Figure 3.5: Sketch of a D0→K−π+ decay depicting the improvement of the impact parameter resolution by the ITS.
meson candidate and b) on the angle between the reconstructed momentum of the D meson candidate and the vector connecting the secondary and primary vertex. The vast improvement due to the background rejection is obvious.
Although the ITS was designed to specifically accomodate the needs of charm reconstruction, all the qualities of the ITS, which were discussed so far, are equally beneficial to a measurement of strange lambda particles as done in this thesis. The ITS also provides particle identification via the measurement of the energy loss. This feature was not exploited in the scope of this thesis. See Section 3.3 for a general discussion of the concept of an energy loss measurement.
3.3 The Time Projection Chamber 49
Figure 3.6: Left: Transverse impact parameter resolution for different collision systems in ALICE. Right: Effect of two topological selection criteria (see text) on the invariant mass spectrum of the D meson candidates. Taken from [216].
derive the position of the gas-traversing particle in the drift direction. The electrons should drift through the gas fast to provide a good event-rate capability of the detector and with low diffusion to give a good spatial resolution of the reconstructed track. In addition, the detector should have a good energy loss resolution to allow for particle identification. The intrinsic low material budget of a gaseous detector is beneficial for the momentum and impact parameter resolution of low pT particles, for which the resolution is dominated by multiple scattering in the material [114]. A low material budget also reduces the production of secondary particles. A comprehensive, general write-up on particle detection including TPCs can be found in [222]. ALICE specific details can be found in the technical design report of the TPC [223]
and e. g. [224]. Some considerations concerning the gas mixture are discussed in Section C.1. A few basics are communicated here.
In ALICE the choice was made to use NeCO2N2 with a mixture of 90 : 10 : 5, i. e. 85.7%
Ne, 9.5% CO2, and 4.8% N2, which was changed to 90% Ne and 10% CO2 in the beginning of 2011 [124]. For ALICE, Ne is used as the noble gas in order to reduce the material budget:
the density of Ne (0.9 g/L @ 0◦C, normal pressure) is half the one of argon (1.8 g/L @ 0◦C, normal pressure). Another gas property is the ion mobility. It depends slightly on the ratio E/N, whereE is the electrical field andN is the neutral gas number density. For an ideal gas, i. e. 6·1023 particles occupying 24 l at ambient conditions, the number density is 2.5·1019cm−3. With the drift fieldE= 400 V/cm, this results in a typicalE/N = 1.6×10−17 V cm2 = 1.6 Td.
Under these conditions, the mobility of Ne+ ions in a Ne gas is about 4.1 cms /cmV while the one of Ar+ in an Ar gas is only around 1.5 cms /cmV [225]. (The same result is given in [226].) The TPC gas is called a cold gas as its diffusion is close to the thermal limit. Fig. 3.7 shows a comparison of the transverse (on the left) and longitudinal (on the right) diffusion coefficients of NeCO2 with other gases. The addition of N2 does not change the diffusion. The diffusion of the TPC gas for both the transverse and longitudinal direction is 220µm/√
cm, which results in a spread over the maximum drift distance (2.5 m) of 3.4 mm laterally and 120 ns in the time direction. The dependence of the drift velocity on the temperature of about 0.05 cmµs K1 is steep which makes temperature control to the 0.1 K level crucial [224].
Figure 3.7: Transverse (left) and longitudinal (right) diffusion coefficients for several gas mixtures as a function of electrical field E over pressureP. Also shown is a dotted line for the thermal limit. Taken from [227].
The gas also meets the needs of the amplification process. The primary ionization produced by a charged particle traversing the TPC gas is only about 43 electron-ion pairs.3 As this charge is too small to be detectable by electronic devices, an internal gas amplification is used.
