Recent Parametric Instability Modeling

1. Recent Parametric Instability Modeling Bill Kells Caltech LIGO G070145-00-Z

2. PI “R” calculation from entire cavity field • Previous: model arm cavity field as discreet SHOs • Cavity specific modes {j}, Qj, Ljm need accurate specification • Proves difficult for modest order HTMs: high loss/distortion • Is a significant “background” PI missed (K. Thorne, W. Kells: aS ~cancels S)? • Now: build on FFT tool, ideally suited to net SS field from <<l static distortions (acoustic surface amplitude from FEA) • Instead of SB(+/- fm) modes: FFT cavity length shifted by for proper Stokes (a-Stokes) simulation. Each acoustic {m} a-Stokes Braginsky, Vyatchanin Stokes G070145-00-Z

3. f Gouy (FSR)/p 2 FSR FSR R See T060207 & suppl. Acoustic mode frequency FFT “R” values: AdvLIGO arm • Complete RS-RaS for AdvLIGO arm FEA generated {m}: fm to few % No flats, ears, wedge ~only 6 R>1 No anomalous “background” All high R values correspond to known HTMs Simple cases agree with analytic & previous results G070145-00-Z

4. Full Ifo: essential Features • Single arm only • PI gain strongly depends on Qm and Qj • For AdL this limits plausible {m} to fm<90kHz, ~3-4000 Stokes dominated modes • Above at least 6th order {j} cavity loss too high • 1st order (tilt) and perhaps 2nd order (curvature) special (control possible). • PRC only (AdL parameters) • ~10x recycling enhancement of PI gain. However: • This peaking is ~10x narrower (+/-2 Hz tune of PI mode from arm res.) • Arms must have nearly same Gouy phase (D ROC <1-2m) • No enhancement (over arm alone PI gain) for > 3d order Pi modes (too lossy) • PRC + SRC (AdL parameters) LIGO-T060159 & G060475 (Braginsky, Vyatchanin, et al TBP) • Peak gain enhancements (& widths) < PRC alone. • Significant “pulling” of peaks with SRC phasing (GW detuning + Gouy multiplet) • Certain phases are dangerous: D ROCarm “protection” obviated Complete survey Via FFT simulation G070145-00-Z

5. ½ x contour 1x 10x 4x 2x Recycled tuning landscape 3d order PI arm mode 1st order PI arm mode 8x contour Arm-Arm D ROC=1m 2x contour Arm-Arm D ROC=1m Arms identical Other arm PI mode detuning Hz PRC alone (unstable) 1x contour SRC detune=.983p (AdL nominal) detune=.95p detune=.8p PI arm detuning Hz detune=.5p, .8p , .9p detune=.5p (same as PRC) G070145-00-Z

6. PI gain normalized to single arm value Even modes > 5x suppression Other arm tune Hz .01 ~10 max .1 1 .04 .5 .02 .2 Odd modes PI arm tune Hz Fine Tuning !? • Incorporating SRC/PRC stability DOF, can AdLIGO optics configuration be “tuned” to mitigate PI? • Generally: no. Special case: confocal PRC + DROC large (D. Ottaway) can suppress all PI mode gains of concern large factor below single arm value. G070145-00-Z

7. Arm alone d=0 Arms+PRC d=0 PI gain relative to Dw=0 arm alone PRC+SRC (detune=.8p) d=200 Hz; Dw shifted 10.3 Hz PI arm detuning Hz PI gain widths ! • SRC increases enhancement ridge “area” in 2 arm tuning • Large SRC Gouy phase range leaves ridge unavoidable for allowed DROC • However, width of ridge is also critical ! Likelihood of “hitting” enhancement: ~(enhancement width)/FSR =4Hz/38kHz x ~6000/2 acoustic modes x 4 TM x 2-3 HTMs = order 3 probable cases • Already PRC reduces width factor 2 • SRC narrows further, so may actually be Advantageous if a very few exact resonances can be avoided (e.g. thermal tuning) G070145-00-Z

8. gain =6 Arg[r]=0.94p Arg[r]=0.8p d (Hz) d (Hz) D (Hz) D (Hz) G070145-00-Z

9. D (Hz) G070145-00-Z