Neutral tritium gas reduction in the KATRIN differential pumping sections

The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to measure the effective electron anti-neutrino mass with an unprecedented sensitivity of $0.2\,\mathrm{eV}/\mathrm{c}^2$, using $\beta$-electrons from tritium decay. The electrons are guided magnetically by a system of superconducting magnets through a vacuum beamline from the windowless gaseous tritium source through differential and cryogenic pumping sections to a high resolution spectrometer and a segmented silicon pin detector. At the same time tritium gas has to be prevented from entering the spectrometer. Therefore, the pumping sections have to reduce the tritium flow by more than 14 orders of magnitude. This paper describes the measurement of the reduction factor of the differential pumping section performed with high purity tritium gas during the first measurement campaigns of the KATRIN experiment. The reduction factor results are compared with previously performed simulations, as well as the stringent requirements of the KATRIN experiment.

fields along the 40 m long STS-beamline. Half of the electrons travel downstream to the SDS, where their energy is measured by an electrostatic spectrometer (MAC-E filter [11]) with ultra-high precision (1 eV at 20 keV). Virtually all remaining tritium gas in the beam tube is pumped out in the transport and pumping section, before it can reach the spectrometer section, where otherwise it would increase the background rate of the measurement. Since only 2 × 10 −13 of all β-electrons have kinetic energies in the last eV below the endpoint of the spectrum, a low background rate is necessary to reach the target sensitivity. Therefore, the initial tritium flow into the WGTS of 1.8 mbar s −1 (here and in the following referenced to 0 • C) has to be reduced by at least 14 orders of magnitude, before reaching the SDS.
An essential part of the STS is the KATRIN Loop System shown in figure 2, which incorporates the pumping systems. It provides a closed inner loop for the ultra-pure and pressure stabilized tritium circulation through the beam tube inside the WGTS cryostat. Simultaneously, the outer loop serves as interlink to the tritium infrastructure of the TLK, where impure tritium gas is cleaned and stored. The transport and pumping section comprises two components. First, the differential pumping section (DPS) employs a chain of turbo molecular pumps (TMP), as shown in figure 2. The TMPs reduce the flow by 7 orders of magnitude. Details are described in the next section. For lower pressures, mechanical pumping becomes inefficient. Therefore, the second part is a cryogenic pumping section (CPS), which cryosorbs the remaining tritium molecules on a 3 K to 4 K cold argon frost layer [12,13]. The Ar frost layer is regenerated regularly, before the accumulated tritium exceeds a maximum activity of 3.7 × 10 10 Bq (=1 Ci). With the nominal tritium flow into the WGTS and the projected flow reduction by the DPS, this limit would be reached after about 60 days. A longer time between regenerations of the CPS increases the possible uptime of the KATRIN experiment. Therefore, an accurate assessment of the actual flow reduction by the DPS is important. This paper is focused on the reduction of the neutral tritium flow rate along the beamline by the differential pumping section, between the inlet into the beam tube at the center of the WGTS to the entrance of the CPS. The overall performance of the differential pumping system of KATRIN was checked during commissioning with deuterium gas, before admitting tritium into the system. The result has been confirmed during the first tritium measurement in 2018 with 1 % DT in deuterium [9]. However, these measurements allow only a rough estimate of the actual tritium reduction efficiency, due to different effective pumping speeds for DT and T 2 . The decay rate of DT in the recovered gas after regenerating the Ar frost was used in the second measurement to determine the amount of gas accumulated in the CPS. The ratio between the accumulated gas and the integrated gas flow into the WGTS provides a measure for the reduction factor of the DPS. However, the small admixture of DT introduced a large statistical uncertainty.  are presented in section 3 and compared to simulations [14] described in the next section.

