The temperature is almost constant in the vacuum system of hydrogen maser. According to The Boyle’s law, the product of the gas volume V and the pressure P is constant if only the pressure changes. Therefore, in a vacuum system, the product P × V is generally used to represent the amount of gas, we can obtain the expression of flow after differentiating time: Q G = V d p d t + P d V d t (1)

The pressure everywhere remains generally constant when the system is stable, and the pressure changes little in a short time interval. At this time, Formula 1 can be written as: Q G = P d V d t (2)

This is the constant pressure expression of flow, unit for Pa⋅m³⋅s⁻¹ or Pa⋅m³⋅s⁻¹.

Figure 3 is a brief schematic diagram of the vacuum system. When the vacuum pump starts pumping, the pressure P at the inlet of the vacuum pump is less than the pressure P 0 in the container, thus the gas flows to the vacuum pump and is collected or discharged out of there. The pumping speed S p of a vacuum pump is the ratio of the gas flow Q G to the pressure P at the pump port: S p = Q G P (3)

The unit is m³⋅s⁻¹ or L⋅s⁻¹. Compared with Formula 2, when the pressure P is constant, S p is approximately equal to d V d t .

Due to the pressure difference between the pumped container and the vacuum pump, there is also a difference between the pumping rate of the vacuum pump and the pumping rate of the gas in the container. To distinguish between them, the pumping speed of the gas in the container is usually called the effective pumping speed, represented by S 0 , it can be obtained by dividing the gas flow Q G by the pressure P 0 in the container: S 0 = Q G P 0 (4)

Hydrogen pressure and flow rate are both small while in the high vacuum state of the hydrogen maser, which make the probability of collision between molecules is much less than with the tube wall. After each collision, molecules will move forward or backward in different directions. Therefore, the flow of hydrogen in the connecting tube is molecular flow.

The calculation of flow conductance is closely related to the shape of the tube. The structure of hydrogen maser is very compact, and short tubes (tube length L /diameter d < 20) are usually used in vacuum systems. The flow conductance calculation formula of air in molecular flow state in a short tube at 20°C can be expressed as follows: U f . 20 ℃ = α ⋅ 116 A 0 (5) Where the α is the Clausing coefficient, which is related to the value of L / d ; A 0 is the cross-sectional area of the tube. Under the same conditions, the conductance of hydrogen and air has the following relationship: U H 2 = 3.78   U A i r (6)

The conversion formula for flow conductance at different temperatures is: U T = U 20 ℃ T 293.15 (7)

Based on Formulas 5ormulas –Formulas 7, we can obtain the relationship between the flow conductance of hydrogen in the short tube and the temperature: U H 2 = 438.48 ⋅ A 0 ⋅ α ⋅ T 293.15 (8)

When the gas flows in the tube, the pressure decreases gradually along the direction of the gas flow, so there is a dynamic pressure difference ( P 1 − P 2 ) , P 1 , and P 2 respectively represents the upstream and downstream gas pressure in the tube. The pressure difference is proportional to the gas flow, the formula is as follows: Q G = U ( P 1 − P 2 ) (9)

In the vacuum system, assuming that there is no air leakage or air source and the air flow is in a stable state, according to the law of conservation of mass, the flow P ⋅ S P at the right end of the conduit (vacuum pump inlet), the flow P 0 ⋅ S 0 at the left end of the conduit (container outlet) and the flow U ( P 1 − P 2 ) at any section in the conduit are equal, that is: U ( P 1 − P 2 ) = U ( P 0 − P ) (10) P 0 S 0 = U ( P 0 − P ) = P S P (11)

After the convention of Formula 11, the following equation can be obtained: 1 S 0 − 1 S P = 1 U (12)

Formula 12 is the basic equation of the vacuum system when the air flow reaches a stable state. It relates the flow conductance U of connecting tube, the pumping rate S p and the effective pumping rate S 0 , and plays an important role in the design of the vacuum system.

As the absorption of hydrogen content in the getter increases, hydrogen atoms at the surface will spread inward at a slower rate, which results in a reduced inspiratory rate. In order to ensure that the suction rate can maintain a good vacuum state of the system after absorbing a certain amount of gas during the required working life, it is necessary to ensure a certain effective suction area. The calculation formula of the effective suction area is as follows: F = Q i m i q i K i (13) Where the Q i is the required one-time inspiratory volume; m i is the mass of getter per unit area; q i is the suction amount of getter when the pump pumping speed tends to be stable; K i is a constant, when only one side is working, the value is 0.9, and when both sides are working, the value is 0.55.

The hydrogen evolution flow rate in hydrogen maser is mainly determined by the nickel tube purifier. We designed a measuring device for hydrogen permeability under different operating currents of nickel tube purifier. As shown in Figure 4A, it is mainly composed of nickel tube purifier, electrode flange, thermostatic circuit board and measuring tube. The right side of the measuring tube is connected with a vacuum pump to maintain the vacuum environment of measuring. The measuring principle is described as follows.

