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Miroslav [email protected]

Term paper:

Estimation of the heat leaks in GBMR test cryostat

Introduction:

GBMR (Gaussian Beam Measurement Range) is a setup for measurement of thebeam pattern of quasioptical receivers for the European Space Agency Project“Herschel Space Observatory”. The project is developed at GARD (Group forAdvanced Receiver Development). Receivers will be part of the HeterodyneInstrument (HIFI) for high-resolution spectroscopy with frequency coverage of 480 to1250 GHz in five receiver bands and 1410 to 1910 GHz in two additional bands. Themixers are SIS for bands 1-5 and HEB type for bands 6l and 6h, which requirescryogenics temperatures for the test measurements. One of the key problems inachieving ultimate performance of the HIFI instrument is the receiver beam coupling

to the antenna with required alignment tolerance of 1% coupling loss per degree of freedom. This entails precise measurement of the MSA input beam with respect to itsmechanical reference to accomplish the required alignment accuracy. Such ameasurement includes complete data on the MSA input Gaussian beams, includingthe sky signal and local oscillator (LO) paths, and comprises orientation of the opticalaxis, position of the waist, size of the waist and the shape of the beam down to –30dBm power level.

1

4

5

6

10

3 98 6 10

2

17

Figure 1. Layout of the Gaussian beam measurement setup. The insert shows 3D

model of the cold plate (the upper left corner).Figure 1 shows the layout of the built system. The MSA (1) together with the

second stage IF amplifier is installed on the cold plate of the cryogenic station (2) atthe temperature of 4K. The receiver under test is operated in super heterodyne modeusing standard optical scheme with LO (3) injected from side and coupled to themixer beam via wire grid (4). The idle LO beam is damped with absorber (5) behindthe grid. We adopted the scalar measuring technique: the beam (6) is scanned by apoint radiation source (7) placed on a hexapod scanner (8). The source emits signal at

wavelength corresponding to the frequency of tested MSA. Normally the measuredbeam should pass through a window on the cryostat; to avoid distortion of the beam,



the test source on the scanner is placed inside cylindrical vacuum chamber (9) withdimensions of 1.2 m long and diameter of 1 m connected via gate-valve of diameterabout 34 cm to the cryostat vacuum chamber. The scanner covers travelling range of 600 mm along the chamber (z axis), 180x180 mm perpendicular to the beam axis (x

and y axis) and 20 degree rotation around x and y with positioning accuracy ±10 µm.

Description of the cryostat:

The cryostat (Infrared Lab HDL series [1]) is shown on in the insert in Table 1. It hasoperating Temperature Range of 1.2K to 4,2K. The dewar contains two cryogenicvessels housed in vacuum chamber. The LN2 vessel directly cools a radiation shieldthat surrounds the LHe vessel and the cold work surface. All interior cryostat surfacesare lined with metal foil in order to provide additional shielding. The diameter of thecold plate is 250mm.The cryostat was ordered with extended capacity of the LHe vessel and circularradiation shields that allows useful height on the cold platform of 100mm.

Specification of the cryostat is given in Table 1.

Dewar Outside Diameter(inches)

11.95

Dewar Height (inches) 13.50

Cold Plate Diameter (inches) 10.18

Work Area Height - "B"Dimension (mm)

100

Weight (pounds) 42.0

LN

2

Capacity (liters) 4.2LN2 Hold Time - standardsupports (hours)

35

LN2 Hold Time - rigid supports(hours)

32

LHe Capacity (liters) 5.2

LHe Hold Time - standardsupports (hours)

135

LHe Hold Time - rigid supports

(hours)

47

Table 1. Specification of the cryostatSupport structure was designed and implemented later. The vacuum chamber wasintegrated to the big vacuum chamber (Figure 1) of the measurement setup viainterface flange. It purposes to match the Infrared Lab vacuum interface to DN320vacuum flange and also to assure enough height to fit the MSA.To accomudate the MSA on the cold plate it is necessary to provide electricalconnections (IF and Bias), RF connection in this case opening toward the probesource and LO connection also opening toward the LO generator. The DC Biasinterface of the MSA consists of three 9 pins MDM connectors. One IF coaxial cableis the down converted signal. To provide enough amplification of that signal it is

required to install second stage IF on the cold plate (Figure 2).



Spectrum

Analizer

LO sourc

4K stage

MSA

Probe

source S c a n n e r

Vacuum

IR window

PC

Beam splitter

Bias supply

unit

Figure 2. RF, IF, and biasing block diagram.

It is powered via an additional 9 pins MDM connector. To that amount of 36 electricalconnections we considered to add 18 more to be used for temperature sensors andheaters plus some additional safety margins. We have chosen Lake Shore Quad-LeadCryogenic wire QL-36. That is a 4-wire "ribbon cable" which makes heat sinking anddressing leads much easier than working with individual wires. The wire is also colorcoded for easy lead identification and can be split to yield two wire pairs. Quad-Leadwire is also useful in standard 4-lead measurements. The insulation is vinyl acetalresin, as a smooth uniform film. It has excellent mechanical properties such as

abrasion resistance and flexibility. The film will stand excessive elongation withoutrupture. Formvar™ can be removed mechanically or chemically during terminalpreparation. Electrical and mechanical properties are summarized in Appendix A,Table A1.Based on previous experience that during the installation of the coaxial cables in tothe cryostat they can be damaged and their RF performance can be destroyed we haveput in 3 stainless steel coaxial cables. Using available data [3] we choose UT-85-B-SSsemi rigid coaxial cable. It has stainless steel outer conductor and PTFE dielectric.The inner conductor is made from steel in silver plated copper shell. The data is givenin Appendix A, TableA2:The DC biasing cables and coaxial cables are thermally anchroated at the top of the

LN vessel (temperature of the boiled N2 gas ~90K), on the bottom of the LN vessel(temperature of the liquid N2 ~77K), at the top of the liquid He vessel (temperature of the boiled He2 gas ~20K) and at the bottom of the He vessel (temperature of the liquidhe gas ~4.2K). The DC cables are soldered to Printed Circuit Board glued onAluminium heat sinks fixed to the cold plate for final heat termination (see Figure 3).

After some changes in the design of the MSA it was necessary to modify the radiationshields to accommodate it on the cold plate. We have made also additionalmechanical support to prevent the inner part of the cryostat from vibrations. Therequired preciseness of the measurement entails no any infrared filters between the300K and 4K stage. Any such a filter would distort the measured beam pattern. The

initial design of the openings is based only on the geometry of the beams of the MSA,



LO and the Triangulation system gave area of few square centimetres looking directlytoward 300K.

Figure 3. a. The cryostat with mounted shield; b. the cold plate.

Estimation of the heat leaks:

In the end of November last year we started the first test of integration of themeasurement equipment and tests of the holding time of the cryostat. Along with theexperiments it was necessary some estimation of the heat leaks in to be made.

To estimate the heat leaks we adopted the following approach. We have made severaltests of the holding time:- the cryostat with the wiring installed and equipped with the original shields. We

have obtained holding time of approximately 54 hours. The vacuum level wasabout 2-3.10-7mbar;

- then we have mounted the new shields with blinded openings. We obtainedslightly shorter holding time that can be due to absence of superinsulationmaterial covering the shields.

- Next experiment was made with openings looking at 300K and 5mm thick copperplate attached to the cold plate at 50mm besides the openings. This experimentdid not show significant dropping of the holding time. This might be explained

with the fact that the copper plate was too near the openings and specularyreflected back significant fraction of the radiation coming from 300K.

- Currently (05/02/2003) we are performing test with all the necessary partsinstalled on the cold plate.

To make calculations for the heat flux into the LHe vessel the following sources mustbe taken into account: Heat conduction through LHe vessel wall; heat convectionbetween the LHe vessel wall and evaporated helium gas; radiation between LHevessel and thermal shields; radiation from 300K towards 4K stage via the openings;heat conduction of residual gas; heat conduction via the cables, filling pipe andsupport structure. The heat balance equation, which accounts the heat transfer via

conductance with temperature dependent thermal conductivity coefficient, heat



convection, radiation and conductance with temperature independent thermalconductivity coefficient is:

( ) ( ) 0)( 214

24

10 =−+−+∂∂

−

∂∂

T T KC T T A x

T C m

x

T T

dx

d A p εσηλ & (1)

where A is the area of the cross section, )(T K is the thermal dependent thermal

conductivity, L is the length and T ∆ is the temperature difference across the heat

conduction path, η is efficiency of heat transfer, m& is mass flow rate of the gas, pC

is specific heat of the gas, ε is the effective emissivity, A is the surface area and428 / 10.67,5 K mW −=σ is Stefan-Boltzman constant and K is thermal independent

conductivity of the residual gasSince the heat conducted by the filling pipe and the heat transferred by the gases arethe same for the original configuration and the configuration of interest we are notgoing to estimate them. Here are some numerical results for the different sources of heat leaks related mainly with the modification of the cryostat that we have made:

- heat flow from the openings looking at 300K;- radiation flow towards 4K stage from the 77K shields;- heat conducted through the wires;- heat conducted through support structure;- contribution from the Joule heating (MSA, second IF and temperature sensors).

1. The heat transfer by radiation per unit time between two bodies at temperatures 1T

and 2T is given with:

( )2121

214

2

4

1.εεεε

εεσ

−+−= T T AQ (2)

where 21, εε are emissivities of the two bodies, A is the surface area and. Below aregiven calculation of the heat transfer obtained with MathCAD:First we calculate the heat transfer from 77K radiation shie ld towards 4K shield

WQ_radiationHN 0.049=Q_radiationHN σ AN⋅ T774

T44−( )⋅ εHN⋅:=

εHN

εH εN⋅

εH εN+ εH εN⋅−:=

m2AH 2 π⋅ Hhr⋅ Hhc⋅( ) π

Hcover

2

2

⋅+:=

m2

Hcover 250 103−⋅:=Hhr

250 103−⋅

2:=Hhc 90 10

3−⋅:=

εH 0.31:=Data for the He part

AN 2 π⋅ Nhr⋅ Nhc⋅( ) πNcover

2

2

⋅+:=

m2

Ncover 260 103−⋅:=Nhr

260 103−⋅

2:=Nhc 100 10

3−⋅:=

εN 0.31:=Data for the N2 part

W/m2k4σ 5.67 108−⋅:=KT4 4.2:=KT77 77:=KT300 300:=

In similar manner we repeat the calculations above but with the geometry of the

modified radiation shields:



Q_radiation_new_HN σ AN⋅ T774

T44−( )⋅ εHN⋅:= Q_radiation_new_HN 0.104= W

The total heat load is doubled installing the new shields, but that is still small fractioncompare to the cooling capacity of the cryostat. During the tests temperaturedifference of 20-25K was measured between temperature sensors (TS) mounted on

the cold plate and TS mounted at the middle at the shield (approximately 150mmfrom the cold plate).

The contribution from the openings looking at 300K can be estimated in two ways:- we consider that luminance areas are the same, but the emissivity of the 300K is

the emissivity of the black body. We have three openings: one circular on theoptical path of the MSA’s beam (diameter 30mm), one for the triangulationsystem (square 25x25mm) and one optical path of the LO. The last one is clearopening on the 4K shield and the opening on 77K shield is covered with IR filtermade of 2mm thick mylar. In this case we get the heat transferred from 77K to4K as

WQ_radiation_77 =Q_radiation_77 σ AN⋅ T774

T44

−⋅ εHN⋅:=

εHN

εH ε300⋅

εH ε300+ εH ε300⋅−:=

m2

AH =AH π dH 0.5⋅( )2

⋅ Hboxl Hboxl⋅+:=

Hboxl 25 103−⋅:=mdH 28 10

3−⋅:=εH 0.01:=Data for the He part

m2

AN 2 π⋅ dN 0.5⋅( )2⋅:=ε300 0.8:=mdN 28 103−⋅:=Data for the N2 part

and the heat transferred from 300K to 4K as:

Q_radiation_300 σ AH⋅ T3004 T4

4−⋅ εHN⋅:= Q_radiation_300 = W

In this calculations we choose the smissiivity of the 4K stage to be bigger (5 times)than that of the aluminum which is the material used for manufacturing of the more

of the parts on the cold plate. The reason for that is that we have to take in to accountthat certain fraction of the incoming radiation is scattered or reflected inside the coldplate. As it is expected the radiation heat inflow is quite substantial for the heat leak from 300K. The result is strongly dependent on the choosen value for the emissivity.

1

2

22 A J

11 A J

112,1A J F

221,2A J F

4

1T σ

4

2T σ

( ) A11

/ 1 εε− ( )222

/ 1 Aεε−2,11 / 1 F A

Figure 4. Radiation heat transfer between two opaque surfaces and the equivalent

radiation network

- We take into account radiation shape factor jiF

, introduced in [5]. It is defined as

the fraction of the radiation that leaves surface i and is incident on surface j. For



the two surfaces shown on Figure 4 the radiation leaving surface 1, 14

11 AT A J σ= ,

which strikes surface 2 is denoted by 112,1 A J F .

Similar expression can be written for the radiation flow in opposite direction. Ingeneral the heat transferred from surface 1 to surface 2 will be:

4

12,12 T AF q incident εσ=

To estimate the radiation transferred from 300K to 4K we use the Radiation shapefactor between parallel disks given in [5]. We consider the opening as a diaphragm.The nearest object on the cold plate is at 50mm. The luminance areas that correspondto the angle between the nearest object at 4K and at 300K can be calculated withsimple geometry. In the worst case, when the gate valve is open and MSA lookstowards the scanner, the distance is 0.8m and the corresponding area will be 0.5m2.

The radiation shape chart gives 89.02,1

=F . To easy the calculations we use the

radiation network approach introduced in [5]. For this case the radiation network is

given in Figure 5 and the heat transfer will be determined by:( )( ) ( )[ ]2222,11111

42

41

/ 1 / 1 / 1 AF A A

T T Q

εεεε

σ

−++−−

= (3)

For the calculations we assume that the values for the emisivity similar to theprevious case emphasizing again on the fact that the result is quite dependent on thechosen value:

Wσ T300

4T4

4−⋅

1 ε1−( )

ε1 A1⋅

1

A1 F12⋅+

1 ε2−( )

ε2 AH⋅+

=

m2

AH =AH π dH 0.5⋅( )2⋅ Hboxl Hboxl⋅+:=

mHboxl 25 10

3−

⋅:=mdH 28 10

3−

⋅:=

Geometry of the openings

ε2 0.1:=

m2

A1 0.5:=F12 0.89:=ε1 0.8:=

We can made simple estimation of the volume helium boiled from such a heat inflow.The heat of vaporization (latent heat) for liquid He at 4.2K is 25.103J/kg. That givesboiling rate of 0,84W/l. So that heat flow will boil off additional quantity of

0.075l/hour.

2. Conductance through cables and support structure.For the coaxial and the DC cables we consider that the heat transfer is given by thefirst term in equation (1):

∂∂

= x

T T

dx

d AQ )(λ (4)

Thus the heat transfer between the ends of a solid bar at temperatures 1T and 2T is:

T x

T T

dx

d A

L

AQ

T

T

∂

∂∂

−= ∫ 2

1

)(λ (5)



In case of metallic alloys, e.g. brass, German silver, stainless steel, available dateenable us to give a fairly accurate estimate of )(T K at any temperature. In this case

we can perform simplified calculations with the mean heat conductivitymK W T K / ),(λ= [4]. The heat transfer can be calculated simplified formula:

T K L

AQ ∆−= .

Final results

Here are present only calculations for the heat leaks due to the different parts of thecoaxial cable. Due to lack of data for the mean conductivity in case of endtemperatures 20K and 4K we have used the data given in [4] for link between 77Kand 4K. These values will give higher heat leaks but we will be on the safe sidecompensating for example bad thermal termination (anchoring) on the top of LHevessel. The calculated values are summarized in a Table 4 including an additional heat

flow to 4K stage from Joule heat. We use a value provided from SRON (Spaceresearch Organisation of Netherlands). The Joule heat dissipated from the temperaturesensors is obtained from the LakeShore data sheets [2].

Additional Heat inflow

min max

Coaxial cable outside and conductor(stainless steel parts total)

6.958E-3

Coaxial cables PTFE 1.285E-4

Coaxial cable Copper shell 1.52E-3

Coaxial cable Silver plating 9.24E-3

DC cables (total 56 wires) 0.0328

Contribution from the in door madeshields

0.05

Openings towards 300K 5.6E-3 0.063

Openings towards 77K 2.4E-5

Joule heat dissipated on the cold platefrom the MSA and Second IF

0.038

Joule heat dissipated from thetemperature sensors and DC wires. ~2E-4

Total 0.144W 0.207W

Table 4. Data for the heat leaks after the modifications.Here we do not consider the heat transfer via the side supports because they willinfluence on the boiling rate of the nitrogen. In the worst case when the gate valve isopen and the cold plate will look towards the scanner the heat leak of 0.207W willcrate additional boiling of 0.439 litres Helium which is quite substantial amount. Theheat load without electrical current and with closed openings is 0.1W. That valueagrees with the experimentally obtained holding time of 50 hours. It will be

interesting to verify with the holding time obtained when all the parts are installed onthe cold plate and the openings are not covered.



References:

[1] http://www.irlabs.com/

[2] http://www.lakeshore.com/temp/acc/am.html

[3]C. Sundblad , Calculation of heat transmission in cales, Project ODIN; Odin Coldbox, 950621

[4] White, “ Experimental techniques in low-temperature physics”, Claredon Press,Oxford, 1979.

[5] W.Schmidt, R. Henderson, C. Wolgemunt, “ Introduction to thermal sciences”,Wiley, 1993



Appendix A

Data for the cables used in the cryostat:

Coefficient of thermal

expansion

1.78 x 10-5

Thermal conductivity 48 W/m • K at 293 K

Electrical resistivity(annealed)

1.15 x 10-7 W-m at 293 K

Specific heat 376.4 J/ kg • K

Stress relief temperature(1 hour)

423 K to 498 K (150 °C to 225 °C)

Chemical composition 94.8% copper, 5% tin, 0.2% phosphorus

Table A1. DC cables specification

Thermal Conductivity

300K-77K 77K-4K

Cable outside diameter (OD) Ø2,2mm

Area OD 1,58mm2

PTFE diametre Ø1,68mm

Area PTFE 2,01mm2

Conductor OD Ø1,68mm

Area conductor 2,01mm2

Copper shell OD Ø0,50mm

Area Cu shell 0,106mm2

Silver plating Ø0,51mm

Area Silver plating 0,007931mm2

Table A2. Data for UT-85-B-SS

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