Description of the differential pumping section
The tritium loop system is distributed along the 40 m long KATRIN STS beam line and interconnects the beam line segments with each other and the TLK infrastructure [15,16]. As shown in figure 2, it consists of the "Inner Loop" (IL) and "Outer Loop" (OL). Components of interest for this paper are: • Windowless Gaseous Tritium Source (WGTS): The source of β-electrons in KATRIN is a gas column of tritium in a 10 m long beam tube with 90 mm diameter. In order to achieve the high statistics required for KATRIN, 1.8 mbar s −1 (40 g/day) of tritium with a purity >95 % is injected in the center of the WGTS beam tube with an inlet pressure of ≈10 −3 mbar. In order to minimize systematic effects, the source tube inside the WGTS cryostat is cooled down to a temperature of ≈30 K. The beam tube temperature, the injection pressure, and the necessary gas throughput have to be kept stable on a level of <0.1 % h −1 .
• Differential Pumping Section 1 (DPS1): Connected on both sides to the WGTS beam tube are the first stages of the differential pumping section, the DPS1 (see figure 3). This section consists of 4 pump ports (PP) inside the WGTS cryostat (DPS1-F1, DPS1-F2, DPS1-R1, DPS1-R2) and one outside of it (PP0). A total of 14 turbomolecular pumps (TMP) of type Leybold MAG-W2800 with a pumping speed of 2100 s −1 for H 2 [17] are connected to these pump ports. Twelve TMPs are arranged symmetrically around the WGTS beam beam tube, starting with 4 TMPs at each end, connected to DPS1-F1 and DPS-R1. The next stage includes two TMPs in DPS1-F2 and DPS1-R2, respectively. The two remaining pumps are located at an additional pump port (PP0) between the WGTS cryostat and the DPS2 in downstream direction. The pump ports are connected via beam tube segments of 1 m length and a diameter of 90 mm.
The fore-vacuum for the MAG-W2800 TMPs is provided by 4 Pfeiffer HiPace300 TMPs with a pumping speed of 220 s −1 for H 2 [18]. These pumps are in turn pumped by cascaded fore-pumps, combining a Normetex R scroll pump and a metal bellows pump [19] (see figure 2). Gas pumped out by this system is purified by a PdAg permeator and then re-injected into the WGTS (see [20] for details). The WGTS beam line and pump ports are part of the IL.
The pumps of the DPS1 reach an ultimate pressure of <5 × 10 −10 mbar in the unbaked, 30 K cold WGTS cryostat, without gas load. When gas is circulating, the pumps reduce the gas flow towards the spectrometer by a factor of ≈10 3 , as is shown in subsection 3.1.
• Differential Pumping Section 2 (DPS2): Separated from the DPS1 via a gate valve, four large, cascaded MAG-W2800 TMPs further reduce the downstream flow of neutral tritium in the DPS2 (PP1-4). The fore-vacuum for these pumps is provided by 2 Pfeiffer HiPace300 TMPs. Of these TMPs, the one pumping the PP3 and PP4 MAG-W2800 is cascaded with the other (see figure 2). The last HiPace300 TMP is in turn pumped by cascaded fore-pumps, combining a Normetex scroll pump and a metal bellows pump. In order to increase the pumping efficiency and prevent a direct line of sight between source and spectrometer, the DPS2 beam tube is arranged in a chicane (see figure 3. Gas pumped out from the DPS2 contains a high fraction of outgassing products, which decrease the purity of the tritium gas. Therefore, it is not re-circulated, but returned to the TLK infrastructure for purification. Hence, the DPS2 beam line and pump ports are part of the Outer Loop (OL).
The pumps of the DPS2 reach an ultimate pressure of <10 −9 mbar in the unbaked system, without gas load. During gas circulation, the pumps reduce the gas flow towards the spectrometer by a factor of ≈10 4 , as is shown in subsection 3.2.
• Cryogenic Pumping Section (CPS): Separated by another gate valve from the DPS2, about 2 /3 of the CPS beamline is operated at a temperature of 3 K to 4 K, working as a cryo-pump for the remaining tritium. The inner surfaces of the cold beam tubes are enlarged by 90 circular fins welded into the beam tubes and covered by a layer of argon frost. Even with conservative assumptions, simulations indicate a reduction factor of at least 10 11 [14], well above the minimum design value of 10 7 . The performance of the CPS is not covered in this paper, but it is used to determine the amount of tritium gas passing the DPS. During the regeneration of the cryo-surfaces the previously sorbed tritium, together with the argon frost, are evaporated and captured in a buffer vessel (B2). The activity of tritium in the gas is measured, allowing the determination of the total amount of tritium gas that passed the DPS.
The connections of the IL and OL to the infrastructure systems of the TLK are shown in figure 2.

