As the flat mirrors i bought are specified for 0 deg i measured the transmission vs angle of one of them (assuming they are both "identical" as they are from the same coating run) as we want to use them at ~42deg as input/output coupler.
Here the simple setup using a large rotational stage, half wave plate to adjust the polarization and the power meter to measure the incident and transmitted power.

Here the results. Error bars for absolute values are probably large as even 1deg was hard to reproduce and read as the scale on the stage had 2deg steps. But better than nothing. It's enough for an order-of-magnitude calculation.

and here the data files

@DMASS: can you please check if my assumption for the angle is correct and make an estimation for the finesse for s and p-pol using the above numbers

Here are the drawings I submitted to the local machine shops for our 1550 nm triangular metal PMC.

The round trip path length is 2 x 6.3 inches. We want to use either 1m or 0.5m curved mirrors in the back, which give a waist size of:

1m => 425 um waist

0.5m => 340 um waist

Cavity FSR is***:

936 MHz

The PZT we have ordered and plan to use, the PI P-016.10H, has a 15 um range with a 1000V max voltage. Assuming linearity gives us 15 nm / V.

The voltage required to move 1.5 FSR is:

1.5 * (dL = L x FSR / f) * V / 15 nm = (6.3" x 0.0254 m/") x 936 MHz / (1.93x10^14 Hz) * V / (10^-8 m) = 77 V

Frank wanted to get some (specific) 60V power supplies, if we use these we only get a 1.17 FSR full range. Is this "good enough?" It means that we might not be able to sweep out two TEM00 modes in the full range unless we tune its length with a heater.

*** I am guessing a tiny bit. Since the FSR of a Fabry Perot of length L is c/2L, and the triangular cavity is like a flat/curved Fabry Perot with 2L = roundtrip length of triangular cavity, I think the FSR of a triangular cavity is c/(roundtrip length)

Unfortunately the concave mirror i've ordered and which was in stock according to their online shop turned out to be out of stock

So i've changed the order to a similar one. The only difference is that the new one doesn't have a wedge which shouldn't matter for our prototype as the transmission is only 50ppm (and it's still AR-coated on the back)

We have been tasked to think about in what ways the two cavity measurement is sensitive to the machining of the Silicon, so that we know if we need to ask for anything special in the machining of t.

Absolute Length

Relative Length

Absolute Diameter

Relative Diameter

Parallelism of Faces

Concentricity of Bore Hole

Flatness of Surface

1. Absolute Length

Sets cavity FSR determines how much frequency shifting we might need.

Magnitude of cavity length noise goes up linearly with length (as described by the half infinite mirror treatment of the problem)

Coating thermal noise coupling (uncorrelated between cavities so no reason to care about this even if we only match the cavity lengths to 10^-1)

Seismic coupling

2.Relative Length

Difference in cavity FSRs (if we could choose this, what would we want it to be)

We get common mode rejection of the laser noise from matching the length of the two cavities (unimportant and at uninteresting frequencies)

Room temperature common mode rejection of thermoelastic changes (also applicable if we are not operating at the zero CTE point at various cryogenic temperatures)

3.Absolute Diameter

Magnitude of cavity length noise goes down as the inverse square of its diameter (as described by the half infinite mirror treatment of the problem)

Seismic coupling

4.Relative Diameter

?

5.Parallelism of Faces

Cavity Mode axis gets shifted, and is no longer such a clean 00 (depending on how far the g-factor is away from 1)

SOME CRUDE CALCULATIONS/DISCUSSION OF THESE EFFECTS

1-1: If we use 100mm for the cavity length (~4 inches), the FSR is c/2L = 1.5 GHz (too much for an AOM)

2-1: If we have a length mismatch of dL, so that the lengths are L and L+dL, the FSR of the cavities will be slightly different (which seems unimportant). The cavities will differ by some number of lambda, (probably ~20 lambda). Worst case scenario here is they differ by (n+1/2) lambda, so if we made one cavity resonant for a laser, the other cavity would be anti resonant. In the picture where we use a single laser and frequency shift it, this would require us to do ~750 MHz of shifting. CAN WE DO THIS WITH AN AOM? If not, then we will either have to individually tune the temperature of the cavities (the absolute temperature of each cavity at room temperature doesn't matter much).

