- Email: [email protected]
Measurement of the pressure differences in a large chamber where the pressure is generated dynamically
Vacuum 67 (2002) 333–338
Measurement of the pressure differences in a large chamber where the pressure is generated dynamically a $ L. Peksaa,*, T. Gronycha, P. Repa , J. Tesar$b a
! 2, 180 00 Praha 8, Czech Republic Faculty of Math & Physics, Charles University of Prague, V Hole$sovi$ckach b Czech Institute of Metrology, Okru$zn!ı 31, 638 00 Brno, Czech Republic
Abstract The need to know the pressure in relatively large vacuum chambers arises at different measurements (calibration of the vacuum gauges, out-gassing measurements, TDS, etc.). Although the uniformity of the gas pressure over some areas in the chamber is crucial for the accuracy of the measurement, it is checked mainly by means of theoretical computations. The experimental determination of the pressure differences between various gauge positions at a chamber of cylindrical shape is described in the paper. The pressure in the chamber was generated dynamically by adjustable gas flow introduced into the chamber, simultaneously pumped by a constant pumping speed. The measurements were performed in the pressure range 1 103–1 106 mbar by means of a spinning rotor gauge and two ionisation gauges; they were connected to various positions and during measurements, mutually changed in order to exclude the influence of the difference between them. The differences between positions at different levels along the axis (i.e. along the gas flow direction) as well as the differences between positions in the same level were followed. The method of data evaluation enabling to recognise the influence of the non-linearities of the gauge was developed. The differences in the order of some per cent between positions in the same level were observed. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Pressure measurement; Pressure distribution; Vacuum gauge calibration
1. Introduction The calibration of the vacuum gauges according to the secondary normal is usually performed in a vacuum chamber where the normal gauge and the calibrated one run simultaneously and their readings are compared while the pressure in the chamber is (usually stepwise) varied over the whole calibration range. One of the most efficient and convenient way is to generate the pressure *Corresponding author. Tel.: +420-2-2191-2302; fax: +4202-6885-095. E-mail address: [email protected] (L. Peksa).
dynamically, i.e. to admit the calibration gas into the chamber and to pump it simultaneously. Two important assumptions should be satisfied in order to justify this process. The gas has to be considered at least locally being near equilibrium state with defined pressure and the pressure is uniform over the positions of the calibrated vacuum gauge and the standard gauge. There are two sources of nonequilibrium and the pressure non-uniformity in the chamber: inlet of the gas and its sink in the pump. In order to suppress their influence, the chamber has to have a suitable shape, it has to be sufficiently large, the gas after admission should be scattered by impinging on the walls, etc. The
0042-207X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 2 ) 0 0 2 2 2 - 1
334
L. Peksa et al. / Vacuum 67 (2002) 333–338
uniformity of the pressure is then checked usually theoretically e.g. by Monte Carlo calculations [1]. These calculations are based on the assumptions of the correctness of the mathematical model (diffusive scattering on the walls, velocity and angular distribution of the gas molecules at the inlet) and the input data about geometrical arrangement, gas purity, temperature distribution, etc. Only seldom are these assumptions checked experimentally [2] and it is difficult to reach sufficient accuracy at such measurements to observe small deviations from the assumptions. The aim of the measurements described in this paper was to check immediately the pressure differences between various positions in a vacuum calibration chamber, where the pressure is generated dynamically.
2. The used vacuum gauges The first attempt to perform such a measurement was described in [3]. The studied differences can be of the order of per cent or tenths of per cent and it is useful to check a very wide range of pressure. Theoretically, such a measurement can be performed using a pair of quite identical gauges by simply measuring pressure simultaneously at two checked positions. Extremely good gauges for this purpose are under certain circumstances two spinning rotor gauges (SRG) but the measurement at a low pressure is influenced by offset and noise caused by vibrations of the measuring apparatus (from the pumps, movement in the laboratory, etc.); thus, in this way, measurement can be performed only at pressure 105opo103 mbar. Moreover, the SRG cannot be immersed into the chamber and thus the pressure differences can occur even at the same flange if a nude gauge is connected instead of the SRG. It is shown in [3] that the gauges need not be identical; it is sufficient if the gauges are linear and stable. Hot cathode ionisation gauges are vibration-resistant, they are linear within certain pressure limits (well above the X-ray limit and the EID limit but below secondary ionisation starts) only the stability, especially the sensitivity changes between two runs after venting apparatus
and the changing gauge position, is questionable. In order to overcome these difficulties, two hot cathode ionisation gauges and one spinning rotor gauge (2 IV+SRG) were used.
