Precision high voltage divider for the KATRIN experiment

The Karlsruhe Tritium Neutrino Experiment (KATRIN) aims to determine the absolute mass of the electron antineutrino from a precise measurement of the tritium beta-spectrum near its endpoint at 18.6 keV with a sensitivity of 0.2 eV. KATRIN uses an electrostatic retardation spectrometer of MAC-E filter type for which it is crucial to monitor high voltages of up to 35 kV with a precision and long-term stability at the ppm level. Since devices capable of this precision are not commercially available, a new high voltage divider for direct voltages of up to 35 kV has been designed, following the new concept of the standard divider for direct voltages of up to 100 kV developed at the Physikalisch-Technische Bundesanstalt (PTB). The electrical and mechanical design of the divider, the screening procedure for the selection of the precision resistors, and the results of the investigation and calibration at PTB are reported here. During the latter, uncertainties at the low ppm level have been deduced for the new divider, thus qualifying it for the precision measurements of the KATRIN experiment.


Introduction
The properties of neutrinos and especially their rest mass play an important role for cosmology, particle physics, and astroparticle physics. At present the most sensitive and model-independent method to determine the neutrino rest mass in a laboratory experiment is the investigation of the energy spectrum of tritium β-decay. Because of neutrino flavour mixing, the neutrino mass appears as an average of all neutrino mass eigenstates contributing to the electron neutrino. At a few eV below the endpoint energy E 0 = 18.6 keV of the β-spectrum the signature of the neutrino rest mass is maximal [1]. Until now only upper bounds on the neutrino mass of m ν < 2 eV/c 2 have been determined [2,3,4]. In 2001 the international collaboration KATRIN [5] was established to build a new tritium β-decay experiment. The KATRIN experiment is based on the experimental experience of its predecessor experiments in Mainz [3] and Troitsk [4] and aims to improve their sensitivity on the neutrino rest mass by one order of magnitude to 0.2 eV/c 2 [7].
KATRIN is using an integrating spectrometer of MAC-E filter type [8,9] for the energy analysis of the β-decay electrons. For such a device the stability of the energy analysis relies primarily on the stability of the electrostatic filter potential [10,11]. The stability of the latter has been identified as one of the five main contributions to the uncertainty of KATRIN [7]. In order to keep the high sensitivity on the neutrino mass, the contribution of the retarding potential to the systematic error has to be limited to ∆m 2 < 0.0075 eV 2 /c 4 . Any unknown filter potential fluctuation with a Gaussian variance σ 2 leads to a shift of the measured squared neutrino rest mass δm 2 ν . The general relation how systematic uncertainties affect the neutrino mass value is [12] δm 2 ν c 4 = −2q 2 σ 2 , with q being the elementary charge. Due to the given systematic error limit this leads to a maximum uncertainty of the filter potential of σ < 0.061 V which corresponds to an allowed relative stability of the voltage monitoring system of ∆U U < 3.3 · 10 −6 at a filter potential of E 0 /q = U = −18.6 kV. This stability limit has to be kept for the anticipated KATRIN measurement time of three years, which corresponds to a calendar time of about five years. The relative precision of the retarding potential is of primary importance, whereas the absolute precision, which includes also the contributions of work-functions and chemical shifts, is of less importance, since the endpoint of the βspectrum is fitted from the data. Still, the KATRIN experiment will use the absolute endpoint position obtained from the data to compare it to the 3 He-3 H mass difference [6], thus serving as an important check of the systematic corrections. By precisely measuring the high voltage potential as well as by measuring the line position of a mono-energetic electron source, two redundant monitoring solutions will be applied [7]. For the latter method the filter potential of the KATRIN main MAC-E filter will be continuously monitored by means of a monitor beam-line consisting of the MAC-E filter setup of the former Mainz neutrino mass experiment. While being connected to the same filter potential as the main filter, mono-energetic electron calibration sources like 83m Kr will be operated at the monitor beam-line. Hence we are able to lock the main filter relative to the electron energy of the calibration source at the monitor filter. For supplying the energy filters at both beam-lines with a stable high voltage potential we use state-of-the-art, commercially available, high voltage equipment with a stability of 5 · 10 −6 per eight hours. High-end measurement equipment to monitor voltages in the 10 V range with a relative precision at the sub-ppm level is commercially available also. What is not available is a precision high voltage divider to scale down the filter potential to the most sensitive 10 V range of the digital multimeter. In [13], a new concept of high voltage divider is reported, reaching 2 · 10 −6 per year relative stability for direct voltages of up to 100 kV. The present paper describes how this concept has been applied to the new KATRIN precision high voltage divider for direct voltages of up to 35 kV using a different resistor technology and a simplified mechanical construction. Finally, the new divider has been investigated and calibrated by comparison with the PTB standard divider of [13].

