. First, the power capacity of higher order TM0n modes is apparently larger than that of TM01 mode. This is quite different from the conclusion got in the foregone report, in which the power capacity of overmoded SWSs is estimated by that of smooth cylindrical waveguides. Second, the rate at which the power capacity of TM01 mode in overmoded SWSs grows with diameter does not slow down as the TM01 field transforms from "volume wave" to "surface wave." Third, once the diameter of overmoded SWSs and the beam voltage are fixed, the power capacity of TM01 wave drops as periodic length L shortens and the generated frequency rises, although the value of D/lambda increases significantly. Therefore, it is necessary to investigate the capability of annular electron beam to interact efficiently with higher order TM0n modes in overmoded SWSs if we want to improve the power capacity of overmoded O-type Cerenkov HPM generators working at high frequency. (C) 2013 AIP Publishing LLC.