Further down the road when we are trying to operate at 120K, we could possibly detune the temperature of one cavity away from the zero CTE point (at the cost of higher temperature noise coupling) and still do useful work like that. If the cavities happen to have a worst case type condition, and we can't get our hands on a frequency shifter which can do the job, we can always move to a 2 laser setup (duplicating other components like a PMC, etc).

2-2: The only common mode rejection of laser frequency noise issue I can think of is the following: if the cavity lengths differ, then the cavity poles differ, and above the cavity pole, we will lose some common mode rejection of the high frequency noise based on this pole shift. Since the cavity pole for a 100 mm Finesse of 10k cavity is FSR/10k = 150 kHz. The difference in rejection between 0.005" and 0.001" seems like it probably doesn't matter for us, since we still have ~60 dB if we match the lengths to 10^-3.

We should also note that most of the loops we are thinking of using to lock the laser to the cavity have a UGF above the cavity pole, so the frequency noise will already be suppressed down at 150 kHz, thought not by all that much (a factor of 3-6 for a 500kHz - 1MHz UGF with 1/f at high frequency).

Since it wasn't clear before: In terms of laser frequency noise, I see no sort length mismatch dependent coupling of laser frequency noise to the beat signal which we should concern ourselves with. In the band of interest for us (1 mHz to 100 Hz), we expect 1/f laser noise, and f^2 or f^3 loop shape, with a ~500kHz UGF. This means we should be shot noise limited in our lock to the cavity, so there is no more classical laser noise.

1-4 and 3-2: The seismic coupling (in m/m of seismic displacement noise to cavity length noise) is dependent on the cavity geometry. If we can match the geometries very well, and they are suspended identically, we can have some rejection of the seismic coupling, since the seismic noise at the cold plate should be somewhat coherent over its length scale at those low frequencies (below 1Hz).

The way to figure out how cavity geometric tolerances couple into the seismic coupling (and therefore the common mode rejection of the seismic noise from the beat signal) seems to be COMSOL.

bought one of the NIR intensified CCDs which have the phosphor coating on the chip as we need at least one good one for mode identification. My home-made ones need still too much power, so you can't identify higher order modes
Edmund has one with 15% discount at the moment, so it's "only" $1700. Also bought two turning mirrors to see how they are. Specs are not bad, but so far i couldn't find any turning mirror not being frosted on the back.
A full beam analyzer for 1550nm is about $6k, which me might wanna buy in the future if we do more 1550nm stuff. For now i think we don't need one.

i thought the company we are talking about is doing everything (drilling, polishing) except the polishing of the part which requires flatness for contacting. The second company is then doing the re-polishing of the end surfaces, right?

Checked the update - w.r.t. a certain company- they were nonresponsive (to use the nomenclature) when I asked them to quote on the spacer. As far as we are concerned, they are just another Si supplier. Your concern about that supplier sounds to me like we are asking them to give us certain surface quality / precise geometry, neither of which I think we need from the raw materials, but from what I understand, we have very limited requirements for the spacer BEFORE machining.

Or did you mean you were concerned that there weren't things like purity, doping, not being broken specifically in the quote. This all seems sort of moot, since it seems like a not-so-hot idea to use something with the fabrication/shipping process and lead times given in the elog.

I asked a certain (unnamed) company whether or not they could do superpolishes, and they told me:

"We believe our silicon surfaces are as good as it gets. We have compared them to 'super polished' sufaces using our white light zygo and do no see any difference but we could be missing something..."

I don't know enough to know whether this is the way you would do a non phase-mapping comparison and totally reasonable, or if this statement is so ridiculous we should consider completely ignoring this company when it comes to mirror polishes.

