From ae3e837d55f45d126b12868e7f8fd4d372b3f114 Mon Sep 17 00:00:00 2001
From: Kevin Kuns <kevin.kuns@ligo.org>
Date: Wed, 2 Jun 2021 20:30:57 +0000
Subject: [PATCH] Residual gas sub-budgets and updates
Adds residual gas damping and additional molecular species to the residual gas calculations. The gas scattering and gas damping are now tracked separately for each species in an excess gas sub-budget. The damping calculation is done in the infinite volume limit by default but adds corrections for squeezed film damping if specified in the yaml file.
H2, N2, H2O, and O2 are considered. The numbers for aLIGO are taken from the link in this commit. The numbers for Aplus and Voyager are copied from aLIGO. For the existing LIGO facilities the O2 numbers are unknown but are suspected to be low, and are therefore set 10x below the expected noise floor.
Closes #63.
---
gwinc/ifo/Aplus/ifo.yaml | 27 +++-
gwinc/ifo/CE1/__init__.py | 3 -
gwinc/ifo/CE1/ifo.yaml | 28 ++++-
gwinc/ifo/CE2silica/__init__.py | 3 -
gwinc/ifo/CE2silica/ifo.yaml | 28 ++++-
gwinc/ifo/CE2silicon/__init__.py | 3 -
gwinc/ifo/CE2silicon/ifo.yaml | 30 ++++-
gwinc/ifo/Voyager/ifo.yaml | 27 +++-
gwinc/ifo/aLIGO/ifo.yaml | 27 +++-
gwinc/ifo/noises.py | 208 ++++++++++++++++++++++++++++---
gwinc/noise/residualgas.py | 115 +++++++++++++----
11 files changed, 434 insertions(+), 65 deletions(-)
diff --git a/gwinc/ifo/Aplus/ifo.yaml b/gwinc/ifo/Aplus/ifo.yaml
index d8e0411..66aa82b 100644
--- a/gwinc/ifo/Aplus/ifo.yaml
+++ b/gwinc/ifo/Aplus/ifo.yaml
@@ -33,9 +33,30 @@ Infrastructure:
Length: 3995 # m
Temp: 290 # K
ResidualGas:
- pressure: 4.0e-7 # Pa
- mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
- polarizability: 7.8e-31 # m^3
+ H2:
+ BeamtubePressure: 2.7e-7 # Pa
+ ChamberPressure: 2.7e-7 # Pa
+ mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
+ polarizability: 7.8e-31 # m^3
+
+ N2:
+ BeamtubePressure: 1.33e-8
+ ChamberPressure: 1.33e-8
+ mass: 4.65e-26
+ polarizability: 1.71e-30
+
+ H2O:
+ BeamtubePressure: 1.33e-8
+ ChamberPressure: 1.33e-8
+ mass: 2.99e-26
+ polarizability: 1.50e-30
+
+ O2:
+ BeamtubePressure: 1e-9
+ ChamberPressure: 1e-9
+ mass: 5.31e-26
+ polarizability: 1.56e-30
+
TCS:
# The presumably dominant effect of a thermal lens in the ITMs is an increased
diff --git a/gwinc/ifo/CE1/__init__.py b/gwinc/ifo/CE1/__init__.py
index 7221756..586d3f7 100644
--- a/gwinc/ifo/CE1/__init__.py
+++ b/gwinc/ifo/CE1/__init__.py
@@ -77,9 +77,6 @@ class Substrate(nb.Budget):
]
-ExcessGas.style['linestyle'] = '-'
-
-
class CE1(nb.Budget):
name = 'Cosmic Explorer 1'
diff --git a/gwinc/ifo/CE1/ifo.yaml b/gwinc/ifo/CE1/ifo.yaml
index 0d3914e..e637093 100644
--- a/gwinc/ifo/CE1/ifo.yaml
+++ b/gwinc/ifo/CE1/ifo.yaml
@@ -26,9 +26,31 @@ Infrastructure:
Length: 40000 # m; whoa
Temp: 293 # K
ResidualGas:
- pressure: 4.0e-7 # Pa
- mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
- polarizability: 0.81e-30 # m^3 (H_2, DOI: 10.1116/1.1479360)
