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Detailed description of the algorithm used for the simulation of the cluster counting. For the studies of CluCou we have used standard programs like MAGBOLTZ, GARFIELD, HEED plus our own C++/Root Montecarlo. Whenever necessary, we have complemented the simulations with
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for the simulation of the cluster counting
For the studies of CluCou we have used standard programs like
MAGBOLTZ, GARFIELD, HEED
plus our own C++/Root Montecarlo.
Whenever necessary, we have complemented the simulations with
data taken from the literature.
(for example: the distribution of the number of electrons per cluster
is not well simulated in the standard programs; many data on Helium
have better recent measurements).
G.F. Tassielli - A gas tracking device based on Cluster Counting for
future colliders. PhD Thesis, Lecce, 2007.
(Available as detached appendix to the 4th LOI).
 http://www.le.infn.it¥ ∼chiodini¥allow listing¥chipclucou¥tesivarlamava.
V. Varlamava. Tesi di Laurea in microelettronica: “Circuito di interfaccia
per camera a drift in tecnologia integrata CMOS 0.13 µm”. Universit`
del Salento (2006-2007).
 http://www.le.infn.it¥ ∼chiodini¥tesi¥Tesi Mino Pierri.pdf.
C. Pierri. Tesi di Laurea in microelettronica: “Caratterizzazione di un dis-
positivo VLSI Custom per l’acquisizione di segnali veloci da un rivelatore
di particelle”. Universit`
a del Salento (2007-2008).
 A. Baschirotto, S. D’Amico, M. De Matteis, F. Grancagnolo, M. Panareo,
R. Perrino, G. Chiodini and G.Tassielli. “A CMOS high-speed front-end
for cluster counting techniques in ionization detectors”. Proc. of IWASI
A 0.13µm CMOS Front-End
for Cluster Counting Technique in Ionization Detectors
S. D’Amico1,3, A. Baschirotto2, M. De Matteis1, F. Grancagnolo3, M. Panareo1,3, R. Perrino3, G. Chiodini3, A.Corvaglia3
A CMOS high-speed front-end
for cluster counting techniques
in ionization detectors
A. Baschirotto1, S. D’Amico1, M. De Matteis1, F. Grancagnolo2, M. Panareo1,2, R. Perrino2, G. Chiodini2, G.
actImpact Parameter Resolution
[0.5 ns units]
The impact parameter b is generally defined as:
where t1 - t0 is the arrival time of the first (few) e–.
b is, with this approach, therefore, systematically overestimated by the quantity:
Poisson statistics tells us that the number N of ionization acts fluctuates with a variance 2(N) = N.
The corresponding variance of = 1/Nis
2() = 1/N42(N) = 1/N3= 3.
For a gas with a density of 12.5 clusters/cm and an ionization length of 1 cm,
N = 12.5 and = 0.080, with (N) = 3.54 and () = 0.023, or (N)/N = ()/ = 28%
Same gas but 2 cm cell gives a factor smaller for both (20%); 0.5 cm cell gives (N)/N = ()/ = 40%.
Obviously, in this last case, the error is more asymmetric.
For a round (or hexagonal) cell, when the impact parameter grows and approaches the edge of the cell, the length of the chord shortens and the relative fluctuations of N and increase accordingly.
Tracks at an angle with respect to the sense wire reduce the error by a factor (sin )-1/2 (e.g. 20% for =45).
Sense wires at alternating stereo angles , even at = 0, reduce the error by a factor (cos 2)-1/2 (a few %).
In our case, N ionizations are distributed over half chord:
1/(2N) = (/2), and, therefore,
(/2) =(/2)3/2= 1/(22)3/2= 1/(22)().
Eventhough < 1> = /4, we’ll assume, conservatively, (1) =(/2)
as defined by the
first cluster only
“equi-drift”Can we do any better in He gas mixtures and small cells?
First of all, let’s get rid of the systematic overestimate of b by calculating b and 1 from d1 and d2
and assume, for simplicity, that thedi’s are not affected by error(no diffusion, no electronics):
from which one gets:
By generalizing this result with the contribution of the i-th (i2) cluster:
the impact parameter can then be calculated by a
weighted average with its proper variance:
as opposed to:
(N = 12.5 / cm)
r = 1.0 cm
pointsWhat about diffusion?
So far, so good!
We have reduced the contribution to theimpact parameter resolutiondue to the ionization statistics at
small impact parameter b (where this contribution is dominant since the uncertainty on the drift distance due to electron diffusion is negligible: we have, in fact, assumed so far no error on di’s).
What happens as b increases?