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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
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?