Experimental ion mobility measurements in Ar-N2

Data on ion mobility is important to improve the performance of large volume gaseous detectors, since the detector signal can be influenced by the drift of the ions, namely in the cases where charge multiplication is used, for example in Multi-Wire Proportional Chambers (MWPCs) and in some Time Projection Chambers (TPCs). In the present work the results for the ion mobility measurements in Ar-N2 mixtures are presented, using an experimental setup and method already tested in previous work. The results for this mixture show the presence of only one peak for all gas ratios of Ar-N2, for reduced electric fields, E/N, in the range of 10–25 Td (2.4–6.1 kV⋅cm−1⋅bar−1), and 8 Torr (10.6 mbar) pressure, at room temperature.


Introduction
Measuring the mobility of ions in gases is relevant in several areas from physics to chemistry, e.g. in gaseous radiation detectors modelling and in understanding the pulse shape [1][2][3][4], since their mobility can affect the performance of these detectors [3] as they influence the rate capability and signal formation of detectors, e.g., of the Multi-Wire Proportional Chambers (MWPCs) [5]. The choice of the gas mixture for most of these detectors is determined by several characteristics such as high electron/ion velocity and low electron diffusion.
The experimental setup used in the present work (described in detail in [6]) allows the measurement of ion mobility in gas mixtures. Initially thought for high pressure, it was converted into a low pressure gas system. Lowering the operation pressure provided a wider scope of application and more detailed information on the fundamental processes involved in the ion transport and also allowed to reduce the inherent operation cost. Still, the results have been consistently in accordance with data obtained at higher pressures [7].

Ion mobility
Under a weak and uniform electric field a group of ions will eventually reach a steady state. In this conditions, the average velocity of this group of ions, also known as drift velocity v d , is proportional to the electric field intensity [4]: where K is the mobility of the ions, expressed in units of cm 2 ·V −1 ·s −1 and E the intensity of the drift electric field. The ion mobility, K, is normally expressed in terms of the reduced mobility K 0 ,

Langevin's theory
According to Langevin's theory [24], one limiting value of the mobility is reached when the electrostatic hard-core repulsion becomes negligible compared to the neutral polarization effect [25]. This limit is given by the following equation, where α is the neutral polarisability in cubic angstroms (α = 1.64 Å 3 for Ar [26] and α = 1.95 Å 3 for N 2 [27]) and µ is the ion-neutral reduced mass in unified atomic mass units. Although the Langevin limit only applies rigorously for real ion-neutral systems in the double limit of low E/N and low temperature, it still predicts the low-field mobility at room temperature with relatively good accuracy [25], which is the case of our experimental conditions. Although generally accepted, Langevin theory has some known limitations in its application, since it fails to provide correct values for the ion's mobility in some cases, namely for gases with low polarizability or for very large molecules [7].

Blanc's law
In binary gaseous mixtures, Blanc's law has proven to be most useful when determining the ions' mobility. According to this law, the reduced mobility of the ion in the binary mixture, K mix , can be expressed as follows: where K g1 and K g2 are the reduced mobility of that same ion in an atmosphere of 100% of gas #1 and #2, respectively and f 1 and f 2 are the molar fraction of each gas in the binary mixture [28].