3. The used apparatus and the process of measurement The chamber for the gauge comparison was of cylindrical shape with nine positions for gauge connection arranged on two levels. They were denoted with letters A–I. The total volume of the chamber was approximately 40 l and this did not change during experiments, because the same vacuum components were always connected to the various flanges. The chamber was pumped by a turbomolecular pump with a pumping speed of 130 l s1 for nitrogen backed by a rotary vane pump in the usual arrangement with a bypass. Between the chamber and the pump there was a gate valve. Full available pumping speed was used, nevertheless, the ratio of the exit orifice area to the total (geometrical) area of the chamber wall was only approximately 0.013. The ultimate pressure of the turbomolecular pump, according to the manufacturer, is 2 1010 mbar, the lowest pressure in the chamber reached during the tests was 7 1010 mbar, and the total leak rate was approximately 1.6 108 mbar l s1. A fine control variable leak valve (VLV) for the calibration gas admission was connected to position A on the upper level of the chamber. A thin bent tube behind the VLV inside the chamber directed the gas stream against the ceiling of the chamber. Argon of 99.996% purity was used as the calibration (test) gas. The VLV could be entirely closed by an integrated serial valve. The vacuum gauges (2 IV+SRG) were mounted at various positions on the lower level of the chamber. Their readings should have been recorded at the same time and at various pressures set by the VLV. After scanning the whole pressure range the positions of some gauges were changed. It was observed that after any touch to the apparatus including adjusting the VLV, the reading of SRG was disturbed and the return to the
L. Peksa et al. / Vacuum 67 (2002) 333–338
correct value lasted more than 10–15 min. That is why the process that did not need any touch to apparatus and the corresponding arrangement were used. A small chamber of volume V consisting of some vacuum fittings, diaphragm gauge and an auxiliary volume was mounted at the input of the VLV. The process of the measurement was as follows. The chamber was baked out 24 h after mounting the gauges on the measuring positions. Then, after cooling down the chamber to the ambient temperature and measuring the background pressure, the small chamber V was several times flushed out by argon gas and pumped down by the diaphragm pump. Finally, the volume V was filled by pure argon up to the pressure 1000 mbar. The VLV was opened so that the pressure in the chamber was between 103 and 102 mbar. No more gas was supplied into the volume V ; but it was pumped out through the VLV into the chamber, which was pumped by turbomolecular pump. Thus, the gas pressure in the volume V decreased slowly, also, both the gas throughput through the VLV and the gas pressure in the chamber decreased. The pressure drop over the whole pressure range lasted approximately 2 days. The readings of the gauges (2 IV+SRG) were recorded regularly after fixed
335
time intervals by computer during this time. No touch to the apparatus was necessary, but usually the VLV was opened more after several hours to accelerate very slow pressure drop at a small pressure in the volume V : It was easy to remove a small part of the data set damaged after this touch. After the pressure in the chamber decreased below 107 mbar, the VLV was closed entirely and the background pressure was checked again. It was always at least 10 times lower than the lowest pressure when the VLV was opened.
4. The obtained data treatment The recorded data were the time-pressure curves. For the data treatment it was necessary to have the dependency of gauge readings on the pressure in the chamber. Due to the noise at a low pressure in SRG readings, the IV curves are much more monotonous. That is why the reading of IV1 was chosen as the measure of pressure in the chamber. Then the time–pressure curves can be replotted as shown in Fig. 1. The used gauges are assumed to be linear, it means their reading is dependent on the pressure in the point of measuring structure according to
Fig. 1. Readings of the SRG, IV1 and IV2 plotted versus readings of IV1—an example. IV1 was at the position D, IV2 was at the position F and SRG was at the position E.
