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Charge state distributions and charge exchange cross sections of carbon in helium at 30–258 keV
Nuclear Instruments and Methods in Physics Research B 361 (2015) 541–547
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Charge state distributions and charge exchange cross sections of carbon in helium at 30–258 keV Sascha Maxeiner ⇑, Martin Seiler, Martin Suter, Hans-Arno Synal Laboratory of Ion Beam Physics, ETH Zurich, 8093 Zurich, Switzerland
a r t i c l e
i n f o
Article history: Received 12 December 2014 Received in revised form 19 February 2015 Accepted 20 February 2015 Available online 14 March 2015 Keywords: Charge state distributions Charge exchange Helium stripping Low energy Accelerator Mass Spectrometry
a b s t r a c t With the introduction of helium stripping in radiocarbon (14C) accelerator mass spectrometry (AMS), higher +1 charge state yields in the 200 keV region and fewer beam losses are observed compared to nitrogen or argon stripping. To investigate the feasibility of even lower beam energies for 14C analyses the stripping characteristics of carbon in helium need to be further studied. Using two different AMS systems at ETH Zurich (myCADAS and MICADAS), ion beam transmissions of carbon ions for the charge states 1, +1, +2 and +3 were measured in the range of 258 keV down to 30 keV. The correction for beam losses and the extraction of charge state yields and charge exchange cross sections will be presented. An increase in population of the +1 charge state towards the lowest measured energies up to 75% was found as well as agreement with previous data from literature. The findings suggest that more compact radiocarbon AMS systems are possible and could provide even higher efficiency than current systems operating in the 200 keV range. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction To perform radiocarbon (14C) mass spectrometry, interfering isobars such as 14N and molecules like 12CH2, 13CH and 7Li2 need to be eliminated. Early measurements revealed, that 14N ions are not stable while stable 14C ion beams can be produced in ion sputter sources [1]. The molecules like the ones mentioned above on the other hand turned out to not have any bound states in charge states P+3 [2]. First radiocarbon accelerator mass spectrometry (AMS) setups around 1980 [3] made use of these facts and accelerated a negatively charged ion beam onto a gas or solid target. By stripping electrons from the ions in the target, different ionization states are produced, including the molecule free +3. The distribution of charge states depends on the thickness of the stripper medium and its compositions as well as the initial ion charge state. The charge exchange processes scale with the ion velocity and atomic number (for example see Ref. [4]). Towards high stripper thickness, a charge exchange equilibrium is established which does not depend on the initial charge state and stripper thickness anymore. The different charge state fractions in this equilibrium region are defined as their yields and are given by the physical charge exchange cross sections. Due to beam losses in a system, a different definition, namely the transmission, is usually of more ⇑ Corresponding author. E-mail address: [email protected] (S. Maxeiner). http://dx.doi.org/10.1016/j.nimb.2015.02.060 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.
use. It is defined as the measured ratio of particles in a specific charge state after stripping to all the injected particles before stripping. It is therefore given by the product of charge state yield and optical ion beam transmission. To achieve a sufficient measurement efficiency for good counting statistics, high acceleration voltages of several MV are needed for AMS in order to populate the higher charge states where no interfering molecules exist. In the following years the use of lower charge states such as 12 2+ C and 12C1+ was discussed. It was shown that the molecule intensity decreases exponentially with stripper thickness due to collisions with the target atoms [5,6]. Furthermore, high transmissions of 12C1+ in N2 gas were observed at 200 keV [7]. At such low energies, increased angular straggling and the reduced phase space compression of the ion beam diminish the transmission and increase the background. The use of helium instead of heavier gases was suggested to overcome this issue as the lower nuclear charge leads to decreased angular straggling while providing sufficient molecular destruction at only slightly higher areal densities [8]. The study of He as a target for ion gas interactions in the keV region goes back to 1954 where Stier et al. [9] investigated the charge state yields of the light ions H, He, N, Ne and Ar. Later, transmission measurements of carbon ions by Hvelplund et al. [4,10] revealed yields of about 50% for the +1 charge state at energies around 300 keV with increasing yield towards lower energies of 100 keV. Experimental data of charge state yields of carbon in helium in the 30–100 keV region is missing and makes it difficult
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to estimate the feasibility of radiocarbon AMS at even lower energies than today’s smallest available AMS systems at 200 keV. To fill this gap we performed transmission measurements on our compact AMS system MICADAS at 144 up to 258 keV stripping energy and our new prototype (A)MS system myCADAS [11] without tandem acceleration at energies as low as 30 keV. To correct the measured transmissions for beam losses, simulations of the beam limiting ion optical elements were performed. By measuring the dependence of charge state fractions 1, +1, +2 and +3 on the stripper density it was possible to determine the charge exchange cross sections. 2. Methods 2.1. Experimental setup Measurements of negative carbon ions passing through a He gas target were performed on two different systems available for radiocarbon dating at ETH Zurich. The experiments at higher energies (P144 keV) were carried out on the MICADAS radiocarbon AMS system [7], while experiments below 50 keV were performed on the new ETH Zurich prototype system myCADAS [11] (Fig. 1). In both AMS systems, the negative ion beam is produced in a Cs sputter source from a graphite target and in all experiments 12C is selected in the 90° injection magnet. To quickly alternate between different deflection radii without changing the magnetic field, a fast, electrostatic beam switching system is available on both systems. This enables the quasi simultaneous measurement of the 12C current Iinject in the off-axis injection Faraday cup (dark green, in the focal plane of the magnet) and the deflection onto the beam reference axis into the gas stripper canal (light green). A beam waist is formed in the center of the stripper in both systems to minimize beam losses. The beam current Ipost stripping of a charge state is finally measured in an analyzing Faraday cup (light green) after selection with either a second 90° magnet (MICADAS) or an electrostatic deflector (myCADAS). The Faraday cups are not equipped with suppressor
electrodes or magnets. To reduce secondary electron losses, the back plane of the charge collecting inner cups are tilted by 60° and the drift length from the cup aperture to the back plane is around 10 cm (5 cm in case of the myCADAS analyzing cup). The entrance aperture radii limit the opening angle seen from the back plane to less than 30 msr (100 msr in case of the myCADAS analyzing cup). Faraday cup currents are integrated on a capacitor over a few microseconds and the resulting voltage is read and converted. The overall precision and accuracy of current readout of this in-house built setup amounts to less than 1‰. Because this integrator setup is not able to read negative currents, a microammeter was used to manually record currents of the negatively charged ion beam. Additionally, the magnet (ESA) polarity needed to be swapped to select the negatively charged fraction of the ions. In all the experiments the value of the transmission was measured, defined as the absolute value of the ratio (Ipost stripping/q)/Iinject, with q being the respective charge state. In the MICADAS system, beam slits are positioned at the focal point of the first magnet and the ion beam is focused into the gas stripper canal at the high voltage potential by acceleration. The high voltage terminal can reach potentials of up to 220 kV and is differentially pumped by a 700 l/s turbo pump. In Fig. 1, the differential pumping region is indicated by the lighter shaded region (blue in the online version). The high voltage platform is supported by a ceramic holder (at the bottom) and vacuum insulated from the outer vessel, which is at ground potential and is pumped by two additional 700 l/s turbo pumps. Stripper gas is fed from ground to the high voltage terminal via a thin glass capillary with a diameter of about 100 lm. This requires a high He gas pressure of up to 30 bar to prevent electrical breakdown in the capillary. The gas flow into the stripper is finally regulated by a valve on the high voltage terminal which can be mechanically controlled from ground via a ceramic rod. After passing the stripper tube the positive (negative) ions are (de)accelerated back to ground. The subsequent high energy (HE) 90° magnet deflects the different beams into a vacuum chamber with
Fig. 1. Overview of the myCADAS (30–50 keV) and MICADAS (144–258 keV) radiocarbon (A)MS setup (seen from the top). Apart from the ion source and beam switching system, all of the myCADAS system is operated at ground potential. The high voltage for the acceleration at MICADAS is supplied by a commercial power supply and uses vacuum insulation. Both systems differentially pump the He stripper housing (lighter shaded region, blue in the online version) to achieve acceptable vacuum in the rest of the system. In case of MICADAS, this is monitored in the accelerator vessel (p1) while for myCADAS the pressure at the ESA (p2) is monitored. The He supply pressure at myCADAS is measured at p0, before it is reduced by a 30 cm tubing (4 mm diameter) and tube connecting parts. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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a Faraday cup for detection of 12C (light green in Fig. 1). Different charge states of 12C were selected by adjusting the magnetic field. Experiments at energies at and below 50 keV were performed on the prototype system myCADAS that is described in more detail in reference [11]. The main difference to the MICADAS setup is the absence of a second acceleration stage as the stripper tube is at ground potential. Because the focusing effect of the acceleration is missing, the center of the stripper canal needs to be at the position of the beam slits of the MICADAS setup. Furthermore, the second magnet is replaced by a 90° electrostatic deflector. Both systems use the same principle for stripping electrons from the incoming ions: the gas stripper canal is a stepped tube with a total length of about 20 cm and with an inner diameter of 3 mm at the center and a maximal diameter of 7 mm at the exit. It is supplied by He gas injected from the center. The gas pressure in the stripper tube drops with increasing distance from the inlet from about 1 mbar in the center to around 104 mbar at the ends. The differential pumping stage (blue in Fig. 1) plus additional turbo pumps further reduce the pressure in the accelerator chamber of the MICADAS and the region of the ESA and first magnet of the myCADAS to the 107–106 mbar range (determined by a Pfeiffer PKR251 Full Range gauge in the cold cathode mode at p1 and p2 in Fig. 1). At the myCADAS system an additional gauge measures the supply pressure in the stripper feeding tubing (p0). As described above, 12C transmissions were determined by measuring the ion currents in the analyzing and injection Faraday cups. Different charge states were measured separately by adjusting the HE magnet (ESA) at the MICADAS (myCADAS) system. Because the neutral part of the beam is not deflected, it could not be measured. Ion optic calculations including Monte Carlo simulations of multiple scattering processes of the (least phase space compressed) +1 ion beam show that in both systems the only beam limiting element is the stripper tube and the apertures connecting the differentially pumped volumes. Thus, the measured transmission can be regarded as the product of the respective charge state yield and the optical beam transmission through the stripper (comprising ion optics and scattering losses). During the experiment, the stripper pressure was varied in order to record the behavior of the transient charge exchange processes in the low density regime as well as the decrease of the transmission in the charge exchange equilibrium region that is caused by increasing angular straggling (see for example Fig. 2). The measured pressure values were corrected with the residual gas pressure in the respective vacuum vessel to account for the influence of stripper gas (He) only.
