From 3a0fd2e17634618c2335615a91a4def7ef5deca8 Mon Sep 17 00:00:00 2001
From: Jameson Graef Rollins <jrollins@finestructure.net>
Date: Fri, 20 Sep 2019 00:44:57 -0700
Subject: [PATCH] substrate brownian noise simplification
substrate_brownian() function updated to calculate thermal noise of a
single suspended optic.
ifo SubstrateBrownian Noise class modified to handle specific case of
Fabry-Perot Michelson.
---
gwinc/ifo/noises.py | 6 ++-
gwinc/noise/substratethermal.py | 88 ++++++++++++++++-----------------
2 files changed, 47 insertions(+), 47 deletions(-)
diff --git a/gwinc/ifo/noises.py b/gwinc/ifo/noises.py
index 3478f3d6..374dd905 100644
--- a/gwinc/ifo/noises.py
+++ b/gwinc/ifo/noises.py
@@ -198,7 +198,11 @@ class SubstrateBrownian(nb.Noise):
)
def calc(self):
- return noise.substratethermal.subbrownian(self.freq, self.ifo)
+ nITM = noise.substratethermal.substrate_brownian(
+ self.freq, self.ifo.Materials, self.ifo.Optics.ITM.BeamRadius)
+ nETM = noise.substratethermal.substrate_brownian(
+ self.freq, self.ifo.Materials, self.ifo.Optics.ETM.BeamRadius)
+ return (nITM + nETM) * 2 * self.ifo.gwinc.dhdl_sqr
class SubstrateThermoElastic(nb.Noise):
diff --git a/gwinc/noise/substratethermal.py b/gwinc/noise/substratethermal.py
index 2919f0df..f8a3f60a 100644
--- a/gwinc/noise/substratethermal.py
+++ b/gwinc/noise/substratethermal.py
@@ -101,90 +101,86 @@ def substrate_thermorefractive(f, materials, wBeam, exact=False):
return psd
-def subbrownian(f, ifo):
- """Strain noise from the Brownian thermal noise due to substrate mechanical loss
+def substrate_brownian(f, materials, wBeam):
+ """Substrate thermal displacement noise spectrum due to substrate mechanical loss
+
+ :f: frequency array in Hz
+ :materials: gwinc optic materials structure
+ :wBeam: beam radius (at 1 / e^2 power)
+
+ :returns: displacement noise power spectrum at :f:, in meters
"""
- wITM = ifo.Optics.ITM.BeamRadius
- wETM = ifo.Optics.ETM.BeamRadius
- Y = ifo.Materials.Substrate.MirrorY
- sigma = ifo.Materials.Substrate.MirrorSigma
+ Y = materials.Substrate.MirrorY
+ sigma = materials.Substrate.MirrorSigma
+ c2 = materials.Substrate.c2
+ n = materials.Substrate.MechanicalLossExponent
+ alphas = materials.Substrate.Alphas
+ kBT = const.kB * materials.Substrate.Temp
- c2 = ifo.Materials.Substrate.c2
- n = ifo.Materials.Substrate.MechanicalLossExponent
- alphas = ifo.Materials.Substrate.Alphas
- kBT = const.kB * ifo.Materials.Substrate.Temp
+ cftm, aftm = substrate_brownian_FiniteCorr(materials, wBeam)
# Bulk substrate contribution
phibulk = c2 * f**n
-
- cITM, aITM = subbrownianFiniteCorr(ifo, 'ITM')
- cETM, aETM = subbrownianFiniteCorr(ifo, 'ETM')
- cbulk = 8 * kBT * (aITM + aETM) * phibulk / (2 * pi * f)
+ cbulk = 8 * kBT * aftm * phibulk / (2 * pi * f)
# Surface loss contribution
- # csurfETM = alphas/(Y*pi*wETM^2);
- # csurfITM = alphas/(Y*pi*wITM^2);
-
- csurfETM = alphas*(1-2*sigma)/((1-sigma)*Y*pi*wETM**2)
- csurfITM = alphas*(1-2*sigma)/((1-sigma)*Y*pi*wITM**2)
- csurf = 8 * kBT * (csurfITM + csurfETM) / (2 * pi * f)
+ # csurf = alphas/(Y*pi*wBeam^2)
+ csurf = alphas*(1-2*sigma)/((1-sigma)*Y*pi*wBeam**2)
+ csurf *= 8 * kBT / (2 * pi * f)
- # account for 2 ITM and 2 ETM, and convert to strain whith 1/L^2
- n = 2 * (csurf + cbulk) * ifo.gwinc.dhdl_sqr
+ return csurf + cbulk
- return n
+def substrate_brownian_FiniteCorr(materials, wBeam):
+ """Substrate brownian noise finite-size test mass correction
-def subbrownianFiniteCorr(ifo, opticName):
- """Amplitude coefficient of mirror thermal noise
+ :materials: gwinc optic materials structure
+ :wBeam: beam radius (at 1 / e^2 power)
- Contribution for finite-size test masses.