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L. Peksa et al. / Vacuum 67 (2002) 333–338
readings of the gauges are
the formula Rgauge ¼ kp þ B;
ð1Þ
where k is a constant ‘‘sensitivity’’ and B is offset. Since SRG was calibrated as transfer normal, kSRG ¼ 1: BSRG is its offset, discussed in many papers about this gauge, plus other external influences decelerating the rotation of the ball. (One can hardly imagine any external vibrations accelerating the rotation.) This offset is graphically visible in Fig. 1. It corresponds to some pressure; let us denote it as BSRG ¼ px : k of the ionisation gauges ought to be also near 1, which is determined by gauge calibration. Since it is considered already as kSRG ¼ 1 and pressure differences between single calibration positions are asumed, kIV1 and kIV2 are unknown. The offset (i.e. residual readings caused by X-ray current EID current, etc.) of the ionisation gauges, on the contrary, can be neglected, i.e. considered as 0. It is caused by X-ray current, EID current, etc., which are much less than the collector currents measured at the pressures during our experiments. Let us consider that the pressure at the position of the SRG is p and the pressure at the position of the IV is q-times higher and Dp greater (q is, nevertheless, near 1 and Dp near 0). Then the
RSRG ¼ p þ px ;
ð2Þ
RIV ¼ kðqp þ DpÞ:
ð3Þ
Then the values of RSRG can be calculated from the curves of IV1 and IV2 according to the formula RIV Dp ð4aÞ þ px RSRG ¼ q kq or RSRG px þ
Dp RIV ¼ : q kq
ð4bÞ
The term px ðDp=kqÞ is of the order of 107 mbar (it is visible in Fig. 1), thus, kq can be estimated from the gauge readings at a pressure of about 1 104 mbar. Dividing the IV1 and IV2 readings by these appropriate values kq and adding a suitable constant, the curves in Fig. 1 become identical—see Fig. 2. The added constant (4.1 107 mbar in Fig. 2) is the first estimation of the term px ðDp=kqÞ which is used at the lefthand side of Eq. (4b). In Fig. 2, it is visible that the curves in the range 4 106–3 104 mbar (reading RIV1 ) that are quite identical differ remarkably from each other
Fig. 2. An example of the treatment of the data plotted in Fig. 1. Readings of SRG recorded at SRG and computed from readings of IV1 and IV2.
L. Peksa et al. / Vacuum 67 (2002) 333–338
above 3 104 mbar. The curve of the SRG here is the lowest. The reason is higher sensitivities of ionisation gauges are caused due to the ionisation by secondary electrons. 4.1. Evaluation of kq Knowing the estimation of the term px ðDp=kqÞ the value kq can be calculated from the data accuretely. Knowing better the value of kq; the term px ðDp=kqÞ can be determined again more accurately and vice verse—the best result can be reached in an iterative way. Since only data in the range 3 106– 3 104 mbar (reading RIV1 ) were taken to determine the value kq; the influence of the changes of the term px ðDp=kqÞ here is only small; thus the accuracy after the first step was sufficient. Let us denote the left-hand side of Eq. (4b) as RSRGCORR : The constant kq has to satisfy condition (5) 2 Z p2 d RIV RSRGCORR dp ¼ 0: ð5Þ dðkqÞ p1 kq (Ideally, the curves RðpÞ=kq and RSRGCORR ðpÞ should be identical. Condition (5) has the least area between these two curves.) In the case of discrete values of p 2 d X RIVi Dpi RSRGCORRi ¼ 0: ð6Þ dðkqÞ kq The data were recorded in fixed time intervals and the pressure differences Dpi decreased—they can be considered as approximately proportional to the pressure. The reading IV1 is taken as pressure.
337
Thus, X is 1 or 2, respectively, for k1 at ionisation gauge IV1 or k2 at ionisation gauge IV2, respectively, P 2 RIVX RIV1 kX q ¼ P : ð7Þ RIVX RSRGCORR RIV1
5. Results The following results in Table 1 were obtained from recorded data by means of the abovedescribed process (the number 1 or 2 at k denotes the number of the ionisation gauge, the first letter after q denotes the position of the ionisation gauge at the chamber, the second letter denotes the position of the SRG t the same time). Positions D, F and H are all in the lower level of the chamber by 1201. Relative deviations of the single values kX q E from a mean value ððkX qDE þ kX qFE þ kX qHEÞ=3 ¼ 100%Þ are shown in Fig. 3. It seems that the pressure differences of order of per cent may occur between the positions.
