\chapter{Reducing differential motion of aLIGO seismic platforms}
\label{CPSdiff}
During 2019, I spent some months working on LIGO Hanford site (Washington, USA). This experience allowed me to be critically involved in the complicated life of a gravitational-wave interferometer. In particular, I was given the opportunity to study how to improve LIGO performances at low-frequency, focussing on the reduction of seismic motion of the platforms where the optics live.\\
In this chapter I will demonstrate how we can modify the software set up of LIGO in order to obtain different and possibly better performances for seismic motion stabilization, faster and longer locking mode and, ultimately, more gravitational waves detections. The detailed computations included in this chapter are original and partially presented to the LIGO community and stored in LIGO DCC \cite{proposal}\cite{technote1} .\\
During 2019, I spent some months working at the LIGO Hanford site (Washington, USA). This experience allowed me to be critically involved in the complicated life of a gravitational-wave interferometer. In particular, I was given the opportunity to study how to improve LIGO performances at low-frequency, focussing on the reduction of seismic motion of the platforms where the optics are located.\\
In this chapter I will demonstrate how we can modify seismic control configuration of LIGO in order to obtain different and possibly better performances for seismic motion stabilization, faster and longer locking mode and, ultimately, more gravitational waves detections. The detailed computations included in this chapter are original and partially presented to the LIGO community and stored in LIGO DCC \cite{proposal}\cite{technote1} .\\
This work has been developed in collaboration with LIGO Hanford and LIGO Livingston laboratories, Stanford University, MIT and UoB and completed at UoB during 2020.\\
This chapter is partially including some technical notes I shared with LIGO collaboration and the contents of this study have been presented at conferences and workshops \cite{chiatalk}.\\
Essential information about the sections of LIGO involved in this study has been exposed in detail in Chapter \ref{LIGO}.
\section{Motivation: Duty cycle on LIGO}
Lock loss events are the main sources of preventing continuous observations for long periods of time: when light loses resonance in the cavities, a lock loss happens and the control systems of the optical cavities are under effort to restore stabilization. This means that during lock loss the interferometer is no longer able to be stable and the observing time is interrupted \cite{biscans}.\\
Duty cycle is one of the main topic where commissioners focus on before starting an observing run \cite{biscans}\cite{kisseltalk1}. It is needed not only to observe more gravitational waves, but also to identify noise sources and improve sensitivity \cite{biscanstalk}.\\
Duty cycle is one of the main topics where commissioners focus on before starting an observing run \cite{biscans}\cite{kisseltalk1}. It is needed not only to observe more gravitational waves, but also to identify noise sources and improve sensitivity \cite{biscanstalk}.\\
Since the number of detected events over a time period N(t) is proportional to the volume of Universe under observation V, the observing time t and the rate R of astrophysical sources that can occur in a certain volume:
\begin{equation}
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@@ -55,7 +55,7 @@ In particular, during O3 run, it was observed that the chambers in the corner st
On another side, reducing the differential motion between the chambers means to reduce a source of noise at low frequency (5-30 Hz), as we will show in the next section: this would improve the sensitivity of the interferometer.
\subsection{ISI stabilization}
Differential motion affects the ISI of the HAM and BSC chambers in the CS: these are then the platforms that we want to stabilize. Several sensors are responsible for sensing the seismic motion, in all degrees of freedom of each stage. They are T240, L4C, GS13, OSEMs and CPS \cite{kisselthesis}.
Differential motion affects the ISI of the HAM and BSC chambers in the CS: these are the platforms that we want to stabilize. Several sensors are responsible for sensing the seismic motion, in all degrees of freedom of each stage. They are T240, L4C, GS13 and CPS \cite{kisselthesis}.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.9]{images/isi.png}
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@@ -63,7 +63,7 @@ Differential motion affects the ISI of the HAM and BSC chambers in the CS: these
\label{isi}
\end{figure}
\noindent
In particular, CPS sensors are placed in every chambers at all stages: it is easy to compare motion between HAM and BSC chambers through the signal of a device sensing the same motion on every chamber \cite{kisseltalk2}.\\
In particular, CPS sensors are placed on every stage of every chamber: it is easy to compare motion between HAM and BSC chambers through the signal of a device sensing the same motion on every chamber \cite{kisseltalk2}.\\
The idea which should stabilize ISIs to follow the ground motion is to lock the chambers to each other, in order to make them move on a synchronized way, following a common motion given by a driver chamber (or block of chambers).