Definition of reduction factor in existing setup
The overall reduction factor R tot in the STS denotes the relative reduction of neutral tritium gas flow Q WGTS,d from the WGTS to the spectrometers. R tot needs to be larger than 10 14 . It incorporates the reduction factors of the differential pumping sections R DPS and of the cryogenic pumping section R CPS , which are both required to reach at least a target value of 10 7 : In addition, R DPS can be subdivided into reduction factors for the inner and outer loops, respectively: with: • R IL is the flow rate reduction between the downstream flow Q WGTS,d from the injection point into the WGTS to the DPS2. This includes DPS1-F1, DPS1-F2, and PP0 up to V1, as shown in figure 3.
• R OL is the flow rate reduction between the flow rate entering PP1 via A3 from the WGTS and the flow rate entering the CPS. In figure 3 this reduction factor is the fraction of gas entering the DPS2 through V1 over the gas exiting via V2.
In previous simulations [21,14] R DPS was subdivided according to the different flow regimes, using laminar and transitional flow up to DPS1-2F and molecular flow in PP0 and DPS2. However, for the measurements the reduction factors have to be split into R IL and R OL .

Results of simulations
The DPS1 is described in Ref. [21], which splits it into three computational domains. For the transition from the laminar flow regime at the injection point towards the transitional flow regime in the first pump ports, a semi-analytical rarefied gas dynamics model [22,23] is used. The transitional flow regime inside DPS1-F1 is simulated using a Direct Simulation Monte Carlo (DSMC) [24] method. Finally, the outermost pump ports are described, using the angular coefficient [25] method to account for the transition from 30 K to room temperature in this domain.
As the focus in [21] was on the precise description of the gas density distribution along the beamline, the reduction factor was not investigated in detail, and therefore no detailed error analysis was given. From the uncertainties given on the simulated pressures and flows, we estimate an uncertainty of about a factor two in both directions, mainly owing to the uncertainty of the effective pumping speed used in the simplified geometry of the model. The value for the gas flow reduction as reported in Ref. [21] is: In order to achieve comparability between measurement and simulation, the DPS2 MolFlow+ simulation performed in [14] has been rerun with slightly different boundary conditions, since the intitial simulation included PP0 as part of the DPS2, while in the measurements it is connected to the IL. MolFlow+ [25] is a Test Particle Monte Carlo (TPMC) simulation code for particle tracking through the geometry of a vacuum chamber in the molecular flow regime. Particles do not interact with each other but only with the walls of the vacuum chamber where they get adsorbed, desorbed or reflected. The geometry is approximated by a mesh of two-dimensional polygon surfaces, called facets. For each facet the number of hits, adsorptions and desorptions is counted. An adsorbing facet represents a pump, a desorbing facet a gas source. Fully transparent (virtual) facets which are not part of the actual physical geometry can be defined providing additional counting of hits at a location of interest. Ratios of counts are used in order to determine transmission probabilities. In figure 3 an overview of the implemented geometry is given. Besides the physical boundaries of the beam line there are several virtual facets implemented. The particle tracking starts at facet A2 downstream of DPS1-F2. Particles are removed from the simulation in three different cases: They • are pumped out by one of the TMPs in the pumping ports DPS1-F2 or PP0-4, or • are pumped out at the CPS cryo-pump downstream of V2.
Consequently, the simulation does not only consist of the DPS2, but also the neighboring sections. Since particle tracking starts already at A2, while only facet counts at A3 and beyond are used in the simulation, it is assured, that boundary effects, such as back reflections or the angular distributions of particle velocities are included correctly. In MolFlow+ pumps are modeled by facets with well-defined sticking probabilities α ∈ [0, 1], corresponding to the pump's gas type dependent pumping probability. For the CPS cryo-pump α = 0.7 was set, which is an established reference value of a well prepared argon layer at 3 K [26]. Particles moving as far back as DPS1-F1, hitting facet A1, are assumed to be pumped off. Consequently, these particles are removed from the simulation by setting α A1 = 1. It has been verified that this simplification of the model does affect the results of the simulation by less than 0.5 %.
The DPS TMPs were included with α = 0.252, corresponding to their estimated pumping probability for particles of mass m = 6 g mol −1 . For this estimate we used the nominal pumping speeds given by the manufaturer, interpolating different particle masses by applying the Malyshev model [27], which assumes that the pumping probability scales with the logarithm of the particle mass M (α ∝ ln(M )). The systematic uncertainty of this method has been taken into account as an uncertainty of 20 % on this pumping probability. It was estimated by comparing the measured and simulated pumping speeds for different gases (based on the nominal pumping speed of the pump manufacturer) in the KATRIN Main Spectrometer. The impact on the resulting reduction factor was obtained by dedicated simulations with 20 % higher and 20 % lower TMP pumping probabilities, respectively.
In table 1 the output of the simulations is shown by giving the important numbers for the reduction factor calculations. Using the number of particles pumped at PP1-4 (N PP1−4 ) and at the CPS (N CPS ) for α = 0.25 the resulting reduction factor is derived by the following equation: The upper and lower uncertainties originate from the simulations with α = 0.20 and α = 0.30 respectively. Since the maximal statistical uncertainty is about 4 % and thus much smaller than the systematic uncertainty of about ≈40 %, it is neglected in the following. The reduction factor of the IL can be derived from R Sim DPS1 in Eq. 3 and the reduction factor of PP0. With the simulated numbers from table 1, the reduction of the gas flow via PP0 is given by the ratio of particles entering PP0 through A3 (N A3 ) and those pumped by the DPS2 (N PP1−4 ) and the CPS (N CPS ): was simulated and how it is operated in the current KATRIN setup. In [21] the simulation ended at the surface A3 with an assumed effective pumping probability of α = 20 % for PP0 and the subsequent DPS2 pumps. This number originated from calculations for the case of only one active TMP at PP0. Currently, both TMPs are operated. So, the A3 effective pumping probability, as simulated with MolFlow+, should be rather 36 % than 20 %. The impact on the final result of R Sim DPS1 has been calculated based on two dedicated MolFlow+ simulations. In each of them A3 is assumed as an opaque facet but with different sticking factors of 20 % and 36 %, respectively. Gas particles are desorbed from facet A1. For both simulations the reduction factors have been calculated by taking the ratio of the number of adsorptions at A3 and hits at A2. The correction factor C A3 for R Sim DPS1 is determined as the ratio of both reduction factors, resulting in a value of C A3 = R 36 % /R 20 % = 0.953 ± 0.003. The corrected IL reduction factor is: In combination with the simulated OL result from equation 4 one can derive the overall simulated reduction factor for the DPS: With the assumption that the uncertainties of the TMP pumping probabilities in DPS1 and DPS2 are correlated, the uncertainties were estimated by multiplying the simulations with the upper and lower bounds of the two reduction factors, respectively, and subtracting the simulation with the central value.

