Design criteria for a beam-driven resonant passive transverse deflector for longitudinal beam diagnostics

Conventional radio-frequency (rf) transverse deflecting structures provide high-resolution longitudinal beam diagnostics, but require externally generated high-power rf, waveguide distribution, synchronization and input coupling at the operating frequency. We propose design criteria for a beam-driven resonant passive transverse deflector that does not require an external rf source. A leading drive bunch excites long-range wakefields in an off-axis periodic copper structure and a delayed witness bunch experiences the transverse wake near a zero crossing. The concept is based on the large temporal slope available from high-frequency wake components. A structure designed for installation after the second bunch compressor in the three-bunch-compressor layout of the European XFEL is optimized to place the zero crossing of the drive-bunch-induced transverse wake potential approximately one rf-bucket spacing of the 1.3 GHz linac, behind the drive bunch. The selected geometry produces a multi-mode transverse kick dominated by TM-like modes. We use time-domain wake simulations, frequency-domain decomposition, cell-number scaling, mechanical-tolerance scans, orbit-offset studies and uniform thermal scaling to determine the operating point and its sensitivity. For this geometry, the zero crossing occurs at s0 = 230.6 mm, with a per-cell temporal slope of Scell = 1.186 mV/(pC fs cell). For a compact 1 m structure operated with a 250 pC drive bunch and a 700 MeV witness beam, the estimated temporal resolution is about 33 fs.