Summary of Rb loss simulations The goal: assess different techniques for optimization density gradient at the ends of plasma cell

Parameters

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, tribution/11/material/slides/1.pdf 50cm at 1-2ms 1D Theory (FM+C) + 1D DSMC Petrenko A, bution/2/material/slides/2.pdf 2D DSMC Petrenko A, contribution/2/material/slides/2.pdf 50cm at 2-3ms 3D DSMC Plyushchev G 50cm at 3ms

Electron trapping Lotov KV, => Length of the transition region should not exceed 10-15cm

Very simple estimation of outflow through orifice

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

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

Analytical tails

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

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

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

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

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

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.

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

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

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

3D DSMC simulation Double Orifice with Source: Flow

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

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

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

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 = 1.27mg. Flow through orifice = mg/sec

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

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)