- Email: [email protected]
Investigation of the magnetic field fluctuation and implementation of a temperature and pressure stabilization at SHIPTRAP
Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Investigation of the magnetic field fluctuation and implementation of a temperature and pressure stabilization at SHIPTRAP C. Droese a,, M. Block b, M. Dworschak b, S. Eliseev c, E. Minaya Ramirez d, D. Nesterenko e, L. Schweikhard a a
Ernst-Moritz-Arndt-Universit¨ at, Institut f¨ ur Physik, 17489 Greifswald, Germany GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany c Max-Planck-Institut f¨ ur Kernphysik, Saupfercheckweg 1, 69117 Heiderlberg, Germany d Helmholtz-Institut Mainz, Johannes Gutenberg-Universit¨ at, 55099 Mainz, Germany e PNPI RAS, Gatchina, Leningrad district 188300, Russia b
a r t i c l e in f o
abstract
Article history: Received 12 October 2010 Received in revised form 15 December 2010 Accepted 18 December 2010 Available online 29 December 2010
Penning traps have proven to be powerful tools for the determination of nuclear masses with high accuracy. A crucial parameter for precision mass measurements in Penning traps is the accurate determination of the magnetic-field strength. However, the magnetic field of a superconducting magnet is not constant in time, but changes due to intrinsic effects of the solenoid and external perturbations. These effects have been investigated for SHIPTRAP. Furthermore, a stabilization of the temperature in the magnet bore as well as of the pressure in the liquid-helium cryostat has been implemented. Thus, the magnetic-field related uncertainties have been reduced to 7(6) 10 11/h. & 2010 Elsevier B.V. All rights reserved.
Keywords: Penning traps Magnetic-field stabilization Temperature stabilization Pressure stabilization SHIPTRAP
1. Introduction
determined via a measurement of the cyclotron frequency
Accurate mass values of radionuclides give valuable information about nuclear-structure properties such as shell closures, halos and pairing effects [1,2]. They are also used to benchmark nuclear models [1]. In astrophysics mass values with uncertainties of less than dm=m 107 are necessary, e.g. for investigations on the rapid-neutron-capture process (r-process [3]) and the rapid-proton-capture process (rp-process [4]). Furthermore, mass values are important input parameters for investigations of the weak interaction [5]. Mass measurements with relative uncertainties of less than dm=m 108 of superallowed b emitters and their daughter nuclei [6] enable tests of the conserved-vector-current hypothesis and the unitarity of the Cabibbo–Kobayashi–Maskawa quarkmixing matrix [7]. Penning traps around the world [8,9] have turned out to be the tools of choice to reach these levels of accuracy. The ions of interest are trapped in a homogeneous magnetic field B and a static electric field. By use of the time-of-flight ion-cyclotron-resonance (ToFICR) detection technique [10] the mass m of an ion with charge q is
nc ¼
Corresponding author. Tel.: +49 6151712114; fax: +49 6151713463.
E-mail address: [email protected] (C. Droese). 0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.12.176
1 qB : 2p m
ð1Þ
Eq. (1) can be used for an accurate mass determination only if the magnetic-field strength at the time of the measurement is known or can be derived. Since the magnetic field is not constant in time, calibration measurements using reference ions with well-known mass are performed before and after each measurement of the nuclide of interest. From these reference measurements the magnetic-field strength at the time of the cyclotron-frequency determination of the nuclide of interest is estimated by linear interpolation [11]. The interpolation takes all linear effects into account such as the so called intrinsic flux creep [12,13]. However, there are several perturbations which are not linear in time and thus lead to a deviation of the actual value from the interpolated. This adds a systematic uncertainty to the final mass value. The production rate of radionuclides investigated at SHIPTRAP can be below one per minute. Thus, with a total efficiency of the whole SHIPTRAP apparatus of about 3% [14] and a minimum number of detected ions of about 50 to obtain a reasonable time-of-flight resonance, the measurement time can add up to several hours. For such long measurement times fluctuations of the magnetic field limit the achievable mass uncertainty [15]. Therefore, regulation systems for the temperature in the bore and the
158
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
pressure in the cryostat of the superconducting solenoid were implemented in a similar way as reported for SMILETRAP [16,17] and ISOLTRAP [18]. A description of the SHIPTRAP experiment is presented in Section 2. Its magnetic-field fluctuations in the absence of the stabilization system are described in Section 3. The SHIPTRAP stabilization systems and their influence on the magnetic field are illustrated in Sections 4 and 5.
2. Experimental setup and precision mass measurements at SHIPTRAP The SHIPTRAP setup [15] is schematically displayed in Fig. 1. The ion beam from the velocity filter SHIP [19] is stopped in a gas cell [20] in ultra-high purity helium (99.9999% purity) at a pressure of 50 mbar. The ions are extracted from the gas cell via a funnel structure through an extraction nozzle and enter the extraction radiofrequency quadrupole (RFQ). The extraction RFQ is followed by a buncher. Both are linear Paul traps [21] filled with helium as the buffer gas. In the buncher the ions are further cooled and accumulated. After a storage time of several milliseconds up to seconds the charged particles are ejected as bunches into the double Penning-trap system [22]. Both cylindrical Penning traps, separated by a 1.5-mm diameter pumping barrier [23], are placed in a 7-T superconducting magnet (MAGNEX SCIENTIFIC MRBR 7.0/160/as [24]). The first trap is a preparation trap where unwanted ions are removed and the ions of interest are centered using mass selective buffer-gas cooling [25]. In the second trap cyclotron-frequency measurements are performed. To this end, the ToF-ICR technique [10] is applied. Fig. 2 shows a cyclotron-frequency resonance curve of 133 Cs þ delivered from a surface ion source. The atomic mass m of a nuclide is determined from ions of charge state z by comparing the measured cyclotron frequency nc to the cyclotron frequency nc,ref of an ion with a well-known mass mref and charge qref ¼ zref e, with the elementary charge e. Typically 133 Cs þ , other alkali ions, or carbon cluster ions [11,27,28] with a similar mass-to-charge ratio as the nuclides of interest are chosen as reference ions. This leads to the following equation: m¼
nc,ref ðmref zref me Þ þ zme nc
interpolated by Bint ðt2 Þ ¼ Bðt1 Þ þ
ðt2 t1 ÞðBðt3 ÞBðt1 ÞÞ : t3 t1
ð3Þ
Fig. 3 illustrates the influence of field fluctuations: For the choice of t1 and t3 the interpolated B-field value at the time t2 is considerably larger than for the choice of tu1 and t3. Thus, small variations of times t1 and t3 respectively the magnetic-field strength B(t1) and B(t3) of the reference measurements lead to a variety of different B-field approximations for the time of interest t2. The fluctuations that cause the deviation of the actual magnetic field from the interpolated value arise from variations of external parameters, in particular the ambient temperature and pressure.