Under certain conditions, the heat conduction capacity of gas molecules is related to the number of gas molecules per unit volume. According to this principle, hydrogen is released from the hydrogen storage alloy bottle into the nickel tube; when the nickel tube is connected to the direct current, the joule temperature rises, and hydrogen diffuses outward into the measuring tube, where the heat exchange with the thermistor and changes the thermistor temperature. The temperature of thermistor corresponds to the resistance value, thus the voltage difference ∆ U between A and B in the bridge also changes accordingly. Therefore, ∆ U can be used to reflect the change in hydrogen flow rate.

In Figure 4B, R 01 and R 02 are standard resistors with resistance values of 100 kΩ. R 1 and R 2 are the same thermistors. The resistance value is 100 kΩ at 25°C, B value is 3950 K. Hydrogen will take away part of the heat from thermistor R 1 while exchanging heat with it in the measuring tube. The heat loss per unit time can be obtained by the following formula: Δ P L o s s = C P ∙ ( T 0 − T H ) ∙ q (14) Where the C P is the hydrogen constant pressure specific heat capacity, the T 0 is the initial temperature of the deprecated thermistor R 1 without hydrogen gas flow, the T H is the temperature of hydrogen; and q is the hydrogen flow. Meanwhile, the heat generated by the thermistor R 1 due to the inflow current in unit time is: Δ P e = ( U 0 R 02 + R 2 ) 2 ∙ R 2 − ( U 0 R 01 + R 1 ) 2 ∙ R 1 = ∆ U 2 ( R 01 R 02 − R 1 R 2 ) R 01 R 02 ( R 2 − R 1 ) (15)

Where the U 0 is the voltage of the direct current supply. It was done experimentally to determine the optimal value as 1.2 V (for details, see Section 1.1 of the Supplementary Materials). According to the law of energy conservation, the heat loss Δ P L o s s between thermistor R 1 and hydrogen is equal to the heat Δ P e generated by thermistor R 1 . Thus, the calculation formula of hydrogen penetration q can be written as follows: q = ∆ U 2 ( R 01 R 02 − R 1 R 2 ) R 01 R 02 ( R 2 − R 1 ) C p ∙ ( T 0 − T H ) (16)

In a vacuum system, the suction capacity and suction rate are the two most important parameters. In order to calculate the specific values of these two parameters, the total gas flow Q G in the system needs to be calculated first. In general, Q G consists of the following parts [17]: Q G = Q l + Q d + Q p + Q b + Q r (17)

Where, Q l is the hydrogen permeation amount in the vacuum system; Q d is the amount of adsorbed gas desorption on the surface of the internal vacuum system; Q p is the amount of gas discharged by diffusion or infiltration of the internal material in vacuum system; Q b is the reflux volume of vacuum pump; Q r is the air emission of the structural components assembled in the inner vacuum system. In the vacuum system of the hydrogen maser, the gas mainly comes from the hydrogen, which is permeated through the nickel tube during the operation, the other items are relatively little that can be ignored, thus Q ≅ Q l .

According to the hydrogen evolution rate experiment of the nickel purifier under different current (in Section 2.2.6), the result (shown in Figure 5) shows that the hydrogen permeability increases with the increase of the working current of the nickel tube purifier. When I = 1.0–3.0 A, the flow increases greatly, until when I = 3.0 A, q = 1.58 × 10^–8 L s⁻¹. Considering the hydrogen maser signal and the impairment to the vacuum pump, the current of the nickel tube purifier is generally set to 3.0 A to get an optimal value of hydrogen flow (for details, see Section 1.2 of the Supplementary Materials).

Based on the hydrogen permeation amount q under this current flow, we can get the total hydrogen flow of the vacuum system Q G = 1.60 × 10^–3 Pa⋅L⋅s⁻¹ from Formula 2 and the ideal gas equation. The total suction amount Q A can be obtained by multiplying Q G with working life. For 10 years, the total inspiration Q A is about 0.5 MPa L.

In the vacuum system, it is a cylindrical stainless-steel tube between the pumped container and the vacuum pump, which is 70 mm in length and 60 mm in diameter. The cross-sectional area A 0 = 2,827.43 mm², L / d = 1.167, according to the table, Clausing coefficient a is 0.488. According to Formula 8, the flow conductance of hydrogen in the tube at 20°C can be calculated: U H 2 = 6050 L s⁻¹.

According to the requirement of hydrogen maser vacuum system, the gas pressure in the pumped container P 0 = 1 × 10^–5 Pa, gas flow Q G = 1.60 × 10^–3 Pa L s⁻¹ and the effective pumping velocity S 0 = 160 L s⁻¹ can be calculated by Formula 4.

According to effective pumping rate S 0 = 160 L s⁻¹ and flow conductance U H 2 = 6050 L s⁻¹, The pump speed S p = 164 L S⁻¹ can be calculated from the basic equation of vacuum system (Section 2.2.4).

Due to the short and large diameter of the tube, the change of gas pressure at both ends is very small, thus the calculated values of S 0 and S p are almost equal, which to some extent reduces the requirement of vacuum pump on pumping speed.

In this work, Zr-V-Fe alloy getter tablets (as shown in Figure 6) is used as the basic material of the getter pump. At the beginning of the operation, there is little internal hydrogen content and the getter tablet has a high pumping rate of hydrogen. With the increase of suction volume, the pumping rate decreases gradually. Under 20° Cand 10^–5 Pa vacuum, the initial inspiration rate of the carrier is over 2,500 cm³ ⋅ s⁻¹ ⋅ g⁻¹; when the inspiratory capacity reaches 5,000 Pa ⋅ L ⋅ g⁻¹, the inspiration rate tends to stabilize at about 900 cm³ ⋅ s⁻¹ ⋅ g⁻¹.

The inner diameter of the single getter tablet is 4.0 mm, the outer diameter is 10.0 mm, the thickness is 1.3 mm, and the mass is 273.8 mg. The calculated effective suction surface area (the upper, lower and outer wall surfaces) of the single tablet is 172.9 mm². Therefore, the mass of getter per unit area m i = 1.59 mg/mm².

According to the one-time inspiratory volume requirement, Q i = Q A = 0.5 MPa L, the suction capacity as the suction rate tends to be stable is taken as the value of q i = 5,000 Pa ⋅ L ⋅ g⁻¹, K i = 0.55 for double-sided suction, thus we obtained the suction surface area F = 1.16 × 10⁵ mm² for 10 years from Formula 13.

According to the previous calculation, the total inspiratory Q A of service hydrogen maser is 0.5 MPa L for 10 years. In order to prevent the getter material from embrittle, it is necessary to retain a certain amount of allowance for use [18]. Meanwhile, for maintaining the required vacuum state, the vacuum pumping rate should be faster than 164 L/s, and the effective area of the getter should be larger than 1.16 × 10⁵ mm².

Considering the balance of cost, performance, weight and allowance reserve, we design a vacuum system for space active hydrogen maser based on the above research and calculations. The pump contains 527 g getter materials with a total number of 1925 getters. The single effective suction surface area is 172.9 mm² and the total effective suction area of about 3.3 × 10⁵ mm².

The inspiratory capacity of single tablet is not less than 5,000 Pa⋅L⋅g⁻¹, thus the capacity of the total getter pump is not less than 2.5 MPa⋅L, meanwhile, the suction rate is about 474 L/s, and the theoretical gas consumption is less than 20% of the full capacity, which fully meets the above performance requirements and can meet the engineering application needs of space active hydrogen maser for more than 10 years.

Based on the performance requirements and our previous work [19], the getter pump structure designed as follows.

The overall structure of the getter pump is shown in Figure 7A, which is mainly composed of a shell, getter tablet and its bracket, and heating devices. The shape of the pump and its overall size is determined by the internal requirements of the active hydrogen maser. The outer diameter is 196.0 mm, the inner diameter is 90.0 mm, and the height is 40.0 mm. The shell of the pump is composed of a Ti metal plate, which is 1.5 mm in thick, to reduce the influence of magnetic field on the performance of the hydrogen maser.

Figure 7B is the schematic diagram of the internal getter structure. There are altogether 175 getter units assembled in six layers, with 25 in the innermost layer and 30 in the outer five layers.

Figure 8A shows the structure of getter unit, which is mainly composed of base, getter tablets, Ti gasket, fixed nut, heating wire, and Ti support. Each getter unit contains 11 getter tablets, as described above, its inner diameter is 4.0 mm, outer diameter is 10.0 mm, thickness is 1.3 mm, and single mass is 273.8 mg (Figure 8B).

Each getter is separated by Ti metal gasket to increase the suction area; The bracket is a hollow structure, with an inner diameter of 3.0 mm, an outer diameter of 3.5 mm and a length of 35.0 mm (Figure 8C). Nickel-chromium alloy hot wire is installed inside the bracket to facilitate the activation of getter.

After the getter is exposed to the atmosphere or used for a long time, a passivation layer will be formed on its surface, which will reduce the rate of hydrogen absorption. Therefore, the getter pump needs to be equipped with a heating device for high temperature treatment to remove the passivation layer and obtain the fresh active surface, this process is called the getter pump activation.

The heating device uses nickel-chromium alloy heating wire with diameter of 1.0 mm and resistivity of 0.832 μΩ m. It has strong corrosion resistance, non-magnetic, and the operating temperature can up to 1,200°C. In the getter pump, the heating wires inside each getter unit are connected in series with a total length of 4.5 m and a resistance of 4.7 Ω. One end is connected with the pump shell as a negative pole, and the other end is connected with the ceramic electrode insulated with the pump shell as a positive pole. The total mass of the getter pump is approximately 4.5 kg, containing 527 g getter materials.