Simulation and Calibration of the ALICE TPC including innovative Space Charge Calculations

ALICE is one of the four main particle detectors located around the LHC accelerator at CERN. It is particularly designed to study the physics of the quark-gluon plasma by means of nucleus--nucleus collisions at center-of-mass energies up to 5.5 TeV per nucleon pair. A Time-Projection Chamber (TPC) was chosen to be its central-sub-detector due to its low mass properties and its capabilities to provide a robust and accurate Particle Identification even within ultra-high multiplicity environments (up to 8000 tracks per unit of eta). To achieve the required physics performance, the space point resolution of the TPC must be in the order of 0.2 mm. Due to its gigantic size of 5~m in diameter and 5~m in length, corrections for static as well as dynamic effects are indispensable in order to accomplish the design goal. The research presented covers all major issues relevant for the final calibration and therefore the enhancement of the TPC performance in terms of resolution. The main focus was to distinguish between the different effects which disturb the electron trajectory within the drift volume by means of quantifying the magnitude of their influences. The effects were parametrized in terms of physical parameters, as opposed to a multivariate fit, in order to minimize the residuals of the cluster positions. The different chapters of the present research work cover static imperfections, like magnetic and electric field inhom ogeneities due to mechanical imperfections, as well as dynamic variations of the drift properties due to pressure, temperature and gas composition variations which manifest themselves as gas density fluctuations. Furthermore, additional challenges were treated which will occur in future high multiplicity nucleus-nucleus collisions. These are the improvement of the two-track resolution as well as the quantification of additional dynamic field deviations due to space charges. Various simulation techniques were used to qualify and quantify the field imperfections due to mechanical deficiencies. Besides the localization and calibration of the field imperfections, the simulations led to optimized voltage settings which minimize the residuals. The different drift velocity v_d dependencies were parametrized to allow a quick estimation of the dynamic $v_d$ variations as a function of the measured ambient conditions. Besides that, the programmable signal shaping algorithm within the Front-End electronics was revised. This is expected to improve the two-track resolution in high multiplicity events. Moreover, novel analytical solutions were derived to allow a fast and precise prediction of additional dynamic field deviations due to ionic-charge pile up within the TPC gas volume. This analytic approach finally permits accurate simulations of additional systematic shifts along the electron trajectory due to any three dimensional space c harge distribution within the TPC. This innovative method is an essential part of the calibration algorithms which are being developed for the future Pb-Pb collisions at LHC

static green's functions for a bisected coaxial cavity

This paper deals with the three-dimensional potential equation in cylindrical coordinates and its Green's function for geometry close to a rather uncommon Time Projection Chamber field-cage, namely a bisected coaxial cavity. The methods used to derive the Green's function for a coaxial cavity (see [CERN-OPEN-2009-003]) were adapted to deduce novel representations for a bisected geometry, where the additional Dirichlet conditions in phi have to be fulfilled. The necessary modifications are described in detail. In combination, these three novel representations allow fast converging calculations of the electric field components and therefore for any desired space charge configuration within this cavity

The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events

The design, construction, and commissioning of the ALICE Time-Projection Chamber (TPC) is described. It is the main device for pattern recognition, tracking, and identification of charged particles in the ALICE experiment at the CERN LHC. The TPC is cylindrical in shape with a volume close to 90 m^3 and is operated in a 0.5 T solenoidal magnetic field parallel to its axis. In this paper we describe in detail the design considerations for this detector for operation in the extreme multiplicity environment of central Pb--Pb collisions at LHC energy. The implementation of the resulting requirements into hardware (field cage, read-out chambers, electronics), infrastructure (gas and cooling system, laser-calibration system), and software led to many technical innovations which are described along with a presentation of all the major components of the detector, as currently realized. We also report on the performance achieved after completion of the first round of stand-alone calibration runs and demonstrate results close to those specified in the TPC Technical Design Report.Comment: 55 pages, 82 figure

Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}= 2.76 TeV

Measurements of charge dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudo-rapidity range $|\eta| < 0.8$ are presented as a function of the collision centrality, particle separation in pseudo-rapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge dependent azimuthal correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at s=0.9\sqrt{s}=0.9, 2.76 and 7 TeV