-
- [cftm, aftm] = subbrownianFiniteCorr(ifo, opticName)
+ :returns: correction factors tuple:
cftm = finite mirror correction factor
aftm = amplitude coefficient for thermal noise:
thermal noise contribution to displacement noise is
S_x(f) = (8 * kB * T / (2*pi*f)) * Phi(f) * aftm
-
+
Equation references to Bondu, et al. Physics Letters A 246 (1998)
227-236 (hereafter BHV) and Liu and Thorne gr-qc/0002055 (hereafter LT)
"""
- # get some numbers
- a = ifo.Materials.MassRadius
- h = ifo.Materials.MassThickness
- w = ifo.Optics[opticName].BeamRadius
- Y = ifo.Materials.Substrate.MirrorY
- sigma = ifo.Materials.Substrate.MirrorSigma
+ a = materials.MassRadius
+ h = materials.MassThickness
+ Y = materials.Substrate.MirrorY
+ sigma = materials.Substrate.MirrorSigma
- # do the work
- r0 = w / sqrt(2) # LT uses e-folding of power
+ # LT uses e-folding of power
+ r0 = wBeam / sqrt(2)
km = zeta/a
- Qm = exp(-2*km*h) # LT eq. 35a
+ Qm = exp(-2*km*h) # LT eq. 35a
Um = (1-Qm)*(1+Qm)+4*h*km*Qm
- Um = Um/((1-Qm)**2-4*(km*h)**2*Qm) # LT 53 (BHV eq. btwn 29 & 30)
+ Um = Um/((1-Qm)**2-4*(km*h)**2*Qm) # LT 53 (BHV eq. btwn 29 & 30)
x = exp(-(zeta*r0/a)**2/4)
- s = sum(x/(zeta**2*j0m)) # LT 57
+ s = sum(x/(zeta**2*j0m)) # LT 57
x2 = x*x
U0 = sum(Um*x2/(zeta*j0m**2))
U0 = U0*(1-sigma)*(1+sigma)/(pi*a*Y) # LT 56 (BHV eq. 3)
- p0 = 1/(pi*a**2) # LT 28
+ p0 = 1/(pi*a**2) # LT 28
DeltaU = (pi*h**2*p0)**2
DeltaU = DeltaU + 12*pi*h**2*p0*sigma*s
DeltaU = DeltaU + 72*(1-sigma)*s**2
- DeltaU = DeltaU*a**2/(6*pi*h**3*Y) # LT 54
+ DeltaU = DeltaU*a**2/(6*pi*h**3*Y) # LT 54
- aftm = DeltaU + U0 # LT 58 (eq. following BHV 31)
+ # LT 58 (eq. following BHV 31)
+ aftm = DeltaU + U0
- # amplitude coef for infinite TM
- # factored out: (8 * kB * T * Phi) / (2 * pi * f)
- aitm = (1 - sigma**2) / (2 * sqrt(2 * pi) * Y * r0) # LT 59
+ # amplitude coef for infinite TM, LT 59
+ # factored out: (8 * kB * T * Phi) / (2 * pi * f)
+ aitm = (1 - sigma**2) / (2 * sqrt(2 * pi) * Y * r0)
# finite mirror correction
cftm = aftm / aitm
--
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