Design of the KATRIN Precision HV Divider
The KATRIN precision high voltage divider is constructed with design parameters similar to those of the PTB standard divider reported in [13], but has been adopted to the requirements of the KATRIN experiment of measuring voltages up to 35 kV and uses a completely different precision resistor technology. The inner setup comprises four sections subdivided by five control electrodes made of polished copper and supported by a set of polyoxymethylene (POM) rods, see figures 1, 2. Because of its high mechanical and dielectric strength, the thermoplastic POM is used as an insulator and a support structure. The high voltage is fed to the top electrode by an appropriate sealed high voltage bushing. The whole structure is supported by POM rods on the bottom flange of the stainless steel vessel. The high-precision divider consists of 106 precision resistors of Bulk Metal Foil technology (see section 3). The layout of the entire divider circuit is shown in figure 3. In the four upper sections of the divider 100 resistors of R 1 = 1.84 MΩ are arranged in a helix structure, each section comprises 25 resistors. The remaining 6 resistors, R 3 = 140 kΩ each, provide two low voltage outputs. Therefore two groups of three resistors in parallel are arranged subsequent to the 100 precision resistors. One such group provides a divider ratio of 3945:1, both together provide 1972:1, thus allowing precise measurements in the 10 V and in the 20 V range, as needed by KATRIN. Except for the top electrode, all copper electrodes have a centred bore to fit an acrylic tube, which -by means of appropriate drillings -is used to provide a fan-driven flow of temperature stabilized insulation gas (N 2 ) at each resistor position. By using a PID KATRIN is measuring β-electrons; therefore, the filter potential has always a negative sign. Since the divider operates at potentials of either sign, we omit the negative sign in its specification. However, all measurements have been performed with negative voltages of up to -35 kV as required for calibration purposes when measuring all the conversion electron lines of 83m Kr up to 32 keV. microprocessor control unit, a PT100 temperature sensor, suitable heat exchangers, and an external peltier cooling and resistive heating setup, the temperature of the insulation gas is kept stable at 25 • C ± 0.15 • C. The precision resistors of the highprecision divider are mounted between PTFE rods in order to be kept under a constant gas flow. The PTFE rods are fixed between the control electrode layers; they are used to prevent or to reduce any leakage and compensating currents between the cylindrical resistor mounts, which are made of nickel-plated brass. A sketch of one electrode layer is shown in figure 1. A POM-insulated feedthrough connects the precision resistor helix of one section with the resistors of the next section. Each pair of copper electrodes is connected via one HV resistor (R 2 = 44 MΩ) and one HV capacitor (C ′ 2 = 2.5 nF), forming a capacitive ohmic control divider in parallel to the high-precision divider. The control divider output consists of two standard resistors of R 4 = 90 kΩ each and does not need to be calibrated. In this way the applied voltage can be monitored with low precision and independent of the precision divider. The HV resistors of the control divider provide a linear voltage distribution in all sections, guaranteeing each precision resistor being placed in an electrostatic potential according to its voltage. The capacitors of the control divider protect the precision resistors of the high-precision divider from transient overloads, e.g. when the direct high voltage is switched on or off (see figure 4).  In the lower part the layout of both precision divider outputs is shown consisting of six precision resistors of R 3 = 140 kΩ each. The control divider is completed by two standard resistors of R 4 = 90 kΩ, which are used to monitor the applied voltage independent of the precision divider.
