Differences between revisions 7 and 8

Thermal noise

Mirror thermal noise
- Mirror coating structure damping (4枚鏡のtotal変位.[m/rtHz])
  - mirrorcoa[f_, tm_, dcoa_, phicoa_, w1_, w2_, E0_] := 5.5*10^-19*(dcoa/15*10^-6)^1/2*(phicoa/1.2*10^-2)^1/2*Sqrt[(10^-2/w1)²*2+ (10^-2/w2)²*2]*(tm/300)^1/2*(7.24*10¹⁰/E0)^1/2*(100/f)^1/2;
  - dcoa:thickness of coating[m], 7.5*10^-6.
  - phicoa:loss angle of coating, 4*10^-4.
  - w1:beam radius of front mirror[m], 4.89*10^-3.
  - w2:beam radius of end mirror[m], 8.48*10^-3.
  - tm:temperature[K], 300K or 20K.
  - E0:Young's modulus of substrate[N/m²], 4*10¹¹.
  - Mathematica関数表記(以下をmathematicaにコピペ利用可能...なはず。)
  - mirrorcoa[f_, tm_, dcoa_, phicoa_, w1_, w2_, E0_] := 5.5*10^{(-19)*(dcoa/(15*10}(-6)))^{(1/2)*(phicoa/(1.2*10}(-2)))^{(1/2)*Sqrt[(10}(-2)/w1)^{2*2 + (10}(-2)/w2)^{2*2]*(tm/300)}(1/2)*(7.24*10^10/E0)(1/2)*(100/f)^(1/2);
- Mirror substrate structure damping (4枚鏡のtotal変位.[m/rtHZ])
  - mirrorhomo[f_, tm_, sigma_, phimir_, w1_, w2_, E0_] := Sqrt[4*kb*tm*(1 - sigma²)*phimir/(Sqrt[Pi]*E0*2*Pi*f)]*Sqrt[1/w1*2 + 1/w2*2];
  - sigma:poisson ratio, 0.27.
  - phimir:loss angle of mirror material, 10^-7 at 300K, 10^-8 at 20K.
  - w1:beam radius of front mirror[m], 4.89*10^-3.
  - w2:beam radius of end mirror[m], 8.48*10^-3.
  - tm:temperature[K], 300K or 20K.
  - E0:Young's modulus[N/m^{2], 4*10}11^.
  - Mathematica関数表記(以下をmathematicaにコピペ利用可能...なはず。)
  - mirrorhomo[f_, tm_, sigma_, phimir_, w1_, w2_, E0_] := Sqrt[4*kb*tm*(1 - sigma^2)*phimir/(Sqrt[Pi]*E0*2*Pi*f)]*Sqrt[1/w1*2 + 1/w2*2];
- Mirror substrate thermoelastic damping
  - thermoelastic dampingの周波数依存性は、ビーム径、基材の熱拡散係数で決まるcur-off frequencyの前後で変化する。
    - f >> cut-off frequency -> thermoelastic dampingの周波数依存性 1/f. 室温では「観測帯域」>> cut-off frequencyが一般に成り立つ.
    - f << cut-off frequency -> thermoelastic dampingの周波数依存性 f. 低温では「観測帯域」<< cut-off frequencyが一般に成り立つ.
    - thelasticFreq[w_, kappa_, spheat_] := (kappa/(spheat w²/2)) (1/(2 Pi)) [Hz]
    - w: beam radius [m], front: 4.89*10^-3, end: 8.48*10^-3.
    - kappa: thermal ocnductivity [W/K/m], 46 at 300K, 15700 at 20K.
    - spheat: specific heat [J/K/m³], 3.09*10⁶ at 300K, 2760 at 20K.
    - Mathematica関数表記(以下をmathematicaにコピペ利用可能...なはず。)
    - thelasticFreq[w_, kappa_, spheat_] := kappa/(spheat w^2/2) 1/(2 Pi)
  - 室温(f >> cut-off frequency)での熱雑音振幅 (鏡1枚分、変位。[m/rtHz])
    - thelasticRoom[f_, t_, alpha_, sigma_, kappa_, spheat_, w_] := (8/Sqrt[2 Pi]) alpha² (1 + sigma)² (kb t² kappa)/((2 Pi f)² spheat²) (Sqrt[2]/w)³

-  ⇤ ← Revision 7 as of 2009-01-02 11:44:35 → 
  Size: 2430
  Editor: TakashiUchiyama
  Comment:
+   ← Revision 8 as of 2009-01-02 11:58:40 → ⇥
  Size: 2971
  Editor: TakashiUchiyama
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 5:
-   * Mirror coating structure damping (4枚鏡のtotal.)
+   * Mirror coating structure damping (4枚鏡のtotal変位.[m/rtHz])
 Line 7:
-    * l:length of cavity[m], 100m.
 Line 18:
-   * Mirror substrate structure damping (4枚鏡のtotal.)
+   * Mirror substrate structure damping (4枚鏡のtotal変位.[m/rtHZ])
 Line 20:
-     * l:length of cavity[m], 100.
-Line 34:
+Line 33:
-     * f >> cut-off frequency -> thermoelastic damping 1/f. 室温では「観測帯域」>>  cut-off frequencyが一般に成り立つ.
     * f << cut-off frequency -> thermoelastic damping f. 低温では「観測帯域」<<  cut-off frequencyが一般に成り立つ.
     * thelasticFreq[w_, kappa_, spheat_] := (kappa/(spheat w^2^/2)) (1/(2 Pi));
     * w: beam radius [m],
     * kappa: thermal ocnductivity [W/K/m],
      * spheat: specific heat [J/K/m^3]
+     * f >> cut-off frequency -> thermoelastic dampingの周波数依存性 1/f. 室温では「観測帯域」>>  cut-off frequencyが一般に成り立つ.
     * f << cut-off frequency -> thermoelastic dampingの周波数依存性 f. 低温では「観測帯域」<<  cut-off frequencyが一般に成り立つ.
     * thelasticFreq[w_, kappa_, spheat_] := (kappa/(spheat w^2^/2)) (1/(2 Pi)) [Hz]
     * w: beam radius [m], front: 4.89*10^-3^, end: 8.48*10^-3^.
     * kappa: thermal ocnductivity [W/K/m], 46 at 300K, 15700 at 20K.
     * spheat: specific heat [J/K/m^3^], 3.09*10^6^ at 300K, 2760 at 20K. 
     * Mathematica関数表記(以下をmathematicaにコピペ利用可能...なはず。)
     * thelasticFreq[w_, kappa_, spheat_] := kappa/(spheat w^2/2) 1/(2 Pi)
    * 室温(f >> cut-off frequency)での熱雑音振幅 (鏡1枚分、変位。[m/rtHz])
     * thelasticRoom[f_, t_, alpha_, sigma_, kappa_, spheat_, w_] := (8/Sqrt[2 Pi]) alpha^2^ (1 + sigma)^2^ (kb t^2^ kappa)/((2 Pi f)^2^ spheat^2^) (Sqrt[2]/w)^3^
      *