A method and apparatus are disclosed for improving resolution and duty-cycle of a multi-reflecting TOF mass spectrometer (MR-TOF) by arranging a cylindrical analyzer having an appropriate radial deflection means, means for limiting ion divergence in the tangential direction and a pulsed source providing ion packet divergence of less than 1 mm*deg. There are disclosed embodiments for fifth-order focusing cylindrical ion minors. Separate embodiments provide parallel tandem MS-MS within a single cylindrical MR-TOF.