Fig. 2. Measured charge state transmissions of 1, +1, +2, +3 at 45 keV (myCADAS) at different areal stripper gas densities. The curves are linear fits to the transmission values of 1, +1, +2 and +3 in charge exchange equilibrium at high areal densities (in logarithmic scaling). For the charge state 1 there is an additional exponential fit to low density values where charge exchange processes are relevant for the exponential decrease and the population of the other charge states.
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2.2. Determination of stripper gas density The areal stripper gas density is the gas density integrated along the path of the ions. It determines the amount of interactions with the gas, both for charge exchange and scattering with gas nuclei. It is therefore crucial to determine the areal density at each transmission data point as accurate as possible to deduce accurate and precise charge exchange cross sections from full transmission profiles (as shown for example in Fig. 2). For both setups, the He gas flow through tubes, stripper, apertures and turbo pumps was estimated from a given reference pressure with the tube conductance formulas of the Knudsen flow (higher pressure) and molecular flow regime (low pressure) according to [12] and [13]. The calculated pressure in all of the geometric elements may then be converted to gas density and finally integrated to the areal gas density in the relevant geometric elements, mainly the stripper canal. Because the formulas used for the Knudsen flow regime are less exact than the formulas for the molecular flow regime, a more accurate determination of the low areal densities is to be expected. 2.2.1. MICADAS Because the MICADAS terminal is at high potential, the pressure in the supply line of the stripper inlet (after the flow reducing valve of the capillary) cannot be measured. The only available reference to the stripper density is a pressure gauge at the accelerator chamber wall (p1 in Fig. 1). To check the calculations, the areal stripper density was also determined by measuring ion beam energy losses (as done in [8]) using energy loss values from Hvelplund [14]. The deviation from the calculated areal density was less than 10% over the whole range of measured pressure values. 2.2.2. myCADAS For the myCADAS setup, the pressure from the gauge located in the stripper gas supply line (p0 in Fig. 1) was used as the reference pressure. To verify the calculations, the calculated final pressure in the outer volume (ESA, LE magnet) was compared to the measurement of a gauge running in cold cathode mode at the ESA (p2). After correction of the measured values for a minimum vacuum pressure (air, 1.3107 mbar) and the correction factor for He of the pressure gauge (the sensitivity for He is a factor of 5.9 lower than for air), the difference was less than 5% up to densities of 1.51016 atoms/cm2 and less than 10% above. 2.3. Loss correction and equilibrium charge state fractions The incident 12C beam exchanges electrons with the He gas so that other charge states get populated until a charge exchange equilibrium is reached. All the measured transmissions show this behavior (example in Fig. 2 up to 1016 He atoms/cm2) and also reveal the rising beam losses at areal gas densities beyond the point of charge exchange equilibrium. The data points need to be corrected for these losses to determine the correct charge state fractions in equilibrium. The ion optics of both systems are designed to form a beam waist in the central part of the stripper tube were it has its smallest diameter (3 mm). Because of the finite beam phase space, a part of the beam is already lost when entering the stripper tube, even without any stripper gas interaction. Phase space measurements at the position of the stripper tube and 40 lA of 12C beam current showed an emittance of around 25 p mm mrad (2r) [15] with an actual waist size and divergence around 1.7 mm15 mrad. With increasing areal stripper gas density, multiple scattering leads to a larger divergence of the outgoing beam and thus to additional losses caused by the finite outgoing acceptance angle of the stripper tube (30 mrad for MICADAS and 32 mrad for myCADAS). The ion optical and
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scattering influences on the beam losses can be described by the two parameters of a linear relationship:
lossesðareal density x; charge state iÞ ¼ bi þ ai x
ð1Þ
With the offset b describing the constant loss of the incident beam, and the slope a describing the increasing losses due to angular straggling. This is a good first order approximation to the exponential decrease which we observe at very high areal densities (not reached with the measurements included in this paper). This exponential behavior is explained by a cross section of single scattering events resulting in angles larger than the acceptance angle of the stripper canal. The measured transmissions in charge exchange equilibrium are modeled by the product of the equilibrium charge state fractions f i;1 and the losses. This model may be finally fitted to the measured transmissions at high areal densities:
transmissionðx; iÞ ¼ f i;1 lossesðx; iÞ ¼ di þ ci x The fit parameters ci and di need to be determined separately for each charge state (1 and +1 to +3) in charge exchange equilibrium and for each energy. The charge state 1 decreases exponentially with areal stripper density at low densities where equilibrium is not yet reached due to the population of the 0 and +1 charge state through single and double electron losses (Fig. 2). Extrapolating this decrease back to zero areal density reveals the offset b1 since no charge exchange processes occur without stripper gas and the initial charge state is 1 only. In case of the myCADAS experiments, no acceleration is involved and the focusing effect of the ESA is the same for all the charge states. This results in the same beam transmission into the analyzing Faraday cup and therefore b1 = b+1 = b+2 = b+3. This means that the charge state yield fi,1 of every charge state at the respective energy is known through
f i;1 ¼
di b1
ð2Þ
In case of the MICADAS measurements, the above described formula is not a valid approach for calculating fi,1, since the 1 charge state loses energy in the second tandem acceleration step back to ground and its re-expanded phase space volume leads to additional beam losses which do not occur for the other (accelerated and therefore phase space compressed) charge states. To determine the offset b+1 = b+2 = b+3, transport and scattering simulations through the stripper tube were used [16] with a known source phase space of 25 p mm mrad (2r, at 45 keV and 40 lA). Beam losses in the magnet after stripping are negligible and were not considered. The effective offset then depends on the focusing of the source lenses which form the ion optical image in front of the first magnet that is then further transported into the stripper tube. For the further calculations, the maximal possible offset was used as the machine was tuned for maximal transmission during the experiments. Offset values of 0.925, 0.955 and 0.975 were determined for the measurements at 144, 192 and 258 keV respectively with uncertainties of ±1% assuming a variation of ±0.1 mm in 2r waist size which we observed during phase space measurements done in [15]. The offset values are given by the maximum optical beam transmission at zero stripper gas density. Since all bi can be deduced this way, the slopes ai follow from the fitted coefficients ci and di and the transmissions can be fully corrected for beam losses. 2.4. Charge exchange cross sections The evolution of the different charge states f i ðxÞ with areal stripper gas density x, as visible in Fig. 3, are explained through charge exchange processes with charge exchange cross sections ri!j :
Fig. 3. Charge state fractions of 12C in He at 45 keV, corrected for scattering losses and losses in beam limiting elements (described in Section 2.3). The data points are plotted against stripper gas areal density calculated from pressure in the stripper supply line (described in Section 2.2). The curves were fitted with single and double electron loss and capture cross sections (described in Section 2.4).