Checked the update - w.r.t. a certain company- they were nonresponsive (to use the nomenclature) when I asked them to quote on the spacer. As far as we are concerned, they are just another Si supplier. Your concern about that supplier sounds to me like we are asking them to give us certain surface quality / precise geometry, neither of which I think we need from the raw materials, but from what I understand, we have very limited requirements for the spacer BEFORE machining.

Or did you mean you were concerned that there weren't things like purity, doping, not being broken specifically in the quote. This all seems sort of moot, since it seems like a not-so-hot idea to use something with the fabrication/shipping process and lead times given in the elog.

Some actual numbers for the pertinent "RC" time constants are discussed in the PSL elog. There has been debate about what the radiative pole from the can to the cavity will be for the cryo cavity, and what it is for the current room temperature cavity. See section titled:

The cryostat window schedule is currently behind. Tommorrow's to do list to help remedy:

Get John from ISI/MDC on the phone to finally give us a firm quote for the brazing process (Meller has the windows we want to use)

Confirm the clear aperture with Dick from Precision Cryo (who is making the window flange) so we know if 1" windows are actually OK to use

Get quotes for an AR coating from American Photonics and VLOC for 8 windows (1 run) (waiting for reply)

Dick seems to think he might have a problem welding Kovar to stainless (he's never done this before)....

The windows we want to get (and were planning on getting) from MDC/ISI are Kovar brazed to Sapphire. MDC seems to be able to weld/bond this to stainless with no problem as their window flanges are stainless. I don't yet know if there is anything tricky about welding stainless to Kovar, but I'll bug MDC about this. If there is some tricky process required to do the joint, it seems our least bad option might be to have Dick ship his custom fab'ed stainless parts to MDC and have them do the joint.

Old window plan:

Meller Sapphire Windows -> MDC for brazing -> coating company for AR coating -> Dick for welding to stainless flange

Possible new plan:

Meller Sapphire Windows -> MDC for brazing -> coating company for AR coating -> MDC for welding to Dicks flange which he also ships to MDC

One might ask why we have a custom flange at all...This is all born from Dick's idea of what is good / bad: He did not want to do a cold CF joint between stainless (the flange) and Cu (the 77K cold shield), his words were "you need one of the surfaces to be stainless in a CF flange". This left us with the choice of either doing a stainless 77K shield, or abandoning CF and having him do something custom. Since Rana and Warren seemed strongly opposed to stainless b/c or thermal gradients (low spatial correlation over the shields surface) I said F it and went for the custom flange.

At this point we will probably have the cryostat before we have windows for the cryostat, so I'm having Dick fab some (simple) covers for the window ports so we can get started on the temperature stabilization once the cryostat gets here.

I have been delinquent about elogging the calculation I did some time ago about what the radiative time constant between the cavity and its can would be.

I added what the numbers I get for the room temperature situation is as well.

[edit: I added the slew rate limit from cooling if we paint everything black]

We had some concerns about being able to get a high enough UGF for the heater around the cavity. The slew rate limit of cooling the heater via direct radiation to the 77K shield, using order of magnitude calculation, seems to be ~0.4 K/second. See section 3 of the attachement for details

I thought I would post a helpful drawing to help anchor my/our (future) discussion of the temperature servo for the cavity heater.

Since we want to know about the closed loop dynamics of the system, I think it makes sense to talk about the whole thing in terms of "equivalent thermal circuits", where we have R's, C's and V's. And dQ/dt=DeltaT/R is our equivalent of Ohm's law.

Initially, I will do the first order thing and make the following assumptions:

Rcond1 is large

Rcond 3 is large

Rcond2 is small

Rcond4 is small

Heat Capacities of the heater and temperature sensor are small

I have been delinquent about elogging the calculation I did some time ago about what the radiative time constant between the cavity and its can would be.

I added what the numbers I get for the room temperature situation is as well.