3. Investigation of the magnetic-field fluctuations The magnetic field of a superconducting solenoid is changing over time. The finite resistance of the superconducting coils leads to a decrease of the magnetic field. This effect is partly compensated by an additional B0(t) of the superconducting field-lock coils inside the solenoid that are continuously charged. For a time span of 440 days the relative magnetic-field decay has been fitted by a linear function to be 4.063(7) 10 10/h (see Fig. 4). This linear component is taken care of by the calibration measurements.
ð2Þ
where me is the mass of an electron. Eq. (2) is only valid if one assumes that the magnetic field is constant. Since the B-field is changing over time it is necessary to approximate the magneticfield strength at the time t2 of the mass determination of the ion of interest. To this end, calibrations are performed before ðt1 o t2 Þ and after ðt3 4 t2 Þ the measurement of the nuclide of interest. The magnetic-field strength B(t2) at the time t2 is then linearly
Fig. 2. Mean time of flight of 133 Cs þ as a function of the excitation frequency with an excitation time of Texc ¼1.8 s. The solid line is a fit of the theoretical line shape to the data [26]. The doubled uncertainty of the cyclotron frequency 2dnc not drawn to scale.
Fig. 1. Experimental setup of the SHIPTRAP apparatus. For details see text.
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
Fig. 3. Schematic explanation of the fluctuations of the magnetic field strength B as a function of time for demonstration of the linear interpolation of the value B(t2). For details see text.
Fig. 4. Magnetic field as a function of time over a period of 440 days (2007–2009). The magnetic field strength was determined with cyclotron resonances of 133 Cs þ . The error bars are smaller than the symbol size. The solid line shows a linear fit to the data.
Fig. 5. Magnetic field strength (points) and temperature in the bore of the superconducting magnet (solid line) as a function of time over a period of 50 h.
159
In addition, there are nonlinear B-field changes on a shorter time scale of 24 h caused by environmental conditions like temperature or pressure variations. Fig. 5 shows the B-field (points) measured via the cyclotron-frequency determination of 133 Cs þ over a period of two days simultaneously with a temperature measurement (solid line) in the bore of the solenoid using a PT100 temperature sensor. There is an obvious correlation between the bore temperature and the magnetic-field strength. Due to these temperature-dependent changes the actual B-field can deviate from the interpolated value leading to a systematic uncertainty of the resulting mass value (Fig. 3). In the following, a method is presented to reduce the temperature fluctuations and, thus, to stabilize the magnetic-field strength to lower the uncertainty of the mass determination, in particular for long measurement durations. To determine the uncertainty due to magnetic-field fluctuations frequency measurements have been continuously performed over periods of several hours up to days. The resulting data was split up into several subsets each containing an equal number of frequency scans to assure comparable statistical uncertainties for all subsets. The magnetic-field magnitude for each subset was determined by use of Eq. (1). The magnetic field at the time tn + 1 ¼(tn + tn + 2)/2 can be interpolated using Eq. (3) and then be compared to the actual value B(tn + 1). The standard deviation of the relative difference between the interpolated and the actual magnetic-field strength ðBðtn þ 1 ÞBint ðtn þ 1 ÞÞ=Bðtn þ 1 Þ for each point is plotted as a function of the time interval tn + 2 tn over which the field was interpolated. The same procedure is repeated for different values of tn + 2 tn. The resulting data points sðDB=BÞ are displayed in Fig. 6. The data up to 6 h are fitted by a straight line. In this range the data points for the unstabilized case follow a linear trend. Its slope describes the uncertainty due to magnetic-field fluctuations per time interval spanned by a mass measurement of the ion of interest (see also Refs. [11,29]). The uncertainty of the linear fit represents the error of the relative magnetic-field uncertainty. For time spans longer than 6 h the magnetic-field strength shows a periodic behaviour which originates from the correlation to the day/night temperature variation in the experimental hall (see Fig. 5), for details of the measurement see next section. As a result the standard deviation of the relative magnetic-field fluctuation s is decreasing again for time spans of more than about 12 h. This also explains the maximum at tn + 2 tn ¼12 h in Fig. 6, i.e. at half of the period for the day/night temperature fluctuations. The finite values for the standard deviations of the relative magnetic-field deviation for vanishing time intervals in Fig. 6 are
Fig. 6. Standard deviation of the relative magnetic-field fluctuation with (circles) and without (squares) stabilized temperature in the bore of the superconducting magnet as a function of time between two measurement points.
160
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
due to the remaining statistical uncertainties for each measurement series. The resulting uncertainty without a temperature stabilization system is so ¼ 3:54ð17Þ 108 =h. From previous investigations [15] the value so ¼ 1:3ð3Þ 109 =h was obtained. The difference between the previous value and so of the present work originates from the different temperature fluctuations during the two measurements. With larger temperature variations the magnetic-field related uncertainty is increasing, too. Note that between the two measurements of the uncertainty without temperature stabilization a quench of the SHIPTRAP solenoid occurred.
4. Temperature stabilization The vacuum tube located inside the bore of the magnet and the bore itself is thermally connected to the air in the experimental hall at GSI. The ambient temperature shows typical day/night fluctuations of plus/minus 2 K. The temperature in the bore follows the ambient temperature with a delay of about 100 min. According to Fig. 5 the magnetic-field fluctuations are correlated with the temperature in the magnet bore. In order to reduce the temperature induced magnetic-field fluctuations a regulation system was set up to stabilize this parameter. A sketch of the temperature stabilization setup is shown in Fig. 7. The temperature in the bore of the solenoid is determined with the temperature sensor (PT100) placed at the horizontal position of the measurement trap. The resistance of the temperature sensor is recorded with a multimeter (Hewlett Packard 3457A) which is connected via an General Purpose Interface Bus (GPIB) connection to a PC. A LabVIEW-based software converts the resistance data to temperature values and provides a software Proportional-Integral-Derivative (PID) loop. The regulation software compares the actual temperature to a set value and calculates a corresponding output voltage. This data is sent via GPIB to a power supply of a heating element. A fan constantly blows heated air into the bore of the magnet. To be effective the set temperature of the stabilization is set to be higher than the temperature in the experimental hall. The parameters of the servo loop are optimized manually according to an algorithm described in Ref. [30]. In order to prevent the magnet bore from overheating in case of malfunctioning of the regulation software, a hardware temperature interlock is installed which interrupts the circuit between the power supply and the heating element if a temperature of 45 3 C is exceeded.