\paragraph*{Role of the mode cleaner}
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@@ -80,7 +80,7 @@ We started our design on the chambers on the X arm. Along this direction, the In
In the next section we will demonstrate that CPS are good witnesses to sense differential motion and that they also can be used to lock the chambers with each other.
\section{Sensing differential motion via CPS}
The Capacitive Position Sensors (CPS) measure the relative motion between two stages of the isolation system. Referring to Fig. \ref{isi}, on HAM chambers they are set between HEPI and ground, and between Stage 1 and HEPI. On BSC chambers they also measure the relative motion between Stage 1 and Stage 2. The plots in Fig. \ref{diff} show the differential motion seen by the CPS between BSC and HAM chambers: the sensors put in evidence that the HAM chambers have a more synchronized motion with respect to the motion between HAM and BSC and BSCs only. This means that the block of HAM chambers on X arm is more stable relatively to the other blocks and can be used as driver for the other chambers, with the mode cleaner acting as witness. We then projected the CPS of the X axis chambers to the suspension point in order to obtain PRCL and Input Model Cleaner Length (IMCL) traces like as they would be sensed by the CPS. For BSCs, we decided to sum the contributions of the CPSs on stage 1 and stage 2 and to project this sum to the suspension point.
The Capacitive Position Sensors (CPS) measure the relative motion between two stages of the isolation system. On HAM chambers they are set between HEPI and ground, and between Stage 1 and HEPI. On BSC chambers they also measure the relative motion between Stage 1 and Stage 2. The plots in Fig. \ref{diff} show the differential motion seen by the CPS between BSC and HAM chambers: the sensors put in evidence that the HAM chambers have a more synchronized motion with respect to the motion between HAM and BSC and BSCs only. This means that the block of HAM chambers on X arm is more stable relatively to the other blocks and can be used as driver for the other chambers, with the mode cleaner acting as witness. We then projected the CPS of the X axis chambers to the suspension point in order to obtain PRCL and Input Model Cleaner Length (IMCL) traces like as they would be sensed by the CPS. For BSCs, we decided to sum the contributions of the CPSs on stage 1 and stage 2 and to project this sum to the suspension point.
\begin{figure}[H]
\centering
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@@ -149,7 +149,7 @@ $x_{p}$ & plant motion\\
We can compute the signal $\textit{$d_{2}$}$ which will be the CPS offset to send to HAM3 chamber. In this case, HAM2 will drive HAM3 to follow its motion. Defining K = PC:\\
In the approximation where K$\rightarrow\infty$, i.e. in a condition of infinite gain, the terms we computed become:\\
\begin{equation}
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@@ -251,11 +254,12 @@ which is what we expect to be the signal of the differential motion sensed by th
\section{Analysis of feasibility}
The next step is to study how to modify the low and high pass filters in order to obtain the best performances from each one in the new configuration of the chambers \cite{technote3}. To do this, we are going to change the blending filters, i.e. those filters whose combination gives the best performance of the set low+high pass filters.\\
If by definition we have L+H=1, we can write it as:
If by definition we have L+H=1\footnote{This definition arises from the need to accounting for unconditional loop stability and noise contributions. For details about blending filters, refer to \cite{kisselthesis}.}, we can write it as:
According to the values of \textit{l} and \textit{h}, we have different order of magnitudes of the binomials, which can be solved for the real part.\\
\noindent
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@@ -274,7 +278,7 @@ All this analysis has been performed through Matlab software.\\
\end{figure}
\subsection{Contributions from CPS and inertial sensors}
To calculate the CPS signal contribution, we need the ground motion and we used the ITMY STS signal on X direction. This is going to be the same motion for every chamber, since there is only one sensor in the Corner Station to measure it, because it has been found that the ground motion is the same everywhere in the Corner Station. From this signal, we separate the contribution given by the tilt ($\theta_g$) from the microseismic frequency (0.08 Hz). Then we subtract the tilt to obtain the ground motion $x_g$ from the STS:\\
To calculate the CPS signal contribution, we need the ground motion and we used the ITMY STS (Streckheisen Tri-axial Seismometer) signal on X direction. This is going to be the same motion for every chamber, since there is only one sensor in the Corner Station to measure it, because it has been found that the ground motion is the same everywhere in the Corner Station. From this signal, we separate the contribution given by the tilt ($\theta_g$) from the microseismic frequency (0.08 Hz). Then we subtract the tilt to obtain the ground motion $x_g$ from the STS:\\
\begin{equation}
x_g = STS - \theta_g.