dfi ¼
X
f rj!i j–i j
X
f r dx: i!j i j–i
ð3Þ
Integration of this set of linear differential equations can be done analytically and results in an exponential of the matrix that contains the exchange cross sections. By fitting the solution to the measured (and loss corrected) transmission profiles, values for the cross sections are determined. The energy loss of the incident ions in the stripper gas was not considered as the charge exchange processes depend on the ion velocity and thus have only a minor (square root of energy) influence on the profiles. Therefore, the cross sections presented here need to be understood as effective cross sections averaging over ion energy and factors such as excitation states of the ions. Only single and double electron loss and capture cross sections were included for the charge states 1 to +3. For fitting, the Levenberg–Marquardt least squares method was used with the levmar library for C/C++ [17] and inequality constraints were set to disable the possibility of negative cross sections which would formally lead to correct fits but are physically not valid. For the residual, the deviation of the single data points from the fitted curves were weighted with the inverse of the data points themselves to account for the large range of orders of magnitude in transmissions. We note that the implementation of the physical motivated constraints resulted in only slightly higher residuals than the formally correct algorithm without any constraints for ri!j . Because of the rather big set of independent fit parameters (14 cross sections), correlations between some of them introduce a dependency of the fit result on the starting values. An example for such a correlation is found for the +3 charge state, whose small transmission allows for different combinations of rþ3!þ2 and rþ3!þ1 . To account for these correlations, several thousand randomly distributed initial values were used to find sets of cross sections. 3. Results Fig. 3 is given as an example for a set of charge state fractions at an ion energy of 45 keV. The data points were calculated from raw transmission measurements (Fig. 2) and the curves represent the functions f i ðxÞ characterized by Eq. (3). The incident 12C beam exchanges electrons with the He gas and an increasing fraction is neutralized (single electron loss) or ionized into higher, positive charge states (multiple electron loss). This leads to an exponential decrease over almost the whole range of densities because the repopulation from higher charge states is very small. The neutral part of the beam could not be measured but can be derived from
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S. Maxeiner et al. / Nuclear Instruments and Methods in Physics Research B 361 (2015) 541–547 Table 1 Equilibrium charge state fractions (Eq. (2)) of 12C in He from measurements at myCADAS (30–50 keV) and MICADAS (144–258 keV). The neutral yield was not measured but is given by the remaining fraction of 100%. Relative uncertainties are estimated to ±3% (myCADAS) and ±1% (MICADAS) respectively, resulting from uncertainties in the transmission correction. Possible systematic errors are discussed in Section 4. E/keV
+1
+2
+3
30 40 45 50 144 192 258
0.76 0.72 0.78 0.75 0.6 0.54 0.5
0.11 0.095 0.1 0.11 0.17 0.18 0.19
0.00029 0.00049 0.00056 0.00065 0.0062 0.0095 0.011
the fractions of the other charge states. It is increasingly populated at low areal densities until not enough negatively charged ions are left to pick up electrons and the ionization of neutral 12C into 12C+ becomes the dominant contribution leading to a decrease again and a maximum around 0.21016 atoms/cm2. The charge state fractions of 1+ to 3+ extend over a large range of order of magnitudes while they rise asymptotically towards their charge exchange equilibrium at high areal densities (around 21016 He atoms/cm2) defined by dfi ¼ 0 in Eq. (3). These charge state yields are reported in Table 1 for all measured energies. Charge exchange cross sections of all measured energies are reported in Tables 2 and 3. To account for the different fit result sets (depending on the initial fit values), mean cross section values are given with errors indicating an interval which covers 95% of all fit results. Cross sections which were fitted to values below 1024 cm2 are not reported. 4. Discussion From the transmission measurements at the AMS instruments it is not possible to determine very accurate equilibrium charge state Table 2 Charge exchange cross sections of
1 ? 0 0?1 1?2 2?3 3?2 2?1 1?0 0 ? 1 1 ? 1 0?2 1?3 3?1 2?0 1 ? 1
12
fractions, since the beam losses especially at low energies strongly depend on the focusing of the ion source and on the angular straggling in the stripper. The focusing can be slightly different for different cathodes because of varying burn-in characteristics of the primary Cs-beam. By applying the angular straggling loss corrections to the transmission versus pressure profiles instead of areal density profiles, +1 equilibrium charge state fractions of around 0.80 are computed. This approach is valid, since the pressure to areal density behavior is almost linear and the linear fits reproduce the data quite well. This suggests a systematic uncertainty which can be estimated to be at least 7%. To estimate uncertainties of current measurements originating from secondary electron losses, the inner charge collecting cylinder of the MICADAS Faraday cups were raised to a +50 V potential. With the potential applied, a measured positive ion current of 70 nA (13C) and 7 lA (12C) decreased by up to 1.5%. Even though the myCADAS analyzing cup is shorter, no difference in current measurement was found in a direct comparison with the other geometries. This suggests that the reported transmission values of positive charge states might be overestimated by up to 3% due to the normalization to underestimated negative injection current. Nevertheless, the increase of the +1 charge state yield towards low energies is significant (Fig. 4) and an important result for low energy AMS developments. The cause for this increase of +1 is found in the relatively stable electron loss cross section of the neutral charge state (r0!þ1 ) with energy and the decreasing electron capture cross section of the +1 charge state (rþ1!0 ) which reduces the population of the neutral beam in favor of the +1 charge state (see Fig. 5). In gases like Ar, this decrease is observed at much lower energies which results in a neutral carbon yield of about 70% at 50 keV while the +1 charge state yield is around 20% [18]. The neutral beam intensity could not be measured, but only reconstructed from the other charge states and therefore crucial information about the total system transmission is missing. The fitted values of the single electron exchange cross section between the +1 and 0 charge state are therefore less reliable in their absolute value. This is particularly valid for the MICADAS
C in He in 1016 cm2 from measurements at myCADAS (30–50 keV).
30 keV
40 keV
45 keV
50 keV
6.625 +0.064/0.16 3.68 +0.39/0.77 0.43 +0.79/0.25 0.018 +0.044/0.018
6.523 +0.066/0.17 2.46 +0.72/0.29 0.76 +0.58/0.56 0.051 +0.074/0.051
6.489 +0.032/0.15 2.979 +0.19/0.095 0.81 +0.95/0.65 0.02 +0.07/0.02
6.23 +0.065/0.038 3.02 +0.045/0.049 0.64 +0.65/0.64 –
16 +15/11 3.5 +5.7/2 0.94 +0.2/0.37 0.01276 +0.0013/6.6E – 4
15.4 +11/9.7 5.9 +4.6/4.3 0.31 +0.48/0.21 0.0297 +5E 3/0.012
15 +11/8.8 6 +6.6/4.7 0.32 +0.13/0.26 0.0293 +0.0012/5E – 3
8.8 +2/4.8 4.6 +4.2/3.9 0.45 +0.13/0.4 0.022 +0.0037/0.0023
0.727 +0.18/0.081 0.3 +0.04/0.12 0.0054 +0.0014/0.0017
0.87 +0.11/0.13 0.28 +0.066/0.072 0.0063 +0.0017/2E 3
0.988 +0.095/0.056 0.313 +0.093/0.13 0.01072 +6.9E 4/0.0027
1.274 +0.028/0.049 0.39 +0.12/0.12 0.008706 +1.6E 4/9.6E 5
5.8 +8.7/5 0.18 +1.1/0.18 –
5.3 +4.7/4 0.68 +1.5/0.66 –
4.5 +4.4/4.5 0.62 +1.8/0.62 –
1.8 +4.7/1.8 0.66 +2.6/0.66 0.00338 +4.4E 4/7.2E 4
546 Table 3 Charge exchange cross sections of
1 ? 0 0?1 1?2 2?3 3?2 2?1 1?0 0 ? 1 1 ? 1 0?2 1?3 3?1 2?0 1 ? 1
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12
C in He in 1016 cm2 from measurements at MICADAS (144–258 keV). 144 keV
192 keV
258 keV
4.591 +0.32/0.084 2.59 +0.48/0.34 1.37 +0.26/0.75 0.34 +0.29/0.27
3.99 +0.44/0.47 2.81 +0.9/1.3 1.36 +0.68/0.91 0.51 +0.29/0.14
4.284 +0.036/0.05 2.56 +0.13/0.15 2.33 +0.27/0.41 0.56 +0.49/0.36
8.4 +5.9/5.4 3.7 +1.4/1.8 0.57 +0.43/0.47 0.08363 +8.3E 4/0.0031
7.2 +6.3/4.3 3.4 +1.8/1.9 1.18 +0.57/0.56 –
8 +6.1/4.4 4.2 +1.6/1.6 0.62 +0.59/0.61 –
1.276 +0.087/0.34 0.12 +0.3/0.11 0.021 +0.013/0.014
1.01 +0.46/0.44 0.28 +0.38/0.28 –
0.267 +0.05/0.037 0.267 +0.05/0.037 0.044 +0.041/0.044
3.7 +2.9/2.9 1.1 +1.3/1 –
2.9 +2.9/2.4 0.76 +1.1/0.66 0.04972 +3.3E 4/2.2E 4
3.6 +2.9/2 2.3 +1.5/1.5 0.08662 +3.1E 4/2.2E 4
(a)
(b) Fig. 4. Equilibrium charge state fraction of +1 (f þ1;1 , top) and +2 (f þ2;1 , bottom) of 12 C in He at different energies. The black data points (boxes, circles) were measured by Hvelplund et al. [4,10]. The red datapoints (diamonds, triangles) are extracted from the corrected myCADAS and MICADAS density profiles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
measurements, where only ray tracing and scattering simulations could be used to estimate beam losses. Since for these measurements also the deceleration back to ground leads to a significantly broadened 1 ion beam on the HE side of the system, the injection loss correction (offset b in Eq. (1)) of this charge state can only be done by extrapolating back to 0 areal stripper density. This approach, in turn, depends on the offset in pressure measurement which is not exactly known and can only be estimated from vacuum readings after long periods of pumping. Furthermore, the additional beam broadening may also lead to secondary beam losses in subsequent electrodes or vacuum tubes (instead of just in one limiting element like the stripper canal). This would invalidate the approach of a linear loss correction with a single slope a (Eq. (1)) over the whole density region. In this case, the 1 ion
Fig. 5. (a) and (b) Single electron exchange cross sections. (a) Electron loss, (b) electron capture of carbon in helium from literature [19–34] (unfilled plot points) and this paper (filled plot points). Error bars indicate the scatter of fit results coming from different initial fit parameters. (see Section 2.4).