+ # polarizabilities from https://cccbdb.nist.gov/pollistx.asp
+ H2:
+ BeamtubePressure: 4.4e-8 # Pa
+ ChamberPressure: 4.1e-7 # Pa
+ mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
+ polarizability: 7.87e-31 # m^3;
+
+ N2:
+ BeamtubePressure: 2.5e-9
+ ChamberPressure: 1.1e-7
+ mass: 4.65e-26
+ polarizability: 1.71e-30
+
+ H2O:
+ BeamtubePressure: 4.0e-9
+ ChamberPressure: 1.4e-7
+ mass: 2.99e-26
+ polarizability: 1.50e-30
+
+ O2:
+ BeamtubePressure: 2.8e-9
+ ChamberPressure: 1.0e-7
+ mass: 5.31e-26
+ polarizability: 1.56e-30
+
BuildingRadius: 10 # m
diff --git a/gwinc/ifo/CE2silica/__init__.py b/gwinc/ifo/CE2silica/__init__.py
index 1029b0f..8cbfa37 100644
--- a/gwinc/ifo/CE2silica/__init__.py
+++ b/gwinc/ifo/CE2silica/__init__.py
@@ -77,9 +77,6 @@ class Substrate(nb.Budget):
]
-ExcessGas.style['linestyle'] = '-'
-
-
class CE2silica(nb.Budget):
name = 'Cosmic Explorer 2 (Silica)'
diff --git a/gwinc/ifo/CE2silica/ifo.yaml b/gwinc/ifo/CE2silica/ifo.yaml
index 2cb7017..2737875 100644
--- a/gwinc/ifo/CE2silica/ifo.yaml
+++ b/gwinc/ifo/CE2silica/ifo.yaml
@@ -26,9 +26,31 @@ Infrastructure:
Length: 40000 # m; whoa
Temp: 293 # K
ResidualGas:
- pressure: 4.0e-7 # Pa
- mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
- polarizability: 0.81e-30 # m^3 (H_2, DOI: 10.1116/1.1479360)
+ # polarizabilities from https://cccbdb.nist.gov/pollistx.asp
+ H2:
+ BeamtubePressure: 4.4e-8 # Pa
+ ChamberPressure: 4.1e-7 # Pa
+ mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
+ polarizability: 7.87e-31 # m^3;
+
+ N2:
+ BeamtubePressure: 2.5e-9
+ ChamberPressure: 1.1e-7
+ mass: 4.65e-26
+ polarizability: 1.71e-30
+
+ H2O:
+ BeamtubePressure: 4.0e-9
+ ChamberPressure: 1.4e-7
+ mass: 2.99e-26
+ polarizability: 1.50e-30
+
+ O2:
+ BeamtubePressure: 2.8e-9
+ ChamberPressure: 1.0e-7
+ mass: 5.31e-26
+ polarizability: 1.56e-30
+
BuildingRadius: 10 # m
diff --git a/gwinc/ifo/CE2silicon/__init__.py b/gwinc/ifo/CE2silicon/__init__.py
index 451a9d7..1c43d3b 100644
--- a/gwinc/ifo/CE2silicon/__init__.py
+++ b/gwinc/ifo/CE2silicon/__init__.py
@@ -78,9 +78,6 @@ class Substrate(nb.Budget):
]
-ExcessGas.style['linestyle'] = '-'
-
-
class CE2silicon(nb.Budget):
name = 'Cosmic Explorer 2 (Silicon)'
diff --git a/gwinc/ifo/CE2silicon/ifo.yaml b/gwinc/ifo/CE2silicon/ifo.yaml
index d001a97..436e0e9 100644
--- a/gwinc/ifo/CE2silicon/ifo.yaml
+++ b/gwinc/ifo/CE2silicon/ifo.yaml
@@ -26,10 +26,32 @@ Infrastructure:
Length: 40000 # m; whoa
Temp: 293 # K; Temperature of the Vacuum
ResidualGas:
- pressure: 4.0e-7 # Pa
- mass: 3.35e-27 # kg, Mass of H_2 (ref. 10)
- polarizability: 0.81e-30 # m^3 (H_2, DOI: 10.1116/1.1479360)
- BuildingRadius: 5 # m
+ # polarizabilities from https://cccbdb.nist.gov/pollistx.asp
+ H2:
+ BeamtubePressure: 4.4e-8 # Pa
+ ChamberPressure: 4.1e-7 # Pa
+ mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
+ polarizability: 7.87e-31 # m^3;
+
+ N2:
+ BeamtubePressure: 2.5e-9