[edit: I added the slew rate limit from cooling if we paint everything black]

We had some concerns about being able to get a high enough UGF for the heater around the cavity. The slew rate limit of cooling the heater via direct radiation to the 77K shield, using order of magnitude calculation, seems to be ~0.4 K/second. See section 3 of the attachement for details

It seems we may want to say something quantitative about how cavity mirror thickness effects the bottom line performance of the reference cavity before we get mirrors for said cavity.

equation (3) gives a single sided PSD (in m^2/Hz) of cavity length noise from mirror substrate thermal noise (under certain assumptions*):

G(f) = 4 k T (1-sigma^2) / (omega sqrt(pi) E w0) Phi_substrate

where sigma is Poisson's ratio, omega is the (optical) angular frequency, E is the Young's modulus, w0 is the spot size on the mirror, Phi_substrate is the loss of the mirror substrate.

The dependence on mirror substrate thickness is contained in Phi_substrate. I talked to Alastair, since he seems to know some things about loss. For fused silica, it seems that the accepted way of thinking about how the bulk loss and surface loss contribute to the total loss is:

Phi_total = Phi_bulk x E_bulk / E_total + Phi_surf x E_surf / E_total

Where the bulk and surface losses are weighted by the fraction of total energy in each respective "zone". I don't see any reason why this equation should hold for an amorphous material but not a crystalline one.

Figure 11 shows various results silicon oscillator Q vs thickness at 4K. Figure 10 shows the temperature dependence of one of the oscillators (7 um thick cantilever). Applying envelope physics to this, it seems we can guess the following about silicon Q's for a mirror (making some assumptions about thickness >> diameter - only semi valid here):

Q(3mm,4K) ~ 10^8

Q(120K) ~ Q(4K)/5

Q(300K) ~ Q(4K)/2.5

And from looking at the graph and doing some rough interpolation, we get:

0.74 log(thickness in um) + 5 = log(Q-factor), or

10^5 x (thickness [um])^0.74= Q-factor

for curiosity of scaling: dQ/dthickness(3mm,4K) ~ 10^5 x 0.74 x (thickness [um])^-0.26

so we have:

Q(3mm,120K) ~ 10^8/5

Q(6mm,120) ~ 10^8/5x 2^0.74

I plugged these numbers into the formulas given for both spacer thermal noise, and substrate thermal noise for 3mm and 6mm substrates. I used a biggish spot (250 um), and a loss of 3e4 for the coating.

In reality the question of thermal noise is more complicated than just using these equations blindly...

As a first pass, my inclination is to say that if we can't get 6mm mirrors without a big PITA, 3mm would be *fine* for cavity version 1, and following some more detailed understanding of the thermal noise couplings, cavity version 2 could be made with bigger mirrors.

TL;DR Bigger mirror substrates are better up to a point, but in a simple analysis of noise couplings, choosing 3mm mirrors doesn't totally screw us.

collection of data and references for noise calculations for ET, including Silicon data from large mirror substrates down to thin cantilever blades.
Two pictures as an overview:

again i've compared the performance of various temp sensors and temp controllers to see which one would be good to start with.
I've assumed that we might wanna start with a commercial solution as we have tons of other problems to solve in the beginning and don't wanna care about designing and building a super low-noise temp sensor readout and control unit. So i've checked what's available and basically found two multi-channel cryo temp controllers which are sold under different names from different companies:

both are 4-sensor input, analog output units with 2 integrated variable DC current sources (up to 100W).
Interfaces to the outside world are analog, USB, Ethernet, serial etc.

I've used the comparison for the control stability from Lakeshore which can be found on page 5 in the manual of the 4-channel cryo temp controller.
The accuracy and noise for both controllers is almost identical. The SRS is slightly better in some things, the Lakeshore in others, so it's good enough for a start.

Here the table with highlighted values for the ELECTRONICS ONLY.

From that we see that using a commercial unit gives us something about +/-1.6mK to +/-4.8mK for super long-term stability (not noise at higher frequencies!).
This is good enough for what i've estimated here some time ago what we can get for the long-term stability. While Germanium is good for low temperatures (e.g. 18K) , platinum RTDs, silicon diodes and Cernox are good for higher temperatures (300K-77K).