Measurement of reduction factors
Two different methods were used to determine the reduction factors R IL and R OL for tritium. Measurements were taken for the nominal column den-sity of 5.0 × 10 21 m −2 (= 100 %) as well as for the settings used during the KNM1 (1.1 × 10 21 m −2= 22 %) and KNM2 (4.2 × 10 21 m −2= 84 %) measurement campaigns. While the reduction factor R IL depends on the pressure in the WGTS beam tube and the temperature, R OL is constant, since the DPS2 is operated at constant room temperature in the molecular flow regime. In contrast to the upper and lower bounds of uncertainty present for the theoretical results, the uncertainties for the derived quantities were calculated using uncertainty propagation assuming gaussian distributed uncertainties of the measured values. The different methods and their results are described below.

Reduction factor of the Inner Loop
The reduction factor R IL is determined from the ratio of the measured gas flow rates into the WGTS and into the DPS2: The gas flow rate in downstream direction Q WGTS,d inside the WGTS is calculated using a MKS 179 mass flow meter 1 (labeled FIR in figure 2), which measures the total flow rate into the WGTS Q WGTS,tot . With the symmetric design of the WGTS beam tube and the DPS1-R and DPS1-F pump ports, equal conductances and effective pumping speeds in upstream and downstream direction can be assumed, leading to an equal split of the flow rate in both directions: The pressure ratio between the point of injection and both ends of the symmetrical sections, DPS1-F2 and DPS1-R2, is around 3 orders of magnitude. Therefore, the small effect of the difference in effective pumping speeds between the Rear Section at the upstream end and DPS2-PP0 at the downstream end can be neglected, compared to the systematic uncertainties of flow and pressure measurements which are on the percent-level. The effective gas flow rate Q DPS2 entering the DPS2 is measured by a pressure rise ∆p /∆t inside the buffer vessel B1 (labeled PIR in figure 2) with a well known volume V B1 , located behind the last cascaded DPS2 TMP: The volume V B1 = (16.53 ± 0.21) has been determined during the commissioning phase via gas expansion from a reference volume. A necessary assumption for applying Eq. 10 is that all gas entering the DPS2 is pumped out by the 4 TMPs connected to the beamline, neglecting the gas entering the CPS. This assumption is justified, since the flow rate into the CPS is reduced by four orders of magnitude in the DPS2, which is much smaller compared to the systematic uncertainties for the flow and pressure measurement in the percent-level (see subsection 3.2). An additional effect is the outgassing of the DPS2 setup. The surfaces of the vacuum chambers, beam line instrumentation such as dipole electrodes or an ion monitor inside the vacuum system of the DPS2, as well as the TMPs themselves cause a non-negligible outgassing rate, leading to an additional pressure rise ∆pog /∆tog in V B1 . In order to correct for this effect, the outgassing rate was measured during operation of the beam line without tritium gas injection and then subtracted from the tritium gas flow induced pressure rise: The outgassing rate (≈ 5 × 10 −7 mbar s −1 ) is determined for each tritium measurement from the latest available outgassing measurement, in order to account for possible changes in the outgassing behavior. The pressure rise data and a linear fit for a column density of 5.0 × 10 21 m −2 can be seen in figure 4. The results for Q DPS2 , Q WGTS,d , and R IL for different column densities are listed in table 2. The monitoring of R IL with resonable accuracy has two direct applications for the operation of the source and transport section. First, with a constant R OL the expected tritium load on the CPS is accessible with a measurement on the time scale of 1 h to 2 h. This allows for reduction factor measurements to be done for different settings of WGTS cryostat temperatures and gas flows, which can change R IL . Second, the fraction of gas which can be recirculated in the IL can be directly derived from this measurement. As such, R IL has a  direct impact on the operation of both the IL and OL.