+ ChamberPressure: 1.1e-7
+ mass: 4.65e-26
+ polarizability: 1.71e-30
+
+ H2O:
+ BeamtubePressure: 4.0e-9
+ ChamberPressure: 1.4e-7
+ mass: 2.99e-26
+ polarizability: 1.50e-30
+
+ O2:
+ BeamtubePressure: 2.8e-9
+ ChamberPressure: 1.0e-7
+ mass: 5.31e-26
+ polarizability: 1.56e-30
+
+ BuildingRadius: 10 # m
TCS:
diff --git a/gwinc/ifo/Voyager/ifo.yaml b/gwinc/ifo/Voyager/ifo.yaml
index 81125d1..67821a9 100644
--- a/gwinc/ifo/Voyager/ifo.yaml
+++ b/gwinc/ifo/Voyager/ifo.yaml
@@ -31,9 +31,30 @@ Infrastructure:
Length: 3995 # m
Temp: 295 # K; Temperature of the Vacuum
ResidualGas:
- pressure: 4.0e-7 # Pa
- mass: 3.35e-27 # kg, Mass of H_2 (ref. 10)
- polarizability: 0.81e-30 # m^3 (H_2, DOI: 10.1116/1.1479360)
+ H2:
+ BeamtubePressure: 2.7e-7 # Pa
+ ChamberPressure: 2.7e-7 # Pa
+ mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
+ polarizability: 7.8e-31 # m^3
+
+ N2:
+ BeamtubePressure: 1.33e-8
+ ChamberPressure: 1.33e-8
+ mass: 4.65e-26
+ polarizability: 1.71e-30
+
+ H2O:
+ BeamtubePressure: 1.33e-8
+ ChamberPressure: 1.33e-8
+ mass: 2.99e-26
+ polarizability: 1.50e-30
+
+ O2:
+ BeamtubePressure: 1e-9
+ ChamberPressure: 1e-9
+ mass: 5.31e-26
+ polarizability: 1.56e-30
+
TCS:
## Parameter describing thermal lensing
diff --git a/gwinc/ifo/aLIGO/ifo.yaml b/gwinc/ifo/aLIGO/ifo.yaml
index 9ffde77..44e50f2 100644
--- a/gwinc/ifo/aLIGO/ifo.yaml
+++ b/gwinc/ifo/aLIGO/ifo.yaml
@@ -33,9 +33,30 @@ Infrastructure:
Length: 3995 # m
Temp: 290 # K
ResidualGas:
- pressure: 4.0e-7 # Pa
- mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
- polarizability: 7.8e-31 # m^3
+ H2:
+ BeamtubePressure: 2.7e-7 # Pa
+ ChamberPressure: 2.7e-7 # Pa
+ mass: 3.35e-27 # kg; Mass of H_2 (ref. 10)
+ polarizability: 7.8e-31 # m^3
+
+ N2:
+ BeamtubePressure: 1.33e-8
+ ChamberPressure: 1.33e-8
+ mass: 4.65e-26
+ polarizability: 1.71e-30
+
+ H2O:
+ BeamtubePressure: 1.33e-8
+ ChamberPressure: 1.33e-8
+ mass: 2.99e-26
+ polarizability: 1.50e-30
+
+ O2:
+ BeamtubePressure: 1e-9
+ ChamberPressure: 1e-9
+ mass: 5.31e-26
+ polarizability: 1.56e-30
+
TCS:
# The presumably dominant effect of a thermal lens in the ITMs is an increased
diff --git a/gwinc/ifo/noises.py b/gwinc/ifo/noises.py
index 8472c6a..f0202e4 100644
--- a/gwinc/ifo/noises.py
+++ b/gwinc/ifo/noises.py
@@ -752,26 +752,204 @@ class SubstrateThermoElastic(nb.Noise):
# residual gas
#########################
-class ExcessGas(nb.Noise):
- """Excess Gas
+# FIXME HACK: it's unclear if a phase noise in the arms like
+# the excess gas noise should get the same dhdL strain
+# calibration as the other displacement noises. However, we
+# would like to use the one Strain calibration for all noises,
+# so we need to divide by the sinc_sqr here to undo the
+# application of the dhdl in the Strain calibration. But this
+# is ultimately a superfluous extra calculation with the only
+# to provide some simplication in the Budget definition, so
+# should be re-evaluated at some point.