In Fig. 8 the temperature in the bore with operating stabilization system and in the experimental hall are compared. The temperature in the hall was determined with a USB thermo-respectively, manometer by ‘Intersema’ (Model MS5534-B) at a distance of 2 m to the solenoid. The ambient temperature shows typical day/night fluctuations of 4 K. During the same time the bore temperature of the magnet was stabilized to a value of 29 3 C with a standard deviation of only 6.3 mK. This is an improvement by a factor of 200 compared to the free running case. To investigate the influence of the temperature on the magnetic-field strength the cyclotron frequency of 133 Cs þ was measured with an excitation time of 1 s over a period of 10 h. The resonance was split up into data subsets of a duration of 11 min each, which corresponds to 10 scans. For each of these subsets the cyclotron frequency nc was determined and plotted as a function of time. During this long-term measurement the set value of the temperature stabilization was varied and the pressure in the helium cryostat was stable to within a standard deviation of 0.05 mbar (see Section 5). The results are displayed in Fig. 9. A correlation between the temperature and the resonance frequency, respectively, the magnetic-field strength, is observed. According to this measurement the average temperature-dependent variation of
Fig. 8. The temperature in the bore of the solenoid with the temperature stabilization system active (solid line) and the temperature in the experimental hall (points) as a function of time.
Magnet
Vacuum tube Bore Temperature sensor
Fan
Temperature delimiter
Heating element U
Fig. 7. Schematic sketch of the temperature stabilization system. For more details see text.
Fig. 9. Cyclotron resonance frequency nc of 133 Cs þ (points) and bore temperature (solid line) as a function of time. For details see text.
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
161
the cyclotron frequency of 133 Cs þ is 2.34(16) 10 4 Hz/mK. This corresponds to a relative magnetic-field change of 2.9(2) 10 10/mK. The magnetic-field related uncertainty was determined in a similar way as described in Section 3. The result with an active temperature regulation system is included in Fig. 6. Obviously, the temperature stabilization has a strong effect on the temporal magnetic-field stability. During the measurement with temperature stabilization the number of detected ions happened to be larger than in the unstabilized case which leads to a lower statistical uncertainty in the determination of the cyclotron frequency of each subset. As a result the fluctuations of the center frequencies of the data subsets are smaller which leads to a reduced standard deviation for the stabilized case and a smaller offset of the curve. The relative magnetic-field related uncertainty could be reduced by a factor of 50 by going from the unstabilized case with so ¼ 3:54ð17Þ 108 =h to the temperature stabilization sT ¼ 7:1ð3Þ 1010 =h. The temperature related magnetic field uncertainty sT compared to so ¼ 1:3ð3Þ 109 =h published in Ref. [15] is by a factor of 2 smaller. Fig. 11. Pressure in the cryostate as a function of time over a period of 48 h. The pressure regulation system was switched on after 19 h and stabilized the pressure to a standard deviation of 0.137 mbar.
5. Pressure stabilization From previous experience [18] it is known that in addition to the ambient temperature, the pressure in the helium cryostat has an influence on the magnetic field. Thus, the regulation was extended by a pressure stabilization system (MKS Instruments [32]). It consists of a temperature-stabilized gauge (MKS, Baratron 627B) and a regulating valve. A voltage corresponding to the pressure in the cryostat is fed to a controller unit (MKS, Model 250E) that contains a PID servo loop. The PID unit compares the actual value to the set value of the pressure and adjusts the gas flow through a needle valve (MKS, model 248A) correspondingly. The parameters of the PID loop are optimized manually according to Ref. [30]. For the case of malfunctioning of the regulation system a safety bypass is added which prevents the pressure from exceeding a certain difference to the ambient pressure. The measured pressure is acquired with a multimeter reading the analogue voltage of the baratron gauge from the controller that is connected via a GPIB Interface to a PC where a LabVIEW based measurement software logs the data. A schematic diagram of the regulation system is presented in Fig. 10. Fig. 11 shows the pressure in the cryostat over a two-days period. The pressure measurement started with an inactive regulation system. After a time span of 19 h the pressure stabilization was switched on. The pressure rises and approaches the set value of 1004 mbar within less than 2 h. The overcompensation and oscillation (inset of Fig. 11) is a typical effect of PID-loop controlled devices for a fast approach of the set value [31]. The pressure can be stabilized to a given value with a standard deviation of 0.1 mbar. To be effective the set pressure of the stabilization is set to be higher
Keithley 2700 Multimeter Controller
p
Gauge p* Helium Electronic valve exhaust line Safety valve Fig. 10. Block diagram of the pressure stabilization system.
Fig. 12. Cyclotron frequency of 133 Cs þ as a function of time (black points) determined for different pressure values in the LHe cryostat (red points). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
than the ambient pressure. The peaks Fig. 11 at 9 and 33 h and in Fig. 12 at 15 h are due to the so called B0-dump of the solenoid which releases a certain amount of helium. The B0-dump is controlled by the Magnex Model E7001 Emergency Discharge Unit. This unit is programmed to discharge the superconducting fieldlock coil each day at 12pm CET. The influence of the pressure on the magnetic field was monitored by measuring the cyclotron frequency of 133 Cs þ with an excitation time of 2 s over a period of 30 h. The measurement was split up into individual sections of 40 min duration each. To avoid temperature effects the temperature of the bore was regulated during the whole measurement with the stabilization system presented in Section 4. Fig. 12 shows the center frequency of each section as a function of time. In parallel the pressure in the helium dewar was measured and varied at certain moments (Fig. 12 solid line). Obviously, the resonance frequency follows the pressure in the LHe cryostat, i.e. the B-field is dependent on the pressure. As the set value is changed from 1011 to 1005 mbar the frequency shifts by 40 mHz. This corresponds to a variation of the relative magnetic-field strength of 1.24(3) 10 8/mbar. If both stabilization systems are active the relative magneticfield uncertainty is reduced from so ¼ 3:54ð17Þ 108 =h to sT þ p ¼ 7:6ð64Þ 1011 =h. This corresponds to a reduction by a
162
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
factor of 460 compared to the present unstabilized case and a factor of 20 in comparison with the value of so published in Ref. [15]. Compared to the results in Section 4 (temperature stabilization only) the pressure stabilization reduces s by one order of magnitude.