The shape of the outer edge of the copper electrodes has been optimized in order to provide a homogeneous electrostatic field at the mounting position of each measuring resistor. All parts and structures are designed with edge radii larger than 4 mm in order to reduce the field strength and to prevent internal discharges. At the precision resistor mounts the maximum field strength is less than 5 kV/cm. Between the 35 kV copper electrode and the grounded stainless steel vessel the maximum field strength is less than 16.5 kV/cm. The divider setup is contained in a cylindrical stainless steel vessel filled at standard atmospheric pressure with dry N 2 as insulation gas. Flowing across the precision resistors, the insulation gas is used for temperature stabilization and heat transfer. Due  to its operation in high magnetic fields close to the main MAC-E filter of the KATRIN experiment, the vessel has to be non-magnetic. It is mounted on top of a mobile 19" rack, which contains the equipment for temperature control and the interface to the KATRIN slow control network (see figure 2).

Precision Resistor Selection and Screening Procedure
High precision hermetically sealed and oil-filled resistors based on the Bulk Metal Foil ¶ technology have been chosen to equip the resistor chain of the high-precision divider. Those resistors are specified for voltages of up to 600V, they are available with temperature coefficients ( of ±5 · 10 −6 in one year shelf life + and ±2 · 10 −5 in load life * . This drift is mainly caused by an ageing effect of the resistor material and is supposed to decrease with time. With these values the resistors are about one order of magnitude less precise than the wire-wound resistors used in the PTB standard divider [13], which are not anymore commercially available. The load life stability can be improved by a special pre-ageing procedure, but this procedure has not been applied to the chosen resistors of type VHA-518/11. Under load each resistor shows a characteristic warm-up deviation of the resistance value which is strongly correlated to the internal temperature increase and the temperature coefficient of resistance. This effect is visible even within the specified TCR and VCR values (see figure 5) and can be reduced by a careful screening procedure. Therefore the 100 resistors of 1.84 MΩ for the high-precision divider have been selected from a lot of 200 resistors by investigating their warm-up deviation. The screening procedure has been performed within a shielded chamber (see figure 6) at a stabilized ambient temperature of 25.0 ± 0.1 • C. The measurement circuit that has been used is shown in figure 6; it consists of a calibrated voltage source, one test resistor at a time, the low resistance reference resistor, and a 8   figure 5 it is shown how the initial warm-up deviation stabilizes after about 10 minutes for a typical resistor sample compared to the unstable characteristic of an exceptional bad resistor. Only resistors whose measured warm-up characteristic matches the following limits are used in the setup: • Reproducible and stable operation after ≈ 15 minutes.
During operation at the KATRIN experiment the nominal voltage across each resistor will be less than 200 V in Tritium measurement mode when measuring energies around 18.6 keV, with a maximum of 350 V during calibration runs when investigating the 83m Kr conversion electrons at energies of up to 32 keV. In order to investigate the maximal warm-up effect, the maximal rated voltage of 600 V per resistor has been applied to the test circuit, i.e. a load of 588.2 V at the test resistor. The relative deviation of the resistance value has been monitored for 25 minutes after switching-on. After the initial warm-up process is finished and the resistor reached thermal equilibrium, the resistance value becomes stable, as shown in figure 5 for 588.2 V load and in figure 7 for 490 V load. By analysing the warm-up deviation against the independently measured TCR value a mean temperature increase of ∆T = 8.5 ± 0.2 • C in each 1.84 MΩ resistor can be deduced (see figure 8).
Within their specification resistors with positive and negative TCR exist, thus positive and negative warm-up deviations occur. This property is a result of the Bulk Metal Foil, since it is based on strain gauge technology. The resistor foil with positive TCR is glued on a ceramic substrate, which shows very low thermal expansion. The thermal expansion of the resistor foil leads to a rise in resistance, but since it is glued on the substrate a mechanical stress occurs, which leads to a decrease of its resistance. The low TCR value of the final resistor is achieved by carefully balancing the expansion factors, the glue method, and the substrate material. Since we investigated the resistors within their specifications, we are sensitive to whether the remaining TCR is positive or negative.
