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\@writefile{toc}{\contentsline {section}{\numberline {1}Executive summary}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Recommendations}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Summary of the reasoning behind the recommendations}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Expected performance of the LCGT SPI}{4}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Suspension Model}{4}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Conceptual diagram of the LCGT suspension system. IP: Inverted Pendulum, PM: Penultimate Mass, MB: Magnet Box, TM: Test Mass, RM: Recoil Mass.}}{4}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces SPI servo's open loop transfer function}}{5}}
\newlabel{fig: SPI OPLTF}{{2}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Seismic noise and the LCGT target sensitivity.}}{5}}
\newlabel{fig: target sense}{{3}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Observation band seismic noise}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}RMS motion}{6}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.1}Displacement RMS}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces RMS displacement noise when the seismic noise is normal. Total Seismic means the overall motion of the mirrors caused by all kinds of seismic vibrations.}}{6}}
\newlabel{fig: SeismicRMS}{{4}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces RMS displacement noise when the micro seismic motion is high. Total Seismic means the overall motion of the mirrors caused by all kinds of seismic vibrations.}}{7}}
\newlabel{fig: SeismicRMS high}{{5}{7}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.2}Hierarchical control}{7}}
\newlabel{section: hierarchical control}{{2.3.2}{7}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.3}Speed RMS}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Mirror RMS speed}}{8}}
\newlabel{fig: Speed RMS}{{6}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Mirror RMS speed when the micro seismic motion is high}}{9}}
\newlabel{fig: Speed RMS high}{{7}{9}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Heat link vibration isolation}{9}}
\newlabel{Heat link vibration isolation}{{3}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Heat-link design}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Estimated vibration introduced from the heat-links}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Breakdown of the seismic noise without SPI}}{10}}
\newlabel{fig: Seismic Breakdown No SPI}{{8}{10}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Cryogenic active vibration isolation}{10}}
\newlabel{Cryogenic active vibration isolation}{{3.3}{10}}
\citation{cryo-pzt}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Breakdown of the seismic noise with SPI}}{11}}
\newlabel{fig: Seismic Breakdown with SPI}{{9}{11}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Conclusion for heat-link vibration isolation}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Cryogenic active vibration isolation}}{12}}
\newlabel{fig:Cryogenic active vibration isolation}{{10}{12}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Lock acquisition}{12}}
\newlabel{section: lock acquisition}{{4}{12}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}LCGT lock acquisition procedure}{12}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Obstacles for arm cavity lock}{13}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.1}Impulse limit velocity for mass lock acquisition}{13}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Critical velocity of mass lock acquisition}}{13}}
\newlabel{table: ciritical velocity}{{1}{13}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.2}Ringing velocity}{14}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Ringing velocity for several arm finesse values}}{14}}
\newlabel{table:ringing velocity}{{2}{14}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.3}Radiation pressure}{14}}
\newlabel{section: lock acquisition radiation pressure}{{4.2.3}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Lock event with the mirror speed of 60\tmspace  +\thinmuskip {.1667em}nm/s in various input powers. 0.2\tmspace  +\thinmuskip {.1667em}\% of the full power corresponds to 1.5\tmspace  +\thinmuskip {.1667em}kW inside the arm cavity when fully locked. 0.5\tmspace  +\thinmuskip {.1667em}\% and 1\tmspace  +\thinmuskip {.1667em}\% correspond to 3.5\tmspace  +\thinmuskip {.1667em}kW and 7\tmspace  +\thinmuskip {.1667em}kW respectively.}}{14}}
\newlabel{fig:sus1}{{11}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Radiation pressure effects on angle motion without alignment control. Left graph is power inside the cavity. After lock is acquired with very low power, input power is ramped up to full power in 15 seconds. The central graph shows the horizontal position of the mirrors moved by radiation pressure. The right graph shows the pitch angle change. $m0$ to $m3$ refer to the four test masses of an advanced LIGO style quad-suspension. Lock is lost due to the pitch offset when the power inside the cavity reaches about 10\tmspace  +\thinmuskip {.1667em}\% of full power.}}{15}}
\newlabel{fig:angle_oscillation}{{12}{15}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.4}Arm lock simulation}{15}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Lock probability with various mirror speeds.}}{15}}
