We report on the research and development of high gradient low frequency closed-cell structures for possible use in a muon cooling channel. The presence of strong magnetic fields precludes the use of superconducting RF. These multi-cell structures have the "beam iris" closed by conducting foils, grids of tubes or other isolating structures. This greatly increases the shunt impedance and also allows the individually powered cells to be set independently to any phase. The isolating structure must be made using a very small amount of low-Z material to avoid unacceptable scattering of the muon beam. Various cell designs and methods of closure are presented and compared. The problems of RF heating and breakdown at high gradient are discussed with regard to the vulnerable isolating structures. RF, thermal and stress analyses are presented and the integration of the RF with the solenoid cryostat and liquid hydrogen absorbers is considered.
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