By combining pairs of resistors with identical but different signed warm-up deviations, we were able to reduce the combined warm-up deviation by more than one order of magnitude, see figure 7. Finally, pairs or even groups of up to four resistors which in sum show the lowest combined warm-up deviation are used for assembling the resistor chain of the high-precision divider. The resistors of those pairs and groups are mounted in adjacent positions in order to have identical ambient conditions should there be instabilities in the internal temperature. Based on the single resistor results, the combined warm-up deviation of the resistance of all 100 selected resistors should be less than 2 · 10 −8 at a load of 588.2 V per resistor, which is a two orders of magnitude improvement on the average value of a single resistor. The six 140 kΩ resistors providing the divider ratios are chosen from a lot of 15 resistors; they are matched by reducing their combined temperature coefficient of resistance as well. No significant warm-up deviation is expected for those resistors because in this part of the divider setup the voltage drop is less than 10 V per resistor.

Investigation of the High-Precision Divider Chain
At the laboratory for instrument transformers and high voltage of the PTB Braunschweig we investigated the new high voltage divider in comparison with the PTB reference divider MT100, one of the most precise high voltage dividers in the world, at direct voltages between −8 kV and −32 kV. Both dividers (MT100, KATRIN) have been connected to a common precision HV source, thus minimizing the influence of high voltage variations. The MT100 divider has been upgraded with an additional scale factor of 3334:1 in order to cover the whole range of the precision voltmeter (HP 3458A, 10 V range) when applying voltages below 35 kV. The MT100 and KATRIN divider output voltages have been monitored by state-of-the-art 8 1 2 digit voltmeters of type HP 3458A and Fluke 8508A, respectively. A 10 V reference source of type Fluke 732A, calibrated against PTB's Josephson voltage standard [14], has been used to re-calibrate both digital voltmeters in order to compensate gain and offset deviations before and after each measurement run. Thermoelectric voltages in particular have to be taken into account when measuring in the 10 V range at 10 −7 relative precision. In order to reduce any thermoelectric influence, only gold-plated or Cu-Te connectors were used for the measurement chain. In addition, by encapsulating readout contact pairs of the same material, we achieve identical thermal gradients on both polarities, thus thermoelectric voltages cancel. The thermoelectric effect inside the divider housing is expected to be negligible, since the internal temperature of the whole setup is being stabilized. In this configuration the externally applied voltage U HV is related to both divider readings U MT100 , U KATRIN and both scale factors M MT100 , M KATRIN according to For the scale factor of the KATRIN divider this yields: Series of measurements have been performed repeatedly with identical settings, but independent from one another. Data sets of these measurements have been combined by compiling a mean value for each time step after applying the voltage. In order to examine the effect of the scale factor uncertainty on the voltage reading, the relative deviation of the scale factor M = M KATRIN based on a reference value M 0 = M 0,KATRIN is of interest: Depending on the objective of the analysis, the initial, the final, or the average value is used for M 0 . The main focus of the investigation at PTB was the switching-on deviation, the linearity, and long-term stability of M KATRIN . During KATRIN measurement runs the nominal voltage to be monitored is −18.6 kV. In order to take advantage of the whole scale  warm up at -32 kV (5 indep. runs) exponential fit Figure 9. Deviation of the scale factor M for the 1972:1 output during the first seven minutes after applying high voltage of −32 kV. Plotted data points represent the average per time step of five independent measurements performed under identical conditions. The error bars denote the standard deviation of the five measurements at each time step. The exponential fit (dashed line) yields a relative initial warm-up deviation of 1 · 10 −6 during the first two minutes. The exponential time constant is 0.7 minutes. After two minutes the scale factor mean value plus standard deviation keeps stable within a relative deviation of ±5 · 10 −7 .

