From 995890ddb4b7efc820d1d528b1afe57d16ce4f51 Mon Sep 17 00:00:00 2001
From: Christopher Wipf <wipf@ligo.mit.edu>
Date: Thu, 23 Aug 2018 15:22:44 -0700
Subject: [PATCH] substratethermal: use adiabatic approx for carrier density &
thermorefractive noises Note: these are cryo-silicon-only noises. The
adiabatic approx is quite accurate and evaluates faster than the exact
integral. See also https://git.ligo.org/rana-adhikari/CryogenicLIGO/issues/37
---
gwinc/noise/substratethermal.py | 58 +++++++++++++++++++++++++++++++--
1 file changed, 55 insertions(+), 3 deletions(-)
diff --git a/gwinc/noise/substratethermal.py b/gwinc/noise/substratethermal.py
index 9129c0bb..a53ef954 100644
--- a/gwinc/noise/substratethermal.py
+++ b/gwinc/noise/substratethermal.py
@@ -9,7 +9,31 @@ from ..const import BESSEL_ZEROS as zeta
from ..const import J0M as j0m
-def carrierdensity(f, ifo):
+def carrierdensity_adiabatic(f, ifo):
+ """strain noise psd arising from charge carrier density
+ fluctuations in ITM substrate (for semiconductor substrates)."""
+
+ Omega = 2*pi*f
+ H = ifo.Materials.MassThickness
+ gammaElec = ifo.Materials.Substrate.ElectronIndexGamma
+ gammaHole = ifo.Materials.Substrate.HoleIndexGamma
+ diffElec = ifo.Materials.Substrate.ElectronDiffusion
+ diffHole = ifo.Materials.Substrate.HoleDiffusion
+ cdDens = ifo.Materials.Substrate.CarrierDensity
+ r0 = ifo.Optics.ITM.BeamRadius/np.sqrt(2)
+ T = ifo.Optics.ITM.Transmittance
+ L = ifo.Infrastructure.Length
+ Finesse = 2*pi/T
+ gPhase = 2*Finesse/pi
+
+ psdElec = 4*H*gammaElec**2*cdDens*diffElec/(pi*r0**4*Omega**2) # units are meters
+ psdHole = 4*H*gammaHole**2*cdDens*diffHole/(pi*r0**4*Omega**2) # units are meters
+ psdMeters = 2 * (psdElec + psdHole) # electrons and holes for two ITMs
+ n = psdMeters / (gPhase*L)**2
+ return n
+
+
+def carrierdensity_exact(f, ifo):
"""Strain noise arising from charge carrier density fluctuations in ITM substrate
For semiconductor substrates
@@ -37,7 +61,7 @@ def carrierdensity(f, ifo):
gPhase = 2*Finesse/pi
omega = 2*pi*f
-
+
def integrand(k, om, D):
return D * k**3 * exp(-k**2 * w**2/4) / (D**2 * k**4 + om**2)
@@ -58,8 +82,34 @@ def carrierdensity(f, ifo):
return n
+carrierdensity = carrierdensity_adiabatic
-def thermorefractiveITM(f, ifo):
+
+def thermorefractiveITM_adiabatic(f, ifo):
+ """strain noise psd arising from thermorefractive
+ fluctuations in ITM substrate (for semiconductor substrates)."""
+
+ Omega = 2*pi*f
+ H = ifo.Materials.MassThickness
+ beta = ifo.Materials.Substrate.dndT
+ kappa = ifo.Materials.Substrate.MassKappa
+ rho = ifo.Materials.Substrate.MassDensity
+ C = ifo.Materials.Substrate.MassCM
+ Temp = ifo.Materials.Substrate.Temp
+ kBT = scipy.constants.k * Temp
+ r0 = ifo.Optics.ITM.BeamRadius/np.sqrt(2)
+ L = ifo.Infrastructure.Length
+ T = ifo.Optics.ITM.Transmittance
+ Finesse = 2*pi/T
+ gPhase = 2*Finesse/pi
+
+ psd = 4*H*beta**2*kappa*kBT*Temp/(pi*r0**4*Omega**2*(rho*C)**2) # units are meters
+ psdMeters = 2*psd # two ITMs
+ n = psdMeters / (gPhase*L)**2
+ return n
+
+
+def thermorefractiveITM_exact(f, ifo):
"""Strain noise from thermorefractive fluctuations in ITM substrate
For semiconductor substrates.
@@ -105,6 +155,8 @@ def thermorefractiveITM(f, ifo):
return n
+thermorefractiveITM = thermorefractiveITM_adiabatic
+
def subbrownian(f, ifo):
"""Strain noise from the Brownian thermal noise due to substrate mechanical loss
--
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