Cernox sensors require calibration. On the other hand platinum RTDs offer high uniform sensitivity with excellent reproducibility. They follow a standard curve above 70 K and are easily interchangeable and cheap. We can also get dual sensors in one unit for in- and out-of-loop measurements at the same point (if we want).

Both controllers support any kind of diode or RTD/thermistor as the sensor so we are totally flexible and can also compare different sensors e.g. mounted to a huge block in vacuum to measure the noise/stability of them and then switch to something we like more later on.

So i would go for platinum RTDs in the beginning and the SRS CTC100c which offers everything we need including data-logging (unlimited on a usb stick, until full) and a graphical display showing graphs for everything we want, so we don't need a data acquisition system at the beginning. That's all for $2600. They also have 4 sensors, so in and out-of-loop for both cavities and two independent heater units. Perfect for our system.

i've checked the change in Q vs thickness for the mirrors. I think we want to go for thicker ones to be on the save side.
The Q for the measured 6mm is still high enough but we don't know how it changes from 6 to 3mm and changing the diameter from 3" to 1".

Here the plot from one of Ronny's publications "High mechanical Q-factor measurements on silicon bulk samples":

Reply from them: "We offer 1"Ø 1M ROC Fused Silica Substrates, which are usually in stock. Or we
could manufacture 1"Ø 1M BK-7 Substrates, which would be a custom job. I understood
your e-mail to be 1"Ø 1M Silicon Substrates, which we are not able to manufacture."

Almaz Optics, Inc. - - QUOTE REQUESTED
www.almazoptics.com

do silicon mirrors all the time for CO2 lasers, surface only >3nm rms, but could buy pre-polished substrates and let them repolish somewhere else

Umicore Laser Optics USA - CAN't DO GOOD SURFACE QUALITY
also known as http://www.ulooptics.com, manufacturer of CO2 laser optics and beam delivery systems

standard quality silicon mirrors (concave) are stock parts, e.g. 10SIS3-05

Reply from them: "We offer 1"Ø 1M ROC Fused Silica Substrates, which are usually in stock. Or we
could manufacture 1"Ø 1M BK-7 Substrates, which would be a custom job. I understood
your e-mail to be 1"Ø 1M Silicon Substrates, which we are not able to manufacture."

Almaz Optics, Inc. - - QUOTE REQUESTED
www.almazoptics.com

do silicon mirrors all the time for CO2 lasers, surface only >3nm rms, but could buy pre-polished substrates and let them repolish somewhere else

Umicore Laser Optics USA - CAN't DO GOOD SURFACE QUALITY
also known as http://www.ulooptics.com, manufacturer of CO2 laser optics and beam delivery systems

standard quality silicon mirrors (concave) are stock parts, e.g. 10SIS3-05

Diameter still pending. Question is which tolerances for raw material are available, e.g. can we buy a 2" crystal and still get a 2" cavity out of it or do we have to buy 3" crystals which are much more expensive.
If we have to go for the larger one we then could go for larger diameter without increasing the cost. Or we go slightly under 2" for the cavity when starting with 2".

Before the happy metal pmc gets finalized, here is some information to stimulate some controversy, and maybe constructive Socratic dialogue...

First image:

Since my hand is still broken, I made a doodle of the algebra involved in the PMC.

I set the total length to 6.3", which seemed to give some OK HOM filtering (elog:96)

Second Image:

This is what I have in solidworks so far

We still need:

O-ring choice for the outside of the mirror - the recession in the clamp is a 1.05" clearance

Mounting bracket / contacts for the spacer (balls a la 40m PMC seem bad, use pins for precise placement?)

PZT - do we need to shrink the back hole to use a reasonable one?

The eventual (aka imminent) plan is to send drawings to local shops...I talked to Ken Mailand, he liked ASCO Engineering
in north hollywood. I also talked to Rich Abbott, and he liked Futrell's in West Covina.

