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The LCLS-II is a high repetition-rate Free-Electron Laser (FEL) facility under construction at SLAC. A new 4-GeV continuous wave (CW) superconducting (SC) L-band linac is being built to provide an electron bunch rate of up to 1 MHz, with bunches rapidly switched between two FEL undulators. It is desirable to provide peak current (i.e., pulse length) control in each FEL independently by varying the RF phase (chirp) prior to the first bunch compressor. However, the high-Q, SCRF, with its 1-ms fill-time, cannot be changed within one bunch spacing (1 us). So to provide a small chirp adjustment from bunch to bunch, we propose a short CW copper RF accelerating cavity, located just after the injector, with < 250-ns fill-time designed to adjust the beam chirp at zero-crossing phase. We examined RF cavity designs spanning RF frequencies from L-band to X-band. We considered both SW and TW structures. We found an optimal solution with 2 cm iris diameter, SW RF cavity, operating at C-band with input power of only 10 kW. If one can afford to operate with smaller diameter, from a wakefield point of view, then similar structure at X-band may require only 500 W with 5 mm iris diameter.
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