Reduction factor of the Outer Loop
The OL reduction factor R OL is calculated in a two step process. First, a combined reduction factor R DPS = R IL · R OL is measured by comparing integral gas activities: Where A WGTS is the integral activity of beta-decays in the gas flow Q WGTS,d , and A CPS is the beta-activity accumulated inside the CPS. The direct relation of the accumulated beta-activity to the integral gas flow into the CPS can be made, as isotopic exchange effects inside the DPS2 are expected to be on the sub-percent-level and therefore insignificant. This expectation is derived from the IL gas composition measurements for which gas passes through WGTS and DPS1, which are comparable to the DPS2 in length, the composition changes are below the percent-level for a single pass through.
To obtain R OL , R DPS is divided by R IL : This measurement method, using the activity of tritium gas, is needed as the cryogenic pumping principle of the CPS does not allow for an easily measurable gas accumulation in situ as described in subsection 3.1. The gas flow entering the CPS is adsorbed on its cryogenic surface and can only be determined after regeneration. During the regeneration procedure, helium is used as a purge gas to remove the argon frost layer together with the captured tritium. This results in a mixture of around ∼6 bar argon, 250 bar helium, and traces of tritium of less than 0.39 mbar , limited by the maximum allowed activity inside the CPS. The entire gas is collected in the buffer vessel B2 (see figure 2). Reliable quantification of the small trace amounts of tritium in this gas mixture is impossible using pressure measurements and very challenging using residual gas analyzers. However, the traces of tritium are quantifiable by counting the beta-activity in the gas with measurement techniques developed by TLK [28,29,30]. Several samples of this gas mixture from the buffer vessel were analyzed, using oxidation on copper oxide (CuO) at 450 • C, followed by liquid scintillation counting to determine the activity concentration of the gas sample with an uncertainty of 10 %. The total activity of the collected purge gas A CPS was calculated by scaling the sample activity with the respective gas amounts.
The determination of the activity A WGTS is not possible via a direct activity measurement. It can be derived from the gas flow Q WGTS,d and the composition of the gas. The gas composition is measured via laser raman spectroscopy [31,32,33]. The composition analysis allows the determination of the fraction of tritium T . Using these two values and the specific activity a T2 = 9.5 × 10 10 Bq/mbar of T 2 , one can calculate the integral activity A WGTS as follows: The measurement results for A WGTS and A CPS for the CPS regenerations after the KNM1 and KNM2 measurement campaigns, as well as the reduction factors R DPS and R OL , are shown in table 3.

