I've taken a look at 18k PI modes after they've had some problematic times over the past few weeks.
1. There are actually 4 modes in the 18035 - 18062 Hz region that are all aliased down from 47kHz, two on ETMY and two on ETMX. See peaks in first attachment. We currently have only two damping modes set up for this range (MODES 27, 28), both driving ETMY and have been mistaking ETMX modes for 'shifting' ETMY modes. Thus, two new damping modes need to be set up to cover the ETMX modes so we do not confuse the peaks. I can do this remotely but am waiting until some down time since this would take us out of Observe.
For reference, the modes in this group are roughly as follows: 18038 Hz ETMY (currently MODE 27), 18041 Hz ETMX, 18056 Hz ETMY (currently MODE 28), 18061 Hz ETMX.
I've looked back through months of alogs and have only found a few times where the ETMX-corresponding 18kHz frequencies have gone unstable. ETMY seems to hold the problematic frequencies, and usually the problem arises when we mistakingly put the damping filters around the ETMX frequencies thinking the peaks shifted.
2. These 18kHz modes shift in frequency roughly twice as much as their respective test mass' drumhead modes. I've looked at the ratio of df/f[18kHz] / df/f[8kHz] over about a dozen long locks; df/f of the two 18kHz modes on ETMX is an average of 1.7x df/f of ETMX 8kHz mode and an average of 2x for ETMY. ETMY has greater variance. The settling time to these values is 6 - 8 hours. For comparison, 15kHz modes shift ~0.7x the 8kHz shift. For example, in one 18 hour lock the 8kHz Drumhead of ETMX shifted 0.08 Hz while the 18061 Hz shifted 0.33 Hz. Thus, long locks and variable temp changes will more greatly change the 18kHz modes' frequencies and hence the additional phase aquired in the static damping bandpass, aka require damping changes. Note that 18kHz modes shift the opposite direction of 8kHz and 15kHz modes since they're aliased.
3. We've already guessed this, but PI problems over the past few months have primarily occured after the previous bad lock saw above average frequency shifts; in numbers, 'bad locks' seem to see df/f of 18kHz modes > 30ppm. This correlates to larger temp shifts as seen by the PEM temp sensors on the chambers - H1:PEM_CS/EX/EY_TEMPERATURE_BSC#_I/ETMX/Y (since resonant frequency is proportional to sqrt Youngs is proportional to temp). Note that the deltaT of these PEM channels is bogus and uncalibrated; I'm just comparing them against other locks.
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We're currently working on a way to automate these larger frequency shifts, but obviously trying to commission some new things now is limited. For prevention going forward, I suggest watching the above PEM channels and regularly stopping at DC READOUT to check mode peak frequencies against BP filters. Both BP filter and PLL Set Frequency need to be shifted accordingly. Most of the PI problems like those we've seen the past months could be prevented with frequency pre checks and some sort of chamber temp monitor/alert system.
I've attached several examples of good and bad locks. Top plots show df/f of 8kHz drumheads, 15kHz, and 18kHz modes. Middle plots show df/f of either 15 or 18kHz mode over df/f of 8kHz mode. Bottom plots show PEM temp sensors on the outside of the optic chambers (with bogus units). 2nd (lock with very little temp change) and 3rd (lock with larger temp change) attachments are good, 4th and 5th are bad. By 'bad' I mean that lock had PI ring up at the end of it or the lock immediately after broke due to PI. 'Good' means we lost lock for unPI reasons and had no problem with the next lock.