+
+
+def calc_total_residual_gas_damping(f, ifo, species, sustf):
+ """Total residual gas damping from all four test masses
+
+ :f: frequency array in Hz
+ :ifo: gwinc IFO structure
+ :species: molecular species structure
+ :sustf: suspension transfer function structure
+
+ :returns: displacement noise
+ """
+ squeezed_film = ifo.Infrastructure.ResidualGas.get('SqueezedFilm', Struct())
+
+ if squeezed_film is None:
+ raise ValueError('Must specify either excess damping or a gap')
+
+ # Calculate squeezed film for ETM and ITM seperately if either is given
+ # explicitly. If only one is given, it is not computed for the other one.
+ if ('ETM' in squeezed_film) or ('ITM' in squeezed_film):
+ squeezed_film_ETM = squeezed_film.get('ETM', Struct())
+ squeezed_film_ITM = squeezed_film.get('ITM', Struct())
+ n_ETM = noise.residualgas.residual_gas_damping_test_mass(
+ f, ifo, species, sustf, squeezed_film_ETM)
+ n_ITM = noise.residualgas.residual_gas_damping_test_mass(
+ f, ifo, species, sustf, squeezed_film_ITM)
+ n = 2 * (n_ETM + n_ITM)
+
+ # Otherwise the same calculation is used for both.
+ else:
+ n = 4 * noise.residualgas.residual_gas_damping_test_mass(
+ f, ifo, species, sustf, squeezed_film)
+
+ return n
+
+
+class ExcessGasScatteringH2(nb.Noise):
+ """Excess gas scattering for H2
"""
style = dict(
- label='Excess Gas',
- color='#add00d',
- linestyle='--',
+ label='H$_2$ scattering',
+ color='xkcd:red orange'
+ )
+
+ def calc(self):
+ cavity = arm_cavity(self.ifo)
+ species = self.ifo.Infrastructure.ResidualGas.H2
+ n = noise.residualgas.residual_gas_scattering_arm(
+ self.freq, self.ifo, cavity, species)
+ dhdl_sqr, sinc_sqr = dhdl(self.freq, self.ifo.Infrastructure.Length)
+ return n * 2 / sinc_sqr
+
+
+class ExcessGasScatteringN2(nb.Noise):
+ """Excess gas scattering for N2
+
+ """
+ style = dict(
+ label='N$_2$ scattering',
+ color='xkcd:emerald'
+ )
+
+ def calc(self):
+ cavity = arm_cavity(self.ifo)
+ species = self.ifo.Infrastructure.ResidualGas.N2
+ n = noise.residualgas.residual_gas_scattering_arm(
+ self.freq, self.ifo, cavity, species)
+ dhdl_sqr, sinc_sqr = dhdl(self.freq, self.ifo.Infrastructure.Length)
+ return n * 2 / sinc_sqr
+
+
+class ExcessGasScatteringH2O(nb.Noise):
+ """Excess gas scattering for H2O
+
+ """
+ style = dict(
+ label='H$_2$O scattering',
+ color='xkcd:water blue'
)
def calc(self):
- n = noise.residualgas.residual_gas_cavity(self.freq, self.ifo)
- # FIXME HACK: it's unclear if a phase noise in the arms like
- # the excess gas noise should get the same dhdL strain
- # calibration as the other displacement noises. However, we
- # would like to use the one Strain calibration for all noises,
- # so we need to divide by the sinc_sqr here to undo the
- # application of the dhdl in the Strain calibration. But this
- # is ultimately a superfluous extra calculation with the only
- # to provide some simplication in the Budget definition, so
- # should be re-evaluated at some point.
