Aidan, Terra

A continuation of alog 30522

Previously we'd found that frequency drift over a lock stretch is mode dependent - differential drumhead mode drifts more than that same optic's drumhead mode - but surmised that the ratio of (change of frequency / frequency) between two modes would be constant. However, this assumed a spacially uniform change in temperature --- f_m = g(T) --- when a more realistic assumption is some radial dependence of T, so: 

f_m = g(T(r)), where r is radial vector

Since the energy distribution of a given mode is also dependent on r, we can expect some modally unique self heating response. In other words, the more overlap between a given mechanical mode and the hot spots of the optic, the larger the frequency drift we'd expect that mode to have. 

I've looked at ETMY 15009 Hz diff drumhead mode shift compared with ETMY 8158 Hz drumhead shift during twelve hours of a recent lock. 15009 Hz relative frequency change is larger than drumhead relative change and the ratio begins to level off towards a constant after about six hours. We expect (and model) the opposite - the drumhead mode would have more thermal overlap and thus would shift more. This assumes a mostly centered beam spot (or equivalently, assumes r = 0 at the center of the optic). Looking at Jenne's recent beam spot investigation, ETMY spot position was fairly centered during this time, off in yaw by a few mm. The 15009 Hz mode is differential in pitch. (I still suspect some dependence on torsional vs. longitudinal mode movement as suggested in alog 30522.)

We've started having operators run a2l more regularly and before and after powerup at times to get assurance of beam spot position.