A High-Performance Wave Guide Cryogenic Thermal Break

We describe a high-performance wave guide cryogenic thermal break. This has been constructed both for Ka band, using WR28 wave guide, and Q band, using WR22 wave guide. The mechanical structure consists of an hexapod (Stewart platform) made from pultruded carbon fibre tubing. We present a tentative examination of the cryogenic Young’s modulus of this material. The thermal conductivity is measured at temperatures above the range explored by Runyan and Jones, resulting in predicted conductive loads through our thermal breaks of 3.7mW to 3K and 17μK to 1K.


I. INTRODUCTION
When designing a cryogenically-cooled microwave system there are conflicting requirements for the transmission line (or lines) between the cooled components and components at higher temperatures.On the one hand low thermal conductance is sought to reduce the conductive heat load on the cooling system.On the other hand low transmission line loss is highly desirable and often essential.These two requirements are, to a large extent, mutually exclusive as, in typical conditions, electrons which carry charge for RF transmission are also effective for electronic transfer of heat.The ratio between RF loss and thermal conductance may be optimized by careful material selection and design geometry, such as using stainless steel coaxial cable or wave guide, with thin cross-section and often a gold flash, not much exceeding a skin depth in thickness.
This technique has commonly been adopted for signal paths that can tolerate higher losses (e.g.IF outputs or LO inputs), for many radio-astronomy cryogenic receivers and diverse other types of cryogenic instrument.
For our cryogenic noise measurement system 1 , with which we have been characterizing LNA noise temperatures over a range of physical temperatures to below 2 K, we found achieving a low enough thermal load on our 4 He sorption fridge to be very challenging using stainless steel wave guide.Also, the addition of an input wave guide for cold source (Keysight Technologies PNA-X option 28) noise measurements doubled the conducted load, and itself added a noise contribution overwhelming that of our LNAs.
However, a wave guide with a physical break part way along its length can provide both extremely low thermal conductance and very low RF loss, without compromise.This has been described, for example, by Weinreb et al. 2 , for circular receiver input wave guide.The method relies upon maintaining a small, accurately-aligned, gap at the wave guide break.If the break closes the thermal isolation will fail.If the gap opens wide or gets misaligned the RF transmission and reflection will degrade.The main difficulty when designing a wave guide thermal break is therefore conceiving a support structure to maintain the a) Simon.Melhuish@manchester.ac.uk gap without itself adding a significant thermal condition path.

II. INITIAL DESIGN
Our thermal break was inspired by a design by J.L. Cano de Diego 3 .At the split in the wave-guide two flanges are held apart by approximately 100 µm.This could result in radiation of the signal from the gap.It is important to keep radiation to a very low level, such that it cannot provide a means of feed-back causing our highgain LNAs to oscillate.Some of our LNAs have gains of nearly 50 dB, so we need to restrict radiation to well below a level of -25 dB, which we achieve by machining a quarter-wave choke ring into one flange.

A. Mechanical and Thermal Design
Whereas Cano de Diego had Rogers RO4003 hydrocarbon ceramic laminate we used a set of four pieces of stainless steel shim to hold apart the flanges of our initial prototype.
Whilst it is obvious that a thin sheet of steel does not strongly constrain movement perpendicular to the plane of the sheet, a square-based arrangement of four sheets, held at each end, is surprisingly stiff.
A simple thermal model predicts a conductive power of 56 µW with one side at 1 K and the other side at 3 K.They were also used from 3 K to 50 K and 50 K to 300 K, for which the modelled powers are 25 and 501 mW respectively.These values are further reduced through the removal of parts of the steel in a pattern of cut-outs, as may be seen in fig. 1.

B. RF Design
The Cano de Diego RF design was verified with modelling in Ansys HFSS.This is illustrated in for our Qband design in Figure 3.
Figure 2 shows S 11 and S 21 measured through four thermal breaks at room temperature.Generally the results are very good, but two have increased loss around 29 GHz.Return loss is generally around 30 dB, but about 20 dB at worst.The device-to-device variations are likely FIG.1: The original prototype using 100 µm-thick stainless steel supports FIG.2: VNA measurements (S 11 and S 21 ) of prototype (shim steel) thermal breaks at room temperature due to differences in the gap size and misalignment of the two parts of wave guide.