6. Conclusions It is possible to measure the pressure distribution in vacuum chambers, where the pressure is generated dynamically, e.g. by the above-described method and in the cases of need, e.g. at an accurate calibration to use correction. In vacuum chambers where the pressure is generated dynamically, measurable pressure differences may occur not only between positions at
Table 1 Products kq
Mean Std. error
k1qIE
k1qHE
k1qFE
k1qDE
k1qDF
k2qFE
k2qHE
k2qDE
k2qEF
1.7875
1.7603 1.7812
1.7471 1.7706
1.8275 1.8168
1.7921
0.9881 0.9733
1.0051 0.9939
0.9237
1.7707 0.0105
1.7589 0.0117
1.8221 0.0054
0.9657 1.0065 0.9834 0.9852 0.0118
0.9807 0.0074
0.9995 0.0056
The subscript figure 1 or 2 after k denotes the number of the ionisation gauge, k is its sensitivity. The first letter after q denotes the position of the ionisation gauge, the second letter denotes the position of the SRG. q is the ratio between the pressure at the position of the ionisation gauge and the pressure at the position of the SRG.
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different levels, but also between the points considered being symmetrical according to the connecting line between the inlet and the sink of gas due to imperfect symmetry.
Acknowledgements This research was supported by GACR Grant No. 202/01/0668.
References Fig. 3. Relative pressure deviations from the mean value at three positions in the lower level of the chamber. The error bars correspond to the standard error se according to the formula qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P se ¼ ðDxÞ2 =nðn 1Þ:
[1] Nesterov SB, Vassiliev YuK, Kryukov AP. Vacuum 1991;53:193–6. [2] Jitschin W, Reich GJ. Vac Sci Technol A 1991;9:2752–6. [3] Repa P, Cespiro Z, Peksa L, Gronych T. Tesar J Metrologia 1999;36:551–4.
Measurement of the pressure differences in a large chamber where the pressure is generated dynamically a $ L. Peksaa,*, T. Gronycha, P. Repa , J. Tesar$b a
! 2, 180 00 Praha 8, Czech Republic Faculty of Math & Physics, Charles University of Prague, V Hole$sovi$ckach b Czech Institute of Metrology, Okru$zn!ı 31, 638 00 Brno, Czech Republic
Abstract The need to know the pressure in relatively large vacuum chambers arises at different measurements (calibration of the vacuum gauges, out-gassing measurements, TDS, etc.). Although the uniformity of the gas pressure over some areas in the chamber is crucial for the accuracy of the measurement, it is checked mainly by means of theoretical computations. The experimental determination of the pressure differences between various gauge positions at a chamber of cylindrical shape is described in the paper. The pressure in the chamber was generated dynamically by adjustable gas flow introduced into the chamber, simultaneously pumped by a constant pumping speed. The measurements were performed in the pressure range 1 103–1 106 mbar by means of a spinning rotor gauge and two ionisation gauges; they were connected to various positions and during measurements, mutually changed in order to exclude the influence of the difference between them. The differences between positions at different levels along the axis (i.e. along the gas flow direction) as well as the differences between positions in the same level were followed. The method of data evaluation enabling to recognise the influence of the non-linearities of the gauge was developed. The differences in the order of some per cent between positions in the same level were observed. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Pressure measurement; Pressure distribution; Vacuum gauge calibration
1. Introduction The calibration of the vacuum gauges according to the secondary normal is usually performed in a vacuum chamber where the normal gauge and the calibrated one run simultaneously and their readings are compared while the pressure in the chamber is (usually stepwise) varied over the whole calibration range. One of the most efficient and convenient way is to generate the pressure *Corresponding author. Tel.: +420-2-2191-2302; fax: +4202-6885-095. E-mail address: [email protected] (L. Peksa).
