## page was renamed from CLIO/NoiseBudgets/Thermalnoise
## page was renamed from CLIO/Technicals/Thermalnoise
## page was renamed from CLIO/req/Thermalnoise
= 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*10^10^/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/m^2^], 4*10^11^.
   

　　 * 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 - sigma^2^)*phimir/(Sqrt[Pi]*E0*2*Pi*f)]*Sqrt[1/w1*2 + 1/w2*2];
     * kb = 1.39 10^-23^; (*Boltzmann's constant [J/K]*) 
     * 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^.
     


   * 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 w^2^/2)) (1/(2 Pi)) [Hz]     
    * 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^
    * 低温(f << cut-off frequency)での熱雑音振幅 (鏡1枚分、変位。[m/rtHz])
     * thelasticCryo[f_, t_, alpha_, sigma_, kappa_, spheat_] := (8/Sqrt[2 Pi]) alpha^2^ (1 + sigma)^2^ (kb t^2^ )/kappa (kappa/(2 Pi f spheat  ))^0.5^
      * kb = 1.39 10^-23^ J/second; (*Boltzmann's constant [J/K]*)
      * t : temperature [K], 300K or 20K.
      * alpha : linerar expansion ratio, 5.4*10^-6^ at 300K, 5.6*10^-9^ at 20K. 
      * sigma : poisson ratio, 0.27.
      * kappa : thermal conductivity [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. 
      * w : beam radius of front mirror [m], front: 4.89*10^-3^, end: 8.48*10^-3^.

   * Mathematicaにコピペで利用可能...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)
    * 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]
    * thelasticFreq[w_, kappa_, spheat_] := kappa/(spheat w^2/2) 1/(2 Pi)
    * 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
    * thelasticCryo[f_, t_, alpha_, sigma_, kappa_, spheat_] := (8/Sqrt[2 Pi]) alpha^2 (1 + sigma)^2 (kb t^2 )/kappa (kappa/(2 Pi f spheat  ))^0.5
    * thelastic[f_, t_, alpha_, sigma_, kappa_, spheat_, w_] := If[f > thelasticFreq[w, kappa, spheat], thelasticRoom[f, t, alpha, sigma, kappa, spheat, w], thelasticCryo[f, t, alpha, sigma, kappa, spheat]] (*Cut-off frequencyを計算し、室温と低温のthermoelastic dampingの熱雑音計算式を選択し、変位を計算する関数。鏡一枚分の変位。[m/rtHz]*)