6. Summary and outlook In this work the external perturbations that lead to fluctuations in the magnetic field were identified and measures were taken to reduce them. Thus, the magnetic-field related uncertainty of the mass determination (frequency measurement) could be significantly reduced. As a consequence the measurement duration can now be significantly increased. Fig. 13 demonstrates the influence of the temperature stabilization on the ToF-resonances with an excitation time of 10 s. The measurement duration for each 133 Cs þ resonance was approximately 4 h. Without a temperature stabilization nc is drifting stronger due to temperature dependent magnetic-field fluctuations during the measurement period. The superposition of all frequency scans leads to a broadened resonance curve with a Full-Width-at-Half-Maximum (FWHM) of DnðFWHMÞ ¼ 0:178 Hz
(from a Gaussian fit). The features of the resonance curve are washed out. In contrast, the resonance on the right was recorded with an active temperature stabilization. Here the typical resonance line shape [26] can be observed with DnðFWHMÞ ¼ 0:089 Hz as expected for an excitation period of Texc ¼10 s [26]. The temperature fluctuations in the bore of the solenoid have a stronger effect on the magnetic-field strength than the pressure fluctuations in the LHe cryostat. For a pressure variation of 10 mbar the B-field magnitude changes by 8:6 107 T. For a typical daily temperature fluctuation of 5 K the magnetic field strength changes by approximately 1 105 T. In fact, the temperature-induced fluctuations have to be reduced in order to observe the correlation between B and p. However, since the helium pressure is independent of the temperature in the bore one would expect a further decrease in the uncertainty if both parameters are regulated. A measurement with both stabilization systems confirms this assumption. For measurement durations of 63 h the relative magnetic-field uncertainty with an operating temperature and pressure stabilization would be only 10% of the systematic uncertainty of the SHIPTRAP setup of ssys ¼ 4:8 108 [28] while the old value of so ¼ 1:3ð3Þ 109 =h is even for short measurement times of 7 h in the same order of magnitude as ssys . This means that if both regulation systems are active the frequency uncertainty due to magnetic-field fluctuations can be neglected for typical measurement durations of 30 h, as required for many heavy radionuclides. High-precision mass measurements of superheavy elements is a future perspective of the SHIPTRAP experiment [33]. However, the reaction cross-section e, i.e., the corresponding production rates of, e.g., 257Rf (e ¼ 40ð5Þnb [34]), 258Db (e ¼ 4:3ð5Þnb [35]) and 261Sg (e ¼ 0:69ð17Þnb [35]) are orders of magnitude smaller compared to the latest experiments of 254No (e ¼ 1,8mb [14]). This, of course, requires longer measurement periods in the order of days or weeks. In this case even the magnetic-field related uncertainty sT þ p including the present regulations would still become rather large. However, a method to even further reduce this uncertainty would be the implementation of a ‘switch mode’. Reference measurements would not only be performed before and after but also during the measurement of the ion of interest to monitor the temporal changes of the magnetic field. After, for instance, 10 frequency scans of the exotic ions a resonance measurement of the reference ion would be inserted. Alternatively, whenever an event with the exotic ion is observed (e.g. in the average one count in several hours) one would automatically switch to a reference scan to determine the B-field value shortly after this event—before returning to the ion of interest. With this expansion of the measurement routine the time interval of the magnetic field interpolation would be drastically reduced and, thus, the uncertainty of the magnetic-field strength would be reduced further. Another promising approach is the implementation of the Fourier-transform ion-cyclotron-resonance (FT-ICR) technique for precision mass spectrometry of exotic nuclei [36]. This nondestructive ion-detection method requires only one ion with a sufficient half life to perform a mass measurement. Thus, the measurement duration is drastically reduced compared to the ToFICR technique. As a result the magnetic-field uncertainty will play a minor role compared to other systematic uncertainties.
Acknowledgements
Fig. 13. Mean time of flight as a function of excitation frequency nexc with a quadrupole excitation time Texc ¼ 10 s without temperature stabilization (Top) and with temperature stabilization (Bottom). The measurement duration for each resonance was 4 h.
We acknowledge the support of the German BMBF under WTZ Grant 06GF186I, 06GF9103I and RUS-07/015 and thank Klaus Blaum and Yuri Novikov for useful discussions. C.D., G.M. and L.S. also thank for support by the GSI F & E program. E.M. thanks the Helmholtz-Institute Mainz. D.N. thanks the Russian Minobrnauki under Grant 2.2.1.
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75 (2003) 1021. V.L. Ryjkov, et al., Phys. Rev. Lett. 101 (2008) 012501. J.J. Cowan, F.-K. Thielemann, J.W. Truran, Phys. Rep. 208 (1991) 267. H. Schatz, Int. J. Mass Spectrom. 251 (2006) 293. K. Blaum, Yu.N. Novikov, G. Werth, Cont. Phys. 51 (2010) 149. T. Eronen, et al., Phys. Rev. Lett. 100 (2008) 132502. J.C. Hardy, I.S. Towner, Phys. Rev. C 79 (2009) 055502. K. Blaum, Phys. Rep. 425 (2006) 1. L. Schweikhard, G. Bollen, Int. J. Mass Spectrom. 251 (2/3) (Special issue). ¨ et al., Z. Phys. A 297 (1980) 35. G. Graff, A. Kellerbauer, et al., Eur. Phys. J. D 22 (2003) 53. P.W. Anderson, Phys. Rev. Lett. 9 (1962) 309. P.W. Anderson, Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39. M. Dworschak, et al., Phys. Rev. C 81 (2010) 064312. M. Block, et al., Eur. Phys. J. D 45 (2007) 39. ¨ I. Bergstrom, et al., Nucl. Instr. and Meth. A 487 (2002) 618. Y. Liu, et al., Int. J. Mass Spectrom. 294 (2010) 28. M. Marie-Jeanne, et al., Nucl. Instr. and Meth. A 587 (2008) 464.
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
[33] [34] [35] [36]
163
¨ S. Hofmann, G. Munzenberg, Rev. Mod. Phys. 72 (2000) 733. J.B. Neumayr, et al., Nucl. Instr. and Meth. B 244 (2006) 489. W. Paul, Rev. Mod. Phys. 62 (1989) 531. L.S. Brown, G. Gabrielse, Rev. Mod. Phys. 58 (1986) 233. D. Neidherr, et al., Nucl. Instr. and Meth. B 266 (2008) 4556. Magnex Scientific LTD Technical Specification, 1999. G. Savard, et al., Phys. Lett. A 158 (1991) 247. ¨ M. Konig, et al., Int. J. Mass Spectrom. Ion Process. 142 (1995) 95. C. Smorra, et al., J. Phys. B 42 (2009) 154028. A. Chaudhuri, et al., Eur. Phys. J. D 45 (2007) 47. J. Ketelaer, et al., Eur. Phys. J. D 58 (2010) 47. J.G. Ziegler, N.B. Nichols, Trans. ASME 64 (1942) 759. K.H. Ang, et al., IEEE Trans. Control Sys. Tech. 13 (2005) 559. MKS Instruments User Manuals /www.mks.comS (a) MKS Type 627B Baratron Temperature regulated Capacitance Manometer. (b) MKS Type 250E Pressure Flow Controller. (c) MKS Type 248A/B/C Control Valve. M. Block, et al., Nature 463 (2010) 785. I. Dragojevic´, et al., Phys. Rev. C 78 (2008) 024605. F.P. Heßberger, et al., Eur. Phys. J. A 41 (2009) 145. J. Ketelaer, et al., Eur. Phys. J. A 42 (2009) 311.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Investigation of the magnetic field fluctuation and implementation of a temperature and pressure stabilization at SHIPTRAP C. Droese a,, M. Block b, M. Dworschak b, S. Eliseev c, E. Minaya Ramirez d, D. Nesterenko e, L. Schweikhard a a
Ernst-Moritz-Arndt-Universit¨ at, Institut f¨ ur Physik, 17489 Greifswald, Germany GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany c Max-Planck-Institut f¨ ur Kernphysik, Saupfercheckweg 1, 69117 Heiderlberg, Germany d Helmholtz-Institut Mainz, Johannes Gutenberg-Universit¨ at, 55099 Mainz, Germany e PNPI RAS, Gatchina, Leningrad district 188300, Russia b
a r t i c l e in f o
abstract
Article history: Received 12 October 2010 Received in revised form 15 December 2010 Accepted 18 December 2010 Available online 29 December 2010
Penning traps have proven to be powerful tools for the determination of nuclear masses with high accuracy. A crucial parameter for precision mass measurements in Penning traps is the accurate determination of the magnetic-field strength. However, the magnetic field of a superconducting magnet is not constant in time, but changes due to intrinsic effects of the solenoid and external perturbations. These effects have been investigated for SHIPTRAP. Furthermore, a stabilization of the temperature in the magnet bore as well as of the pressure in the liquid-helium cryostat has been implemented. Thus, the magnetic-field related uncertainties have been reduced to 7(6) 10 11/h. & 2010 Elsevier B.V. All rights reserved.