Method and experimental setup
The mobility measurements were obtained using the experimental system described in [6]. A UV flash lamp with a frequency of 10 Hz emits photons that impinge on a 250 nm thick CsI film deposited on the top of a GEM that is inside a gas vessel. The photoelectrons released from the CsI film are guided through the GEM holes, ionizing the gas atoms/molecules along their paths. While electrons are collected at the GEM bottom electrode, cations formed will drift across a uniform electric field region towards a double grid; the first of these acts as a Frisch grid while the second, at ground voltage, collects the ions' charge. A pre-amplifier is used to convert the charge collected into a voltage signal, and the time spectra are recorded in a digital oscilloscope. After electronic background subtraction from the signal, gaussian curves are fitted to the time-of-arrival spectra from which the peak centroids are obtained. Since the peaks' centroid correspond to the average drift time of the ions along a known fixed distance (4.273 cm), the drift velocity and mobility can then be -2 -calculated. One important feature of the system is the capability of controlling the voltage across the GEM (V GEM ), which limits the maximum energy gained by the electrons as they move across the GEM holes, narrowing the variety of primary ions possibly produced. Identifying the primary ions will allow to pinpoint secondary reaction paths that lead to the identification of the detected ions. This experimental setup has already provided correct and consistent results for several gases and their mixtures.
Since impurities play an important role in the ions' mobility, before each experiment the vessel was vacuum pumped down to pressures of 10 −6 to 10 −7 Torr and a strict gas filling procedure was carried out. No measurement was considered until the signal stabilised, and all measurements were done in a 2-3 minutes time interval to ensure minimal contamination of the gas mixture, mainly due to outgassing processes.
The method described together with the knowledge of the ions' dissociation channels, the product distribution and rate constants of the possible secondary reactions represent a valid solution to the ion identification problem.

Results and discussion
The mobility of the ions originated in Ar-N 2 mixtures has been measured at different reduced electric fields E/N (10 Td and 25 Td) and 8 Torr pressure at room temperature (293 K).

Argon-nitrogen (Ar-N 2 ) mixtures
In argon-nitrogen (Ar-N 2 ) mixtures, only one peak is observed in the different time spectra throughout the entire mixture range studied, with a bump appearing on the left side of the peak for Ar concentrations above 70%, as seen in figure 1. The drift spectra for several Ar-N 2 mixtures (5%, 50%, 70% and 95% of Xe) are shown in figure 1, at a pressure of 8 Torr, temperature of 293 K, reduced electric field of 15 Td and V GEM of 25 V. There are three striking changes that result from the increase in Ar concentration: the first is a decrease observed in the mobility of ions, the second is an increase in the peak amplitude and the third is the appearance of the referred bump, for Ar concentrations above 70%.
To understand which ions are responsible for the peak and bump observed, a Monte Carlo simulation was performed, to have an insight on how the proportion of the primary ions formed (from N 2 and Ar ions) evolve with the mixture composition. This information together with the reaction rates available in literature, allows to obtain a clear picture of the ions drifting in this mixture.
The Monte Carlo simulation code used is described in detail in [31], and as in [21], a uniform field was considered inside the GEM holes, between anode and cathode. Although this is an approximation of the real field geometry, it has already provided valuable information for this purpose in previous studies. The simulation reproduces the drift of 10 8 photoelectrons released from a CsI photocathode into Ar-N 2 mixtures and their collisions with the gas atoms/molecules (at the typical pressure of 8 Torr and temperature of 293 K) until they reach the anode, 50 µm away, and calculates the proportion of primary ions (N + 2 and Ar + ) produced by these electrons for the different gas mixtures. The cross-sections used in the simulation code are displayed in figure 2. For the scattering of electrons by Ar atoms these are the same as those adopted in [32]. For N 2 molecules, crosssections used are based on the data from [33,34]. For rotational excitation, data was taken from [33,35]; superelastic collisions corresponding to these rotational transitions were taken into account, considering the principle of detailed balance. Regarding vibrational excitation, data from [36] was used to complement data from [33]. Electron dissociative attachment cross-section was taken from [37]. For electronic excitation, the partial cross-sections were taken from [34]. For ionization, the simulation used the partial cross-sections for N + 2 and N + production from [33]. All electron collisions with molecules are assumed to be isotropic, however anisotropy of elastic scattering is accounted for using momentum transfer cross-section [33] instead of integral.
The simulation results obtained are displayed in figure 3. According to these results, N + 2 ions are produced more abundantly up to about 35% Ar, while above this concentration Ar + ions are the ones preferentially produced. Knowing the ions' relative initial abundance and comparing the different reaction rates summarized in table 1, it can be concluded that the reactions leading to the formation of ArN + 2 are faster than any other competing channel, which means that in our experimental conditions the formation of ArN + 2 is favoured.   However, in the very low and very high Ar concentration limit, a transition is expected to occur in the dominant ion. For very low Ar concentrations, where the production of N + 2 (primary ion) is predominant, the dominant ion, N + 4 , is expected to change gradually to ArN + 2 , when increasing Ar concentration, while for very high Ar concentrations, ArN + 2 gradually gives way to Ar + 2 , when increasing Ar concentration. The appearance of a bump at the left side of the main peak for Ar concentrations above 70% might be due to a hetero-nuclear associative ionization of the molecule involving a highly excited state of the Ar atom and a N 2 molecule [42], expressed by: This reaction leads to the formation of the same ion product, ArN + 2 , but through a different channel. This being the case, this ion should in fact appear at the left side of the main peak, as ArN + 2 will be always the same drifting ion, while through the other channel (involving Ar + 2 ), its mobility (ArN + 2 ) will be affected by the predecessor ions (Ar + and Ar + 2 ) which have a lower mobility. This seems a plausible explanation for the bump, since from the Monte Carlo simulation we concluded that about 10% of the total Ar * produced in the GEM holes have enough energy to originate ArN + 2 ions. In figure 4 the reduced mobility obtained for the ions produced in Ar-N 2 mixtures is plotted as a function of Ar percentage, for 8 Torr and 15 Td, at room temperature (293 K), together with Blanc's law prediction for N + 4 (red dashed line), Ar + 2 (orange dashed line) and ArN + 2 (green dashed line). K g1 and K g2 in Blanc's law (eq. (1.4)), were obtained either using experimental values from literature or, when not possible, from Langevin formula (eq. (1.3)). Figure 4 shows that the ion -6 -2018 JINST 13 P11016 mobility experimentally obtained generally follows, within error bars, Blanc's law prediction for the most abundant ion, ArN + 2 , for most of the Ar percentages studied. In fact, from pure N 2 up to 5% Ar, the ion observed displays a considerable decrease in mobility which reflects the change from N + 4 to ArN + 2 in the final ion. For Ar concentration above 10%, the mobility is consistent with Blanc's law prediction for ArN + 2 , deviating towards Ar + 2 for Ar concentrations above 80%. The slight differences observed in the drift time from pure N 2 up to 5% Ar and from pure Ar down to 80% are related with the slower production of ArN + 2 at these concentrations conditions, that, throughout its drift, has its mobility affected by the predecessor ions, N + 2 and Ar + , resulting in an increase (N + 2 ) or decrease (Ar + ) in the mobility of ArN + 2 . Due to the great uncertainties associated with a Gaussian fitting of the bump, this was not considered in the analysis. Table 2 summarizes the results. No significant variation of the mobility was observed for the E/N range studied (10-25 Td).  -7 -

Conclusion
In the present work we measured the reduced mobility of ions originated by electron impact in Ar-N 2 mixtures at pressures ranging from 6 to 8 Torr, low reduced electric fields (10-25 Td) and different mixture ratios. The experimental results show that, from pure N 2 to pure Ar and concentrations in between, only one peak is observed in all drift spectra. The ion responsible is ArN + 2 , as confirmed by Blanc's law, except for concentrations below 5% Ar and above 80% Ar, where a gradual change from the expected theoretical mobility of ArN + 2 to N + 4 and Ar + 2 was observed, as would be expected. For concentrations above 70% of Ar, a bump emerged on the left side of the peak, which was attributed also to ArN + 2 , yet produced through hetero-nuclear associative ionization, involving highly excited Ar states and the neutral N 2 . This hypothesis was consistent with the higher mobility of this bump, and corroborated by the Monte Carlo simulation.
Future work is expected with different gaseous mixtures of known interest such as: Ar-iC 4 H 10 , Ar-CF 4 -iC 4 H 10 and Ne-CF 4 .