beam losses would be underestimated. This could be an explanation for the behavior of the r0!1 cross section which could not be fitted with the data at the highest energy (its fitted value was numerically zero). The electron exchange between the charge
S. Maxeiner et al. / Nuclear Instruments and Methods in Physics Research B 361 (2015) 541–547
states +1, +2 and +3 on the other hand fit well into literature trends and even extend them to low energies, due to the almost loss-less measurement of these charge states. To determine the charge exchange cross sections even better, different initial charge states would have been needed to further constrain the degrees of freedom in the fit procedure. Also a more precise knowledge of the beam losses or the detection of neutral beam particles would increase the overall accuracy. Because the calculated cross sections are inversely proportional to the determined areal stripper density, a relative error in the conversion of pressure to areal stripper density propagates directly. By comparing the values presented here to data from literature, this error seems to be quite small, much smaller than the variations introduced by different initial fit parameters (error bars in Fig. 5). This supports the validity of the approach of calculating the areal stripper gas density from pressure readings and gas flow calculations. Literature values on the other hand also suffer from systematic errors as is particularly visible for the electron capture of +2, where values from various groups differ by up to a factor of 3. This makes the calculation of charge state yields from exchange cross sections unreliable. Some of the cross sections are of particular interest for AMS applications. If stripper gas leaks into acceleration sections, charge exchange processes during acceleration alter the energy of particles. Low energetic molecular breakup fragments for example could gain just the right energy to pass the subsequent filter element. Hence, these processes are possible sources for background and their influence may be estimated from the corresponding cross sections. Because scattering cross sections are higher at lower energies, the increase in beam losses partially compensates the gain in charge state yield. To estimate the total transmission versus energy, we performed ray tracing and scattering simulations of the current MICADAS stripper tube and multiplied the resulting transmissions with charge state yields at corresponding energies. The results suggest a constant overall transmission of 12C in He into 12C+ around 47% from 300 keV down to about 80 keV which drops to 35% at 45 keV. This in turn encourages further experiments with acceleration voltages around 50–80 kV (i.e., stripping energies around 80– 100 keV) which would allow even more compact radiocarbon AMS designs. 5. Conclusion Single and double electron loss and capture cross sections for C in He were determined in the range of 30 keV up to 258 keV for the 1 up to +3 charge state from sets of transmission versus areal stripper gas density measurements. Not precisely known beam losses and the lack of measurement of the neutral charge state limit the accuracy of the values. Nevertheless, they are able to explain the trend of the charge state yields with energy and extend the knowledge of the single electron loss cross sections of charge states +2 and +3 to the region below 400 keV. The charge state yields of +1, +2 and +3 could be determined from the same sets of measurements and are compatible with earlier measurements at 100 keV and above by Hvelplund et al. [4,10]. At the lowest measured stripping energies around 30 keV, +1 charge state yields of up to 75% were evaluated. At this very low
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stripping energy however, angular and energy loss straggling are dominant and significantly reduce the total transmission. This suggests that there is an optimal energy range which maximizes transmission and enables a more compact AMS machine design. Rough estimates of beam losses with scattering simulations at different energies suggest an energy of around 100 keV for the next generation of radiocarbon AMS systems. Acknowledgment The author is funded by the Swiss National Science Foundation. References [1] C.L. Bennett, R.P. Beukens, M.R. Clover, H.E. Gove, R.B. Liebert, A.E. Litherland, K.H. Purser, W.E. Sondheim, Science 198 (1977) 508. [2] K.H. Purser, US Patent: 4037100, Appl. No.: 662968 (1977). [3] K.H. Purser, R.B. Liebert, C.J. Russo, Radiocarbon 22 (1980) 794. [4] A.B. Wittkower, H.D. Betz, At. Data 5 (1973) 113. [5] H.W. Lee, A. Galindo-Uribarri, K.H. Chang, L.R. Kilius, A.E. Litherland, Nucl. Instr. Meth. Phys. Res., Sect. B 5 (1984) 208. [6] Ref. [34], in: A.E. Litherland, Nucl. Instr. Meth. Phys. Res., Sect. B 5 (1984) 100. [7] H.A. Synal, M. Stocker, M. Suter, Nucl. Instr. Meth. Phys. Res., Sect. B 259 (2007) 7. [8] T. Schulze-König, M. Seiler, M. Suter, L. Wacker, H.-A. Synal, Nucl. Instr. Meth. Phys. Res., Sect. B 269 (2011) 34. [9] P.M. Stier, C.F. Barnett, G.E. Evans, Phys. Rev. 96 (1954) 973. [10] P. Hvelplund, E. Lægsgaard, E. Horsdal Pedersen, Nucl. Instr. Meth. 101 (1972) 497. [11] H.-A. Synal, T. Schulze-König, M. Seiler, M. Suter, L. Wacker, Nucl. Instr. Meth. Phys. Res., Sect. B 294 (2013) 349. [12] M. Wutz, H. Adam, W. Walcher, K. Jousten, Handbuch Vakuumtechnik, 7th ed., Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, 2000. [13] J.M. Lafferty, Foundations of Vacuum Science and Technology, John Wiley & Sons Inc., New York, 1998. [14] P. Hvelplund, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 38 (1971) 1. [15] M. Seiler, Accelerator Mass Spectrometry for Radiocarbon at very Low Energies (Ph.D. thesis), ETH Zurich, 2014. [16] S. Maxeiner, M. Suter, M. Christl, and H.-A. Synal, Simulation of ion beam scattering in a gas stripper, in: AMS13 Proceedings, unpublished. [17] M.I.A. Lourakis, Retrieved 31 Jan. 2005. From:. [18] J.H. Ormrod, W.L. Michel, Can. J. Phys. 49 (1971) 606. [19] I.S. Dmitriev, Y.A. Teplova, Y.A. Belkova, N.V. Novikov, Y.A. Fainberg, At. Data Nucl. Data Tables 96 (2010) 85. [20] Y. Nakai, M. Sataka, J. Phys. B: At. Mol. Opt. Phys. 24 (1991) L89. [21] L.M. Rottmann, R. Bruch, P. Neill, C. Drexler, R.D. Dubois, L.H. Toburen, Phys. Rev. A 46 (1992) 3883. [22] L.D. Gardner, J.E. Bayfield, P.M. Koch, I.A. Sellin, D.J. Pegg, R.S. Peterson, M.L. Mallory, D.H. Crandall, Phys. Rev. A 20 (1979) 766. [23] E. Unterreiter, J. Schweinzer, H. Winter, J. Phys. B: At. Mol. Opt. Phys. 24 (1991) 1003. [24] K. Ishii, A. Itoh, K. Okuno, Phys. Rev. A 70 (2004) 042716. [25] T. Iwai, Y. Kaneko, M. Kimura, N. Kobayashi, S. Ohtani, K. Okuno, S. Takagi, H. Tawara, S. Tsurubuchi, Phys. Rev. A 26 (1982) 105. [26] E.C. Montenegro, G.M. Sigaud, W.E. Meyerhof, Phys. Rev. A 45 (1992) 1575. [27] W.S. Melo, M.M. Sant’anna, A.C.F. Santos, G.M. Sigaud, E.C. Montenegro, Phys. Rev. A 60 (1999) 1124. [28] A.C.F. Santos, G.M. Sigaud, W.S. Melo, M.M. Sant’anna, E.C. Montenegro, Phys. Rev. A 82 (2010) 012704. [29] N.V. Novikov, Y.A. Teplova, Retrieved 3 Oct. 2014. From: . [30] I.M. Fogel, V.A. Ankudinov, D.V. Pilipenko, Sov. Phys. JETP-USSR 8 (1959) 601. [31] T. Kusakabe, Y. Mizumoto, K. Katsurayama, H. Tawara, J. Phys. Soc. Jpn. 59 (1990) 1987. [32] Y. Huang, G. Li, Y. Gao, E. Yang, M. Gao, F. Lu, X. Zhang, Phys. Lett. A 355 (2006) 55. [33] H. Luna, F. Zappa, M.H.P. Martins, S.D. Magalhães, G. Jalbert, L.F.S. Coelho, N.V. De Castro Faria, Phys. Rev. A 63 (2001) 052716. [34] R.K. Janev, R.A. Phaneuf, H.T. Hunter, At. Data Nucl. Data Tables 40 (1988) 249.