A sketch can be found in Fig. 3.8 (left). The drifting electrons created by an ionizing particle follow the electrical field lines. The uniform drift field ofE = 400 V/cm inzdirection is created between the central electrode and the cathode. Here, the electrons move with a constant drift velocity, vD = 2.83 cm/µs, and the number of electrons stays approximately constant. The gating grid can be open or closed. When closed, it has an alternating voltage of VG±∆V and
3The energy loss of a minimum ionizing particle in Ne is 1.56 keV/cm [228]. The energy lost per created electron-ion pair, which amounts to 36 eV for Ne [229], is larger than the ionization energy since a significant part will be transfered to gas excitations. This means 43 electron-ion pairs are created per cm.
3.3 The Time Projection Chamber 51
acts as the anode for the electrons: all the drift field lines end on the positively biased gating grid wires. Therefore, all drifting electrons get absorbed by the gating grid; no read out takes place. In the open state the voltage isVG for all wires, which was chosen such that the grid is completely transparent for the electrons, and they drift undisturbed to the cathode. The gating grid is usually closed and only opens for 100 µs upon a trigger. The opening time matches the maximum drift time for electrons of 2.83 cm·µs2.5 m −1 = 88µs. The main purpose of the gating grid is to prevent the positively charged ions from drifting back into the gas volume. Such an ion back flow would result in large distortions caused by the space charge of the ions. At the anode, the electrical field strength increases dramatically and the drifting electrons start a cascade amplifying the number of electron-ion pairs by a factor∼2·104. The dependence on the applied high voltage of the gain factors for the two operating gas mixtures in the ALICE TPC are shown in Fig. 3.8 (right). Adding N2 to the Ne-CO2 mixture allows for a higher gas gain, but demands an increased amplification voltage. In other words: the removal of N2 from the Ne-CO2-N2 can prove favorable if the high voltage has to be reduced. The vast majority of the electron-ion pairs will be produced directly at the anode, where the highly mobile electrons will quickly be absorbed. The ions in contrast, which are a factor of 103 slower4, induce an image charge on the pad plane. The height of the pad signal is proportional to the generated charge [223]. Two signal processing methods that potentially improve the detector performance are discussed in Section C.2.
gating ! central ! grid
electrode
z anode
cathode pads
drift amplification
ionizing particle
drift electrons r
Figure 3.8: Left: Sketch of the path of drifting electrons from an ionizing particle in the transverse (r) and longitudinal (z) plane. Details see text. Right: Gas gain for the two gases utilized before and after beginning of 2011. One observes that the addition of N2 allows for a higher gas gain, though the applied high voltage must be significantly increased to achieve it. Taken from [230].
The energy loss of a given particle with an energy typical for a heavy-ion collision experiment
4Compare the ion mobility of 1.1 cms /cmV multiplied by the electrical drift field of 400 cmV resulting in an ion drift velocity of 0.44·10−3 cmµs to the electron drift velocity of 2.83cmµs.
can be parametrized with the Bethe formula [32]:
h−dE/dxi=Kz2Z A
1 β2
1
2ln(2mec2β2γ2Tmax
I2 )−β2−δ(βγ) 2
, (3.1)
with the variables defined in Table 3.2. The Bethe-Bloch formula results from the Bethe formula with the approximationI ≈Z ·10 eV. Today, this approximation is often replaced by more accurate measurements. Nevertheless, the name Bethe-Bloch formula prevails. Data from muons on copper together with various parametrizations, including the Bethe formula, are shown in Fig. 3.9. One distinguishes mainly between the 1/β2 region which extends from the beginning of the validity of the Bethe formula (the grey vertical band atβγ∼0.05) toβγ≈1 (a function f(x)∼1/x2 is linear in a double-log plot), the region of minimum ionization, and the relativistic rise following this minimum. Particles with different masses will appear as separate bands in a hdE/dxi vs. momentum plot. This feature is exploited for particle identification.
Figure 3.9: Stopping power (=h−dE/dxi) for µon Cu. Taken from [32].
The collisional energy loss of a particle in a gas theoretically follows a Landau distribu-tion [231]:
L(ζ) = 1 π
Z ∞ 0
etlnt−ζt sin(πt) dt, (3.2)
L(ζ)≈M(ζ) = 1 2πexp
−1
2(ζ+e−ζ)
, (3.3)
ζ = (x−x)/σ¯ (3.4)