Initial deviation after switching-on
Directly after applying the high voltage to the divider, a small warm-up deviation is expected. This is due to the residual warm-up effect occurring even after the mutual matching has been performed according to the individual warm-up characteristics and the TCRs of the single resistors. For the MT100 divider it has been demonstrated that this initial warm-up effect is < 5 · 10 −8 independent of the applied voltage [13]. For the KATRIN divider the warm-up deviation has been investigated at −18 kV and −32 kV for both scale factors. In all cases, the relative warm-up deviation of the scale factor is about 1 · 10 −6 during the first two minutes of operation; in addition a reproducibility in the 10 −7 range has been observed relative to the absolute scale factor values. An example is shown in figure 9; here the warm-up effect at the 1972:1 output at −32 kV is plotted as a function of time after applying high voltage. Five independent measurements have been performed, the average of all measurements per time step is plotted as well as statistical error bars. The remaining fluctuations are dominated by noise from the voltmeter reading. The exponential fit (dashed line) gives a relative amplitude of about 1 · 10 −6 for the warm-up effect with an exponential time constant of 0.7 min. The scale factor stabilizes after two minutes -after one it is not quite at equilibrium. This effect has been taken into account in the measurements reported in section 4.2. The remaining deviation of the mean value plus standard deviation keeps stable within a relative deviation of ±5 · 10 −7 . Since there are five measurements averaged this is a direct demonstration of a reproducibility in the 10 −7 range. It can be summarized that after a short warm-up time the initial scale factor deviation is negligible and stabilizes with a relative reproducibility in the low 10 −7 range, independent of the chosen divider output or operation voltage. Additionally, since the warm-up effect measured in 2005 has been reproduced in the 2006 measurements, we conclude that it is stable and reproducible for at least 13 months. Each of the voltage steps has been applied for two minutes, whereas only the data of the second minute has been evaluated due to the initial warm-up effect which is reported in section 4.1. The combined result of all five independent linearity investigations is shown in figure 10. Each plotted scale factor incorporates the average of all measurements for the same voltage setting. As expected, the spread and the uncertainty increase at voltages |U| ≤ 10 kV. At voltages |U| > 10 kV and especially at a wide band around the Tritium endpoint energy, the linearity of the divider is in the 10 −7 range. Here, the spread is less than 3 · 10 −7 , which has been reproduced in all five independent measurement runs. The slope at the high voltage end indicates a voltage dependence that has to be investigated in more detail. Since the wattage increases quadratically with the applied voltage, the self heating of each resistor should increase quadratically as well. The fit function accounts for this case and yields a zero voltage scale factor M(0) and the wattage coefficient ε. In figure 10 the fit of (5) to the data delivers M(0) = 1972.4805(2) and ε = −7.4(1.2) · 10 −10 kV −2 with a reduced χ 2 of 0.8. The result of this evaluation has large uncertainties since the measurement time and statistics of the linearity scan is limited. Therefore, nine independent long-term measurements with a voltage stepping of −8 kV, −16 kV, −24 kV, and −32 kV have been performed. In order to assure stable measurement conditions and higher statistics, each voltage setting has been applied and monitored for four hours. Figure 11 shows the result of all measurements at the 1972:1 output by plotting the evaluated average per measurement and voltage and the overall average per voltage. In order to account for the wattage effect a quadratic fit (5) is applied. It yields a zero voltage scale factor of M(0) = 1972.4807(1) and a wattage coefficient of ε = −8.1(6) · 10 −10 kV −2 which is in agreement with the linearity measurement done earlier. In the voltage range of −8 kV to −32 kV this leads -if unaccounted -to a relative deviation of 0.77(9) · 10 −6 due to the voltage dependence and the wattage effect accordingly. Taking into account the whole voltage range from zero to −35 kV the relative deviation increases to 0.99(10) · 10 −6 , which is