Signal cable ringing and impedance matching

In pulse counting mode, prominent afterpulse ringing in the pulse signal will possibly lead to the unfavorable situation of double or multiple counting a single primary particle incidence in the CEM detector. Similar to the considerations of subsection 3.4.2, this will result in ad-

3.4. Particle counting and CEM operation pulse height [mV] time [ns] -160 -120 -80 -40 0 40 pulse height [mV] time [ns] 0 100 200 300 -200 -100 -80 -60 -40 -20 0 20 -100 0 -120 150 100 50 (b) (a) -140 400 200 100 0 -100 500

Figure 3.10: (a) Measured single CEM pulse trace of a CEM detector, displaying significant afterpulse ringing in the CEM signal cable caused by an unmatched cable impedance. Inset: Damped Sine fit of the afterpulse ringing. (b) Single pulse trace of a similar CEM detector arrangement with only minor afterpulse ringing due to improved impedance matching.

ditional spurious counts with the corresponding CEM detector. However, the observed after- pulse ringing even for comparably unmatched signal cables is generally small. Figure 3.10(a) shows a sample single CEM pulse trace of a previous CEM detector setup, displaying signifi- cant afterpulse ringing presumably caused by an unmatched cable impedance. The depicted trace is obtained with a comparably long signal cable in the UHV, with a cable length of l > 50 cm up to the connections of the electrical UHV-feedthrough (see section 4.2). As illustrated in fig. 3.10(a), the ringing indicates internal cable backreflections caused by an unmatched cable impedance. The inset in fig. 3.10(a) shows a damped Sine fit of the corre- sponding afterpulse ringing. The fit enables to determine a defined central frequencyf, and a corresponding 1/e-decay parameter, which likewise allows improved impedance matching of the unmatched signal cable via additional electronic circuitry [167, 168]. In the contrast to that, fig. 3.10(b) displays the single pulse trace of an already quasi-matched signal cable of another CEM detector arrangement, only yielding minor afterpulse ringing. In this case, a comparably short signal cable (l < 5 cm) is used, leading to much faster ringing oscillations with lower amplitude.

In the case of accidental multiple counting of a single primary particle incidence in the CEM detector, some of the first ringing oscillations succeeding the main pulse will eventally still surpass the trigger level of the subsequent discriminator unit (fig. 3.10(a)). However, in pulse counting mode the integral dead time19 twmt = 80±20 nsof the discriminator unit prevents possible multiple counting of a single pulse incidence (shaded area; fig. 3.5(b)). This follows as even for primary particle incidences with large pulse amplitudes - after a dead time of80 ns- most pulse ringing oscillation amplitudes will be well below the trigger level of−20 mV(dashed line; fig. 3.5(b)). Therefore, by using a discriminator unit with a considerable integral dead time and a correspondingly adjusted trigger level, no double or multiple counting of single primary particle incidences should be observed. This will result in no additional spurious counts due to an eventual afterpulse ringing for counting applications with the current setup.

19_{In general, any dead time t}

wmt of the subsequent pulse processing electronics will inhibit the counting of

3.4.4. Maximum count rate and resolution of two consecutive pulses

For several single particle counting applications, the efficient and reproducible counting of continuous high count rates resembles an important quantity. This follows as particularly an eventual loss of a considerable number of counting incidences at elevated count rates will sig- nificantly affect the observed count rateN0 compared to the true count rateN. Additionally, also the detailed resolution of two or more consecutive pulse incidences within a certain time period is a relevant parameter for single particle counting applications.

Non-extendable dead time correction

In the aspect of high count rates, there is intrinsically no detector-based20 dead time for the CEM detector itself (see subsection 3.2.2), but the CEM amplifies two or more tempo- rally close, incident primary particles only by a reduced gain value (eq. 3.8). Accordingly, an eventual counting loss of incident primary particles can be prevented by adjusting the trigger level of the subsequent pulse processing electronics to lower pulse height amplitudes, correspondingly.

In pulse counting mode, the counting of consecutive pulses at elevated count rates is thus in principle not constrained by the amplification response of the CEM detector itself. Conse- quently, the relevant parameter for any possible dead time correction in pulse counting mode is only the dead time τ of any subsequent pulse processing electronics as, e.g., the integral dead time of an associated discriminator unit. Therefore, a possible correction of the true count rate N at the CEM detector due to the dead time of any subsequent pulse processing electronics can be calculated. Accordingly, for the registration of elevated count rates in pulse counting mode, the dead time correction of the observed count rate N0 is defined as

N0 =N/(1 +N τ) (3.9)

for a discriminator unit with an non-extendable dead time [169, 170]. In the previous equa- tion,N represents the true count rate, while the quantityN0 denotes the observed count rate, and the parameter τ yields the corresponding dead time of the subsequent pulse processing electronics. In the context of this thesis, the constraining time τ is the dead time of the discriminator unit τ ≡ twmt = 80 ns (fig. 3.5(b)). At elevated count rates (Ni,e ≤ 104s−1) as typically obtained from photoionisation (see, e.g., section 5.4), this will correspond to a dead time correction ratio of N0/N = 0.9992, i.e., theoretically leaving only eight out of

10000 events eventually uncounted. However, applying faster pulse processing electronics with shorter dead times of, e.g., τ ∼ 10 ns, will result in a dead time correction ratio of N0/N = 0.9999for count rates of(Ni,e≤104s−1), although at the cost of increased eventual afterpulsing due to the shorter dead time (see subsection 3.4.3).

Resolution of two consecutive pulses

The resolution limit of two consecutive pulses is derived from the temporal pulse width of the respective single pulses (see subsection 3.2.2). Correspondingly, the average pulse width of several single pulses can be deduced from the pulse width histogram (fig. 3.6(b)), yielding an average pulse width oftfwhm= 12.0 ns for the respective CEM detector (fig. 3.6(d)). Note 20_{This implies that the CEM detector is at no point in time ’blind’ to an incident primary particle at the CEM}

3.4. Particle counting and CEM operation

that in the latter histogram, a Gaussian shape of the individual single pulses is assumed (fig. 3.5(d)). According to their average temporal width tfwhm, consecutive single incidences corresponding to count rates exceeding 80 MHz should therefore theoretically be resolved. In comparison, in the experiment sample traces of two or more pulses within, e.g., a time window below100 ns, are occasionally observed21 (ion-CEM; fig. 5.3(a)). This indicates that the CEM detector is principally able to operate on count rates of at least10 MHz. Moreover, similar temporal pulse resolutions of multiple consecutive CEM pulses are stated by, e.g. [85, 139, 154].