\end{equation}\\
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@@ -326,7 +330,7 @@ In order to compute the platform motion for the single chambers in isolation and
\centering
\includegraphics[scale=0.3]{images/bscblend.png}
\includegraphics[scale=0.3]{images/hamblend.png}
\caption[Blending filters]{Plots of all possible costs built with different combinations of blending filters. Orders of magnitude are between l =[1,4] and h = [1,4].}
\caption[Blending filters]{Plots of all possible costs built with different combinations of blending filters. The orders of magnitude are indicated by the low and high pass indices l and h of the binomial filter in \ref{binomial} and the are going between l =[1,4] and h = [1,4].}
\label{blend}
\end{figure}
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@@ -375,7 +379,7 @@ The plot in Fig. \ref{diffham} shows the differential motion of HAM2 and HAM3 in
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/diffham.png}
\caption[Ham chambers in isolation]{Ham chambers in isolation: motion of HAM2 as a reference. The purple trace is the differential motion between HAM2 and HAM3 that we are interested in reducing.}
\caption[HAM chambers in isolation]{Ham chambers in isolation: motion of HAM2 as a reference. The purple trace is the differential motion between HAM2 and HAM3 that we are interested in reducing.}
\label{diffham}
\end{figure}
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@@ -488,7 +492,7 @@ Through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambe
\label{chamb}
\end{figure}
\noindent
The same work is foreseen to be done for the other cavities: the very short period of time available during the commissioning break allowed us to modify only the software for PRCL. Moreover, during the commissioning break, time is also used to work on the chambers, profiting of the out-of-lock mode. This means that, for every attempt of software modification, a locking trial was needed, to see if the new configuration of the instrument was giving better performances and, also, if it was affecting negatively other sides of the instrument. To try to lock LIGO, we needed people not to work besides the chambers. This was a huge and collaborative work, which involved many people on site, and their time. Despite these challenges, the results obtained are encouraging and validated the analysis of feasibility exposed.
The same work is foreseen to be done for the other cavities: the very short period of time available during the commissioning break allowed us to modify only the control loop for PRCL. Moreover, during the commissioning break, time is also used to work on the chambers, profiting of the out-of-lock mode. This means that, for every attempt of software modification, a locking trial was needed, to see if the new configuration of the instrument was giving better performances and, also, if it was affecting negatively other sides of the instrument. To try to lock LIGO, we needed people not to work besides the chambers. This was a huge and collaborative work, which involved many people on site, and their time. Despite these challenges, the results obtained are encouraging and validated the analysis of feasibility exposed.
\paragraph{The Power Recycling Cavity Length (PRCL)}
We need to connect the ISI to the cavity and to do it we need to know how the PR cavity is going to communicate with the ISI (refer to Chapter \ref{LIGO} for details on the PR cavity). The block diagram in Fig. \ref{prcl} illustrates the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers.\\
