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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 239873, 6459]*) (*NotebookOutlinePosition[ 240627, 6486]*) (* CellTagsIndexPosition[ 240583, 6482]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ This notebook can be used to calculate LIGO thermal noise estimates. \ \>", "Text"], Cell[BoxData[ \(<< Graphics`\)], "Input"], Cell["Material properties are set in this section", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Sapphire\ = \ {\[Alpha] -> \ 8.5*10\^\(-6\), \[Rho] \[Rule] 3980, \ C \[Rule] 790, \[Kappa] \[Rule] 40, \[Sigma]\ -> \ .29, \[Phi] \[Rule] \ 10\^\(-8\), E0 \[Rule] 4\ 10\^11, \ rvertex\ -> \ 0.06/\@2, \[IndentingNewLine]rend\ -> \ 0.06/\@2};\)\), "\[IndentingNewLine]", \(\(Silica\ = {\[Alpha] -> \ 5.5\ 10\^\(-7\)\ , \[Rho]\ -> \ 2200, C\ -> \ 770, \[Kappa]\ \[Rule] 1.3, \[Sigma]\ -> \ 0.17, d\ -> \(20\ 10\^\(-6\)\)\/\(4\ 1.45\), \[Phi] \[Rule] \ 10\^\(-8\), E0 -> 7.2\ 10\^10, rvertex\ \[Rule] \((\ 0.035/\@2)\), \[IndentingNewLine]rend\ \[Rule] \ \((0.045/\@2)\ \)};\)\), "\[IndentingNewLine]", \(Silica2\ = {\[Alpha] -> \ 5.5\ 10\^\(-7\)\ , \[Rho]\ -> \ 2200, C\ -> \ 770, \[Kappa]\ \[Rule] 1.3, \[Sigma]\ -> \ 0.17, d\ -> \(20\ 10\^\(-6\)\)\/\(4\ 1.45\), \[Phi] \[Rule] 3*\ 10\^\(-7\), E0 -> 7.2\ 10\^10, rvertex\ \[Rule] \((\ 0.035/\@2)\), \[IndentingNewLine]rend\ \[Rule] \ \ \((0.045/\@2)\)}\), "\[IndentingNewLine]", \(\(Tantala\ = {\[Alpha]\ \[Rule] 3.6\ 10\^\(-6\), \[Rho]\ \[Rule] 8000, C\ \[Rule] 700, \[Kappa]\ \[Rule] 7, \[Sigma]\ \[Rule] 0.2, d\ \[Rule] \(20\ 10\^\(-6\)\)\/\(4\ 2.1\)};\)\ (*\ 3.6\ or\ - \(\(44\)\(?\)\)\ *) \), "\[IndentingNewLine]", \(Coating\ = \ {\[Alpha] \[Rule] \(\((\[Alpha]\ d /. Silica)\)\ + \ \((\ \[Alpha]\ d /. Tantala)\)\)\/\(\((d /. Silica\ )\)\ + \ \((d /. Tantala)\)\)\ \ , \[Phi] \[Rule] 10\^\(-4\), \[Rho] \[Rule] \(\((\[Rho] /. Silica)\)\ \ + \((\ \ \[Rho] /. Tantala)\)\)\/2, C\ \[Rule] \(\((C /. Silica)\)\ \ + \((C /. Tantala)\)\)\/2, \ \[Kappa]\ \[Rule] 2, \[Sigma]\ \[Rule] \(\((\[Sigma] /. Silica)\)\ \ + \((\ \ \[Sigma] /. Tantala)\)\)\/2, \[Beta] \[Rule] \(2.1*\ 1.45 \((\(-1.5\)\ \ 10\^\(-5\)\ + \ \ 1.2\ 10\^\(-4\))\)\)\/\(4 \((\ 2.1\^2 - 1.45\^2)\)\), E0 \[Rule] 2.9\ 10\^11}\)}], "Input"], Cell[BoxData[ \({\[Alpha] \[Rule] 5.5`*^-7, \[Rho] \[Rule] 2200, C \[Rule] 770, \[Kappa] \[Rule] 1.3`, \[Sigma] \[Rule] 0.17`, d \[Rule] 3.448275862068966`*^-6, \[Phi] \[Rule] 3\/10000000, E0 \[Rule] 7.2`*^10, rvertex \[Rule] 0.024748737341529162`, rend \[Rule] 0.03181980515339464`}\)], "Output"], Cell[BoxData[ \({\[Alpha] \[Rule] 1.7957746478873238`*^-6, \[Phi] \[Rule] 1\/10000, \[Rho] \[Rule] 5100, C \[Rule] 735, \[Kappa] \[Rule] 2, \[Sigma] \[Rule] 0.185`, \[Beta] \[Rule] 0.0000346397616468039`, E0 \[Rule] 2.9`*^11}\)], "Output"] }, Open ]], Cell["Properties which do not depend on the test mass", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(h\ = 2\ \[Pi]\ 10\^\(-34\);\)\), "\[IndentingNewLine]", \(\(c\ = \ 3\ 10\^8;\)\), "\[IndentingNewLine]", \(dend\ = \((\((d /. Silica\ )\)\ + \ \((d /. Tantala)\))\)\), "\[IndentingNewLine]", \(\(dvertex\ = \ dend\ *\ 16\ /\ 38;\)\), "\[IndentingNewLine]", \(\(kB = 1.38\ 10\^\(-23\);\)\), "\[IndentingNewLine]", \(\(T\ = \ 300;\)\), "\[IndentingNewLine]", \(\(\[Lambda] = 10\^\(-6\);\)\), "\[IndentingNewLine]", \(Pabs\ = N[Sqrt[800000*\ 5\ 10\^\(-7\)*h*\ c\ /\ \[Lambda]]]\), "\[IndentingNewLine]", \(\(armLength\ = \ 4000;\)\)}], "Input"], Cell[BoxData[ \(5.829228243021347`*^-6\)], "Output"], Cell[BoxData[ \(2.7458736985913073`*^-10\)], "Output"] }, Open ]], Cell["\<\ All the noise models, in units of length noise (rms meters) per arm\ \>", "Text"], Cell[BoxData[{ \(\(bulkStructural = Sqrt[\(\(\(\ \)\(kB\ T\ \[Phi]\ \((1 - \[Sigma]\^2)\)\)\)\/\(\(\((2\ \ \[Pi])\)\^\(3/ 2\)\)\(\ \)\(f\)\(\ \)\(E0\)\(\ \)\)\) \((1\/\(\(\ \)\ \(rvertex\)\) + 1\/rend)\)];\)\), "\[IndentingNewLine]", \(\(coatingStructural = Sqrt[\(\(\(2\)\(\ \)\(kB\)\(\ \)\(T\)\(\ \)\(\[Phi]\)\(\ \ \)\)\/\(\[Pi]\^2\ E0\ \ f\)\) \((dvertex\/\(\(\ \)\(rvertex\^2\)\) + dend\/rend\^2)\)];\)\), "\[IndentingNewLine]", \(\(bulkThermoelastic\ = \(\(\[Alpha]\)\(\ \)\((1 + \[Sigma])\)\(\ \)\(T\ \)\(\ \)\)\/\(2\ \[Pi]\ f\ \ \[Rho]\ C\)\ Sqrt[\(\(8\)\(\ \)\)\/\@\(2\ \ \[Pi]\)\ kB\ \[Kappa] \((1\/\(\(\ \)\(rvertex\^3\)\) + 1\/rend\^3)\)];\)\), "\[IndentingNewLine]", \(\(coatingThermoelastic\ = \ Sqrt[\(\(4\ \(\@2\) \((\[Alpha]\^2\ /. Coating)\) kB\ T\^2\ \((1 + \[Sigma])\)\^2\)\/\(\[Pi]\ \@\(2\ \[Pi]\ \ \[Rho]\ C\ f\ \[Kappa]\)\)\) \((dvertex\^2\/\(\(\ \)\(rvertex\^2\)\) + dend\^2\/rend\^2)\)];\)\), "\[IndentingNewLine]", \(\(thermorefractive\ = \ Sqrt[\(\(\(\ \)\(\(\@2\) \((\ \[Beta]\^\(\(2\)\(\ \)\) /. Coating)\) \(\[Lambda]\^2\) kB\ T\^2\)\)\/\(\[Pi]\ \@\(2\ \[Pi]\ \[Rho]\ C\ f\ \[Kappa]\ \)\)\) \((1\/\(\(\ \)\(rvertex\^2\)\) + 1\/rend\^2)\)];\)\[IndentingNewLine]\), \ "\[IndentingNewLine]", \(\(shape[\[CapitalOmega]_] = \(1\/\[Pi]\) Integrate[\(\(u\^2\) E\^\(\(-u\^2\)/2\)\)\/\(\((u\^2 + \ v\^2)\) \ \((u\^2 + \ v\^2 + I\ \[CapitalOmega])\)\), {u, 0, \[Infinity]}, {v, \(-\[Infinity]\), \[Infinity]}];\)\), "\ \[IndentingNewLine]", \(\(bulkPhotothermal\ = Pabs\ \(\@2\/\[Pi]\) \(\(\[Alpha]\ \((1 + \[Sigma])\)\)\/\[Kappa]\) shape[\(2\ \[Pi]\ f\ \[Rho]\ C\ rvertex\^2\)\/\[Kappa]];\)\), "\ \[IndentingNewLine]", \(\(bulkPhotothermal2\ = \ Pabs\ \(\(\[Alpha]\ \((1 + \[Sigma])\)\)\/\(\@2\ \[Pi]\)\) \(1\/\(\ \[Rho]\ C\ \[Pi]\ \ f\)\) Sqrt[1\/rvertex\^4 + 1\/rend\^4];\)\), "\[IndentingNewLine]", \(\(coatingPhotothermal\ = \(\(\(\ \)\(\(Pabs\)\(\ \)\(\[Alpha]\)\(\ \ \)\)\)\/\(\(\ \)\(\[Pi]\)\(\ \)\)\) \(1\/\(\(\ \)\(\(\[Rho]\)\(\ \)\(C\)\(\ \ \)\((2\ \[Pi]\ I\ f)\)\(\ \)\)\)\) Sqrt[\((\(1 - E\^\(\(-dend\)\ \ \@\(\(I\ \[Rho]\ C\ 2\ \[Pi]\ f\)\/\ \[Kappa]\)\)\)\/rend)\)\^4 + \((\(1 - E\^\(\(-dvertex\)\ \ \@\(\(I\ \[Rho]\ C\ \ 2\ \[Pi]\ f\)\/\[Kappa]\)\)\)\/rvertex)\)\^4];\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(coatingPT2\ = \(\(\((\[Alpha]\ /. 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