III. IMPROVED DESIGN
The initial design was effective enough for a series of noise temperature measurement experiments, but degraded over time due to mechanical stresses during handling and cooling.We therefore sought to improve the mechanical arrangement to provide more accurate maintenance of the gap with greater robustness but even lower thermal conductance.
FIG. 3: HFSS E-field simulation of Q-band thermal break

A. Support Material
For a given minimum stiffness and heat conduction of the support structure we are not bound to choose the stiffest or least conducting material.Instead we seek a material with a high ratio of Young's modulus to thermal conductivity and then size the tube cross-sectional area as appropriate.
Runyan and Jones 4 examined several polymeric and composite structural materials, evaluating their Young's modulus (E) to conductivity ratios.They found pultruded carbon fibre tubes to be a useful class of materials with a high ratio.However, one aspect of their analysis was that room-temperature Young's modulus measurements had to be used.We therefore designed a simple experiment with our undergraduate students to verify that cryogenic values of E did not suffer with respect to room-temperature values.We used pultruded carbonfibre tubes from UK supplier, Easy Composites Ltd.

B. Cryogenic Young's Modulus of Carbon Fibre Tubing
A CAD model of the experiment is shown in figure 4. A carbon fibre rod is glued to a brass fixture at its top end and attached to the second cooling stage of our Gifford McMahon cooler at a temperature of approximately 4 K.At the lower end a steel bob is attached.This has threaded attachment holes for a heater and diode thermometer.
The Dewar system is mounted on a yoke to allow tilting in any direction away from vertical.The test sample is mounted co-axially within a copper pipe.As the Dewar is tilted the weight of the bob bends the carbon fibre tube off-axis.If the tilt is sufficient to displace the bob 7.5 mm sideways it makes contact with the copper pipe.
The thermometer on the bob serves two purposes.It measures the temperature of the bob, which may be increased by passing a current through the adjacent heating resistor.It also indicates when the bob touches the copper pipe, as its anode is shorted to ground.In practise the thermometer was switched off between measurements because the thermal isolation provided by the carbon fibre tube was so good that the ∼ 10-µW bias power significantly increased the bob temperature.During cold measurements the bottom end of the tube cooled to 6 K.
The length of tube emerging from the fixed end to the centre of mass of the bob was 310 mm.
The tilt angles required for contact are collected around a full rotation about the vertical axis.A leastsquares fit of a circle to this pattern of contact points is made.Due to imperfect alignment of the tubing to the jig axis this circle may not be centred on the origin, but the best-fit radius provides the tilt angle for the Young's Modulus calculation.
Our results are presented in Table I.Here the errors on the E values are derived from the fitting parameter errors.They do not take account of uncertainty in the tube cross-sections, but these should be the same for measurements on the same tubes.
The 3-mm tube was at the limit of stiffness for the original set-up, with one rotation angle not able to bring the bob into contact even with the Dewar horizontal, when cold.Therefore this tube was re-measured with additional weight on the bob.
All the other measurements exhibit an increase in the required tilt angle, and therefore small increase in stiffness, when the apparatus is cooled.
It will be noted that the measurements for the two smaller tubes are very different from the larger tubes.This is due to the assumption that our experimental scheme is equivalent to the usual horizontal cantilever problem, where a downwards-acting weight pushes the beam down.We equate the small sideways-acting component of the bob weight, when the tube axis is tilted off vertical, to the cantilever weight.However, the longitudinal component becomes very significant for thinner tubes as it pulls them into a tight bend at the top.This becomes obvious when considering an arbitrarilythin tube, which will hang vertically like a string with a small weight.Therefore we discount the 1.0 and 1.5-mm values as true measurements of E, although they do illustrate a stiffening upon cooling.The quoted errors are therefore not representative of the true E-value errors, but are useful for consideration of the significance of the hot/cold variation.
In conclusion we detect a small (3 to 8%) increase in modulus upon cooling, as might be expected.Our samples appear slightly stiffer than the 134 GPa (tension) and 131 GPa (compression) moduli quoted by Runyan and Jones.