still well within the requirements of the KATRIN experiment. For the 3945:1 output one gets a similar result with M(0) = 3944.9612(1) and ε = −7.5(4) · 10 −10 kV −2 , which corresponds to a relative deviation of 0.72(6) · 10 −6 in total for the voltage range −8 kV to −32 kV. Accordingly, the relative deviation over the whole voltage range from zero to −35 kV is 0.91(7) · 10 −6 , which is still well within the requirements of the KATRIN experiment as well. The voltage dependence results for both scale factors agree within their uncertainty and since this result has been measured in 2005 and reproduced in 2006 we can conclude that the effect is stable and that the scale factor deviations due to voltage dependence and wattage effect are well below the uncertainty limit for the KATRIN experiment. Moreover, based on these results linearized voltage coefficients of both scale factors can be derived from 1 M

Linearity and voltage coefficient
for a certain retarding potential U ′ . In the case of KATRIN the most commonly monitored voltage will be U ′ = −18.6 kV which corresponds to the energy filter setting at the tritium endpoint. At this voltage (6)

Temperature dependence
Although the new divider is equipped with a sophisticated temperature control, showing a maximum fluctuation of only 0.1 K, the temperature dependence of both outputs has been investigated at 25 • C and at 30 • C. During this test the environmental temperature in the lab was stable at (21 ± 1) • C. In the beginning, the whole setup has been operated at a stable temperature control set-point of 25 • C. After several hours of stable operation the temperature has been increased to 30 • C by adjusting the temperature control setpoint. After the scale factor reading had settled and the divider has been running under stable conditions again, the high temperature scale factor value was measured for several hours. Finally, the temperature control set-point has been set back to the initial value of 25 • C in order to reproduce the initial scale factor value. The relative temperature deviation found for the 1972:1 output is 1 M ∂M ∂T = −8.1(6) · 10 −8 K −1 . The result for the 3945:1 output is 1 M ∂M ∂T = 1.71(73) · 10 −7 K −1 . Both values are far lower than the temperature coefficients of any commercial high voltage divider, which is again a measure for the quality achieved by the screening and matching procedure of the precision resistors. In order to check the performance of the internal temperature stabilization, the divider has been operated at environmental temperatures between 20 • C and 30 • C with a temperature control set-point of 25 • C. In this test it has been demonstrated that the internal temperature stabilization is able to maintain stable conditions at environmental temperatures of up to 27 • C. Since we expect temperatures of (21±3) • C in the laboratory environment of KATRIN, we can expect a stable operation of the divider without any temperature dependence. We conclude that with respect to the fluctuations of the temperature control, the temperature dependence of both outputs as well as of the complete set-up under laboratory conditions is negligible. On the other hand the difference in sign and value between both scale factors indicates the technical limit of the matching procedure of the precision resistors used in the low voltage tap of the divider.

Medium-term measurements
In order to investigate the scale factor stability during medium-term measurement runs, a series of three 15 hours long overnight measurements has been performed at a voltage of −18 kV and at stable environmental conditions. All measurements have been averaged time-step by time-step, the result is plotted in figure 12. In order to investigate the presence of a time dependent drift of the scale factor, a linear fit has been applied yielding Hence, no significant drift can be observed as long as the environmental conditions are stable. Changing the room temperature conditions results in a small deviation, see the deviation at t > 14 h when the door of the laboratory has been opened in the morning. This is no effect of the voltage divider, but of auxiliary equipment like the digital voltmeters. With this result the one day stability of the divider can be rated as significantly lower than the KATRIN stability limit. Nevertheless, no statement on the scale factor drift or an extrapolation over longer time periods is reasonable, based on this kind of medium-term measurements.