+ cavity = arm_cavity(self.ifo)
+ species = self.ifo.Infrastructure.ResidualGas.H2O
+ n = noise.residualgas.residual_gas_scattering_arm(
+ self.freq, self.ifo, cavity, species)
dhdl_sqr, sinc_sqr = dhdl(self.freq, self.ifo.Infrastructure.Length)
return n * 2 / sinc_sqr
+
+
+class ExcessGasScatteringO2(nb.Noise):
+ """Excess gas scattering for O2
+
+ """
+ style = dict(
+ label='O$_2$ scattering',
+ color='xkcd:grey'
+ )
+
+ def calc(self):
+ cavity = arm_cavity(self.ifo)
+ species = self.ifo.Infrastructure.ResidualGas.O2
+ n = noise.residualgas.residual_gas_scattering_arm(
+ self.freq, self.ifo, cavity, species)
+ dhdl_sqr, sinc_sqr = dhdl(self.freq, self.ifo.Infrastructure.Length)
+ return n * 2 / sinc_sqr
+
+
+class ExcessGasDampingH2(nb.Noise):
+ """Residual gas damping for H2
+
+ """
+ style = dict(
+ label='H$_2$ damping',
+ color='xkcd:red orange',
+ linestyle='--',
+ )
+
+ @nb.precomp(sustf=precomp_suspension)
+ def calc(self, sustf):
+ species = self.ifo.Infrastructure.ResidualGas.H2
+ return calc_total_residual_gas_damping(self.freq, self.ifo, species, sustf)
+
+
+class ExcessGasDampingN2(nb.Noise):
+ """Excess gas damping for N2
+
+ """
+ style = dict(
+ label='N$_2$ damping',
+ color='xkcd:emerald',
+ linestyle='--',
+ )
+
+ @nb.precomp(sustf=precomp_suspension)
+ def calc(self, sustf):
+ species = self.ifo.Infrastructure.ResidualGas.N2
+ return calc_total_residual_gas_damping(self.freq, self.ifo, species, sustf)
+
+
+class ExcessGasDampingH2O(nb.Noise):
+ """Excess gas damping for H2O
+
+ """
+ style = dict(
+ label='H$_2$O damping',
+ color='xkcd:water blue',
+ linestyle='--',
+ )
+
+ @nb.precomp(sustf=precomp_suspension)
+ def calc(self, sustf):
+ species = self.ifo.Infrastructure.ResidualGas.H2O
+ return calc_total_residual_gas_damping(self.freq, self.ifo, species, sustf)
+
+
+class ExcessGasDampingO2(nb.Noise):
+ """Excess gas damping for O2
+
+ """
+ style = dict(
+ label='O$_2$ damping',
+ color='xkcd:grey',
+ linestyle='--',
+ )
+
+ @nb.precomp(sustf=precomp_suspension)
+ def calc(self, sustf):
+ species = self.ifo.Infrastructure.ResidualGas.O2
+ return calc_total_residual_gas_damping(self.freq, self.ifo, species, sustf)
+
+
+class ExcessGas(nb.Budget):
+ """Excess Gas
+
+ """
+ style = dict(
+ label='Residual Gas',
+ color='#add00d',
+ linestyle='-',
+ )
+
+ noises = [
+ ExcessGasScatteringH2,
+ ExcessGasScatteringN2,
+ ExcessGasScatteringH2O,
+ ExcessGasScatteringO2,
+ ExcessGasDampingH2,
+ ExcessGasDampingN2,
+ ExcessGasDampingH2O,
+ ExcessGasDampingO2,
+ ]
diff --git a/gwinc/noise/residualgas.py b/gwinc/noise/residualgas.py
index 1b03693..df00e09 100644
--- a/gwinc/noise/residualgas.py
+++ b/gwinc/noise/residualgas.py
@@ -5,18 +5,21 @@ from __future__ import division
from numpy import sqrt, log, pi
from .. import const
+from .. import Struct
-def residual_gas_cavity(f, ifo):
- """Residual gas noise strain spectrum in an evacuated cavity.
+def residual_gas_scattering_arm(f, ifo, cavity, species):
+ """Residual gas noise strain spectrum due to scattering from one arm
Noise caused by the passage of residual gas molecules through the
- laser beams in a cavity.
+ laser beams in one arm cavity due to scattering.
:f: frequency array in Hz
:ifo: gwinc IFO structure
+ :cavity: arm cavity structure
+ :species: molecular species structure
- :returns: arm displacement noise power spectrum at :f:
+ :returns: arm strain noise power spectrum at :f:
The method used here is presented by Rainer Weiss, Micheal
E. Zucker, and Stanley E. Whitcomb in their paper Optical
@@ -28,26 +31,19 @@ def residual_gas_cavity(f, ifo):
expansion of exp, to speed it up.
