Test Method for Vacuum Pump Speed of Cryogenic Titanium Getter Pump with Complex Geometry

(under construction)

Abstract:

Tri Alpha Energy has developed liquid nitrogen cooled titanium getter pumps (cryoboxes) for high speed pumping (120,000 L/sec and 60,000 L/sec) of hydrogen and deuterium in divertors of the new C2W plasma fusion machine. The complex shape of these cryoboxes makes it difficult to perform classic pumping speed tests and obtain experimental data for these cryoboxes. Therefore, the goal of this research is to develop a pumping speed test method by simulating actual equipment in Molflow+, a monte carlo simulation software for ultra high vacuum. The results show that although pressure and density measurements vary around an ultra high vacuum test chamber, the rate of pump down does not.

Introduction:

Tri Alpha Energy developed liquid nitrogen cooled titanium getter boxes (cryoboxes) in order to achieve a high pump speed inside the four Divertors of the new C2W plasma fusion machine. According to Harra and Redhead et al^1,2 , a titanium getter surface cooled down to liquid nitrogen temperature of 77K can obtain a sticking factor of 40% for hydrogen and 20% for deuterium per square centimeter of area. We can obtain the pumping speed from a table given in Capture Pumping Technology³ by Kimo M. Welch (Page 208, Table 3.2.1) which presents sticking factors and corresponding pumping speeds per square cm. Additionally, we can use the corresponding equation given in Monte Carlo Simulations of Ultra High Vacuum and Synchrotron Radiation for Particle Accelerators by Marton Ady (Page 18, Section 1.2.15) to find the equivalent pump speed per cm²:

S_pump = α * ν_avg / 4 * A_m2

S_pump = Pump Speed in m³/sec

α = sticking factor

ν_avg = sqrt(k_B * T / m) ; thermal average velocity according to maxwell-boltzmann distribution

A_m2 = Pumping Area in m²

We divide by the A_m2 , multiply by 1000 L / m³ , and divide by 10000 cm² / m² to get pumping speed per cm², to get pumping speed in L / sec per cm²:

S_pump/cm2 = α * ν_avg / 40

For a hydrogen molecule (m = 2): ν_avg = 1782.1 m/s

Therefore, for a sticking factor of 40%:

S_pump/cm2 = 17.821 L/s per cm²

This result agrees with Hara et al's results shown in Table 3.2.1 in Capture Pumping Technology³ .

Tri Alpha's cryobox design has a pumping surface area of around 7000 cm², which implies a pumping speed of:

S_cryobox ≅ 120,000 L/s

The Problem

Theoretically, a pumping speed of 120,000 L/s is achievable with a cryobox. However, it is imperative that physical experimentation is done. Because of the asymmetry and complex shape as shown in Figure 1, however, classic pump speed methods such as the rate of pump down cannot be used because the conductance into the pump is difficult to obtain. Additionally, the single and three gauge dome method are also impractical because of the shape of the cryobox and because it was to be tested in a cylindrical tank (test tank) of approximately 2530 L,shown in Figure 2.

Figure 1: Cryobox Geometry. The inside surface is the pumping surface and is a multifaceted surface for maximum surface area per volume.

Figure 2: Simplified cryobox geometry placed inside the experimental test tank (SolidWorks)

Therefore, Molflow+, a monte carlo simulation software developed by CERN for UHV, was used to model the cryobox inside the test tank. Pressure and density measurements were made and observed in order to see if there was any correlation between any measurements and actual pump speed. More precisely, the density measurements are taken to be analogous to Ion Guage measurements, therefore, the density measurements in Molflow+ inside the test tank as the cryobox is pumping down should correspond to the physical density measurements in the same places by ion gauges in a real experiment.

However, it is difficult to tell the effects of conduction so the goal of this paper is to collect the simulated density measurements at random locations inside the test tank where ion gauges would be placed to the actual pump speed theoretically calculated, and correlate those measurements to the actual pump speed calculated above.

