Figure 1. During the transient the power in the arms increased by 1%. This is most likely the sign that the input beam is not well mode matched with the arms, and that for different end mirror radius of curvature the matching becomes better. As we change only the end mirror radius of curvature, this corresponds to a mode that has the same wavefront curvature at the level of the input mirror (parallel to the mirror surface), but a different beam radius at the level of the input mirror.

Figure 2 shows the effect on the mode order 2 frequency. Purple is before the step, blue and red are roughly when the power in the arms is maximum during the transient (red is RH cooling and blue is RH warming), green is the maximum excursion of the RH change, ie two minutes before the ring heater was put back to the nominal correction. The maximum excursion corresponds to an 800Hz change in the mode frequency, which should correspond to a 14 meter change in radius of curvature. The peak in arm powers corresponds to 500Hz frequency change, or 8 meters in radius of curvature.

Using equation (53) of [H. Kogelnik and T. Li, "Laser Beams and Resonators," Appl. Opt. 5, 1550-1567 (1966) ] an 8 meter increase in EM radius of curvature correspond to 2.5% decrease in the resonant mode radius at the surface of the input mirror. Which means that to match the arm mode in nominal condition the input beam radius at the IM surface needs to be increased by 2.5%.

Figure 3 and 4 shows mode order 6 and 7, they are moving in opposite direction to the order 2 mode, which is not what one would expect from a simple radius of curvature change. And they also move by a smaller amount, about 1kHz instead of 2kHz. This means that the mode order 9 most likely did not move by the expected 3kHz. This effect of modes moving in opposite direction has already been seen for previous steps https://logbook.virgo-gw.eu/virgo/?r=66937. My guess is that it means the ring heater actuation far from the mirror center is not well approximated by a simple radius of curvature change (parabolic change), but that there is a more complicated shape and modes of high order are able to sense that.

Figure 5 in the meantime there was not a significant decrease in glitches during that test at any time, if anything there was an increase for part of that time.

Figure 6 is a simple histogram of the glitches with SNR>10 during that day with bins of 30 minutes, without taking into account that the interferometer is not locked some of the time. There is no significant improvement during the test on that figure either. A year ago such a histogram would have 1 or 2 glitches per bin (the 25 minute glitches).

Figure 1During the step of the ring heater on June 20 the modes order 7 and 11 have moved in opposite direction, while simple simulations of a single arm would expect for all modes to move in the same direction in the arm FSR, with the change in the FSR smaller for very high order modes as they start to be clipped in the arm.

I have reused the Finesse 3 simulation that Augustin has been developping for scattered light (https://git.ligo.org/augustin.demagny/finesse-simulation-04)  to look instead at the CARM to B1 transfer function. These simulations include a misalignment of SR by 2urad. I have added appertures of 170mm in radius to add realistic losses to very high order modes, and simulated with the max TEM number of 10.

Figure 2 shows the result around the first FSR for a nominal end mirror radius of curvature of 1683 meters, while Figure 3 shows the same for 1679m radius of curvature for both end mirrors. It shows the same effect that the two HOM spanning around the first FSR of the arm move in opposite directions, which is counterintuitive, but similar to what has been observed experimentally on figure 1. Note that peak in the middle of the figure is slightly above 50kHz, while the analytical calculation predicts an FSR with a spacing of 49'969 Hz (slightly below 50kHz). Does this mean that the peak we see is not the FSR, but something else? What is strange is that it remains in the simulation when the max TEM is reduced to 0, so it cannot be the order 9 mode. The side modes around 44kHz and 56kHz, also remain present for max TEM 1, and disappear for max TEM 0, so this is actually two images of the order 1 mode, and then it makes sense that they move in opposite direction when the RoC is changed.

Figure 4 and 5 shows the frequency range of modes order 1-3, respectively for 1683m on EM and 1679m. These modes behave as expected, moving to lower frequency for a shorter radius of curvature.

Figure 6 and 7 shows the frequency range of modes 4-6, the picture is confused with more modes than one would expect. Some of the modes move to higher frequency for a shorter RoC, while others move to lower frequency. In particular the mode around 33kHz, which could be the order 6 mode moves to higher frequency, so the opposite of the low order modes.

I will add the modified code into git under 'high order mode - CARM.ipynb'.