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Charge state distributions and charge exchange cross sections of carbon in helium at 30–258 keV Sascha Maxeiner ⇑, Martin Seiler, Martin Suter, Hans-Arno Synal Laboratory of Ion Beam Physics, ETH Zurich, 8093 Zurich, Switzerland
a r t i c l e
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Article history: Received 12 December 2014 Received in revised form 19 February 2015 Accepted 20 February 2015 Available online 14 March 2015 Keywords: Charge state distributions Charge exchange Helium stripping Low energy Accelerator Mass Spectrometry
a b s t r a c t With the introduction of helium stripping in radiocarbon (14C) accelerator mass spectrometry (AMS), higher +1 charge state yields in the 200 keV region and fewer beam losses are observed compared to nitrogen or argon stripping. To investigate the feasibility of even lower beam energies for 14C analyses the stripping characteristics of carbon in helium need to be further studied. Using two different AMS systems at ETH Zurich (myCADAS and MICADAS), ion beam transmissions of carbon ions for the charge states 1, +1, +2 and +3 were measured in the range of 258 keV down to 30 keV. The correction for beam losses and the extraction of charge state yields and charge exchange cross sections will be presented. An increase in population of the +1 charge state towards the lowest measured energies up to 75% was found as well as agreement with previous data from literature. The findings suggest that more compact radiocarbon AMS systems are possible and could provide even higher efficiency than current systems operating in the 200 keV range. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction To perform radiocarbon (14C) mass spectrometry, interfering isobars such as 14N and molecules like 12CH2, 13CH and 7Li2 need to be eliminated. Early measurements revealed, that 14N ions are not stable while stable 14C ion beams can be produced in ion sputter sources [1]. The molecules like the ones mentioned above on the other hand turned out to not have any bound states in charge states P+3 [2]. First radiocarbon accelerator mass spectrometry (AMS) setups around 1980 [3] made use of these facts and accelerated a negatively charged ion beam onto a gas or solid target. By stripping electrons from the ions in the target, different ionization states are produced, including the molecule free +3. The distribution of charge states depends on the thickness of the stripper medium and its compositions as well as the initial ion charge state. The charge exchange processes scale with the ion velocity and atomic number (for example see Ref. [4]). Towards high stripper thickness, a charge exchange equilibrium is established which does not depend on the initial charge state and stripper thickness anymore. The different charge state fractions in this equilibrium region are defined as their yields and are given by the physical charge exchange cross sections. Due to beam losses in a system, a different definition, namely the transmission, is usually of more ⇑ Corresponding author. E-mail address: [email protected] (S. Maxeiner). http://dx.doi.org/10.1016/j.nimb.2015.02.060 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.
use. It is defined as the measured ratio of particles in a specific charge state after stripping to all the injected particles before stripping. It is therefore given by the product of charge state yield and optical ion beam transmission. To achieve a sufficient measurement efficiency for good counting statistics, high acceleration voltages of several MV are needed for AMS in order to populate the higher charge states where no interfering molecules exist. In the following years the use of lower charge states such as 12 2+ C and 12C1+ was discussed. It was shown that the molecule intensity decreases exponentially with stripper thickness due to collisions with the target atoms [5,6]. Furthermore, high transmissions of 12C1+ in N2 gas were observed at 200 keV [7]. At such low energies, increased angular straggling and the reduced phase space compression of the ion beam diminish the transmission and increase the background. The use of helium instead of heavier gases was suggested to overcome this issue as the lower nuclear charge leads to decreased angular straggling while providing sufficient molecular destruction at only slightly higher areal densities [8]. The study of He as a target for ion gas interactions in the keV region goes back to 1954 where Stier et al. [9] investigated the charge state yields of the light ions H, He, N, Ne and Ar. Later, transmission measurements of carbon ions by Hvelplund et al. [4,10] revealed yields of about 50% for the +1 charge state at energies around 300 keV with increasing yield towards lower energies of 100 keV. Experimental data of charge state yields of carbon in helium in the 30–100 keV region is missing and makes it difficult
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to estimate the feasibility of radiocarbon AMS at even lower energies than today’s smallest available AMS systems at 200 keV. To fill this gap we performed transmission measurements on our compact AMS system MICADAS at 144 up to 258 keV stripping energy and our new prototype (A)MS system myCADAS [11] without tandem acceleration at energies as low as 30 keV. To correct the measured transmissions for beam losses, simulations of the beam limiting ion optical elements were performed. By measuring the dependence of charge state fractions 1, +1, +2 and +3 on the stripper density it was possible to determine the charge exchange cross sections. 2. Methods 2.1. Experimental setup Measurements of negative carbon ions passing through a He gas target were performed on two different systems available for radiocarbon dating at ETH Zurich. The experiments at higher energies (P144 keV) were carried out on the MICADAS radiocarbon AMS system [7], while experiments below 50 keV were performed on the new ETH Zurich prototype system myCADAS [11] (Fig. 1). In both AMS systems, the negative ion beam is produced in a Cs sputter source from a graphite target and in all experiments 12C is selected in the 90° injection magnet. To quickly alternate between different deflection radii without changing the magnetic field, a fast, electrostatic beam switching system is available on both systems. This enables the quasi simultaneous measurement of the 12C current Iinject in the off-axis injection Faraday cup (dark green, in the focal plane of the magnet) and the deflection onto the beam reference axis into the gas stripper canal (light green). A beam waist is formed in the center of the stripper in both systems to minimize beam losses. The beam current Ipost stripping of a charge state is finally measured in an analyzing Faraday cup (light green) after selection with either a second 90° magnet (MICADAS) or an electrostatic deflector (myCADAS). The Faraday cups are not equipped with suppressor
electrodes or magnets. To reduce secondary electron losses, the back plane of the charge collecting inner cups are tilted by 60° and the drift length from the cup aperture to the back plane is around 10 cm (5 cm in case of the myCADAS analyzing cup). The entrance aperture radii limit the opening angle seen from the back plane to less than 30 msr (100 msr in case of the myCADAS analyzing cup). Faraday cup currents are integrated on a capacitor over a few microseconds and the resulting voltage is read and converted. The overall precision and accuracy of current readout of this in-house built setup amounts to less than 1‰. Because this integrator setup is not able to read negative currents, a microammeter was used to manually record currents of the negatively charged ion beam. Additionally, the magnet (ESA) polarity needed to be swapped to select the negatively charged fraction of the ions. In all the experiments the value of the transmission was measured, defined as the absolute value of the ratio (Ipost stripping/q)/Iinject, with q being the respective charge state. In the MICADAS system, beam slits are positioned at the focal point of the first magnet and the ion beam is focused into the gas stripper canal at the high voltage potential by acceleration. The high voltage terminal can reach potentials of up to 220 kV and is differentially pumped by a 700 l/s turbo pump. In Fig. 1, the differential pumping region is indicated by the lighter shaded region (blue in the online version). The high voltage platform is supported by a ceramic holder (at the bottom) and vacuum insulated from the outer vessel, which is at ground potential and is pumped by two additional 700 l/s turbo pumps. Stripper gas is fed from ground to the high voltage terminal via a thin glass capillary with a diameter of about 100 lm. This requires a high He gas pressure of up to 30 bar to prevent electrical breakdown in the capillary. The gas flow into the stripper is finally regulated by a valve on the high voltage terminal which can be mechanically controlled from ground via a ceramic rod. After passing the stripper tube the positive (negative) ions are (de)accelerated back to ground. The subsequent high energy (HE) 90° magnet deflects the different beams into a vacuum chamber with
