The Powered Resonance Tube (PRT) actuator, in which a high-speed jet impinges on the open end of a quarter-wavelength resonance tube, is an effective device for producing high-amplitude pressure oscillations. For low frequency applications, however, the size of the PRT actuator can be quite large, due to the length of the quarter-wavelength tube. In order to reduce the actuator size, we propose an alternative design in which the quarter-wavelength tube is replaced by a Helmholtz resonator. The Helmholtz resonator has a narrow neck coupled to a backing cavity of much larger diameter. The resonant frequency is determined by the ratio of fluid stiffness in the backing cavity to fluid mass in the neck; proper choice of geometry leads to a resonator length that is small compared to the length of a quarter-wavelength tube. We present an analysis of Helmholtz resonator behavior which predicts the influence of geometry on the resonant frequency and the capacity of the resonator to absorb an unsteady volume flux. Comparisons are made with companion numerical simulations for a Helmholtz PRT actuator.