(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2693682, 33552]*) (*NotebookOutlinePosition[ 2694353, 33575]*) (* CellTagsIndexPosition[ 2694309, 33571]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Integration of ", StyleBox["Mathematica", FontSlant->"Italic"], " in the Large Hadron Collider" }], "Title"], Cell["\<\ J. Beauquis E. Wildner\ \>", "Author"], Cell[TextData[{ "The ", ButtonBox["CERN", ButtonData:>{ URL[ "http://www.cern.ch"], None}, ButtonStyle->"Hyperlink"], " Large Hadron Collider (LHC) is the major project in particle physics in \ the world. The particle accelerator is a 27 km ring where many thousands of \ superconducting magnets keep protons on track. Results from complex \ measurements of, for example, the magnetic field and the geometry of the main \ bending and focusing magnets are stored in databases for analysis and quality \ control. The geometry of the 15 m long main bending magnet weighing almost 30 \ tons has to be controlled within tenths of mm. All measurements are stored in \ ORACLE data bases. They are organized in two types: raw and derived data. Raw \ data come from the measurement devices and derived data describe quality \ measures calculated from the raw measurements. For example, the transverse \ position of the beam tube center relative to the theoretical axis of the \ accelerator is measured along the magnet. This data is used to simulate \ improvements or to calculate quality criteria, used in the daily quality \ checks of all produced magnets. The positions of the corrector magnets housed \ inside the magnet assembly are measured in industry before the closing of the \ magnet cold mass; they have to be calculated from reference points on the \ outside of the cold mass one measured after delivery to CERN. The results \ from these calculations are re-injected into the data base for easy access. \ The calculations cannot be performed by the ORACLE query language. There \ comes the interest of ", StyleBox["Mathematica", FontSlant->"Italic"], ", which is easy to interface with the existing ORACLE and Java \ environment. Maintenance and improvements of calculations are comfortable due \ to ", StyleBox["Mathematica", FontSlant->"Italic"], "\[CloseCurlyQuote]s explicit functional language." }], "Abstract", TextJustification->1], Cell[CellGroupData[{ Cell["Introduction", "SectionFirst"], Cell[TextData[{ "In the future Large Hadron Collider, currently under construction at CERN, \ Geneva, two counter rotating beams will provide proton-proton collisions at 7 \ TeV center of mass energy. One of the major efforts toward the accelerator \ completion is the manufacturing of the 1232 superconducting twin aperture \ magnets required to bend the particle beams along the 27 km long circular \ trajectory. The manufacturing procedure of each 15m long, 0.5m wide and 30 \ ton heavy magnet is strongly driven by the respect of the tight geometrical \ tolerances imposed by the accelerator beam performance. In order to ensure \ the maximum transverse clearance for the circulating particles with the \ minimum coil size, the central part of the magnet is bent in the horizontal \ plane of about 5mrad. In addition, to compensate for systematic \ field-harmonics in the dipole field, multipolar correctors are placed in one \ or both ends of each dipole. Thus, to satisfy the geometrical tolerances \ imposed on the dipole shape, the central part should be enclosed in a torus \ of 1.3 mm radius and the ends in two cylinders of 0.6 mm radius with respect \ to the geometric axis of the dipole. On the other hand all the correctors \ should stay in average within 0.3 mm from the geometric axis with a", StyleBox[" standard deviation of the error", FontVariations->{"CompatibilityType"->0}], " not in excess of 0.5 mm.\nThe dipole geometry must be preserved \ throughout the assembly (in industry and at CERN), transport and testing \ circumstances (cold test) till the positioning in the tunnel and the start of \ the operative stages.\nWe will focus on two aspects of the geometry: the \ calculation of the sagitta of the bent magnet and of the overall shape of the \ excursion of the magnet center along the magnet, to show the how we use a ", StyleBox["Mathematica ", FontSlant->"Italic"], StyleBox[" package to update our data base with derived parameters not \ possible to calculate within the data base.", FontVariations->{"CompatibilityType"->0}] }], "Text", TextJustification->1] }, Open ]], Cell[CellGroupData[{ Cell["Description of the problem", "Section"], Cell[CellGroupData[{ Cell["LHC dipole geometry", "Subsection"], Cell[TextData[StyleBox["The theoretical geometry of the twin aperture dipole \ is shown in figure. The (x,y) plane is the plane of the accelerator. The two \ theoretical beam-trajectories consist of an arc of a circle, extending over \ the magnetic field, with the angle \[CapitalTheta] and the radius \[Rho] and \ of straight lines between magnets. The 3 dimensional measurements of the \ centre of the two cold bore tubes, in which the beams are circulating, are \ fit to the two theoretical curves. 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", FontFamily->"Times New Roman"]], "Text"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", " ", RowBox[{\(Table\ 1 : Dipole\ geometry\ parameters\ at\ room\ and\ operational\ \ temperature\), "\[IndentingNewLine]", " ", TagBox[ FrameBox[GridBox[{ {"Parameter", "Symbol", \(Value\ warm\), \(Value\ cold\), "Unit"}, {\(Bending\ angle\ per\ dipole\), "\[CapitalTheta]", "5.099998", "5.099988", "mrad"}, {\(Magnetic\ length\ of\ each\ aperture\), "lm", "14.34", "14.30", "m"}, {\(Radius\ of\ curvature\), "r", "2812.36", "2803.93", "m"}, {\(Separation\ of\ tube\ centers\), "d", "194.52", "194.00", "mm"}, {"Sagitta", "s", "9.14", "9.12", "mm"} }, RowLines->True, ColumnLines->True], BoxMargins->0.1], DisplayForm], "\[IndentingNewLine]"}]}]], "Text", GeneratedCell->False, CellAutoOverwrite->False, Background->GrayLevel[1]], Cell["\<\ The sagitta is used to evaluate the quality of the geometry. The sagitta \ change with respect to the nominal sagitta is estimated by using the fact \ that the difference between two arcs (the nominal and the measured) can be \ expressed as a second order polynomial. 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