dynamically, i.e. to admit the calibration gas into the chamber and to pump it simultaneously. Two important assumptions should be satisfied in order to justify this process. The gas has to be considered at least locally being near equilibrium state with defined pressure and the pressure is uniform over the positions of the calibrated vacuum gauge and the standard gauge. There are two sources of nonequilibrium and the pressure non-uniformity in the chamber: inlet of the gas and its sink in the pump. In order to suppress their influence, the chamber has to have a suitable shape, it has to be sufficiently large, the gas after admission should be scattered by impinging on the walls, etc. The
0042-207X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 2 ) 0 0 2 2 2 - 1
334
L. Peksa et al. / Vacuum 67 (2002) 333–338
uniformity of the pressure is then checked usually theoretically e.g. by Monte Carlo calculations [1]. These calculations are based on the assumptions of the correctness of the mathematical model (diffusive scattering on the walls, velocity and angular distribution of the gas molecules at the inlet) and the input data about geometrical arrangement, gas purity, temperature distribution, etc. Only seldom are these assumptions checked experimentally [2] and it is difficult to reach sufficient accuracy at such measurements to observe small deviations from the assumptions. The aim of the measurements described in this paper was to check immediately the pressure differences between various positions in a vacuum calibration chamber, where the pressure is generated dynamically.
2. The used vacuum gauges The first attempt to perform such a measurement was described in [3]. The studied differences can be of the order of per cent or tenths of per cent and it is useful to check a very wide range of pressure. Theoretically, such a measurement can be performed using a pair of quite identical gauges by simply measuring pressure simultaneously at two checked positions. Extremely good gauges for this purpose are under certain circumstances two spinning rotor gauges (SRG) but the measurement at a low pressure is influenced by offset and noise caused by vibrations of the measuring apparatus (from the pumps, movement in the laboratory, etc.); thus, in this way, measurement can be performed only at pressure 105opo103 mbar. Moreover, the SRG cannot be immersed into the chamber and thus the pressure differences can occur even at the same flange if a nude gauge is connected instead of the SRG. It is shown in [3] that the gauges need not be identical; it is sufficient if the gauges are linear and stable. Hot cathode ionisation gauges are vibration-resistant, they are linear within certain pressure limits (well above the X-ray limit and the EID limit but below secondary ionisation starts) only the stability, especially the sensitivity changes between two runs after venting apparatus
and the changing gauge position, is questionable. In order to overcome these difficulties, two hot cathode ionisation gauges and one spinning rotor gauge (2 IV+SRG) were used.
3. The used apparatus and the process of measurement The chamber for the gauge comparison was of cylindrical shape with nine positions for gauge connection arranged on two levels. They were denoted with letters A–I. The total volume of the chamber was approximately 40 l and this did not change during experiments, because the same vacuum components were always connected to the various flanges. The chamber was pumped by a turbomolecular pump with a pumping speed of 130 l s1 for nitrogen backed by a rotary vane pump in the usual arrangement with a bypass. Between the chamber and the pump there was a gate valve. Full available pumping speed was used, nevertheless, the ratio of the exit orifice area to the total (geometrical) area of the chamber wall was only approximately 0.013. The ultimate pressure of the turbomolecular pump, according to the manufacturer, is 2 1010 mbar, the lowest pressure in the chamber reached during the tests was 7 1010 mbar, and the total leak rate was approximately 1.6 108 mbar l s1. A fine control variable leak valve (VLV) for the calibration gas admission was connected to position A on the upper level of the chamber. A thin bent tube behind the VLV inside the chamber directed the gas stream against the ceiling of the chamber. Argon of 99.996% purity was used as the calibration (test) gas. The VLV could be entirely closed by an integrated serial valve. The vacuum gauges (2 IV+SRG) were mounted at various positions on the lower level of the chamber. Their readings should have been recorded at the same time and at various pressures set by the VLV. After scanning the whole pressure range the positions of some gauges were changed. It was observed that after any touch to the apparatus including adjusting the VLV, the reading of SRG was disturbed and the return to the