"""
- Lambda = ifo.Laser.Wavelength
L = ifo.Infrastructure.Length
kT = ifo.Infrastructure.Temp * const.kB
- P = ifo.Infrastructure.ResidualGas.pressure
- M = ifo.Infrastructure.ResidualGas.mass
- alpha = ifo.Infrastructure.ResidualGas.polarizability
- R1 = ifo.Optics.Curvature.ITM
- R2 = ifo.Optics.Curvature.ETM
-
- rho = P /(kT) # number density of Gas
- v0 = sqrt(2*kT / M) # mean speed of Gas
-
- g1 = 1 - L/R1 # first resonator g-parameter of the ITM
- g2 = 1 - L/R2 # second resonator g-parameter of the ETM
- waist = L * Lambda / pi
- waist = waist * sqrt(((g1*g2)*(1-g1*g2))/((g1+g2-2*g1*g2)**2))
- waist = sqrt(waist) # Gaussian beam waist size
- zr = pi*waist**2 / Lambda # Rayleigh range
- z1 = -((g2*(1-g1))/(g1+g2-2*g1*g2))*L # location of ITM relative to the waist
- z2 = ((g1*(1-g2))/(g1+g2-2*g1*g2))*L # location of ETM relative to the waist
+ P = species.BeamtubePressure
+ M = species.mass
+ alpha = species.polarizability
+
+ rho = P / (kT) # number density of Gas
+ v0 = sqrt(2*kT / M) # mean speed of Gas
+
+ waist = cavity.w0 # Gaussian beam waist size
+ zr = cavity.zr # Rayleigh range
+ z1 = -cavity.zBeam_ITM # location of ITM relative to the waist
+ z2 = cavity.zBeam_ETM # location of ETM relative to the waist
# The exponential of Eq. 1 of P940008 is expanded to first order; this
# can be integrated analytically
@@ -60,3 +56,78 @@ def residual_gas_cavity(f, ifo):
zint[zint < 0] = 0
return zint
+
+
+def residual_gas_damping_test_mass(f, ifo, species, sustf, squeezed_film):
+ """Noise due to residual gas damping for one test mass
+
+ :f: frequency array in Hz
+ :ifo: gwinc IFO structure
+ :species: molecular species structure
+ :sustf: suspension transfer function structure
+ :squeezed_film: squeezed film damping structure
+
+ :returns: displacement noise
+ """
+ sus = ifo.Suspension
+ if 'Temp' in sus.Stage[0]:
+ kT = sus.Stage[0].Temp * const.kB
+ else:
+ kT = sus.Temp * const.kB
+
+ mass = species.mass
+ radius = ifo.Materials.MassRadius
+ thickness = ifo.Materials.MassThickness
+ thermal_vel = sqrt(kT/mass) # thermal velocity
+
+ # pressure in the test mass chambers; possibly different from the pressure
+ # in the arms due to outgassing near the test mass
+ pressure = species.ChamberPressure
+
+ # infinite volume viscous damping coefficient for a cylinder
+ # table 1 of https://doi.org/10.1016/j.physleta.2010.06.041
+ beta_inf = pi * radius**2 * pressure/thermal_vel
+ beta_inf *= sqrt(8/pi) * (1 + thickness/(2*radius) + pi/4)
+
+ force_noise = 4 * kT * beta_inf
+
+ # add squeezed film damping if necessary as parametrized by
+ # Eq (5) of http://dx.doi.org/10.1103/PhysRevD.84.063007
+ if squeezed_film.keys():
+ # the excess force noise and diffusion time are specified directly
+ if 'ExcessDamping' in squeezed_film:
+ # ExcessDamping is the ratio of the total gas damping noise at DC
+ # to damping in the infinite volume limit (in amplitude)
+ DeltaS0 = (squeezed_film.ExcessDamping**2 - 1) * force_noise
+ if DeltaS0 < 0:
+ raise ValueError('ExcessDamping must be > 1')
+
+ try:
+ diffusion_time = squeezed_film.DiffusionTime
+ except AttributeError:
+ msg = 'If excess residual gas damping is given a diffusion ' \
+ + 'time must be specified as well'
+ raise ValueError(msg)
+
+ # if a gap between the test mass and another object is specified
+ # use the approximate model of section IIIA and B
+ elif 'gap' in squeezed_film:
+ gap = squeezed_film.gap
+
+ # Eq (14)
+ diffusion_time = sqrt(pi/2) * radius**2 / (gap * thermal_vel)
+ diffusion_time /= log(1 + (radius/gap)**2)
+
+ # Eq (11) factoring out the low pass cutoff as in (5)
+ DeltaS0 = 4 * kT * pi*radius**2 * pressure * diffusion_time / gap
+
+ else:
+ raise ValueError('Must specify either excess damping or a gap')
+
+ # Eq (5)
+ force_noise += DeltaS0 / (1 + (2*pi*f*diffusion_time)**2)
+
+ # convert force to displacement noise using the suspension susceptibility
+ noise = force_noise * abs(sustf.tst_suscept)**2
+
+ return noise
--
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