We propose a novel method to generate femtosecond and sub-femtosecond photon pulses in a freeelectron laser by selectively spoiling the transverse emittance of the electron beam. Its merits are simplicity and ease of implementation. When the system is applied to the Linac Coherent Light Source, it can provide x-ray pulses the order of 1 femtosecond in duration containing about 10 10 transversely coherent photons. † Emma@SLAC.Stanford.edu ‡ On leave from Deutches Elektronen Synchrotron (DESY),

We consider the impedance of a structure with rectangular, periodic corrugations on two opposing sides of a rectangular beam tube. Using the method of field matching, we find the modes in such a structure. We then limit ourselves to the case of small corrugations, but where the depth of corrugation is not small compared to the period. For such a structure we generate analytical approximate solutions for the wave number k, group velocity v g , and loss factor for the lowest (the dominant) mode which, when compared with the results of the complete numerical solution, agreed well. We find if w a, where w is the beam pipe width and a is the beam pipe half-height, then one mode dominates the impedance, with k 1= w p ( is the depth of corrugation), 1 ÿ v g =c , and 1=aw, which (when replacing w by a) is the same scaling as was found for small corrugations in a round beam pipe. Our results disagree in an important way with a recent paper of Mostacci et al. [A. Mostacci et al., Phys. Rev. ST Accel. Beams 5, 044401 (2002)], where, for the rectangular structure, the authors obtained a synchronous mode with the same frequency k, but with . Finally, we find that if w is large compared to a then many nearby modes contribute to the impedance, resulting in a wakefield that Landau damps.