Fig. 1. Overview of the myCADAS (30–50 keV) and MICADAS (144–258 keV) radiocarbon (A)MS setup (seen from the top). Apart from the ion source and beam switching system, all of the myCADAS system is operated at ground potential. The high voltage for the acceleration at MICADAS is supplied by a commercial power supply and uses vacuum insulation. Both systems differentially pump the He stripper housing (lighter shaded region, blue in the online version) to achieve acceptable vacuum in the rest of the system. In case of MICADAS, this is monitored in the accelerator vessel (p1) while for myCADAS the pressure at the ESA (p2) is monitored. The He supply pressure at myCADAS is measured at p0, before it is reduced by a 30 cm tubing (4 mm diameter) and tube connecting parts. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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a Faraday cup for detection of 12C (light green in Fig. 1). Different charge states of 12C were selected by adjusting the magnetic field. Experiments at energies at and below 50 keV were performed on the prototype system myCADAS that is described in more detail in reference [11]. The main difference to the MICADAS setup is the absence of a second acceleration stage as the stripper tube is at ground potential. Because the focusing effect of the acceleration is missing, the center of the stripper canal needs to be at the position of the beam slits of the MICADAS setup. Furthermore, the second magnet is replaced by a 90° electrostatic deflector. Both systems use the same principle for stripping electrons from the incoming ions: the gas stripper canal is a stepped tube with a total length of about 20 cm and with an inner diameter of 3 mm at the center and a maximal diameter of 7 mm at the exit. It is supplied by He gas injected from the center. The gas pressure in the stripper tube drops with increasing distance from the inlet from about 1 mbar in the center to around 104 mbar at the ends. The differential pumping stage (blue in Fig. 1) plus additional turbo pumps further reduce the pressure in the accelerator chamber of the MICADAS and the region of the ESA and first magnet of the myCADAS to the 107–106 mbar range (determined by a Pfeiffer PKR251 Full Range gauge in the cold cathode mode at p1 and p2 in Fig. 1). At the myCADAS system an additional gauge measures the supply pressure in the stripper feeding tubing (p0). As described above, 12C transmissions were determined by measuring the ion currents in the analyzing and injection Faraday cups. Different charge states were measured separately by adjusting the HE magnet (ESA) at the MICADAS (myCADAS) system. Because the neutral part of the beam is not deflected, it could not be measured. Ion optic calculations including Monte Carlo simulations of multiple scattering processes of the (least phase space compressed) +1 ion beam show that in both systems the only beam limiting element is the stripper tube and the apertures connecting the differentially pumped volumes. Thus, the measured transmission can be regarded as the product of the respective charge state yield and the optical beam transmission through the stripper (comprising ion optics and scattering losses). During the experiment, the stripper pressure was varied in order to record the behavior of the transient charge exchange processes in the low density regime as well as the decrease of the transmission in the charge exchange equilibrium region that is caused by increasing angular straggling (see for example Fig. 2). The measured pressure values were corrected with the residual gas pressure in the respective vacuum vessel to account for the influence of stripper gas (He) only.
Fig. 2. Measured charge state transmissions of 1, +1, +2, +3 at 45 keV (myCADAS) at different areal stripper gas densities. The curves are linear fits to the transmission values of 1, +1, +2 and +3 in charge exchange equilibrium at high areal densities (in logarithmic scaling). For the charge state 1 there is an additional exponential fit to low density values where charge exchange processes are relevant for the exponential decrease and the population of the other charge states.
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2.2. Determination of stripper gas density The areal stripper gas density is the gas density integrated along the path of the ions. It determines the amount of interactions with the gas, both for charge exchange and scattering with gas nuclei. It is therefore crucial to determine the areal density at each transmission data point as accurate as possible to deduce accurate and precise charge exchange cross sections from full transmission profiles (as shown for example in Fig. 2). For both setups, the He gas flow through tubes, stripper, apertures and turbo pumps was estimated from a given reference pressure with the tube conductance formulas of the Knudsen flow (higher pressure) and molecular flow regime (low pressure) according to [12] and [13]. The calculated pressure in all of the geometric elements may then be converted to gas density and finally integrated to the areal gas density in the relevant geometric elements, mainly the stripper canal. Because the formulas used for the Knudsen flow regime are less exact than the formulas for the molecular flow regime, a more accurate determination of the low areal densities is to be expected. 2.2.1. MICADAS Because the MICADAS terminal is at high potential, the pressure in the supply line of the stripper inlet (after the flow reducing valve of the capillary) cannot be measured. The only available reference to the stripper density is a pressure gauge at the accelerator chamber wall (p1 in Fig. 1). To check the calculations, the areal stripper density was also determined by measuring ion beam energy losses (as done in [8]) using energy loss values from Hvelplund [14]. The deviation from the calculated areal density was less than 10% over the whole range of measured pressure values. 2.2.2. myCADAS For the myCADAS setup, the pressure from the gauge located in the stripper gas supply line (p0 in Fig. 1) was used as the reference pressure. To verify the calculations, the calculated final pressure in the outer volume (ESA, LE magnet) was compared to the measurement of a gauge running in cold cathode mode at the ESA (p2). After correction of the measured values for a minimum vacuum pressure (air, 1.3107 mbar) and the correction factor for He of the pressure gauge (the sensitivity for He is a factor of 5.9 lower than for air), the difference was less than 5% up to densities of 1.51016 atoms/cm2 and less than 10% above. 2.3. Loss correction and equilibrium charge state fractions The incident 12C beam exchanges electrons with the He gas so that other charge states get populated until a charge exchange equilibrium is reached. All the measured transmissions show this behavior (example in Fig. 2 up to 1016 He atoms/cm2) and also reveal the rising beam losses at areal gas densities beyond the point of charge exchange equilibrium. The data points need to be corrected for these losses to determine the correct charge state fractions in equilibrium. The ion optics of both systems are designed to form a beam waist in the central part of the stripper tube were it has its smallest diameter (3 mm). Because of the finite beam phase space, a part of the beam is already lost when entering the stripper tube, even without any stripper gas interaction. Phase space measurements at the position of the stripper tube and 40 lA of 12C beam current showed an emittance of around 25 p mm mrad (2r) [15] with an actual waist size and divergence around 1.7 mm15 mrad. With increasing areal stripper gas density, multiple scattering leads to a larger divergence of the outgoing beam and thus to additional losses caused by the finite outgoing acceptance angle of the stripper tube (30 mrad for MICADAS and 32 mrad for myCADAS). The ion optical and
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scattering influences on the beam losses can be described by the two parameters of a linear relationship:
lossesðareal density x; charge state iÞ ¼ bi þ ai x
ð1Þ
With the offset b describing the constant loss of the incident beam, and the slope a describing the increasing losses due to angular straggling. This is a good first order approximation to the exponential decrease which we observe at very high areal densities (not reached with the measurements included in this paper). This exponential behavior is explained by a cross section of single scattering events resulting in angles larger than the acceptance angle of the stripper canal. The measured transmissions in charge exchange equilibrium are modeled by the product of the equilibrium charge state fractions f i;1 and the losses. This model may be finally fitted to the measured transmissions at high areal densities:
transmissionðx; iÞ ¼ f i;1 lossesðx; iÞ ¼ di þ ci x The fit parameters ci and di need to be determined separately for each charge state (1 and +1 to +3) in charge exchange equilibrium and for each energy. The charge state 1 decreases exponentially with areal stripper density at low densities where equilibrium is not yet reached due to the population of the 0 and +1 charge state through single and double electron losses (Fig. 2). Extrapolating this decrease back to zero areal density reveals the offset b1 since no charge exchange processes occur without stripper gas and the initial charge state is 1 only. In case of the myCADAS experiments, no acceleration is involved and the focusing effect of the ESA is the same for all the charge states. This results in the same beam transmission into the analyzing Faraday cup and therefore b1 = b+1 = b+2 = b+3. This means that the charge state yield fi,1 of every charge state at the respective energy is known through
f i;1 ¼
di b1
ð2Þ
In case of the MICADAS measurements, the above described formula is not a valid approach for calculating fi,1, since the 1 charge state loses energy in the second tandem acceleration step back to ground and its re-expanded phase space volume leads to additional beam losses which do not occur for the other (accelerated and therefore phase space compressed) charge states. To determine the offset b+1 = b+2 = b+3, transport and scattering simulations through the stripper tube were used [16] with a known source phase space of 25 p mm mrad (2r, at 45 keV and 40 lA). Beam losses in the magnet after stripping are negligible and were not considered. The effective offset then depends on the focusing of the source lenses which form the ion optical image in front of the first magnet that is then further transported into the stripper tube. For the further calculations, the maximal possible offset was used as the machine was tuned for maximal transmission during the experiments. Offset values of 0.925, 0.955 and 0.975 were determined for the measurements at 144, 192 and 258 keV respectively with uncertainties of ±1% assuming a variation of ±0.1 mm in 2r waist size which we observed during phase space measurements done in [15]. The offset values are given by the maximum optical beam transmission at zero stripper gas density. Since all bi can be deduced this way, the slopes ai follow from the fitted coefficients ci and di and the transmissions can be fully corrected for beam losses. 2.4. Charge exchange cross sections The evolution of the different charge states f i ðxÞ with areal stripper gas density x, as visible in Fig. 3, are explained through charge exchange processes with charge exchange cross sections ri!j :
Fig. 3. Charge state fractions of 12C in He at 45 keV, corrected for scattering losses and losses in beam limiting elements (described in Section 2.3). The data points are plotted against stripper gas areal density calculated from pressure in the stripper supply line (described in Section 2.2). The curves were fitted with single and double electron loss and capture cross sections (described in Section 2.4).