L. Peksa et al. / Vacuum 67 (2002) 333–338
correct value lasted more than 10–15 min. That is why the process that did not need any touch to apparatus and the corresponding arrangement were used. A small chamber of volume V consisting of some vacuum fittings, diaphragm gauge and an auxiliary volume was mounted at the input of the VLV. The process of the measurement was as follows. The chamber was baked out 24 h after mounting the gauges on the measuring positions. Then, after cooling down the chamber to the ambient temperature and measuring the background pressure, the small chamber V was several times flushed out by argon gas and pumped down by the diaphragm pump. Finally, the volume V was filled by pure argon up to the pressure 1000 mbar. The VLV was opened so that the pressure in the chamber was between 103 and 102 mbar. No more gas was supplied into the volume V ; but it was pumped out through the VLV into the chamber, which was pumped by turbomolecular pump. Thus, the gas pressure in the volume V decreased slowly, also, both the gas throughput through the VLV and the gas pressure in the chamber decreased. The pressure drop over the whole pressure range lasted approximately 2 days. The readings of the gauges (2 IV+SRG) were recorded regularly after fixed
335
time intervals by computer during this time. No touch to the apparatus was necessary, but usually the VLV was opened more after several hours to accelerate very slow pressure drop at a small pressure in the volume V : It was easy to remove a small part of the data set damaged after this touch. After the pressure in the chamber decreased below 107 mbar, the VLV was closed entirely and the background pressure was checked again. It was always at least 10 times lower than the lowest pressure when the VLV was opened.
4. The obtained data treatment The recorded data were the time-pressure curves. For the data treatment it was necessary to have the dependency of gauge readings on the pressure in the chamber. Due to the noise at a low pressure in SRG readings, the IV curves are much more monotonous. That is why the reading of IV1 was chosen as the measure of pressure in the chamber. Then the time–pressure curves can be replotted as shown in Fig. 1. The used gauges are assumed to be linear, it means their reading is dependent on the pressure in the point of measuring structure according to
Fig. 1. Readings of the SRG, IV1 and IV2 plotted versus readings of IV1—an example. IV1 was at the position D, IV2 was at the position F and SRG was at the position E.
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L. Peksa et al. / Vacuum 67 (2002) 333–338
readings of the gauges are
the formula Rgauge ¼ kp þ B;
ð1Þ
where k is a constant ‘‘sensitivity’’ and B is offset. Since SRG was calibrated as transfer normal, kSRG ¼ 1: BSRG is its offset, discussed in many papers about this gauge, plus other external influences decelerating the rotation of the ball. (One can hardly imagine any external vibrations accelerating the rotation.) This offset is graphically visible in Fig. 1. It corresponds to some pressure; let us denote it as BSRG ¼ px : k of the ionisation gauges ought to be also near 1, which is determined by gauge calibration. Since it is considered already as kSRG ¼ 1 and pressure differences between single calibration positions are asumed, kIV1 and kIV2 are unknown. The offset (i.e. residual readings caused by X-ray current EID current, etc.) of the ionisation gauges, on the contrary, can be neglected, i.e. considered as 0. It is caused by X-ray current, EID current, etc., which are much less than the collector currents measured at the pressures during our experiments. Let us consider that the pressure at the position of the SRG is p and the pressure at the position of the IV is q-times higher and Dp greater (q is, nevertheless, near 1 and Dp near 0). Then the
RSRG ¼ p þ px ;
ð2Þ
RIV ¼ kðqp þ DpÞ:
ð3Þ
Then the values of RSRG can be calculated from the curves of IV1 and IV2 according to the formula RIV Dp ð4aÞ þ px RSRG ¼ q kq or RSRG px þ
Dp RIV ¼ : q kq
ð4bÞ
The term px ðDp=kqÞ is of the order of 107 mbar (it is visible in Fig. 1), thus, kq can be estimated from the gauge readings at a pressure of about 1 104 mbar. Dividing the IV1 and IV2 readings by these appropriate values kq and adding a suitable constant, the curves in Fig. 1 become identical—see Fig. 2. The added constant (4.1 107 mbar in Fig. 2) is the first estimation of the term px ðDp=kqÞ which is used at the lefthand side of Eq. (4b). In Fig. 2, it is visible that the curves in the range 4 106–3 104 mbar (reading RIV1 ) that are quite identical differ remarkably from each other
Fig. 2. An example of the treatment of the data plotted in Fig. 1. Readings of SRG recorded at SRG and computed from readings of IV1 and IV2.