C. Thermal Conductivity
Runyan and Jones 4 conducted thermal Conductivity measurements from 0.3 to 4 K.They performed a fit to the conductivity over this range using a modified power law.Whilst the conductivity for carbon fibre tubing was higher than most of their trial materials, the ratio of conductivity to (room temperature) Young's modulus was beaten only by Macor (machinable glass ceramic), and that only below approximately 1 K.
Because of the limited temperature range of the Runyan and Jones evaluation compared with the intended operational conditions for our thermal breaks we engaged in our own conductivity measurements.Our simple test jig (figure 5) comprised a sample of carbon fibre tubing glued to high-conductivity copper attachment points at each end and at the mid point.A resistor heats the tube sample through the top attachment.There may be some ∆T across the glue joint.A rhodium iron thermometer is used to measure the temperature at the mid point of the tube.Here there is essentially zero heat flow across the joint so our reading should accurately reflect the temperature of the tube.The bottom stage provides our mounting point to the Dewar cold plate.We assume that the tube cold end temperature is the same as the Dewar cold plate.In fact there will be a small temperature drop here, but because the bond is very thin and the carbon fibre tube has low conductivity anyway, this will not be large.Adding another well-calibrated thermometer to an extra stage separated from the bottom connection would be preferable for ultimate accuracy.Radiative loss from the top stage has been calculated to be at most 7 × 10 −5 of the applied power at the highest power level, assuming worst-case black-body emission.Even with some oxidation the metal emissivity should be no more than a few percent, so the power loss is negligible.Measurements of mid-point temperature as a function of applied power were made over the range 2.7 K to 70 K.The power values scaled according to the test geometry yield integrated conductivities as plotted against temperature in figure 6.The BSpline fit curve is also tabulated in table II.Temperature reading errors due to the RhFe thermometer are insignificant.The variation of ∆T at the base glue joint has not been characterized.An uncertainty in power at a level of a few per cent arises from changes in the R heater to R wires ratio which has not been characterized.To obtain conductance values P (T )  readings were interpolated and the derivative taken.The choice of interpolating function has a significant influence on the resulting derivative.We used a cubic spline interpolation, which resulted in some excess scatter in the results, but this was no worse than, for example, various degrees of polynomial fitting.Results are given in figure 7.No error bars are given as the input T errors are small compared with the scatter generated by the differentiation process.Above 4 K it is apparent that initially the Runyan and Jones fit holds well.However, by 10 K the conductiv-ity should be starting to turn over, but in fact we find it is rising.With the number of free parameters available the Runyan and Jones form can be contrived to fit, but instead we present simple polynomial fits to log 10 (k) as a function of log 10 (T ).The 8-term model typical of NIST measurements seems adversely affected by the scatter over this relatively truncated T range, so our preferred fit with a fourth-order polynomial is presented in the plot and in equation 1. Fit residuals are at the 10 to 20% level below 10 K, but peak at nearly 50% at 20 K. log 10 (k) = − 0.24 + 6.701 log 10 (T ) − 10.361 log 10 (T ) 2 + 6.983 log 10 (T ) 3 − 1.553 log 10 (T ) 4 (1) It is apparent that up to 70 K the conductivity is still increasing.We would like to take measurements at higher temperatures still because this may indicate that carbon fibre is less appropriate for higher temperature applications.
For our LNA measurements we were not limited by cooling power on our first stage, so for simplicity we used the same carbon fibre tubing for thermal breaks to room temperature as well as the colder stages.
We do not quote an expected conduction load for the thermal breaks from room temperature to the first stage.Using our measurements we expect a conductive load from 50 K to 3 K of 3.7 mW per thermal break.Using the Runyan and Jones model we expect a conductive load from 3 K to 1 K of 17 µW per thermal break.

D. Thermal Contraction
The purpose of the support structure is to maintain the accurate separation of the wave guides.Whilst some slight increase in the gap size could be tolerated and a reduction in the gap size would even be beneficial it is crucial that the gap should not close completely.This depends upon the relative contraction of the supports and the copper wave guide.
For a separate application we constructed a 200-mm high hexapod using the same carbon fibre tubing.To measure cryogenic thermal contraction the hexapod was cooled to 77 K in a bucket of liquid nitrogen.The height was measured using a height gauge on the bench before cooling and again afterwards, very quickly before the structure warmed up.No change in height could be  As the thermal break is 1/4 the height this demonstrates that closure of the 100-µm gap is unlikely.
In practice we found that the gap did not close, so contraction of the carbon-fibre must be less than 100 µm in excess of the contraction of 50 mm of copper.Thus we can set an upper limit of 5.5×10 −5 fractional contraction, cooling from 293 K to 1.4 K.
If we assume that the carbon fibre tubes do not con-tract when cooled the contraction of the other parts will cause the gap to open.In this case we calculate that the gap would become 137 µm.
Our HFSS model predicts a very low leakage level by radiation through the gap.With a 100-µm gap we expect this to be -48.0dB (total into 4π steradians).Whilst the worst-case (no tube contraction) increase in gap size could increase this to -41.1 dB, there should be an accompanying obvious worsening of S 11 , which is not observed.

E. Support Geometry
The original geometry for the shim steel supports formed a square tube (with the corners missing).Whilst this is much stiffer than the individual sheets a geometry with several tubes could be better.We investigated two tube-based geometries: a 6-tube hexapod (Stewart platform) and an 8-tube octapod (square truss).These were modelled in Autodesk Inventor and a finite element stress analysis conducted on each, for a range of tube dimensions.In figures 8a and 8b we compare the reaction of the octapod and hexapod geometries to a 10-N force applied in shear.The tube modelled has 2-mm outside diameter and 1-mm inside diameter.Each tube is 55 mm long.The octapod displacement is lower, as should be expected because it has more struts.For comparison figure 8c shows the large displacement modelled for our original shim steel design.We modelled the tubes with a Young's modulus of 135 GPa.The higher measured E value will reduce the expected displacement for the hexapod to approximately 12 µm (warm or cold).
Whilst the 8-legged design is evidently stiffer we judged that the hexapod would be sufficient, whilst slightly easing construction by providing easier access to the gap and having 3/4 the thermal conductance.

F. Realization
The four flanges of the thermal break, two at the break and two at the ends for connection to standard flanges, were manufactured from brass.A jig was made to facilitate drilling of the holes for the carbon fibre tubes at the correct angles.The wave guides were cut from copper lengths and silver soldered to the flanges.Mandrels were made to align the two sections to their common axis.Gap separation was set using a 100-µm shim between the inner flanges.With the wave guides held together across the shim using clamps the six carbon fibre tubes were glued in place using Stycast, curing at approximately 60 • C. Finally the clamps, shim and mandrels were removed.Two completed thermal breaks are pictured in Figure 9.

IV. PERFORMANCE
S-parameter measurements of each thermal break were taken using the PNA-X VNA for both Ka and Q-band designs.In figure 10 we show the input match and transmission of one of the Ka-band breaks at room tempera-ture.Performance is improved with respect to the original prototype, with a flatter response in S 21 and a lower and flatter S 11 .In addition, we subject the device to a sideways load of 500 g.It is apparent that the effect of even this large force is minimal.
In figure 11 we present measurements of the entire wave guide chain.Here we put a U-bend in place of any "device under test", adding loss of 0.1 dB or more below 35 GHz increasing to 0.5 dB at higher frequencies.Additional wave guide lengths bring the loss to approximately 0.8 dB below 35 GHz.When the assembly is cooled to 4 K the loss decreases to around 0.5 dB and the high-frequency effect of the U-bend is reduced.
Assuming that the U-bend loss reduces by the same proportion as the overall loss, we may deduce a loss per thermal break of approximately 0.07 dB.However, this will include each associated straight wave guide section to the next break.This is an average value -the loss from the warmer breaks will likely be greater than that from the colder breaks.
Measuring this small loss directly for a single thermal break whilst cold is quite demanding.The loss of intermediate warmer sections is larger.Every disconnection and reconnection operation, as required to perform a swap from the part under test to a baseline comparison, provides an opportunity for small variations in alignment and associated changes in loss, on a scale similar to the loss of the break.Cycling the test system between warm, cold and back to warm takes at least a day, so maintaining sufficiently consistent calibration over this time-scale is also problematical.
Various configurations were tried to make this measurement.The most consistent results were achieved using brass wave guides between the room-temperature parts and the 3-K stage (the extra thermal load caused a temperature increase to approximately 5 K).A measurement through the U-bend was made cold, for use as a reference baseline.The measurement in figure 12 was then taken, showing the relative increase in loss as a single thermal break and straight wave guide section of matching length were added above the U-bend.The increase in loss is very small but consistent with our 0.07-dB average value.
The performance of the Q-band thermal breaks is very similar.Room-temperature S 21 measurements are given in figure 13, showing a loss of around 0.1 dB.

V. CONCLUSIONS
Starting with a crude design using thin steel supports we developed a very effective thermal break, much improved in stiffness by using carbon-fibre tubes.We demonstrated that the Young's modulus increased slightly upon cooling these tubes.However, the thermal conductivity, whilst very low below 10 K, is not as low as we had hoped at higher temperatures.
This confirms that pultruded carbon-fibre tubing is a useful material to consider for cryogenic structures below 10 K.
The thermal breaks were shown to have a good RF  FIG.13: Q-band thermal breaks, measured warm characteristics at room temperature, with useful improvement when cooled.However, for testing of the most sensitive cryogenic LNAs, assuming the loss is evenly divided between sections at different temperatures, the thermal RF noise contributed by warmer sections will still be significant.A 0.1-dB loss at room temperature would contribute nearly 7 K to the noise temperature.Therefore further reduction is desirable.Some improvement should be obtainable by, for example, gold-plating the wave guide parts.This would not degrade the thermal performance because of the gap.
We have not measured the coupling (cross-talk) between adjacent thermal breaks.From our HFSS modelling we expect this to be too small to measure with our apparatus.For even smaller radiation we could consider adopting a more-sophisticated choke design.

FIG. 4 :
FIG.4: Experimental design for carbon-fibre Young's Modulus measurement.As the assembly is tilted away from vertical the steel weight bends the carbon-fibre tube until contact is made with the copper tube.
FIG. 5: Assembly for carbon-fibre conductivity measurements: The top stage is heated and the bottom stage cooled to constant temperature.The temperature at the mid point is measured to determine conductance.

Poly4FIG. 7 :
FIG. 7: Conductivity results for carbon fibre tubing.Measurement points overlay the Runyan & Jones fit, an 8th-order polynomial and a 4th-order polynomial fit to log 10 (k) as a function of log 10 (T ) FIG. 8: FEA of three design geometries showing modelled displacement for an applied 10-N shear force.