Cryogenic Pipe Calculations VB Jan 2008

Cryogenic Pipe Calculations VB Jan 2008

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

basic concept cryocoolers insulation pipe 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

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)

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.

Cryocooler Performance Curve used in calculations (1.0 watts @ 4 K) 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

Heat Capacity Handbook of Chemistry & Physics – page 2357 for low temp behavior for lead

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)

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

Results – data1 – temp contours

Results – data1 – temp vs. time Uptime 85% 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

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

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

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

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

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

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

Cryocooler - Vibrations Information from

Vibration Reduction Methods: Active Cancellation [13]

Vibration reduction – PT cryocoolers

CC sizes Sumitomo Heavy Industries 50 cm scale

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)

CC Spec Sheet Sumitomo Heavy Industry

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

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, De tectors and Associated Equipment Volume 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 Cathode flattop 18 mm Anode flattop 2 mm 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.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, De tectors and Associated Equipment Volume 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

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, De tectors and Associated Equipment Volume 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 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? 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).

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment Volume 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