[en] Rapid cycling proton synchrotrons, such as the proposed LAMPF II accelerator, require approximately 10 MV per turn rf with 17% tuning range near 50 MHz. The traditional approach to ferrite-tuned cavities uses a ferrite which is longitudinally biased (rf magnetic field parallel to bias field). This method leads to unacceptably high losses in the ferrite. At Los Alamos, we are developing a cavity with transverse bias (rf magnetic field perpendicular to the bias field) that makes use of the tensor permeability of the ferrite. Initial tests of a small (10-cm-diam) quarter-wave singly re-entrant cavity tuned by several different ferrites indicate that the losses in the ferrite can be made negligible compared with the losses due to the surface resistivity of the copper cavity