Keywords: Penning traps Magnetic-field stabilization Temperature stabilization Pressure stabilization SHIPTRAP
1. Introduction
determined via a measurement of the cyclotron frequency
Accurate mass values of radionuclides give valuable information about nuclear-structure properties such as shell closures, halos and pairing effects [1,2]. They are also used to benchmark nuclear models [1]. In astrophysics mass values with uncertainties of less than dm=m 107 are necessary, e.g. for investigations on the rapid-neutron-capture process (r-process [3]) and the rapid-proton-capture process (rp-process [4]). Furthermore, mass values are important input parameters for investigations of the weak interaction [5]. Mass measurements with relative uncertainties of less than dm=m 108 of superallowed b emitters and their daughter nuclei [6] enable tests of the conserved-vector-current hypothesis and the unitarity of the Cabibbo–Kobayashi–Maskawa quarkmixing matrix [7]. Penning traps around the world [8,9] have turned out to be the tools of choice to reach these levels of accuracy. The ions of interest are trapped in a homogeneous magnetic field B and a static electric field. By use of the time-of-flight ion-cyclotron-resonance (ToFICR) detection technique [10] the mass m of an ion with charge q is
nc ¼
Corresponding author. Tel.: +49 6151712114; fax: +49 6151713463.
E-mail address: [email protected] (C. Droese). 0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.12.176
1 qB : 2p m
ð1Þ
Eq. (1) can be used for an accurate mass determination only if the magnetic-field strength at the time of the measurement is known or can be derived. Since the magnetic field is not constant in time, calibration measurements using reference ions with well-known mass are performed before and after each measurement of the nuclide of interest. From these reference measurements the magnetic-field strength at the time of the cyclotron-frequency determination of the nuclide of interest is estimated by linear interpolation [11]. The interpolation takes all linear effects into account such as the so called intrinsic flux creep [12,13]. However, there are several perturbations which are not linear in time and thus lead to a deviation of the actual value from the interpolated. This adds a systematic uncertainty to the final mass value. The production rate of radionuclides investigated at SHIPTRAP can be below one per minute. Thus, with a total efficiency of the whole SHIPTRAP apparatus of about 3% [14] and a minimum number of detected ions of about 50 to obtain a reasonable time-of-flight resonance, the measurement time can add up to several hours. For such long measurement times fluctuations of the magnetic field limit the achievable mass uncertainty [15]. Therefore, regulation systems for the temperature in the bore and the
158
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
pressure in the cryostat of the superconducting solenoid were implemented in a similar way as reported for SMILETRAP [16,17] and ISOLTRAP [18]. A description of the SHIPTRAP experiment is presented in Section 2. Its magnetic-field fluctuations in the absence of the stabilization system are described in Section 3. The SHIPTRAP stabilization systems and their influence on the magnetic field are illustrated in Sections 4 and 5.
2. Experimental setup and precision mass measurements at SHIPTRAP The SHIPTRAP setup [15] is schematically displayed in Fig. 1. The ion beam from the velocity filter SHIP [19] is stopped in a gas cell [20] in ultra-high purity helium (99.9999% purity) at a pressure of 50 mbar. The ions are extracted from the gas cell via a funnel structure through an extraction nozzle and enter the extraction radiofrequency quadrupole (RFQ). The extraction RFQ is followed by a buncher. Both are linear Paul traps [21] filled with helium as the buffer gas. In the buncher the ions are further cooled and accumulated. After a storage time of several milliseconds up to seconds the charged particles are ejected as bunches into the double Penning-trap system [22]. Both cylindrical Penning traps, separated by a 1.5-mm diameter pumping barrier [23], are placed in a 7-T superconducting magnet (MAGNEX SCIENTIFIC MRBR 7.0/160/as [24]). The first trap is a preparation trap where unwanted ions are removed and the ions of interest are centered using mass selective buffer-gas cooling [25]. In the second trap cyclotron-frequency measurements are performed. To this end, the ToF-ICR technique [10] is applied. Fig. 2 shows a cyclotron-frequency resonance curve of 133 Cs þ delivered from a surface ion source. The atomic mass m of a nuclide is determined from ions of charge state z by comparing the measured cyclotron frequency nc to the cyclotron frequency nc,ref of an ion with a well-known mass mref and charge qref ¼ zref e, with the elementary charge e. Typically 133 Cs þ , other alkali ions, or carbon cluster ions [11,27,28] with a similar mass-to-charge ratio as the nuclides of interest are chosen as reference ions. This leads to the following equation: m¼
nc,ref ðmref zref me Þ þ zme nc
interpolated by Bint ðt2 Þ ¼ Bðt1 Þ þ
ðt2 t1 ÞðBðt3 ÞBðt1 ÞÞ : t3 t1
ð3Þ
Fig. 3 illustrates the influence of field fluctuations: For the choice of t1 and t3 the interpolated B-field value at the time t2 is considerably larger than for the choice of tu1 and t3. Thus, small variations of times t1 and t3 respectively the magnetic-field strength B(t1) and B(t3) of the reference measurements lead to a variety of different B-field approximations for the time of interest t2. The fluctuations that cause the deviation of the actual magnetic field from the interpolated value arise from variations of external parameters, in particular the ambient temperature and pressure.
