development of micro-pattern gaseous detectors – gem - LMU

6.1. Time Resolution 67
The signal by cosmic muons can now be seen as a set of locally discrete charges distributed over the
entire drift region. To this end we consider the maxima in the rise time histograms shown earlier as
the width of an associated probability distribution of all signal times. In the case of X-ray generated
events the shown signal time represents the width σt local of locally produced charges that is smeared
out due to diffusion effects. Furthermore, the drift time of electrons in 4 mm drift space characterizes
the width σ t dri ft
of a corresponding probability function if one considers all realizable drift times.
Following this argument, the combination of these statistically distributed signal and drift times results
in the signal rise time σ t µ of muon events. Mathematically, this is implemented by the convolution of
the corresponding distribution relating the standard deviations quadratically:
(σ t local )2 + (σ t dri ft )2 = σ t µ
Considering signals recorded with the CATSA82 preamplifier and operation parameters as in Fig.
6.1 and Fig. 6.2 one derives theoretically rise times that are shown in Tab. 6.1. Additionally, the
experimental results and the the characteristics of the used preamplifiers are denoted.
Preamplifier X-ray: mean
rise time[ns]
Cosmics:
mean rise
time [ns]
Cosmics:
theoretical
rise time [ns]
(6.1)
Ccoup [nF] Preamplifier:
rise time [ns]
CATSA82 166.2 182 194 50 10
ELab 105.2 121.5 145 1.5 10
Table 6.1: Mean rise time for Cosmic and X-ray measuements with CASTA82 and ELab preamplifier, respectively.
The theoretically derived rise times are also shown. The preamplifier characteristics Ccoup and rise time
are required for following considerations.
Both theoretically derived approximations overestimate the experimental result slightly. This might
be an effect of the simplified field configurations used in the simulation of drift velocities. By reversing
the above stated equation one derives an experimental average value for the drift velocity
of electrons of 5.4 cm/µs and 6.6 cm/µs both representing the drift in an electric field of
Eind = 1.25 kV/cm. The MAGBOLTZ simulation yields a drift velocity 4 cm/µs. Nevertheless,
the estimation reproduces the correct range and it is assumable that the signal rise time of cosmic
muon events can be considered as an ensemble of single localized charge clusters distributed over the
complete drift space.
Now the question arises how these signal rise times of 55 Fe measurements are created. The data for
locally limited generated charges recorded via the CATSA82 preamplifier show a mean rise time that
is 60 ns longer than samples taken with the ELab preamplifier for an equal setup of fields between
the GEM foils. Thus one can conclude that the total signal rise time for 55 Fe events is not only based
on the presence of liberated charges in the detector but also depending on the connected electronics.
It is assumed that the rise time distribution recorded with the ELab preamplifier represents the real
rise time accurately. The rise time of the CATSA82 preamplifier is limited due to its big coupling
capacity Ccoup which can be shown with the following consideration. Assuming that the signal line
contributes an effective output resistance R = 2.5Ω would lead to an internal rise time τ of the
preamplifier:
τ = R · Ccoupl = 2.5Ω · 50 nF = 125 ns (6.2)