dfi ¼
X
f rj!i j–i j
X
f r dx: i!j i j–i
ð3Þ
Integration of this set of linear differential equations can be done analytically and results in an exponential of the matrix that contains the exchange cross sections. By fitting the solution to the measured (and loss corrected) transmission profiles, values for the cross sections are determined. The energy loss of the incident ions in the stripper gas was not considered as the charge exchange processes depend on the ion velocity and thus have only a minor (square root of energy) influence on the profiles. Therefore, the cross sections presented here need to be understood as effective cross sections averaging over ion energy and factors such as excitation states of the ions. Only single and double electron loss and capture cross sections were included for the charge states 1 to +3. For fitting, the Levenberg–Marquardt least squares method was used with the levmar library for C/C++ [17] and inequality constraints were set to disable the possibility of negative cross sections which would formally lead to correct fits but are physically not valid. For the residual, the deviation of the single data points from the fitted curves were weighted with the inverse of the data points themselves to account for the large range of orders of magnitude in transmissions. We note that the implementation of the physical motivated constraints resulted in only slightly higher residuals than the formally correct algorithm without any constraints for ri!j . Because of the rather big set of independent fit parameters (14 cross sections), correlations between some of them introduce a dependency of the fit result on the starting values. An example for such a correlation is found for the +3 charge state, whose small transmission allows for different combinations of rþ3!þ2 and rþ3!þ1 . To account for these correlations, several thousand randomly distributed initial values were used to find sets of cross sections. 3. Results Fig. 3 is given as an example for a set of charge state fractions at an ion energy of 45 keV. The data points were calculated from raw transmission measurements (Fig. 2) and the curves represent the functions f i ðxÞ characterized by Eq. (3). The incident 12C beam exchanges electrons with the He gas and an increasing fraction is neutralized (single electron loss) or ionized into higher, positive charge states (multiple electron loss). This leads to an exponential decrease over almost the whole range of densities because the repopulation from higher charge states is very small. The neutral part of the beam could not be measured but can be derived from
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S. Maxeiner et al. / Nuclear Instruments and Methods in Physics Research B 361 (2015) 541–547 Table 1 Equilibrium charge state fractions (Eq. (2)) of 12C in He from measurements at myCADAS (30–50 keV) and MICADAS (144–258 keV). The neutral yield was not measured but is given by the remaining fraction of 100%. Relative uncertainties are estimated to ±3% (myCADAS) and ±1% (MICADAS) respectively, resulting from uncertainties in the transmission correction. Possible systematic errors are discussed in Section 4. E/keV
+1
+2
+3
30 40 45 50 144 192 258
0.76 0.72 0.78 0.75 0.6 0.54 0.5
0.11 0.095 0.1 0.11 0.17 0.18 0.19
0.00029 0.00049 0.00056 0.00065 0.0062 0.0095 0.011
the fractions of the other charge states. It is increasingly populated at low areal densities until not enough negatively charged ions are left to pick up electrons and the ionization of neutral 12C into 12C+ becomes the dominant contribution leading to a decrease again and a maximum around 0.21016 atoms/cm2. The charge state fractions of 1+ to 3+ extend over a large range of order of magnitudes while they rise asymptotically towards their charge exchange equilibrium at high areal densities (around 21016 He atoms/cm2) defined by dfi ¼ 0 in Eq. (3). These charge state yields are reported in Table 1 for all measured energies. Charge exchange cross sections of all measured energies are reported in Tables 2 and 3. To account for the different fit result sets (depending on the initial fit values), mean cross section values are given with errors indicating an interval which covers 95% of all fit results. Cross sections which were fitted to values below 1024 cm2 are not reported. 4. Discussion From the transmission measurements at the AMS instruments it is not possible to determine very accurate equilibrium charge state Table 2 Charge exchange cross sections of
1 ? 0 0?1 1?2 2?3 3?2 2?1 1?0 0 ? 1 1 ? 1 0?2 1?3 3?1 2?0 1 ? 1
12
fractions, since the beam losses especially at low energies strongly depend on the focusing of the ion source and on the angular straggling in the stripper. The focusing can be slightly different for different cathodes because of varying burn-in characteristics of the primary Cs-beam. By applying the angular straggling loss corrections to the transmission versus pressure profiles instead of areal density profiles, +1 equilibrium charge state fractions of around 0.80 are computed. This approach is valid, since the pressure to areal density behavior is almost linear and the linear fits reproduce the data quite well. This suggests a systematic uncertainty which can be estimated to be at least 7%. To estimate uncertainties of current measurements originating from secondary electron losses, the inner charge collecting cylinder of the MICADAS Faraday cups were raised to a +50 V potential. With the potential applied, a measured positive ion current of 70 nA (13C) and 7 lA (12C) decreased by up to 1.5%. Even though the myCADAS analyzing cup is shorter, no difference in current measurement was found in a direct comparison with the other geometries. This suggests that the reported transmission values of positive charge states might be overestimated by up to 3% due to the normalization to underestimated negative injection current. Nevertheless, the increase of the +1 charge state yield towards low energies is significant (Fig. 4) and an important result for low energy AMS developments. The cause for this increase of +1 is found in the relatively stable electron loss cross section of the neutral charge state (r0!þ1 ) with energy and the decreasing electron capture cross section of the +1 charge state (rþ1!0 ) which reduces the population of the neutral beam in favor of the +1 charge state (see Fig. 5). In gases like Ar, this decrease is observed at much lower energies which results in a neutral carbon yield of about 70% at 50 keV while the +1 charge state yield is around 20% [18]. The neutral beam intensity could not be measured, but only reconstructed from the other charge states and therefore crucial information about the total system transmission is missing. The fitted values of the single electron exchange cross section between the +1 and 0 charge state are therefore less reliable in their absolute value. This is particularly valid for the MICADAS
C in He in 1016 cm2 from measurements at myCADAS (30–50 keV).