3. Investigation of the magnetic-field fluctuations The magnetic field of a superconducting solenoid is changing over time. The finite resistance of the superconducting coils leads to a decrease of the magnetic field. This effect is partly compensated by an additional B0(t) of the superconducting field-lock coils inside the solenoid that are continuously charged. For a time span of 440 days the relative magnetic-field decay has been fitted by a linear function to be 4.063(7) 10 10/h (see Fig. 4). This linear component is taken care of by the calibration measurements.
ð2Þ
where me is the mass of an electron. Eq. (2) is only valid if one assumes that the magnetic field is constant. Since the B-field is changing over time it is necessary to approximate the magneticfield strength at the time t2 of the mass determination of the ion of interest. To this end, calibrations are performed before ðt1 o t2 Þ and after ðt3 4 t2 Þ the measurement of the nuclide of interest. The magnetic-field strength B(t2) at the time t2 is then linearly
Fig. 2. Mean time of flight of 133 Cs þ as a function of the excitation frequency with an excitation time of Texc ¼1.8 s. The solid line is a fit of the theoretical line shape to the data [26]. The doubled uncertainty of the cyclotron frequency 2dnc not drawn to scale.
Fig. 1. Experimental setup of the SHIPTRAP apparatus. For details see text.
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
Fig. 3. Schematic explanation of the fluctuations of the magnetic field strength B as a function of time for demonstration of the linear interpolation of the value B(t2). For details see text.
Fig. 4. Magnetic field as a function of time over a period of 440 days (2007–2009). The magnetic field strength was determined with cyclotron resonances of 133 Cs þ . The error bars are smaller than the symbol size. The solid line shows a linear fit to the data.
Fig. 5. Magnetic field strength (points) and temperature in the bore of the superconducting magnet (solid line) as a function of time over a period of 50 h.
159
In addition, there are nonlinear B-field changes on a shorter time scale of 24 h caused by environmental conditions like temperature or pressure variations. Fig. 5 shows the B-field (points) measured via the cyclotron-frequency determination of 133 Cs þ over a period of two days simultaneously with a temperature measurement (solid line) in the bore of the solenoid using a PT100 temperature sensor. There is an obvious correlation between the bore temperature and the magnetic-field strength. Due to these temperature-dependent changes the actual B-field can deviate from the interpolated value leading to a systematic uncertainty of the resulting mass value (Fig. 3). In the following, a method is presented to reduce the temperature fluctuations and, thus, to stabilize the magnetic-field strength to lower the uncertainty of the mass determination, in particular for long measurement durations. To determine the uncertainty due to magnetic-field fluctuations frequency measurements have been continuously performed over periods of several hours up to days. The resulting data was split up into several subsets each containing an equal number of frequency scans to assure comparable statistical uncertainties for all subsets. The magnetic-field magnitude for each subset was determined by use of Eq. (1). The magnetic field at the time tn + 1 ¼(tn + tn + 2)/2 can be interpolated using Eq. (3) and then be compared to the actual value B(tn + 1). The standard deviation of the relative difference between the interpolated and the actual magnetic-field strength ðBðtn þ 1 ÞBint ðtn þ 1 ÞÞ=Bðtn þ 1 Þ for each point is plotted as a function of the time interval tn + 2 tn over which the field was interpolated. The same procedure is repeated for different values of tn + 2 tn. The resulting data points sðDB=BÞ are displayed in Fig. 6. The data up to 6 h are fitted by a straight line. In this range the data points for the unstabilized case follow a linear trend. Its slope describes the uncertainty due to magnetic-field fluctuations per time interval spanned by a mass measurement of the ion of interest (see also Refs. [11,29]). The uncertainty of the linear fit represents the error of the relative magnetic-field uncertainty. For time spans longer than 6 h the magnetic-field strength shows a periodic behaviour which originates from the correlation to the day/night temperature variation in the experimental hall (see Fig. 5), for details of the measurement see next section. As a result the standard deviation of the relative magnetic-field fluctuation s is decreasing again for time spans of more than about 12 h. This also explains the maximum at tn + 2 tn ¼12 h in Fig. 6, i.e. at half of the period for the day/night temperature fluctuations. The finite values for the standard deviations of the relative magnetic-field deviation for vanishing time intervals in Fig. 6 are
Fig. 6. Standard deviation of the relative magnetic-field fluctuation with (circles) and without (squares) stabilized temperature in the bore of the superconducting magnet as a function of time between two measurement points.
160
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
due to the remaining statistical uncertainties for each measurement series. The resulting uncertainty without a temperature stabilization system is so ¼ 3:54ð17Þ 108 =h. From previous investigations [15] the value so ¼ 1:3ð3Þ 109 =h was obtained. The difference between the previous value and so of the present work originates from the different temperature fluctuations during the two measurements. With larger temperature variations the magnetic-field related uncertainty is increasing, too. Note that between the two measurements of the uncertainty without temperature stabilization a quench of the SHIPTRAP solenoid occurred.
4. Temperature stabilization The vacuum tube located inside the bore of the magnet and the bore itself is thermally connected to the air in the experimental hall at GSI. The ambient temperature shows typical day/night fluctuations of plus/minus 2 K. The temperature in the bore follows the ambient temperature with a delay of about 100 min. According to Fig. 5 the magnetic-field fluctuations are correlated with the temperature in the magnet bore. In order to reduce the temperature induced magnetic-field fluctuations a regulation system was set up to stabilize this parameter. A sketch of the temperature stabilization setup is shown in Fig. 7. The temperature in the bore of the solenoid is determined with the temperature sensor (PT100) placed at the horizontal position of the measurement trap. The resistance of the temperature sensor is recorded with a multimeter (Hewlett Packard 3457A) which is connected via an General Purpose Interface Bus (GPIB) connection to a PC. A LabVIEW-based software converts the resistance data to temperature values and provides a software Proportional-Integral-Derivative (PID) loop. The regulation software compares the actual temperature to a set value and calculates a corresponding output voltage. This data is sent via GPIB to a power supply of a heating element. A fan constantly blows heated air into the bore of the magnet. To be effective the set temperature of the stabilization is set to be higher than the temperature in the experimental hall. The parameters of the servo loop are optimized manually according to an algorithm described in Ref. [30]. In order to prevent the magnet bore from overheating in case of malfunctioning of the regulation software, a hardware temperature interlock is installed which interrupts the circuit between the power supply and the heating element if a temperature of 45 3 C is exceeded.