Inner Loop reduction factor
The simulated IL reduction factor for the nominal column density of 5 × 10 21 m −2 (= 100 %) as derived in this work (see subsection 2.3) is: Comparing this to the measured value of the IL reduction factor, R IL = (6.68 ± 0.14) × 10 3 , one can see that the measured value is close to the simulated value for the central value of the pumping probability α = 0.25, and well within the uncertainty of the simulation. An effect which had not been expected initially, is the significantly different reduction factor at the low column density setting of 1.1 × 10 21 m −2 (≈ 22 %) used during KNM1 (see table 2). This strong dependence of the reduction factor on the column density, and thereby pressure and flow, can be attributed to the changes of flow regime inside the WGTS. With decreasing column density, the pressure inside the pump ports decreases, shifting the flow regime from the Knudsen flow regime further towards the free molecular flow regime. In the Knudsen flow regime more scattering of gas molecules inside the DPS1-F1 is present. The narrow and long geometry of the beam line between the injection point and DPS1-F1 produces a distinct molecular beam. Thus, radial movement is suppressed and molecules only receive a strong radial momentum by scattering with other molecules. Since gas particles are only pumped if they move radially towards the TMPs, less scattering produces lower reduction factors. This effect is the most likely reason for the smaller reduction factors of the IL at low column densities. Various measurements of R IL at different column densities and beam line temperatures showed that there is no strong influence of the temperature, but a clear correlation with the column density (see table 2). As the DSMC simulations for the Knudsen flow regime are computationally intensive, and low column densities are not of interest for normal KATRIN operation, a detailed parameter study was not undertaken.

Outer Loop reduction factor
The simulated OL reduction factor, as derived in this work (see subsection 2.3), is: Comparing this to the value of the OL reduction factor derived in the KNM2 measurement campaign, one can see that the values match well within their respective uncertainties. In contrast to R IL , no dependance of R OL on the column density can be inferred from the data, considering the measurement uncertainties. This is in good agreement with the underlying assumption of free molecular flow inside the OL section of the differential pumping section.

Impact of the reduction factor on CPS operation
While there is no data on the combined reduction factor for the differential pumping sections R DPS at nominal column densitiy of 5 × 10 21 m −2 , an estimation can be made using the data gained from KNM2 with a column density of 4.2 × 10 21 m −2 . The difference between R IL for both column densities is negligable, and R OL does not depend on the column density value. As such, the R DPS measured during KNM2, can be used as a good estimate for the reduction factor at nominal conditions, which is very promising with regards to the CPS runtime. The runtime of the CPS is limited by the maximal allowed amount of N CPS,max = 0.39 mbar (= 1 Ci) of accumulated tritium gas. At the nominal tritium gas flow rate of Q WGTS,d = 0.98 mbar s −1 from the point of injection in downstream direction, this leads to a maximum operation time before regeneration of: This value surpasses the initial design goal of a CPS regeneration every 60 days by a factor of 7.4. With this rather large safety margin, the measurement interval between subsequent regenerations can be relaxed, allowing for longer neutrino mass runs, and more flexibilty in scheduling of measurements in general.

Summary and conclusion
The KATRIN experiment requires a reduction of the tritium flow in the beamline between the point of injection in the WGTS and the spectrometer and detector section by at least 14 orders of magnitude. Otherwise, the additional background rate would worsen the ultimate sensitivity for the neutrino mass. The huge gas flow reduction is achieved by two sequential pumping systems, each reducing the flow by a factor of at least 10 7 , using turbo-molecular pumps (DPS) and cryosorption on 3 K cold argon frost (CPS), respectively.
For the initial design layout, radiation safety considerations required a regeneration of the cryogenic pumping section after no more than 60 days. A sound knowledge of the actual reduction factor of the DPS allows for a more accurate estimate of the time interval between regenerations, helping to optimize the time available for neutrino mass measurements. Therefore, extensive gas flow simulations were performed, taking into account the different flow regimes along the beamline, from laminar and transitional flow to molecular flow. The simulation of the DPS resulted in a reduction factor of 8 +17 −6 × 10 7 , well above the minimum requirement. To validate the simulations, the tritium reduction factor of the differential pumping sections was measured for the first time in 2019 for different flow rates, with a tritium purity well above 97 %.
The measured value for a tritium column density of 4.2 × 10 21 m −2 in the beamtube of the WGTS is R DPS = (9.63 ± 1.00) × 10 7 . This reduction factor, measured at 84 % of the nominal column density, as used during the most recent neutrino runs, is well above the minimum requirement of 10 7 and is in good agreement with the simulated value.
In conclusion, the good performance of the final design of the differential pumping section of the KATRIN experiment could be demonstrated both by simulation and measurement for the first time. This performance allows the long-term operation of the cryogenic pumping section as intended, enabling the KATRIN experiment to accumulate the necessary amount of measurement runs for its scientific goals.