Note: In order to reduce simulation time, the cryobox was simplified to be a flat open box as shown in Figure 2, as compared to Figure 1. Because of this however, a proportional sticking factor was needed to account for the missing pumping surfaces in the simplified model. The physical cryobox has a pumping surface of 7000 cm², but the simplified model had approximately 5600 cm². Therefore, by eliminating the multifaceted surfaces inside the cryobox, one would need to set the simplified sticking factor to:

S_{ActualSurface} ∝ α_actual * A_actual = S_{SimpleSurface} ∝ α_simple * A_simple

Therefore:

α_simple = 0.4 * 7000/5600 = 0.5

Results

Diagnostic facets were placed in various spots around the cryobox and inside the test tank to take measurement of the density over time. A puff of hydrogen was injected into the test tank at one end for 0.5 seconds and at a flat rate of 20 Tor * L /sec. One can see the dynamic change in density over time as the puff of hydrogen gas is injected into the system and the cryobox pumps down in Figure 3.

Figure 3: Simulation of gas being injected and pumped down inside the test tank with a cryobox

Figure 4 shows the resulting particle density over time at different locations inside the test tank.

Initially, one may think that pump speed can easily be measured by puffing in gas continuously and waiting for the pressure (or density) to reach equilibrium:

Q_puff = P * S_cryobox

Or by using the ideal gas las, we can replace pressure (P) with particle density (#/m³) multiplied by boltzmann constant and 300K temperature:

Q_puff = n_density*k_B*T * S_cryobox

We can then find the measured pump speed:

S_cryobox = Q_puff / ( n_density*k_B*T )

In figure 4 (top),one can see where the injection of gas and the cryobox reach an equilibrium: between 0.05 seconds and 0.5 seconds. On average, during this time, the density stays static in the respective part of test tank. In principle, one can just use a measured density from any of the listed places in the graph and find the cryobox pump speed. However, one can see that this method is unreliable because the equilibrium density is not constant everywhere in the test tank. For example, at the entrance of the cryobox, the equilibrium density is approximately 4.5E+16 #/m³, while at the center of the test tank, it is averaging at 6E+16 and at a 10" Nipple Flange, it is floating above 6.15E+16. Therefore, using the equilibrium state between the gas injected and pumping speed of the cryobox is unreliable and cannot be used to obtain the absolute pumping speed of the cryobox without more assesment.

Figure 4: (Top) Shows dynamics of the test tank when 20 Torr * L/sec of gas is injected for 0.5 seconds while the cryobox is pumping. (Bottom) Shows the top graph zoomed in from 0.5 seconds, after the puff of hydrogen gas is injected to 0.6 seonds

Although one cannot reliably find the pumping speed while the system is in equilibrium, one can see that once the puff injection is shut off after 0.5 seconds, that the particle density begins to fall at a nominal rate, rate of pump down. More surprisingly, as shown in Figure 4 (Bottom), the rate of pump down seems to be, on average, the same at all locations tested within the test tank.

A logarithmic line of best fit was drawn for all 5 measurement locations between 0.5 and 0.6 seconds. Then those lines were averaged to obtain:

n_density = (1E+27) exp( -48.27 * t)

Now the first number out front in the exponential (1E+27) is unimportant. The exponent itself gives us the information we need.

The exponential term -48.27 is the time constant (τ) with units of sec^-1. With this time constant, one can obtain the pump speed as follows:

τ = - S / V

-48.27 = - S_cryobox / 2530 L

S_cryobox = 122,123 L/s

This is approximately the pump speed calculated from theoretical values 120,000 L/s shown in the introduction.

Conclusion

Using Molflow+, it was shown that the actual absolute pump speed of a asymmetric pump with complex geometry can be measured within a test volume. To do this, density was measured within the simulation at different points (where ion gauges could be placed) as a puff of hydrogen gas was injected and the cryobox was pumping.

One could see that although it is logical that it would be possible to measure the pumping speed by taking measurements while the gas being injected has reached equilibrium with the cryobox, this would require the absolute density everywhere in the test tank chamber. From the results, obtaining the absolute density throughout the test tank would require more assessment if not impossible.

However, after the gas puff injected was shut off, one saw that although the density measured differently at various locations, the rate of pump down did not. A logarithmic line of best fit was drawn and averaged out for all locations to obtain a rate of pump down which was then used to calculate a pump speed that corresponded fairly accurately without the theoretical pump speed of 120,000 L/sec.

To conclude, during a physical experiment, the placement of ion gauges within the test tank has no importance. After a certain amount of gas is injected, the rate of pump down can be measured by ion gauges and used to obtain the absolute pump speed.

AVS Symposium 2016 Poster