In Fig. 8 the temperature in the bore with operating stabilization system and in the experimental hall are compared. The temperature in the hall was determined with a USB thermo-respectively, manometer by ‘Intersema’ (Model MS5534-B) at a distance of 2 m to the solenoid. The ambient temperature shows typical day/night fluctuations of 4 K. During the same time the bore temperature of the magnet was stabilized to a value of 29 3 C with a standard deviation of only 6.3 mK. This is an improvement by a factor of 200 compared to the free running case. To investigate the influence of the temperature on the magnetic-field strength the cyclotron frequency of 133 Cs þ was measured with an excitation time of 1 s over a period of 10 h. The resonance was split up into data subsets of a duration of 11 min each, which corresponds to 10 scans. For each of these subsets the cyclotron frequency nc was determined and plotted as a function of time. During this long-term measurement the set value of the temperature stabilization was varied and the pressure in the helium cryostat was stable to within a standard deviation of 0.05 mbar (see Section 5). The results are displayed in Fig. 9. A correlation between the temperature and the resonance frequency, respectively, the magnetic-field strength, is observed. According to this measurement the average temperature-dependent variation of
Fig. 8. The temperature in the bore of the solenoid with the temperature stabilization system active (solid line) and the temperature in the experimental hall (points) as a function of time.
Magnet
Vacuum tube Bore Temperature sensor
Fan
Temperature delimiter
Heating element U
Fig. 7. Schematic sketch of the temperature stabilization system. For more details see text.
Fig. 9. Cyclotron resonance frequency nc of 133 Cs þ (points) and bore temperature (solid line) as a function of time. For details see text.
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
161
the cyclotron frequency of 133 Cs þ is 2.34(16) 10 4 Hz/mK. This corresponds to a relative magnetic-field change of 2.9(2) 10 10/mK. The magnetic-field related uncertainty was determined in a similar way as described in Section 3. The result with an active temperature regulation system is included in Fig. 6. Obviously, the temperature stabilization has a strong effect on the temporal magnetic-field stability. During the measurement with temperature stabilization the number of detected ions happened to be larger than in the unstabilized case which leads to a lower statistical uncertainty in the determination of the cyclotron frequency of each subset. As a result the fluctuations of the center frequencies of the data subsets are smaller which leads to a reduced standard deviation for the stabilized case and a smaller offset of the curve. The relative magnetic-field related uncertainty could be reduced by a factor of 50 by going from the unstabilized case with so ¼ 3:54ð17Þ 108 =h to the temperature stabilization sT ¼ 7:1ð3Þ 1010 =h. The temperature related magnetic field uncertainty sT compared to so ¼ 1:3ð3Þ 109 =h published in Ref. [15] is by a factor of 2 smaller. Fig. 11. Pressure in the cryostate as a function of time over a period of 48 h. The pressure regulation system was switched on after 19 h and stabilized the pressure to a standard deviation of 0.137 mbar.
5. Pressure stabilization From previous experience [18] it is known that in addition to the ambient temperature, the pressure in the helium cryostat has an influence on the magnetic field. Thus, the regulation was extended by a pressure stabilization system (MKS Instruments [32]). It consists of a temperature-stabilized gauge (MKS, Baratron 627B) and a regulating valve. A voltage corresponding to the pressure in the cryostat is fed to a controller unit (MKS, Model 250E) that contains a PID servo loop. The PID unit compares the actual value to the set value of the pressure and adjusts the gas flow through a needle valve (MKS, model 248A) correspondingly. The parameters of the PID loop are optimized manually according to Ref. [30]. For the case of malfunctioning of the regulation system a safety bypass is added which prevents the pressure from exceeding a certain difference to the ambient pressure. The measured pressure is acquired with a multimeter reading the analogue voltage of the baratron gauge from the controller that is connected via a GPIB Interface to a PC where a LabVIEW based measurement software logs the data. A schematic diagram of the regulation system is presented in Fig. 10. Fig. 11 shows the pressure in the cryostat over a two-days period. The pressure measurement started with an inactive regulation system. After a time span of 19 h the pressure stabilization was switched on. The pressure rises and approaches the set value of 1004 mbar within less than 2 h. The overcompensation and oscillation (inset of Fig. 11) is a typical effect of PID-loop controlled devices for a fast approach of the set value [31]. The pressure can be stabilized to a given value with a standard deviation of 0.1 mbar. To be effective the set pressure of the stabilization is set to be higher
Keithley 2700 Multimeter Controller
p
Gauge p* Helium Electronic valve exhaust line Safety valve Fig. 10. Block diagram of the pressure stabilization system.
Fig. 12. Cyclotron frequency of 133 Cs þ as a function of time (black points) determined for different pressure values in the LHe cryostat (red points). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
than the ambient pressure. The peaks Fig. 11 at 9 and 33 h and in Fig. 12 at 15 h are due to the so called B0-dump of the solenoid which releases a certain amount of helium. The B0-dump is controlled by the Magnex Model E7001 Emergency Discharge Unit. This unit is programmed to discharge the superconducting fieldlock coil each day at 12pm CET. The influence of the pressure on the magnetic field was monitored by measuring the cyclotron frequency of 133 Cs þ with an excitation time of 2 s over a period of 30 h. The measurement was split up into individual sections of 40 min duration each. To avoid temperature effects the temperature of the bore was regulated during the whole measurement with the stabilization system presented in Section 4. Fig. 12 shows the center frequency of each section as a function of time. In parallel the pressure in the helium dewar was measured and varied at certain moments (Fig. 12 solid line). Obviously, the resonance frequency follows the pressure in the LHe cryostat, i.e. the B-field is dependent on the pressure. As the set value is changed from 1011 to 1005 mbar the frequency shifts by 40 mHz. This corresponds to a variation of the relative magnetic-field strength of 1.24(3) 10 8/mbar. If both stabilization systems are active the relative magneticfield uncertainty is reduced from so ¼ 3:54ð17Þ 108 =h to sT þ p ¼ 7:6ð64Þ 1011 =h. This corresponds to a reduction by a
162
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
factor of 460 compared to the present unstabilized case and a factor of 20 in comparison with the value of so published in Ref. [15]. Compared to the results in Section 4 (temperature stabilization only) the pressure stabilization reduces s by one order of magnitude.