Try to summarize how to estimate the contribution from surface figure, quality (scratch dig) and roughness to the performance of the cavity including a short description of the individual parameter: This is required to estimate the minimum requirements for the mirror surface for a high finesse silicon cavity.
The problem is that standard values we ask for FS mirrors all the time are hard, almost close to impossible to get for silicon substrates.
e.g. standard surface figure for a silicon mirror at 1um is lambda (!), a good one L/2. Even cheap Thorlabs mirrors usually have L/10 at 633nm for comparison. Same for the other two parameters.

1) surface roughness

surface roughness is typically given as a single rms value without any information about the boundaries for the integrated spatial frequencies.
What i got from talking to Hiro is that without having this particular information the number is kind of useless, it could mean anything without further information how they measured it (same situation as for the linewidth for lasers)

So we have two options: ask the company for the PSD vs spatial frequency or for some rms numbers measured for different lower spatial frequency, e.g. approx our beam size on the mirrors

As this might be difficult or might take too long i prefer a third option:

We assume that a very good polished mirror has a similar PSD shape as the ones we have for several optics from LIGO/VIRGO

the region of interest for small optics can be fitted by a simple linear equation (see T070052)

the ones which are worse have higher noise levels for high frequencies and are about the same for low frequencies (simply changing the slope of the fit)

we then can calculate the loss with the given formula

2) surface quality

surface quality (scratch dig) is described by two numbers, one for scratches, one for digs/bubbles. Description copied from google search:

Purpose: This document defines surface quality on optical components per MIL-O-13830.

Definitions:

SCRATCH:Any marking or tearing of the part surface.

DIG:A small rough spot on the part surface similar to a pit in appearance. A bubble is considered a dig.

SLEEK SCRATCH:A hairline scratch.

CRUSH or RUB SCRATCH:A surface scratch or a series of small scratches.

Method: The size of a defect is to be measured through the use of an optical comparator:
Surface quality is to be specified by a number such as 60/40. The first digits relate to the maximum width allowance of a scratch as measured in microns. The next digits indicate to maximum diameter allowance for a dig in hundredths of a millimeter. Thus, as can be seen from the table below, a surface quality callout of 60/40 would permit a scratch width of .06 mm (60 micron -or- 0.0024") and a dig diameter of .40 mm (400 micron -or- 0.0158").

Scratch or
Dig Number

Maximum
Scratch Width

Maximum Dig
or Bubble Diameter

Dig or Bubble
Separation Distance

#

mm

inch

mm

inch

mm

inch

120

0.12

0.0047

1.20

0.0473

20

0.787

80

0.08

0.0031

0.80

0.0315

20

0.787

60

0.06

0.0024

0.60

0.0236

20

0.787

50

0.05

0.0020

0.50

0.0196

20

0.787

40

0.04

0.0016

0.40

0.0158

20

0.787

30

0.03

0.0012

0.30

0.0118

20

0.787

20

0.02

0.0008

0.20

0.0079

20

0.787

15

0.015

0.0006

0.15

0.0059

20

0.787

10

0.010

0.0004

0.10

0.0039

1.0

0.040

5

0.005

0.0002

0.05

0.0020

1.0

0.040

3

0.003

0.00012

0.03

0.0012

1.0

0.040

The formula for calculating the loss from such surface errors is given in one of Hiros talks, e.g. G1000484. The two missing parameter needed is the depth of the defect and the length, but we could use some average/typical number for a start.

i've polished the back of one of our turning mirrors (Newport 10D20DM.8) which originally come with a frosted back surface.
Used one of the "bad" mirrors which has some slight scratches at the outer area. Used first contact to protect the HR coating while polishing.
Now i was able to measure the transmission of those mirrors.

Reply from them: "We offer 1"Ø 1M ROC Fused Silica Substrates, which are usually in stock. Or we
could manufacture 1"Ø 1M BK-7 Substrates, which would be a custom job. I understood
your e-mail to be 1"Ø 1M Silicon Substrates, which we are not able to manufacture."

Almaz Optics, Inc. - CAN ONLY SUPPLY BLANKS, MAYBE GOOD FOR SPACER
www.almazoptics.com

the Q-measurements were done with doped Cz-grown silicon (see thesis) so i don't see why we should go for the super-expensive, super-pure FZ-grown stuff.