Measurements of the sphericity of primary charged particles in minimum bias proton--proton collisions at $\sqrt{s}=0.9$, 2.76 and 7 TeV with the ALICE detector at the LHC are presented. The observable is linearized to be collinear safe and is measured in the plane perpendicular to the beam direction using primary charged tracks with $p_{\rm T}\geq0.5$ GeV/c in $|\eta|\leq0.8$. The mean sphericity as a function of the charged particle multiplicity at mid-rapidity ($N_{\rm ch}$) is reported for events with different $p_{\rm T}$ scales ("soft" and "hard") defined by the transverse momentum of the leading particle. In addition, the mean charged particle transverse momentum versus multiplicity is presented for the different event classes, and the sphericity distributions in bins of multiplicity are presented. The data are compared with calculations of standard Monte Carlo event generators. The transverse sphericity is found to grow with multiplicity at all collision energies, with a steeper rise at low $N_{\rm ch}$, whereas the event generators show the opposite tendency. The combined study of the sphericity and the mean $p_{\rm T}$ with multiplicity indicates that most of the tested event generators produce events with higher multiplicity by generating more back-to-back jets resulting in decreased sphericity (and isotropy). The PYTHIA6 generator with tune PERUGIA-2011 exhibits a noticeable improvement in describing the data, compared to the other tested generators.Comment: 21 pages, 9 captioned figures, 3 tables, authors from page 16, published version, figures from http://aliceinfo.cern.ch/ArtSubmission/node/308

Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}=2.76 TeV

The elliptic, $v_2$, triangular, $v_3$, and quadrangular, $v_4$, azimuthal anisotropic flow coefficients are measured for unidentified charged particles, pions and (anti-)protons in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV with the ALICE detector at the Large Hadron Collider. Results obtained with the event plane and four-particle cumulant methods are reported for the pseudo-rapidity range $|\eta|<0.8$ at different collision centralities and as a function of transverse momentum, $p_{\rm T}$, out to $p_{\rm T}=20$ GeV/$c$. The observed non-zero elliptic and triangular flow depends only weakly on transverse momentum for $p_{\rm T}>8$ GeV/$c$. The small $p_{\rm T}$ dependence of the difference between elliptic flow results obtained from the event plane and four-particle cumulant methods suggests a common origin of flow fluctuations up to $p_{\rm T}=8$ GeV/$c$. The magnitude of the (anti-)proton elliptic and triangular flow is larger than that of pions out to at least $p_{\rm T}=8$ GeV/$c$ indicating that the particle type dependence persists out to high $p_{\rm T}$.Comment: 16 pages, 5 captioned figures, authors from page 11, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/186

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

Centrality dependence of charged particle production at large transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm{NN}}} = 2.76 TeV

The inclusive transverse momentum ($p_{\rm T}$) distributions of primary charged particles are measured in the pseudo-rapidity range $|\eta|<0.8$ as a function of event centrality in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV with ALICE at the LHC. The data are presented in the $p_{\rm T}$ range $0.15<p_{\rm T}<50$ GeV/$c$ for nine centrality intervals from 70-80% to 0-5%. The Pb-Pb spectra are presented in terms of the nuclear modification factor $R_{\rm{AA}}$ using a pp reference spectrum measured at the same collision energy. We observe that the suppression of high-$p_{\rm T}$ particles strongly depends on event centrality. In central collisions (0-5%) the yield is most suppressed with $R_{\rm{AA}}\approx0.13$ at $p_{\rm T}=6$-7 GeV/$c$. Above $p_{\rm T}=7$ GeV/$c$, there is a significant rise in the nuclear modification factor, which reaches $R_{\rm{AA}} \approx0.4$ for $p_{\rm T}>30$ GeV/$c$. In peripheral collisions (70-80%), the suppression is weaker with $R_{\rm{AA}} \approx 0.7$ almost independently of $p_{\rm T}$. The measured nuclear modification factors are compared to other measurements and model calculations.Comment: 17 pages, 4 captioned figures, 2 tables, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/284

Two-pion Bose-Einstein correlations in central Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.Comment: 17 pages, 5 captioned figures, 1 table, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/388