Summary:
I came aross an interesting suggestion by Yutaro that KAGRA's lowfrequency ALS noise could be limited by the fact that the IMC comes between the point where the frequencies of the PSL and AUX lasers are sensed (i.e. the ALS beat note), and the point where we want them to be equal (i.e. the input of the arm cavity). I wanted to see if the same effect could be at play in the 40m ALS system. A first estimate suggests to me that the numbers are definitely in the ballpark. If this is true, we may benefit from lower noise ALS by picking off the PSL beam for the ALS beat note after the IMC.
Details:
Even though the KAGRA phase lock scheme is different from the 40m scheme, the algebra holds. I needed an estimate of how much the arm cavity moves, I used data from a POX lock to estimate this. The estimate is probably not very accurate (since the arm cavity length is more stable than the IMC length, and the measured ALS noise, e.g. this elog, is actually better than what this calculation would have me believe), but should be the right order of magnitude. From this crude estimate, it does look like for f<10 Hz, this effect could be significant. I assumed an IMC pole of 3.8 kHz for this calculation.
I've indicated a "target" ALS performance where the ALS noise would be less than the CARM linewidth, which would hopefully make the locking much easier. Seems like realizing this target will be touchandgo. But if we can implement length feedforward control for the arm cavities using seismometers, the low frequency motion of the optics should go down. It would be interesting to see if the ALS noise gets better at low frequencies with length feedforward engaged.
* Some updates were made to the plot:
 Took data from Kiwamu's paper for the seismic noise
 Overlaid measured ALS noise