30 keV
40 keV
45 keV
50 keV
6.625 +0.064/0.16 3.68 +0.39/0.77 0.43 +0.79/0.25 0.018 +0.044/0.018
6.523 +0.066/0.17 2.46 +0.72/0.29 0.76 +0.58/0.56 0.051 +0.074/0.051
6.489 +0.032/0.15 2.979 +0.19/0.095 0.81 +0.95/0.65 0.02 +0.07/0.02
6.23 +0.065/0.038 3.02 +0.045/0.049 0.64 +0.65/0.64 –
16 +15/11 3.5 +5.7/2 0.94 +0.2/0.37 0.01276 +0.0013/6.6E – 4
15.4 +11/9.7 5.9 +4.6/4.3 0.31 +0.48/0.21 0.0297 +5E 3/0.012
15 +11/8.8 6 +6.6/4.7 0.32 +0.13/0.26 0.0293 +0.0012/5E – 3
8.8 +2/4.8 4.6 +4.2/3.9 0.45 +0.13/0.4 0.022 +0.0037/0.0023
0.727 +0.18/0.081 0.3 +0.04/0.12 0.0054 +0.0014/0.0017
0.87 +0.11/0.13 0.28 +0.066/0.072 0.0063 +0.0017/2E 3
0.988 +0.095/0.056 0.313 +0.093/0.13 0.01072 +6.9E 4/0.0027
1.274 +0.028/0.049 0.39 +0.12/0.12 0.008706 +1.6E 4/9.6E 5
5.8 +8.7/5 0.18 +1.1/0.18 –
5.3 +4.7/4 0.68 +1.5/0.66 –
4.5 +4.4/4.5 0.62 +1.8/0.62 –
1.8 +4.7/1.8 0.66 +2.6/0.66 0.00338 +4.4E 4/7.2E 4
546 Table 3 Charge exchange cross sections of
1 ? 0 0?1 1?2 2?3 3?2 2?1 1?0 0 ? 1 1 ? 1 0?2 1?3 3?1 2?0 1 ? 1
S. Maxeiner et al. / Nuclear Instruments and Methods in Physics Research B 361 (2015) 541–547
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C in He in 1016 cm2 from measurements at MICADAS (144–258 keV). 144 keV
192 keV
258 keV
4.591 +0.32/0.084 2.59 +0.48/0.34 1.37 +0.26/0.75 0.34 +0.29/0.27
3.99 +0.44/0.47 2.81 +0.9/1.3 1.36 +0.68/0.91 0.51 +0.29/0.14
4.284 +0.036/0.05 2.56 +0.13/0.15 2.33 +0.27/0.41 0.56 +0.49/0.36
8.4 +5.9/5.4 3.7 +1.4/1.8 0.57 +0.43/0.47 0.08363 +8.3E 4/0.0031
7.2 +6.3/4.3 3.4 +1.8/1.9 1.18 +0.57/0.56 –
8 +6.1/4.4 4.2 +1.6/1.6 0.62 +0.59/0.61 –
1.276 +0.087/0.34 0.12 +0.3/0.11 0.021 +0.013/0.014
1.01 +0.46/0.44 0.28 +0.38/0.28 –
0.267 +0.05/0.037 0.267 +0.05/0.037 0.044 +0.041/0.044
3.7 +2.9/2.9 1.1 +1.3/1 –
2.9 +2.9/2.4 0.76 +1.1/0.66 0.04972 +3.3E 4/2.2E 4
3.6 +2.9/2 2.3 +1.5/1.5 0.08662 +3.1E 4/2.2E 4
(a)
(b) Fig. 4. Equilibrium charge state fraction of +1 (f þ1;1 , top) and +2 (f þ2;1 , bottom) of 12 C in He at different energies. The black data points (boxes, circles) were measured by Hvelplund et al. [4,10]. The red datapoints (diamonds, triangles) are extracted from the corrected myCADAS and MICADAS density profiles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
measurements, where only ray tracing and scattering simulations could be used to estimate beam losses. Since for these measurements also the deceleration back to ground leads to a significantly broadened 1 ion beam on the HE side of the system, the injection loss correction (offset b in Eq. (1)) of this charge state can only be done by extrapolating back to 0 areal stripper density. This approach, in turn, depends on the offset in pressure measurement which is not exactly known and can only be estimated from vacuum readings after long periods of pumping. Furthermore, the additional beam broadening may also lead to secondary beam losses in subsequent electrodes or vacuum tubes (instead of just in one limiting element like the stripper canal). This would invalidate the approach of a linear loss correction with a single slope a (Eq. (1)) over the whole density region. In this case, the 1 ion
Fig. 5. (a) and (b) Single electron exchange cross sections. (a) Electron loss, (b) electron capture of carbon in helium from literature [19–34] (unfilled plot points) and this paper (filled plot points). Error bars indicate the scatter of fit results coming from different initial fit parameters. (see Section 2.4).
beam losses would be underestimated. This could be an explanation for the behavior of the r0!1 cross section which could not be fitted with the data at the highest energy (its fitted value was numerically zero). The electron exchange between the charge
S. Maxeiner et al. / Nuclear Instruments and Methods in Physics Research B 361 (2015) 541–547
states +1, +2 and +3 on the other hand fit well into literature trends and even extend them to low energies, due to the almost loss-less measurement of these charge states. To determine the charge exchange cross sections even better, different initial charge states would have been needed to further constrain the degrees of freedom in the fit procedure. Also a more precise knowledge of the beam losses or the detection of neutral beam particles would increase the overall accuracy. Because the calculated cross sections are inversely proportional to the determined areal stripper density, a relative error in the conversion of pressure to areal stripper density propagates directly. By comparing the values presented here to data from literature, this error seems to be quite small, much smaller than the variations introduced by different initial fit parameters (error bars in Fig. 5). This supports the validity of the approach of calculating the areal stripper gas density from pressure readings and gas flow calculations. Literature values on the other hand also suffer from systematic errors as is particularly visible for the electron capture of +2, where values from various groups differ by up to a factor of 3. This makes the calculation of charge state yields from exchange cross sections unreliable. Some of the cross sections are of particular interest for AMS applications. If stripper gas leaks into acceleration sections, charge exchange processes during acceleration alter the energy of particles. Low energetic molecular breakup fragments for example could gain just the right energy to pass the subsequent filter element. Hence, these processes are possible sources for background and their influence may be estimated from the corresponding cross sections. Because scattering cross sections are higher at lower energies, the increase in beam losses partially compensates the gain in charge state yield. To estimate the total transmission versus energy, we performed ray tracing and scattering simulations of the current MICADAS stripper tube and multiplied the resulting transmissions with charge state yields at corresponding energies. The results suggest a constant overall transmission of 12C in He into 12C+ around 47% from 300 keV down to about 80 keV which drops to 35% at 45 keV. This in turn encourages further experiments with acceleration voltages around 50–80 kV (i.e., stripping energies around 80– 100 keV) which would allow even more compact radiocarbon AMS designs. 5. Conclusion Single and double electron loss and capture cross sections for C in He were determined in the range of 30 keV up to 258 keV for the 1 up to +3 charge state from sets of transmission versus areal stripper gas density measurements. Not precisely known beam losses and the lack of measurement of the neutral charge state limit the accuracy of the values. Nevertheless, they are able to explain the trend of the charge state yields with energy and extend the knowledge of the single electron loss cross sections of charge states +2 and +3 to the region below 400 keV. The charge state yields of +1, +2 and +3 could be determined from the same sets of measurements and are compatible with earlier measurements at 100 keV and above by Hvelplund et al. [4,10]. At the lowest measured stripping energies around 30 keV, +1 charge state yields of up to 75% were evaluated. At this very low
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stripping energy however, angular and energy loss straggling are dominant and significantly reduce the total transmission. This suggests that there is an optimal energy range which maximizes transmission and enables a more compact AMS machine design. Rough estimates of beam losses with scattering simulations at different energies suggest an energy of around 100 keV for the next generation of radiocarbon AMS systems. Acknowledgment The author is funded by the Swiss National Science Foundation. References [1] C.L. Bennett, R.P. Beukens, M.R. Clover, H.E. Gove, R.B. Liebert, A.E. Litherland, K.H. Purser, W.E. Sondheim, Science 198 (1977) 508. [2] K.H. Purser, US Patent: 4037100, Appl. No.: 662968 (1977). [3] K.H. Purser, R.B. Liebert, C.J. Russo, Radiocarbon 22 (1980) 794. [4] A.B. Wittkower, H.D. Betz, At. Data 5 (1973) 113. [5] H.W. Lee, A. Galindo-Uribarri, K.H. Chang, L.R. Kilius, A.E. Litherland, Nucl. Instr. Meth. Phys. Res., Sect. B 5 (1984) 208. [6] Ref. [34], in: A.E. Litherland, Nucl. Instr. Meth. Phys. Res., Sect. B 5 (1984) 100. [7] H.A. Synal, M. Stocker, M. Suter, Nucl. Instr. Meth. Phys. Res., Sect. B 259 (2007) 7. [8] T. Schulze-König, M. Seiler, M. Suter, L. Wacker, H.-A. Synal, Nucl. Instr. Meth. Phys. Res., Sect. B 269 (2011) 34. [9] P.M. Stier, C.F. Barnett, G.E. Evans, Phys. Rev. 96 (1954) 973. [10] P. Hvelplund, E. Lægsgaard, E. Horsdal Pedersen, Nucl. Instr. Meth. 101 (1972) 497. [11] H.-A. Synal, T. Schulze-König, M. Seiler, M. Suter, L. Wacker, Nucl. Instr. Meth. Phys. Res., Sect. B 294 (2013) 349. [12] M. Wutz, H. Adam, W. Walcher, K. Jousten, Handbuch Vakuumtechnik, 7th ed., Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, 2000. [13] J.M. Lafferty, Foundations of Vacuum Science and Technology, John Wiley & Sons Inc., New York, 1998. [14] P. Hvelplund, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 38 (1971) 1. [15] M. Seiler, Accelerator Mass Spectrometry for Radiocarbon at very Low Energies (Ph.D. thesis), ETH Zurich, 2014. [16] S. Maxeiner, M. Suter, M. Christl, and H.-A. Synal, Simulation of ion beam scattering in a gas stripper, in: AMS13 Proceedings, unpublished. [17] M.I.A. Lourakis, Retrieved 31 Jan. 2005. From: