First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher-order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. One proposed technique to stabilize parametric instability is active damping of acoustic modes. We report here the first demonstration of damping a parametrically unstable mode using active feedback forces on the cavity mirror. A 15 538 Hz mode that grew exponentially with a time constant of 182 sec was damped using electrostatic actuation, with a resulting decay time constant of 23 sec. An average control force of 0.03 nN was required to maintain the acoustic mode at its minimum amplitude.

Figure 1

Schematic of the gold ESD comb on the reaction mass (RM), the ring heater (RH), and the end test mass (ETM) with exaggerated deformation due to the 15 538 Hz mode. The color represents the magnitude of the displacement (red is large, blue is small). The laser power in the arm cavity is depicted in red (ARM). Suspension structures are not shown and, while the scale is marked to the left, the distance between the RM and the ETM is exaggerated by a factor of 10.

Figure 2

The relative location of the optical and mechanical modes during Advanced LIGO observation run 1. Mechanical modes measured in transmission of the output mode cleaner shown in blue with mode surface deformation generated from FEM modeling overlay. These modes appear in groups of four, one for each test mass. They have linewidths $\sim 1\mathrm{mHz}$. The optical transfer function for a simplified single cavity is shown in bold red with the ring heater on and turned off in dashed red. The shape of the ${\mathrm{TEM}}_{03}$ mode simulated with oscar [15] is inset below the peak.

Figure 3

The ESD comb pattern printed on the reaction mass (left panel) and the force distribution on the test mass (right panel) with the same voltage on all quadrants.

Figure 4

A simplified schematic of Advanced LIGO showing key components for damping PI in the ETMY. Components shown include input (ITM) and end test masses (ETM), beam splitter (BS), power (PRM) and signal recycling mirrors (SRM), the laser source (LS), quadrant photodetectors, the output mode cleaner (OMC), the OMC transmission photodetector (OMC-PD). While four reaction masses exist, only the $Y$ end reaction mass (ERMY) is shown with key components of the damping loop. These components generate a signal from the vertically orientated differential signal from the quadrant photodetector in transmission of ETMY (QPDY), filter the signal with a 10 Hz wide bandpass centered on 15 538 Hz, apply a gain $K_m$ and a phase $\varphi$ (digitally controlled), then differentially drive the upper right $Q1$ and lower left $Q3$ ESD quadrants.

Figure 5

Damping of parametric instability. (Upper panel) The 15 538 Hz ETMY mode is unstable, ringing up with a time constant of $182\pm 9\sec$ and an estimated parametric gain of $R_m=2.4$. Then, at 0 sec, control gain is applied, resulting in an exponential decay with a time constant of $23\pm 1\sec$ and an effective parametric gain $R_{\mathrm{eff},m}=0.18$. (Lower panel) The control force over the same period.