1. transport of 3 He by heat flush measurement of 3 He concentration tests of heat flush George Seidel Brown University

2. outline 3 He transport – heat flush introduction of polarized 3 He to measuring cells removal of 3 He from measuring cells concentrating 3 He for measurement and disposal measurement of 3 He concentration cryogenic methods location heat flush tests reasons methods engineering issues removal of 3 He replacement of 4 He evaporative purifier valves pressurization thermal isolation – heat switches Seidel 2/08

3. 3 He transport – heat flush obtain temperature distribution T(x) for given boundary conditions, geometry and heat flow { A(x) and Q(x) } C dT/dt = Q with Q = K(T) A dT/dx then obtain concentration distribution as function of time c(x,t) for initial conditions and conservation dN/dt = (D dc/dx + v  c) A with D(x) and v(x) being functions of T, hence of x In steady state, (D dc/dx + v  c) = 0 If D and v were independent of position, c(x) = c 0 exp(-v  x/D) With dependences of D and v on T, dT/dx, C, A c(x)  c 0 exp { -6.7×10 2 T 3 (Q/A) x } Also need to be concerned about time dependence Seidel 2/08

4. 3 He transport – heat flush 1. from injection cell into secondary volume secondary volume required because injection cell must operate at 0.38 K and measuring cells are at 0.40 K also essential if pressurization is needed 2. from secondary volume into measuring cells 3.from measuring cells into holding volume holding volume required because cannot concentrate by 100 directly from measuring cells; higher temperatures needed 4.concentrate by 100 to 500 from holding volume to small extraction volume Seidel 2/08

5. injection cell 1 liter secondary volume 4 liters (11.3 cm ID, 40 cm long) holding volume 8 liters (7.1 cm ID, 200 cm long) measuring cells 3.9 liters each 1 cm wall extraction volume ~ 25 cm 3 schematic of 3 He transport system components and sizes tubing (3.81 cm ID, 200 cm long) tubing (1.0 cm ID, 20 cm long) tubing (3.81 cm ID, 100 cm long) tubing (3.81 cm ID, 5.08 cm OD 100 cm long) 2 tubes each (3.81 cm ID, 5.08 cm OD 50 cm long) a large number of variables calculations are only illustrative of what is possible, not defining Seidel 2/08

6. heat flush from injection cell to secondary volume tubing (3.81 cm ID, 200 cm long) Seidel 2/08

7. heat flush from injection cell to secondary volume injection cell – 1 liter, held at 0.380 K, heat input 6 mW secondary volume – 4 liter heat removal 6 mW 0.360 K 200 cm 3.81 cm ID tubing fraction of 3 He remaining in injection cell plus 40 cm of tubing Seidel 2/08

8. heat flush from secondary volume to measuring cells tubing (3.81 cm ID, 200 cm long) tubing (3.81 cm ID, 5.08 cm OD 100 cm long) 2 tubes each (3.81 cm ID, 5.08 cm OD 50cm long) Seidel 2/08

9. heat flush from secondary volume to measuring cells bath.400 K heat removal 8 mW helium in measuring cells.415 K heat input 8 mW.432 K secondary volume.422 K Seidel 2/08

10. heat flush from measuring cells into holding volume tubing (3.81 cm ID, 5.08 cm OD 100 cm long) 2 tubes each (3.81 cm ID, 5.08 cm OD 50 cm long) tubing (3.81 cm ID, 100 cm long) Seidel 2/08

11. heat flush from measuring cells into holding volume 8 mW heat removal.356 K bath.400 K heat input 8mW helium in measuring cells.384 K Seidel 2/08

12. heat flush from holding volume to extraction volume tubing (3.81 cm ID, 100 cm long) tubing (1.0 cm ID, 20 cm long) Seidel 2/08

13. heat flush from holding volume to extraction volume heat input 8mW.502 K holding volume.500 K extraction volume heat removal 8 mW.414 K Seidel 2/08

14. removal of liquid with high concentration of 3 He and replacement with pure 4 He extraction volume ~ 25 cm 3 1 cm ID tube transfer liquid via capillary, 0.05 cm, from extraction volume to evaporator ~60 J to evaporate 25 cm 3 recover gas for analysis evaporator heat above 1 K fill pure 4 He via capillary from reservoir at 1.2 K  H ~.2 J provision for filling system initially? evaporative purifier becomes irrelevant heat transfer via helium in capillaries is small Seidel 2/08

15. conclusions of simulations complete cycle appears reasonable at 400 mK (but at 350 mK ??) can search parameter space for better operating conditions to proceed need constraints - times, geometries, refrigeration,  need results of tests

16. measurement of 3 He concentration cryogenic methods surface tension vortex nucleation location of measurement main cryostat auxiliary cryostat Seidel 2/08

17. measurement of 3 He concentration low temperature surface concen- trations of 1.0 and 1.4 × 10 14 cm -2 surface tension energy of 3 He atom is 2.3 K lower on a free surface than in the bulk liquid; 3 He condenses on the surface below 200 mK influencing surface tension with a surface to volume ratio of 0.1 cm -1 a surface conc. of 1 × 10 14 cm -2 corresponds to a volume conc. of 5 × 10 -10 cm -3 pro: with a heat flush concentration of 100 a 3 He concentration of 1 ×10 -12 can easily be measured con: requires T of 100 mK measurement by velocity of surface waves or capillary rise in parallel plate capacitor Seidel 2/08

18. vortex nucleation electron bubbles create rotons and vortex rings depending on pressure above ~11 bar first create rotons but matrix elements are small so that in modest E fields vortex nucleation also occurs 3 He has lower energy in orbiting states around electron bubble; presence of 3 He, even temporarily, in such states strongly increases probability of vortex nucleation bubble remains attached to vortex ring and velocity drops to a very low value Seidel 2/08

19. vortex nucleation cont. pulse shape analysis field emission control grids ~400 V, I > nA Seidel 2/08

20. resolution of 1×10 2 s -1 (12% of intrinsic nucleation rate) corresponds to a concentration of 2×10 -9 3 He pro: operates at 400 mK con: requires heat flush concentration of 500 to achieve 1×10 -12 requires pressure > 11 bar vortex nucleation cont. influence of 3 He 23 bar pure 4 He, 23 bar nucleation rate s -1 1.0×10 5 V m -1 Seidel 2/08

21. measurement of 3 He concentration location main cryostatauxiliary cryostat pro:overall simplicityease of modification results in real time? con:more difficultmore expensive to to repairbuild and operate nEDM experiment – surface tension in auxiliary cryostat test of heat flush – work at high concentrations with 3 He refrigerator vortex nucleation in single cryostat Seidel 2/08

22. test of heat flush reasons for tests application in unexplored parameter space phonons vs. rotons parameters of importance not known with sufficient certainty appear in exponents – diffusion, slip coefficient, drift velocity, etc. calculations are approximations; do not account for various features, e.g., mean free path of 3 He comparable to tube diameter Seidel 2/08

23. measurement – concentration at one end of a tube with and without heat flow simple configuration 1 cm ID tube, 50 cm long; Q = 2 mW, symmetric ends T cold =.40 K; T hot =.47 K; c c /c h = 2100 with natural He (2×10 -7 ) ; c c = 4×10 -7 ; c h = 2×10 -10 measure concentration using vortex nucleation, preferably at hot end vary temperature, heat flux, area complications pressure 3 He scattering sensitivity heat flush tests c(x) ~ c 0 exp { -6.7×10 2 T 3 (Q/A) x } Seidel 2/08

24. complications in heat flush test pressure apply through fill capillary from gas at room temperature in applying pressure, change concentration (apply at cold end) heat flush depends on pressure possible solutions # 1 – insert porous plug # 2 – apply pressure with bellows # 3 – calculate heat flush at pressure for comparison with experiment Seidel 2/08

25. 3 He- 3 He scattering mfp from 3 He- 3 He < mfp from 3 He-phonon influences heat flush  = 1/(n  ) ; with   10 -15 cm 2 = 0.5 cm for c = 1×10 -7 from phonon scattering at.4 K – 0.5 cm need concentrations less than in natural He possible solutions # 1 – start with 3 He concentration of < 10 -7 # 2 – a more complex system - remove and sequester portion of 3 He # 3 – calculate influence of 3 He- 3 He scattering on heat flush complications (cont.) Seidel 2/08

26. concentration limited on high side by scattering, on low side by sensitivity should have sufficient flexibility to make relevant tests sensitivity literature – 2×10 -9 improvements(?) – current, stability flat plate, field emission cathode longer drift space? alternative: reduce heat flux ~1 cm ~1  m Seidel 2/08 complications (cont.)

27. pressurization (if required because of breakdown) 2 bellows one attached to secondary volume another attached to holding volume or perhaps to extraction volume could be at 1.2 K and connected by capillaries (require another valve) (could conceive of using gas at room temperature) valves 4 for operation of heat flush system none required to be superfluid leak tight probably need leakage < 10 -5 cm 3 s -1 of liquid 3 in contact with polarized 3 He require moderately low thermal conductance when closed, K~10 -4 W K -1 other valves – V1, etc. engineering issues Seidel 2/08

28. heat switches on secondary volume – transfer 6 mW at.36 K provide thermal isolation at.42 K on holding volume – transfer 8 mW at.36 K provide thermal isolation at.50 K employ liquid helium with variable acrylic restriction; ratio > 10 4 engineering issues Seidel 2/08