The time resolution

The time resolution is proportional to the drift field, but inversely proportional to the temperature [122]. According to the Einstein relation (Eq. (2.2)), the diffusion coeffi- cient is proportional to the gas temperature at “low-field” conditions. At a constant

E/nvalue, relatively high gas temperatures result in broadened ATD peaks and reduce the time resolution of the spectrometer. In addition, decreasing the drift field causes the ions to drift for a longer time period inside the cell, which results in broadened peaks due to diffusion (compare the time spectra shown in Fig. 6.5 (left plot)). Hence, the major factors determining IMS peak shape are the initial time distribution of the bundle of ions starting to drift inside the cell and the diffusional broadening of the bundle as it travels to the detector [123]. If the initial time distribution of the ions is

Chapter 6: Investigation of the time resolution by RIS methods 67

of Gaussian shape, the resolving powerhtdi/F W HMtd can be calculated as [124, 125]

Rd =htdi/F W HMtd = 1 r³ w0 βPcell ´₂ + ³ 16 ln 2 kBT qEdd ´, (6.3)

with the drift cell pressure Pcell, the ion charge q, the drift distance dd, the electric

field strength E and the absolute temperature T. The parameter w0 in Eq. (6.3) describes the temporal FWHM of the initial time distribution of the ions created via RIS methods, whereas the coefficient β = td/Pcell is a linearity constant that can be

obtained by measuring the time spectra at different buffer gas pressures. The term

³ w0

βPcell ´₂

in Eq. (6.3) describes the contribution to the resolving power solely due to the temporal shape of the initial pulse. The contribution caused by diffusion for an infinitely narrow initial pulse is given by the term (16 ln 2 kBT /qEdd) [123].

Equation (6.3) shows that at constantT andE, the resolving power generally increases with pressure. However, for the narrowest initial pulse width w0, it rapidly stagnates at a value, which is mainly determined by the applied electric fieldE, the temperature

T and the drift distance dd [124]. For ionization using laser beams of 1 mm diameter,

the term

³ w0

βPcell ´₂

in Eq. (6.3) is about 200 times smaller than the diffusion term (16 ln 2kBT /qEdd) and may be neglected [6]. Hence, the electric field strength E is

the only parameter that limits the resolving power for a specific drift length at room temperature. The highest applicable fieldEmax, however, is practically limited by the

insulation length of the used electrical feedthroughs inside the drift cell, see Sect.4.1.1. The field Emax is found to be about 18 V/cm at 40 mbar argon, which results in the

highest achievable resolving power of≈45 for q =e, dd= 32 cm and kBT = 25 meV.

Instead of Eq. (6.2), using Gaussian fit routines in the analysis of measured time spectra allows for a rather good prediction of the ATD meanhtaiand its corresponding standard

deviationσa. By neglecting the peak broadening due to the initial time distribution of

the ions, the resolving power may be related to the normalized standard deviation of the arrival time σa/htai via

Rd = 1 2.35·σd/htdi ≈ 1 2.35·σa/htai , (6.4)

whereas the normalized standard deviation of the drift timeσd/htdiis approximated by

σa/htai. The latter approximation is justifiable only for a negligibly small transit timett

with respect to the drift timetd, see also Sect.6.4. The normalized standard deviation

of the arrival time obtained with the developed apparatus is found to be one order of magnitude less than the one obtained in Ref. [51] and [113]. The drift cell described in these references is designed mainly for laser spectroscopy experiments on the actinides and transactinides and has not been optimized for mobility measurements. It exhibited a relatively smaller drift distance dd, which inevitably results in higher σa/htai values

even though other experimental parameters like Pcell,T andE are approximately equal

Figure 6.6: Normalized standard deviations of ATDsσa/htaifor Er+drifting in 40 mbar

argon vs. different electric fields inside the cell. The higher values at the same fields (◦) are obtained when the potential difference between the neighboring QPIG segments inside the extraction chamber is decreased to 2.16 V instead of the usually applied 10 V (O).

Figure 6.6 showsσa/htai values for Er+ vs. different electric fields inside the cell. The

time spectra are obtained by using a narrow ionizing laser beam of 1 mm diameter shining on the top of the Er-filament at 32 cm distance from the extraction nozzle. Generally, increasing the field results in smaller σa/htai values

³

∼p1/Ecell ´

as can be inferred from Eq. (6.3) and Eq. (6.4). Nevertheless, the potential gradient between the QPIG segments is found to be a crucial parameter, which strongly influences the time spectra at a background pressure of P1section = 4.5·10−2mbar in the first pumping

section. Increasing the potential gradient between the QPIG segments in that section results in significantly smaller transit time values, and hence in less peak broadening due to diffusion. In Fig. 6.6, the higher value (marked in red) at the same drift field is obtained when the potential difference between each neighboring QPIG segments inside the extraction chamber is set to ∆UQ = 2.16 V. For mobility measurements, however,

smallest line widths are envisaged such that ∆UQ is increased to 10 V (triangles in the

same figure) between the first six QPIG segments. In fact, increasing ∆UQwould reduce

the transit time values further and further, resulting in less diffusional broadening of the ATD peaks. Elevated ∆UQ values, however, bear the risk of gas discharges between

Chapter 6: Investigation of the time resolution by RIS methods 69

Figure 6.7: Left: Gas number density n obtained for a cell pressure of about 40 mbar and a filament temperature of TF il = 1220 K. Right: ATDs of Ho+ ions

drifting in ≈ 40 mbar argon at a mean field of 17.9 V/cm. The pressure difference of about 1.3 mbar leads to a time shift of 1 ms in the measured ATD peaks.

the QPIG segments and have not been tested so far. According to Fig. 6.6, diffusion processes inside the extraction chamber may deteriorate the relative width of the ATD peaks and result in a lower resolving power of the apparatus, especially at small guiding potentials and elevated background (see also Sect.6.4).

Furthermore, the cell pressure is an important parameter as well, not only due to Eq. (6.3), but also because it is desirable to keep the drifting ions in the “low-field” limit such that the Einstein relation (Eq. (2.2)) still applies. At high fields the mobility depends on the drift voltage, such that it is considerably more difficult to relate the mobility to the geometry [2]. So in order to substantially increase the voltage across the drift tube, it is necessary to increase the buffer gas pressure.