J. Kissel, R. Kumar, B. Weaver

This aLOG continues, and puts to rest, the investigations as to why the H1SUSFC1 P2 and P3 modes -- and more concerningly the inter-mode zero -- are still high in frequency (see yesterday's LHO:60787 and older LHO:60766), even after the errant M2 to M3 wire thickness was swapped for "nominal" (see LHO:60741). Recall "nominal" thickness / diameter is supposed to be 0.0047 [inches] (i.e. 4.7 [thousandths of an inch] or "[thou]", or a wire radius of 59.7e-6 [m]).

After a team huddle this morning, Betsy, Rahul, and I uncovered that when, in LHO:60741, Rahul says "[...] replacing the wire with correct thickness (0.005 inch diameter, verified using calipers) [...]" there was no rounding involved in the statement -- the wires have been replaced with 0.005" thickness wires, not the nominal 0.0047".

Surprised that a difference of 0.0003" diameter (3.8e-6 [m]) makes this much of a difference, I've played around with the model to confirm (thanks to a handy-dandy script I wrote in 2012, comparetripleparams.m, and reminding myself of which variable means what with T040072) that:
    (a) Changing the nominal model's "r3" parameter (the radius of the M2 to M3 wire) from 59.7e-6 [m] to 63.5e-6 [m] (from diameter of 4.7 [thou] to 5 [thou]) indeed moves up the P2 mode and the adjacent zero right with it, exactly on top of the current H1SUSFC1 data.
    (b) As a quick "will it still work if we don't fix it?" test -- I use a generic set damping loops that come with the production triple model (some old 2012 velocity damping filters from L1 SUS MC2, that might still be in place honestly...), I confirm there's evidence that this level of plant change will cause loss in stability or any less Q reduction in the damping loops with this change.
    (c) I also recall that these modes are sensitive to the d1 distance between the M1 to M2 blade tip / breakoff point height w.r.t the M1 center of mass -- but importantly, changing this d1 by a lot in either direction only changes the P2 and P3 mode resonances, not the intermode zeros. I would guess that some linear combination of M1 to M2 blade tip height and manufacturers differences in thickness of the M2 to M3 wires would cause the spread that's otherwise seen in the rest of the suspensions see in the whole collection shown in LHO:60787.

Conclusion
    The unintended M2 to M3 wire parameter change of H1SUSFC1 from 4.7 [thou] to 5.0 [thou] diameter is acceptable and will function as any other HSTS does without much extra thought at all. We should and shall carry on as is.

Proof is in the Plots
    I demonstrate (a) with the first attachment, triplemodelcomp_2021-11-30_HSTS_r3exploration_M1_P2P.pdf. Compare nominal solid, thin, orange "nominal" r3 "=" 4.7 [thou] model and solid, thin, maroon r3 "=" 5 [thou] model against the latest measurement of FC1 in solid, thick, red latest H1SUSFC1 measurement. One can see that the latest H1SUSFC1 measurement solid, thin, maroon model, with 5 [thou] agree rather exquisitely, just like the solid, thin, plum r3 "=" 8 [thou] model agreed with the solid, thick, plum measurement of FC1 when it had the corresponding wire thickness.

(b) is demonstrated in the same first attachment with the damped versions of dashed, thin, orange "nominal" r3 "=" 4.7 [thou] model and dashed, thin, maroon r3 "=" 5 [thou] models. One can see that the same damping loop filters will do similar things to these similar plants. Makes sense, as this damping loop filter design is *very* generic, with no features that are tuned to these specific mode frequeuncies. Also, while I haven't explicitly looked at the phase margin change between these different plants, I that suspect even a low-noise design, where we push the phase margin harder with more aggressive ~10 Hz low passes would also be fine, given that the highest P3 mode remains relatively unchanged with a 5 [thou] M2 to M3 wire.

I demonstrate (c) in the second attachment, triplemodelcomp_2021-11-30_HSTS_d1exploration_M1_P2P.pdf. I see the following from this:
   (1) There's no change in the intermode zero, regardless of the change in d1. 
   (2) Comparing the change in response in *other* degrees of freedom -- see third and fourth attachments,
        r3 change -- triplemodelcomp_2021-11-30_HSTS_r3exploration_M1.pdf and
        d1 change -- triplemodelcomp_2021-11-30_HSTS_d1exploration_M1.pdf
       the d1 change has *much* more impact on other DOFs than the r3 change, which is consistent with the various FC1 data we have, and
   (3) Looking at the lowest and highest frequency collection modes we've seen in solid, thick, magenta H1SUSMC1 and solid, thick, cyan H1SUSSR2, they span a range of d1 = nominal + (adjustment, as indicated in the legend) being as low as d1 = 2 + (-3) = -1 [mm] or as high as d1 = 2 + (+4) = 6 [mm].


The story behind 5 [thou] instead of 4.7 [thou]
    I'm parroting what Rahul told me this morning, but when the materials for building HSTSs for A+ were inventoried, Bartlett and Kumar found the 4.7 [thou] spool of wire that we used for all aLIGO HSTSs, but there was concern that it was old and fragile, having been purchased in 2012. As a result, we went out for quote for 4.7 [thou] wire, but at the time could not find it, and someone made the decision that 5 [thou] was good enough (is there a RODA? an ECR / Resolved IIET? Dunno). As such, here we are today, a few years after the SUS was built circa 2019 (LHO:52425the A+ HSTSs were some of the first A+ SUS built, since "we knew how to build them" and we had the person power during O3), uncovering this lil' nugget. 

Rahul also recalls that since LLO went out for quote on their A+ SUS HSTS parts ~a year later, they *were* able to push hard on vendors and find the nominal 4.7 [thou] wire thickness. We should confirm this.