L. Peksa et al. / Vacuum 67 (2002) 333–338
above 3 104 mbar. The curve of the SRG here is the lowest. The reason is higher sensitivities of ionisation gauges are caused due to the ionisation by secondary electrons. 4.1. Evaluation of kq Knowing the estimation of the term px ðDp=kqÞ the value kq can be calculated from the data accuretely. Knowing better the value of kq; the term px ðDp=kqÞ can be determined again more accurately and vice verse—the best result can be reached in an iterative way. Since only data in the range 3 106– 3 104 mbar (reading RIV1 ) were taken to determine the value kq; the influence of the changes of the term px ðDp=kqÞ here is only small; thus the accuracy after the first step was sufficient. Let us denote the left-hand side of Eq. (4b) as RSRGCORR : The constant kq has to satisfy condition (5) 2 Z p2 d RIV RSRGCORR dp ¼ 0: ð5Þ dðkqÞ p1 kq (Ideally, the curves RðpÞ=kq and RSRGCORR ðpÞ should be identical. Condition (5) has the least area between these two curves.) In the case of discrete values of p 2 d X RIVi Dpi RSRGCORRi ¼ 0: ð6Þ dðkqÞ kq The data were recorded in fixed time intervals and the pressure differences Dpi decreased—they can be considered as approximately proportional to the pressure. The reading IV1 is taken as pressure.
337
Thus, X is 1 or 2, respectively, for k1 at ionisation gauge IV1 or k2 at ionisation gauge IV2, respectively, P 2 RIVX RIV1 kX q ¼ P : ð7Þ RIVX RSRGCORR RIV1
5. Results The following results in Table 1 were obtained from recorded data by means of the abovedescribed process (the number 1 or 2 at k denotes the number of the ionisation gauge, the first letter after q denotes the position of the ionisation gauge at the chamber, the second letter denotes the position of the SRG t the same time). Positions D, F and H are all in the lower level of the chamber by 1201. Relative deviations of the single values kX q E from a mean value ððkX qDE þ kX qFE þ kX qHEÞ=3 ¼ 100%Þ are shown in Fig. 3. It seems that the pressure differences of order of per cent may occur between the positions.
6. Conclusions It is possible to measure the pressure distribution in vacuum chambers, where the pressure is generated dynamically, e.g. by the above-described method and in the cases of need, e.g. at an accurate calibration to use correction. In vacuum chambers where the pressure is generated dynamically, measurable pressure differences may occur not only between positions at
Table 1 Products kq
Mean Std. error
k1qIE
k1qHE
k1qFE
k1qDE
k1qDF
k2qFE
k2qHE
k2qDE
k2qEF
1.7875
1.7603 1.7812
1.7471 1.7706
1.8275 1.8168
1.7921
0.9881 0.9733
1.0051 0.9939
0.9237
1.7707 0.0105
1.7589 0.0117
1.8221 0.0054
0.9657 1.0065 0.9834 0.9852 0.0118
0.9807 0.0074
0.9995 0.0056
The subscript figure 1 or 2 after k denotes the number of the ionisation gauge, k is its sensitivity. The first letter after q denotes the position of the ionisation gauge, the second letter denotes the position of the SRG. q is the ratio between the pressure at the position of the ionisation gauge and the pressure at the position of the SRG.
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L. Peksa et al. / Vacuum 67 (2002) 333–338
different levels, but also between the points considered being symmetrical according to the connecting line between the inlet and the sink of gas due to imperfect symmetry.
Acknowledgements This research was supported by GACR Grant No. 202/01/0668.
References Fig. 3. Relative pressure deviations from the mean value at three positions in the lower level of the chamber. The error bars correspond to the standard error se according to the formula qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P se ¼ ðDxÞ2 =nðn 1Þ:
[1] Nesterov SB, Vassiliev YuK, Kryukov AP. Vacuum 1991;53:193–6. [2] Jitschin W, Reich GJ. Vac Sci Technol A 1991;9:2752–6. [3] Repa P, Cespiro Z, Peksa L, Gronych T. Tesar J Metrologia 1999;36:551–4.