It is shown that the low‐power linear behavior of a cavity (here a spherical one) partially filled with plasma plays a fundamental role in understanding the formation of an rf plasma inside it athigher powerlevels. The rf plasma is found to be sustained in one of the linear resonant states of the system. With moderate rf power (10–100 w), it is possible to sustain bounded plasmas in the cavity having densities far above the critical one. The value of the density depends, as is theoretically predicted, essentially on the frequency and only slightly on the power level of the exciting signal.