6. Summary and outlook In this work the external perturbations that lead to fluctuations in the magnetic field were identified and measures were taken to reduce them. Thus, the magnetic-field related uncertainty of the mass determination (frequency measurement) could be significantly reduced. As a consequence the measurement duration can now be significantly increased. Fig. 13 demonstrates the influence of the temperature stabilization on the ToF-resonances with an excitation time of 10 s. The measurement duration for each 133 Cs þ resonance was approximately 4 h. Without a temperature stabilization nc is drifting stronger due to temperature dependent magnetic-field fluctuations during the measurement period. The superposition of all frequency scans leads to a broadened resonance curve with a Full-Width-at-Half-Maximum (FWHM) of DnðFWHMÞ ¼ 0:178 Hz
(from a Gaussian fit). The features of the resonance curve are washed out. In contrast, the resonance on the right was recorded with an active temperature stabilization. Here the typical resonance line shape [26] can be observed with DnðFWHMÞ ¼ 0:089 Hz as expected for an excitation period of Texc ¼10 s [26]. The temperature fluctuations in the bore of the solenoid have a stronger effect on the magnetic-field strength than the pressure fluctuations in the LHe cryostat. For a pressure variation of 10 mbar the B-field magnitude changes by 8:6 107 T. For a typical daily temperature fluctuation of 5 K the magnetic field strength changes by approximately 1 105 T. In fact, the temperature-induced fluctuations have to be reduced in order to observe the correlation between B and p. However, since the helium pressure is independent of the temperature in the bore one would expect a further decrease in the uncertainty if both parameters are regulated. A measurement with both stabilization systems confirms this assumption. For measurement durations of 63 h the relative magnetic-field uncertainty with an operating temperature and pressure stabilization would be only 10% of the systematic uncertainty of the SHIPTRAP setup of ssys ¼ 4:8 108 [28] while the old value of so ¼ 1:3ð3Þ 109 =h is even for short measurement times of 7 h in the same order of magnitude as ssys . This means that if both regulation systems are active the frequency uncertainty due to magnetic-field fluctuations can be neglected for typical measurement durations of 30 h, as required for many heavy radionuclides. High-precision mass measurements of superheavy elements is a future perspective of the SHIPTRAP experiment [33]. However, the reaction cross-section e, i.e., the corresponding production rates of, e.g., 257Rf (e ¼ 40ð5Þnb [34]), 258Db (e ¼ 4:3ð5Þnb [35]) and 261Sg (e ¼ 0:69ð17Þnb [35]) are orders of magnitude smaller compared to the latest experiments of 254No (e ¼ 1,8mb [14]). This, of course, requires longer measurement periods in the order of days or weeks. In this case even the magnetic-field related uncertainty sT þ p including the present regulations would still become rather large. However, a method to even further reduce this uncertainty would be the implementation of a ‘switch mode’. Reference measurements would not only be performed before and after but also during the measurement of the ion of interest to monitor the temporal changes of the magnetic field. After, for instance, 10 frequency scans of the exotic ions a resonance measurement of the reference ion would be inserted. Alternatively, whenever an event with the exotic ion is observed (e.g. in the average one count in several hours) one would automatically switch to a reference scan to determine the B-field value shortly after this event—before returning to the ion of interest. With this expansion of the measurement routine the time interval of the magnetic field interpolation would be drastically reduced and, thus, the uncertainty of the magnetic-field strength would be reduced further. Another promising approach is the implementation of the Fourier-transform ion-cyclotron-resonance (FT-ICR) technique for precision mass spectrometry of exotic nuclei [36]. This nondestructive ion-detection method requires only one ion with a sufficient half life to perform a mass measurement. Thus, the measurement duration is drastically reduced compared to the ToFICR technique. As a result the magnetic-field uncertainty will play a minor role compared to other systematic uncertainties.
Acknowledgements
Fig. 13. Mean time of flight as a function of excitation frequency nexc with a quadrupole excitation time Texc ¼ 10 s without temperature stabilization (Top) and with temperature stabilization (Bottom). The measurement duration for each resonance was 4 h.
We acknowledge the support of the German BMBF under WTZ Grant 06GF186I, 06GF9103I and RUS-07/015 and thank Klaus Blaum and Yuri Novikov for useful discussions. C.D., G.M. and L.S. also thank for support by the GSI F & E program. E.M. thanks the Helmholtz-Institute Mainz. D.N. thanks the Russian Minobrnauki under Grant 2.2.1.
C. Droese et al. / Nuclear Instruments and Methods in Physics Research A 632 (2011) 157–163
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75 (2003) 1021. V.L. Ryjkov, et al., Phys. Rev. Lett. 101 (2008) 012501. J.J. Cowan, F.-K. Thielemann, J.W. Truran, Phys. Rep. 208 (1991) 267. H. Schatz, Int. J. Mass Spectrom. 251 (2006) 293. K. Blaum, Yu.N. Novikov, G. Werth, Cont. Phys. 51 (2010) 149. T. Eronen, et al., Phys. Rev. Lett. 100 (2008) 132502. J.C. Hardy, I.S. Towner, Phys. Rev. C 79 (2009) 055502. K. Blaum, Phys. Rep. 425 (2006) 1. L. Schweikhard, G. Bollen, Int. J. Mass Spectrom. 251 (2/3) (Special issue). ¨ et al., Z. Phys. A 297 (1980) 35. G. Graff, A. Kellerbauer, et al., Eur. Phys. J. D 22 (2003) 53. P.W. Anderson, Phys. Rev. Lett. 9 (1962) 309. P.W. Anderson, Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39. M. Dworschak, et al., Phys. Rev. C 81 (2010) 064312. M. Block, et al., Eur. Phys. J. D 45 (2007) 39. ¨ I. Bergstrom, et al., Nucl. Instr. and Meth. A 487 (2002) 618. Y. Liu, et al., Int. J. Mass Spectrom. 294 (2010) 28. M. Marie-Jeanne, et al., Nucl. Instr. and Meth. A 587 (2008) 464.
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
[33] [34] [35] [36]
163
¨ S. Hofmann, G. Munzenberg, Rev. Mod. Phys. 72 (2000) 733. J.B. Neumayr, et al., Nucl. Instr. and Meth. B 244 (2006) 489. W. Paul, Rev. Mod. Phys. 62 (1989) 531. L.S. Brown, G. Gabrielse, Rev. Mod. Phys. 58 (1986) 233. D. Neidherr, et al., Nucl. Instr. and Meth. B 266 (2008) 4556. Magnex Scientific LTD Technical Specification, 1999. G. Savard, et al., Phys. Lett. A 158 (1991) 247. ¨ M. Konig, et al., Int. J. Mass Spectrom. Ion Process. 142 (1995) 95. C. Smorra, et al., J. Phys. B 42 (2009) 154028. A. Chaudhuri, et al., Eur. Phys. J. D 45 (2007) 47. J. Ketelaer, et al., Eur. Phys. J. D 58 (2010) 47. J.G. Ziegler, N.B. Nichols, Trans. ASME 64 (1942) 759. K.H. Ang, et al., IEEE Trans. Control Sys. Tech. 13 (2005) 559. MKS Instruments User Manuals /www.mks.comS (a) MKS Type 627B Baratron Temperature regulated Capacitance Manometer. (b) MKS Type 250E Pressure Flow Controller. (c) MKS Type 248A/B/C Control Valve. M. Block, et al., Nature 463 (2010) 785. I. Dragojevic´, et al., Phys. Rev. C 78 (2008) 024605. F.P. Heßberger, et al., Eur. Phys. J. A 41 (2009) 145. J. Ketelaer, et al., Eur. Phys. J. A 42 (2009) 311.