High brightness linear accelerators typically produce electron beams with peaks in the head and/or tail of the current profile. These current horns are formed after bunch compression due to non-linear correlations in the longitudinal phase space and the higher order optics of the compressor. It has been suggested that this higher order compression can be corrected by inserting an octupole magnet near the center of a bunch compressor. However, this scheme provides a correlated transverse kick leading to growth of the projected emittance. We present here a method whereby octupole magnets are inserted into two sequential bunch compressors. By tuning a $pi$ betatron phase advance between the two octupoles, the correlated transverse kick from the first octupole can be corrected by the second, while providing a cummulative adjustment of the higher order compression.
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