Long-term stability
As pointed out in section 4.4, it was not feasible to derive a significant long-term deviation by a single measurement nor by the entire measurement campaign at PTB. In order to make a reasonable statement on the long-term stability a longer time interval is needed, therefore the absolute scale factor results of both measurement campaigns in  values of both years♯ we derive a relative scale factor drift of 6.0 · 10 −7 /month for the 1972:1 output and 5.6 · 10 −7 /month for the 3945:1 output. These values are supported by a comparison of measurements of the K-32 conversion electrons of 83m Kr in 2006 and 2007 [15]. It is obvious that those small values are not detectable in a single day measurement nor over several days of measurements. A possible explanation for this drift is the ageing effect of the precision resistors, which have not been pre-aged during the production process. According to their specifications (see section 3) this drift will decrease with time, but as of now it requires a re-calibration of the scale factors on a frequent basis at least twice per year in order to keep the relative uncertainty within the KATRIN limit of 3.3 · 10 −6 . In future voltage dividers it is strongly recommended to use pre-aged resistors.

Estimation of uncertainty
The uncertainty of the scale factors of the KATRIN HV divider was estimated according to the ISO Guide [16]. Following the concept of the ISO Guide, a measurement yields only an approximate value of the measurand and the uncertainty of the measurement characterizes the interval that encompasses a large fraction of all probable values (coverage probability). In general, the value and uncertainty of a measurand depends on a number of input quantities, and their functional relationship is expressed by the model function. Table 1 shows an example of estimating the uncertainty for the 1972:1 output of the KATRIN HV divider at −18.6 kV, i.e. the voltage at the endpoint of the tritium β-spectrum. The model equation for the divider scale factor and its uncertainty determined by comparison with the PTB standard divider is based on (3). In addition to the uncertainty of the PTB standard divider [13] five uncertainty contributions have been considered. The uncertainty was calculated under the assumption that there is no correlation among the input quantities, using a commercial software [17]. The scale factor of the KATRIN HV divider and its expanded uncertainty at −18.6 kV is:  (7). This illustrates that the error calculation of (7) is correct. Applying the long-term stability corrections as described in section 4.5, we conclude that the divider fulfils the requirement on the stability of the KATRIN HV monitoring system.

Conclusion and outlook
Summarizing the investigation of the KATRIN precision high voltage divider compared with the reference divider of PTB Braunschweig, it is obvious that the resistor screening and matching according to the warm-up deviation was successful. It was possible to improve the stability of the combined set-up by more than one order of magnitude compared to the properties of a single resistor. In addition the temperature dependence of the divider is one order of magnitude lower than that of a single resistor. Due to the temperature stabilization of the whole set-up and its independence of the lab temperature in a certain range, the net temperature dependence of the voltage reading is negligible. The warm-up deviation of the KATRIN divider has been reduced to about 1 · 10 −6 relative to the scale factor and remained stable over all measurements in 2005 and 2006. The voltage and wattage dependence of the scale factors over the specified  Long-term stability 6.0 · 10 −7 /month 5.6 · 10 −7 /month voltage range has even been reduced to a relative deviation of less than 1 · 10 −6 if not corrected, otherwise it is even smaller. Moreover, at the voltage setting for tritium endpoint investigations at −18.6 kV the linearized voltage coefficient is negligible. With these properties the new divider fulfils the requirement of the KATRIN experiment of a relative stability of less than 3.3 · 10 −6 . Especially during one cycle of data taking, i.e. one cycle of the source of 60 days, the precision and stability is better than specified. But since a long-term drift of the setup of 6.0·10 −7 /month (1972:1 output) has been observed, it is recommended to re-calibrate the scale factors twice a year or to perform an on-line calibration during data taking in order to compare different data taking cycles with each other. The latter will be done with the KATRIN monitor spectrometer in parallel with the KATRIN main beam-line. While measuring the tritium spectrum at the main beam-line, it is intended to monitor a mono-energetic conversion electron source based on the isomeric state of the isotope 83m Kr at the monitor spectrometer. In this way it is possible to monitor the scale factor drift of the divider and to re-calibrate it frequently. However, independent re-calibration investigations will be performed at PTB as well. For redundancy reasons and in order to prevent down-time of the KATRIN measurement during the calibration at PTB, a second divider is being built. Several improvements applied to its design, especially the use of pre-aged and optimized precision resistors of the same brand, promise further improvement in overall and in long-term stability.