1. Density gradient at the ends of plasma cell The goal: assess different techniques for optimization density gradient at the ends of plasma cell

2. Parameters

3. Fast valve, No orifice (iris) Fast valve: 10ms What is depletion length? Shakhov EM, Non-stationary rarefied gas flow into vacuum from a circular pipe closed at one end 15cm at 0.67ms 50cm at 3-4ms Kersevan R, https://indico.cern.ch/event/328455/con tribution/11/material/slides/1.pdf 50cm at 1-2ms 1D Theory (FM+C) + 1D DSMC Petrenko A, https://indico.cern.ch/event/357090/contri bution/2/material/slides/2.pdf 2D DSMC Petrenko A, https://indico.cern.ch/event/357090/ contribution/2/material/slides/2.pdf 50cm at 2-3ms 3D DSMC Plyushchev G 50cm at 3ms

4. Electron trapping Lotov KV, http://arxiv.org/pdf/1408.4448v1.pdf => Length of the transition region should not exceed 10-15cm

5. Very simple estimation of outflow through orifice

6. Less simple estimation of outflow through orifice Accounts for rarefaction, for molecular regime = 1 Orifice radius Pressure Mass of Rb

7. Summary of leak rate values Molecular flow theory: 0.67mg/sec Rarefied flow:0.77mg/sec Continuum flow: 1.01mg/sec Simple continuum estimation: 1.09mg/sec Simulation: 0.52mg/sec Possible explanation of error: we don’t have infinitely large volume

8. Analytical tails

9. 3D DSMC simulation Double Orifice no Source: boundary conditions The idea : To have large volume between both orifice to drive outflow to gain some time Symmetry wall Thermal wall 50cm 4cm1cm 20cm 4cm Fast valve

10. 3D DSMC simulation Double Orifice no Source: density profile (1e6 particles) 0.00ms 0.66ms 1.33ms 4.65ms 9.96ms 15.3ms 19.9ms 25.2ms 30.0ms Approximately 15cm at 30ms

11. 3D DSMC simulation Double Orifice no Source: density profile (1e7 particles) 0.00ms 0.66ms 1.33ms 5.31ms 9.96ms 15.3ms 19.9ms 25.2ms 29.9ms Approximately 15cm at 30ms

12. 3D DSMC simulation Double Orifice no Source: density profile (1e7 particles) Density profile integrated over last 4ms (25.9-29.9ms) in order to increase statistics: Red line: theory for infinitely large volume Blue lines: orifice 1 and 2

13. 3D DSMC simulation Double Orifice no Source: density profile (1e7 particles) Time, sec Density in plasma cell, a.u.

14. 3D DSMC simulation Single Orifice with Source: boundary conditions Symmetry wall Thermal wall Source (constant flux) 50cm 4cm1cm 20cm 2cm DSMC: hard sphere model

15. 3D DSMC simulation Single Orifice with Source: results Convergence reached at around 0.5sec (with plasma cell tube initially filled) Simulation inflow (=outflow): 0.52mg/sec. This equivalent to 45g/day. If orifice will be open only 3 seconds each 30 seconds: 4.5g/day.

16. 3D DSMC simulation Single Orifice with Source: density profile Density profile in the center of plasma cell (inside r=4mm)

17. 3D DSMC simulation Double Orifice with Source: boundary conditions Symmetry wall Thermal wall Source (constant flux) 50cm 4cm1cm 10cm 2cm The idea of second orifice: 1. Prevent any possible vortex creation 2. Both orifices are symmetrically placed with respect to source tube => the symmetry simplifies the understanding of problem (in case with low collisions between particles, it could be considered as superposition of source and two orifices with plasma cell with orifice at the end

18. 3D DSMC simulation Double Orifice with Source: results Results are very similar to the simulation with single orifice:leak rate:0.52mg/sec convergence:0.5sec

19. 3D DSMC simulation Double Orifice with Source: Flow

20. 3D DSMC simulation Double Orifice with Source (constant density): results 7x10 20 m -3 10x10 20 m -3 8x10 20 m -3 9x10 20 m -3 Conclusions: 1. In this case (stationary case) the density near the source is higher that the density in plasma cell. 2. Thus the injection tube (between Rb source and plasma cell) should be very short and should have large diameter in order to have smaller density gradient difference. 3. The injection tube should be as close as possible to orifice

21. Challenge 1 For Rb vapor, pressure depends on temperature Pressure near the source should be higher, then in plasma cell. => source should be as close as possible to plasma cell (and to iris) Can our source provide this constant flux (~0.77mg/sec)? Steck, D.A., Rubidium 85 D Line Data

22. Temperature, K Density, 10 20 m -3 Surface, m 2 Flux = 0.77mg/sec Evaporation rate Pound G.M., Selected Values of Evaporation and Condensation Coefficients for Simple Substances

23. Challenges: 2 If we going to have orifice system (or source system) from both ends of plasma cell => the both sources should be perfectly aligned (to avoid density ramp)

24. Future work Simulate source with constant density instead of constant flow Simulation with fine grid Simulation with variable hard sphere model Experiment to verify simulation

25. Summary + Steady state solution - Constant Rb loss of 0.52mg/sec + Good agreement with theory + Sharp gradient density profile (in agreement with theory) ? Could our source provide this flux? ? Is our source stable enough for this solution? - Fast valve should be used + Gradient density profile length of ~15cm for up to 30ms + With Rb source the gradient should be even sharper + If our source is not very stable, this solution will work - Density is not uniform after 10ms.

26. Possible practical application Source (constant flux) 10m Valve 1Valve 2 Questions: 1. If valve 1 and 2 close, what is the time to fill this volume with Rb source from one end? (Initially plasma cell is empty!) (for particular geometry it is > 5sec) 2. If valve 2 is closed and valve 1 is open, what is the time to reach the equilibrium? (Initially plasma cell is filled with Rb!) (for particular geometry it is > 8sec, see next slide) Total mass of Rb in 10m@4cm = 1.27mg. Flow through orifice = 0.52 - 0.77mg/sec

27. If valve 2 is closed and valve 1 is open time to reach the equilibrium? Preliminary Results In particular geometry!!! Density in plasma cell, a.u. Time, ms

28. Possible closed loop Rb vapor system: A valve which is normally closed and opened to let beams pass. It’s not necessary for this valve to be leak tight and fast. At 70 °C equilibrium vapor pressure of Rb is 2000 times lower than at 200 °C. Rb in this system is in the closed loop because it’s either in a liquid or in a vapor form. The amount of liquid Rb in the reservoir can be limited to ~ 10 cm 3 (15 g). The main question is how much liquid Rb will stick to 70 °C walls before it starts to flow down to the reservoir? Let’s assume the 70 °C surface is ~ πR 2 = 3.14*(10 cm) 2 = 300 cm 2 and Rb layer is 1 mm thick => V = 300 cm 2 * 0.1 cm = 30 cm 3 => The total mass of Rb is likely to be below 100 g. Rb flow is 0.5 mg/sec = 100 g / 2 days => Another option may be a cycled operation – 70 °C tank will be heated up once a day or so. R ~ 10 cm Rb 70 °C 200 °C oil tank 190 °C 70 °C