According to literature the linear thermal expansion coefficient is identical for all crystal orientations [100], [110] and [111] as the structure is cubic (e.g. see here).
So regarding the zero CTE point we can use any orientation. However, the Q is different for different orientations, but i think high enough in all cases (but should recalculate noise model for worst case values).

Quote:

I was giving the cryo poster at the LV meeting, and one of our references wandered up (Ronny Norwaldt). He asked me what type ofsilicon we were going to use, and I had no idea, so I turned to wikipedia. It seems there are potentially 3 types of Silicon (different fab processes) we might use for the cavity spacer.

I was giving the cryo poster at the LV meeting, and one of our references wandered up (Ronny Norwaldt). He asked me what type ofsilicon we were going to use, and I had no idea, so I turned to wikipedia. It seems there are potentially 3 types of Silicon (different fab processes) we might use for the cavity spacer.

i think it has to be (T_{1} + T_{2} )( T_{1}^{2} - T_{2}^{2} ) and then whatever i said below is right. Not temp difference, no net heat exchange, infinity resistance

hmm, the sign seems to be right

Quote:

i didn't read it carefully but my guess is that you are using a formula which doesn't work in that special case.
The reason is that this formula might be derived from the simple Boltzmann equation with two surfaces for different (!!) temperatures.

If you start using the formula with the view factor to calculate the amount of heat transferred between both surfaces
q_{1-2}=sigma(T_{14}-T_{24}) divided by the rest like epsilon, view factor etc, same as in your formula you see that the heat transfer is zero.
So if you do it for both directions, q_{1-2, }q_{2-1 }both are zero ! So where does the formula come from is the question. But no temp difference no radiative heat transfer (at least that's what i learned years ago)
I guess the only reason why you get anything is that epsilon and the surface is not identical for both sides.
I think you can't use that simplified formula as this might be based on sigma(T_{14}-T_{24}) in the fist place assuming both temperatures are not identical.

But that's just a guess

Quote:

I did a couple calculations today to figure out the radiative pole for the proposed cryostat design.

The first REALLY simple one was just radiative heat transfer ignoring radiosity. This was pretty clearly a poor approximation, as it yielded an answer for tau which is independent of the emissivity of the radiative shield.

Next, I tried to use the equivalent thermal resistance to find the pole. I have attached that calculation, and suspect some glaring typo I carried through, since its answer was 3 months for the time constant.

1$ to anyone who finds the typo(s) / bad assumption(s) which make the answer no longer wrong or comes up with evidence that this is correct.

i didn't read it carefully but my guess is that you are using a formula which doesn't work in that special case.
The reason is that this formula might be derived from the simple Boltzmann equation with two surfaces for different (!!) temperatures.

If you start using the formula with the view factor to calculate the amount of heat transferred between both surfaces
q_{1-2}=sigma(T_{14}-T_{24}) divided by the rest like epsilon, view factor etc, same as in your formula you see that the heat transfer is zero.
So if you do it for both directions, q_{1-2, }q_{2-1 }both are zero ! So where does the formula come from is the question. But no temp difference no radiative heat transfer (at least that's what i learned years ago)
I guess the only reason why you get anything is that epsilon and the surface is not identical for both sides.
I think you can't use that simplified formula as this might be based on sigma(T_{14}-T_{24}) in the fist place assuming both temperatures are not identical.

But that's just a guess

Quote:

I did a couple calculations today to figure out the radiative pole for the proposed cryostat design.

The first REALLY simple one was just radiative heat transfer ignoring radiosity. This was pretty clearly a poor approximation, as it yielded an answer for tau which is independent of the emissivity of the radiative shield.

Next, I tried to use the equivalent thermal resistance to find the pole. I have attached that calculation, and suspect some glaring typo I carried through, since its answer was 3 months for the time constant.

1$ to anyone who finds the typo(s) / bad assumption(s) which make the answer no longer wrong or comes up with evidence that this is correct.