ABSTRACT
We have studied the power dependence of superfluid Helmholtz resonators in flat (750 and 1800 nm) rectangular channels. In the A phase of superfluid ^{3}He, we observe a nonlinear response for velocities larger than a critical value. The small size of the channels stabilizes a static uniform texture that eliminates dissipative processes produced by changes in the texture. For such a static texture, the lowest velocity dissipative process is due to the pumping of surface bound states into the bulk liquid. We show that the temperature dependence of the critical velocity observed in our devices is consistent with this surface-state dissipation. Characterization of the force-velocity curves of our devices may provide a platform for studying the physics of exotic surface bound states in superfluid ^{3}He.