\newlabel{tbl:lockability}{{3}{15}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Advanced lock acquisition techniques}{15}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.3.1}Offset locking}{15}}
\newlabel{section: offset lock}{{4.3.1}{15}}
\citation{GreenLock}
\citation{FiberNoiseCancel}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Transmitted light, $1/\sqrt  {P_{\mathrm  {trans}}}$ + offset vs Cavity microscopic length. $P_{\mathrm  {trans}}$ is normalized with the transmission power at the full lock.}}{16}}
\newlabel{fig:offset lock error signal}{{13}{16}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.3.2}Green laser pre-lock}{16}}
\newlabel{section: green laser lock}{{4.3.2}{16}}
\citation{Vacuum}
\@writefile{toc}{\contentsline {paragraph}{Benefits of green laser pre-lock}{17}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Cavity length conditions for successful offset lock}}{17}}
\newlabel{fig:lock point}{{14}{17}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Conclusion for lock acquisition}{17}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Vacuum tubes}{17}}
\@writefile{toc}{\contentsline {section}{\numberline {A}Design of the LCGT Suspension Point Interferometer}{19}}
\newlabel{section: SPI}{{A}{19}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Working Principle}{19}}
\newlabel{section Working Principle of the SPI}{{A.1}{19}}
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces A conceptual configuration of suspension-point interferometers installed to a Fabry-Perot Michelson interferometer}}{19}}
\newlabel{SPI-FP-MI}{{15}{19}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Rigid bar picture of SPI.}}{20}}
\newlabel{SPI rigid}{{16}{20}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.1.1}Rigid Bar Picture}{20}}
\newlabel{Rigid Bar Picture}{{A.1.1}{20}}
\newlabel{CMRR approx}{{9}{20}}
\newlabel{H1}{{10}{20}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Design of the LCGT SPI}{20}}
\newlabel{Design of LCGT SPI}{{A.2}{20}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.1}Interferometer Configuration}{20}}
\newlabel{Interferometer Configuration}{{A.2.1}{20}}
\citation{LCGT-BW}
\citation{aso-phd}
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Frequency dependence of CMRR: The blue line shows the CMRR with all asymmetries included. The green circles show the CMRR with only $\Delta l$. The red line is the CMRR with only $\Delta m$. The pink triangles show the CMRR with only $\Delta \gamma $. All asymmetries are 1\%.}}{21}}
\newlabel{CMRR plot}{{17}{21}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.2}Location of SPI in the Suspension Chain}{22}}
\newlabel{Location of SPI in the Suspension Chain}{{A.2.2}{22}}
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces A conceptual diagram of the LCGT cryogenic suspension.}}{22}}
\newlabel{SPI-Location}{{18}{22}}
\citation{LCGT Design Doc}
\citation{LCGT Design Doc}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.3}Suspension Design}{23}}
\newlabel{Suspension Design}{{A.2.3}{23}}
\newlabel{fig:ActuatorNoise}{{A.2.3}{23}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Actuator noise of the main mirror and the classical noise of LCGT}}{23}}
\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces A conceptual design of the SPI mirror suspension}}{24}}
\newlabel{fig:SPI-Mirror}{{20}{24}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.4}Noise Requirement}{24}}
\newlabel{SPI Noise Requirement}{{A.2.4}{24}}
\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces Noise requirement of the LCGT SPI. This requirement is calculated from the LCGT classical noises, a transfer function of the final stage suspension ($f_{\mathrm  {c}}=0.8\tmspace  +\thinmuskip {.1667em}\mathrm  {Hz}, Q=1000$) and a safety factor of 10.}}{25}}
\newlabel{Noise requirememt, SPI noise requirement}{{21}{25}}
\@writefile{toc}{\contentsline {paragraph}{Thermal noise of suspension:}{25}}
\@writefile{toc}{\contentsline {paragraph}{Thermal noise of mirror:}{25}}
\@writefile{toc}{\contentsline {paragraph}{Coil driver noise:}{25}}
\@writefile{toc}{\contentsline {paragraph}{Shot noise:}{26}}
\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces Shot noise. Laser power and finesse of the arm cavities can be chosen relatively freely.}}{26}}
\newlabel{Noise requirememt, Shot noise}{{22}{26}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.5}Input Optics}{26}}
\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces Optical configuration (A). The laser light for the SPI is picked off from the main laser.}}{27}}
\newlabel{Input optics, a fraction of main laser}{{23}{27}}
\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces Optical configuration (B). A dedicated laser, which is phase-locked to the main laser, is used for the SPI.}}{27}}
\newlabel{Input optics, another laser}{{24}{27}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.6}Comments on technical feasibility}{27}}
\bibcite{cryo-pzt}{1}
\bibcite{VirgoHierarchical}{2}
\bibcite{Miyakawa06}{3}
\bibcite{GreenLock}{4}
\bibcite{FiberNoiseCancel}{5}
\bibcite{LCGT Design Doc}{6}
\bibcite{Vacuum}{7}
\bibcite{aso-phd}{8}
\bibcite{LCGT-BW}{9}
\@writefile{toc}{\contentsline {section}{\numberline {B}Members of the working group}{28}}
\@writefile{toc}{\contentsline {section}{\numberline {C}Acronyms}{28}}