I have done a quickie look at Optickle to see how the linewidth of an arm cavity changes versus the configuration.
To do this, I make different configurations, and do a sweep of ETMX. For each configuration, I find the max peak value, and then find the points that are at half that value. The distance between them is the full width at half max.
FWHM_DRFPMI = 3.8750e-11 meters
FWHM_PRFPMI = 3.8000e-11 meters
FWHM_SRFPMI = 2.3200e-09 meters
FWHM_FPMI = 1.1900e-09 meters
So, for the ALS to hold within 1/10th of a linewidth for the full IFO configuration, we want the ALS noise to be on the order of 3 picometers RMS. If I recall correctly, that's about an order of magnitude better than we currently have.
EDIT 8 Nov 2013, JCD: New log-y plot: