Cryogenic Pipe Calculations

1. Cryogenic Pipe Calculations VB Jan 2008

2. idea • Use superconducting pipe for atomic beam experiments • advantages • cryopumping for better vacuum • exclusion of magnetic fields inside pipe • disadvantages • cost & complications • cryopump vibrations

3. basic concept cryocoolers • use simple pipe with superinsulation (MLI) & two cryocoolers • no liquids in the system (except in the cryocoolers themselves) • use two cryocoolers (~ 1W cooling @ 4 K) • use lead pipe (used for calculations) • device is NOT a magnet • Type I superconductor • high critical temp ( ~ 7 K) • Niobium has even higher critical temp (~9 K) • Can probably use Type-II superconductors below lower critical temp pipe insulation

4. performance calculations • use MATLAB to simulate pipe performance • heat capacity as a function of temperature • cryocooling as a function of temperature • load map • heat conductivity constant • insulation on pipe + heat leak at pipe ends • pipe divided into longitudinal segments • program calculates new temp profile every fraction of a second • for each segment • conduction from adjacent segments • heat gain through insulation • arbitrary heat gain in a any segment (used for ends) • cryocooling heat loss (if present for the segment) • cryopumps turn on at an upper temp and off at a lower temp (for any segment) • temp cannot go below 4 K (cryopump limit)

5. Superinsulation • http://www.cryogenicsociety.org/cryo_central/cryogenic_insulation/ • An insulation material's performance under a large temperature difference is given in terms of milliwatt per meter-kelvin (mW/m-K) and is referred to as the apparent thermal conductivity or k-value.  To compare k-values for different materials one must understand the warm and cold boundary temperatures, the vacuum level, the residual gas composition, and the installed thickness.  The designer has a very wide range of k-values with which to work: as low as 0.03 mW/m-K for perforated MLI blankets up to approximately 40 mW/m-K for cellular glass.  As in all good designs, the performance must justify the cost.  The performance of the total thermal insulation system as it is actually put to use is defined as the overall k-value for actual field installation or koafi. • Several test methods are usually needed to adequately test and evaluate the overall performance of an insulation system.  Standardized material test methods can be employed for basic thermal, mechanical, and compatibility properties.  Cryostat test methods provide the apparent thermal conductivity values for the insulation systems.  Prototype testing is then needed to determine the actual performance for a specific mechanical system.  The use of MLI systems illustrates the need for this three step testing process.  The k-value for an MLI system under ideal laboratory conditions may be around 0.05 mW/m-K while the koafi can easily be 10 times worse.

6. Cryocooler Performance SHI Cryogenics Group, a global manufacturer that includes the Cryogenics Division of Sumitomo Heavy Industries, Ltd. and the former APD Cryogenics, delivers innovative solutions to the semiconductor, research, optical coating, and medical industries.   http://www.shicryogenics.com/index.php?option=com_content&task=blogcategory&id=22&Itemid=169 Curve used in calculations(1.0 watts @ 4 K)

7. Heat Capacity • Handbook of Chemistry & Physics • page 2357 for low temp behavior for lead

8. Heat Conductivity • Handbook of Chemistry & Physics • page 2528 for lead, relatively flat, ~ 0.1 cal per sec per cm**2 for 1 cm thickness • http://prola.aps.org/pdf/PR/v80/i5/p859_1 • evidence of superconducting behavior of heat capacity (factor of 2.5 enhancement of the heat conduction in the 4-15 K temprange) Used a constant value in calculations (0.5 or 1.0)

9. MATLAB simulations parameters (data1) • rateloss=0.00003 % insulation heat loss W/meter/K • ncool=1.0 % de-rating factor for the 1.0 watt cryocooler • initT = 10 % starting temperature for the pipe • roomT = 300 % temperature of the laboratory • lowT = 5 % turn-off temp of cryocooler • highT = 5.75 % turn-back-on temp of cryocooler • Tmin=4.0 % min cryocooler temp • maxIn = 30000 % number of seconds to run simulation • pradius = 5.0 % pipe radius in cm • pthick = 1.0 % pipe thickness in cm • plength = 1000 % pipe length in meters • pdensity = 13 % density of pipe g/cc • nsegs = 100 % number of pipe segments in length • cooling(8)=0.5 ; cooling(72)=0.5; % cryocooler power in segments • heatleak(1)=0.1; heatleak(100)=0.0; % heat leak in segments • secsegs = 2 ; % number of time segments in a second • hcond=1.0 ; % heat conductivity

10. Results – data1 – temp contours

11. Results – data1 – temp vs. time Times on are 439 310 303 301 300 300 300 300 300 300 Times off are 2065 1769 1772 1771 1770 1770 1770 1770 1770 Uptime=85%

12. Cooldown from 300 K • Would be nice to get faster cooling • Pre-cooling • Better distribution 100 hour timescale

13. MATLAB simulations parameters (data2) • rateloss=0.0001 % insulation heat loss W/meter/K • ncool=0.67 % de-rating factor for the 1.0 watt cryocooler • initT = 10 % starting temperature for the pipe • roomT = 300 % temperature of the laboratory • lowT = 5 % turn-off temp of cryocooler • highT = 5.75 % turn-back-on temp of cryocooler • Tmin=4.0 % min cryocooler temp • maxIn = 30000 % number of seconds to run simulation • pradius = 5.0 % pipe radius in cm • pthick = 1.0 % pipe thickness in cm • plength = 1000 % pipe length in meters • pdensity = 13 % density of pipe g/cc • nsegs = 100 % number of pipe segments in length • cooling(8)=0.5 ; cooling(72)=0.5; % cryocooler power in segments • heatleak(1)=0.1; heatleak(100)=0.0; % heat leak in segments • secsegs = 2 ; % number of time segments in a second • hcond=1.0 ; % heat conductivity

14. Results – data2 Times on are 714 608 606 602 602 601 602 601 602 601 Times off are 1203 1084 1085 1084 1084 1084 1084 1084 1084 Uptime=64%

15. Results – data2 – secsegs=10 Times on are 713 608 606 603 603 603 603 603 603 603 Times off are 1203 1084 1085 1085 1085 1085 1085 1085 1085 uptime=64%

16. MATLAB simulation parameters (data4) • rateloss=0.0001 % insulation heat loss W/meter/K • ncool=1.0 % de-rating factor for the 1.0 watt cryocooler • initT = 10 % starting temperature for the pipe • roomT = 300 % temperature of the laboratory • lowT = 5 % turn-off temp of cryocooler • highT = 5.75 % turn-back-on temp of cryocooler • Tmin=4.0 % min cryocooler temp • maxIn = 30000 % number of seconds to run simulation • pradius = 5.0 % pipe radius in cm • pthick = 1.0 % pipe thickness in cm • plength = 1000 % pipe length in meters • pdensity = 13 % density of pipe g/cc • nsegs = 100 % number of pipe segments in length • cooling(8)=0.5 ; cooling(72)=0.5; % cryocooler power in segments • heatleak(1)=0.2; heatleak(100)=0.0; % heat leak in segments • secsegs = 2 ; % number of time segments in a second • hcond=1.0 ; % heat conductivity

17. Results – data4 Times on are 275 268 265 265 264 265 264 264 264 Times off are 511 502 501 501 501 501 501 501 500 Uptime=65%

18. Cryocooler - Vibrations Information from …

19. Vibration Reduction Methods: Active Cancellation [13]

20. Vibration reduction – PT cryocoolers

21. CC sizes Sumitomo Heavy Industries ~ 50 cm scale

22. Mounting & Other Issues • Need a system to support pipe vertically • Need to connect cryocoolers to pipe • Copper collars (Cu conductivity ~ 5-10 higher) • Can we use flexible metal hose between collars and cryocoolers (reduce vibrations) • How many points on the pipe do we connect • What happens at the “warm” end that is connected to rest of the apparatus • ES&H issues with lead? • We have other options for metals (e.g. Nb)

23. CC Spec Sheet Sumitomo Heavy Industry

24. Summary • Simple model of pipe shows promise • Timescales look reasonable • “brute force” vibration control (i.e. CC off) works • Still have options to improve cooling and vibrations • Next step – get professional help

25. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated EquipmentVolume 538, Issues 1-3, 11 February 2005, Pages 33-44 Reduction of field emission dark current for high-field gradient electron gun by using a molybdenum cathode and titanium anode Enhancement effect of dark current by electron and ion impact on electrodes. (1) Primary field emission, (2) Desorption of ions and molecules by electron bombardment, (3) Ionization by electron impact, (4) Back bombardment, (5) Emission of secondary ions and electrons. Cathode flattop = 18 mm Anode flattop = 2 mm

26. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated EquipmentVolume 538, Issues 1-3, 11 February 2005, Pages 33-44 Reduction of field emission dark current for high-field gradient electron gun by using a molybdenum cathode and titanium anode

27. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated EquipmentVolume 538, Issues 1-3, 11 February 2005, Pages 33-44 Reduction of field emission dark current for high-field gradient electron gun by using a molybdenum cathode and titanium anode 1 nA plots The free parameter α was adjusted in each case, but had an average value of 0.4±0.02 for Ti and 1.0±0.04 for Mo. This constancy of α over the entire range of dark current indicates that the gap separation dependence is well approximated by Eq. (2). E(I,10mm) = 124/(1+4) = 25 MV/m for Ti E(I,10mm) = 170/(1+10) = 15.5 MV/m for Mo Can we make a flat beam??

28. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated EquipmentVolume 538, Issues 1-3, 11 February 2005, Pages 33-44 Reduction of field emission dark current for high-field gradient electron gun by using a molybdenum cathode and titanium anode Sacrificing some gradient can greatly reduce the dark current Surface preparation and cleaning is critically important