(************** 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). 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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[ 1965053, 28923]*) (*NotebookOutlinePosition[ 1966420, 28965]*) (* CellTagsIndexPosition[ 1966376, 28961]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Optimization of Neutrino Rates in a new Beta Beam Complex", StyleBox["\n", FontFamily->"CMR12", FontSize->10] }], "Title"], Cell["\<\ Elena Wildner Michael Benedikt Natalia Emelianenko Adrian Fabich Steven Hancock Mats Lindroos\ \>", "Author"], Cell[TextData[{ "The beta beam concept for the production of intense (anti-)neutrino beams \ is now well established. A baseline design has recently been published for a \ beta-beam facility at CERN. It has the virtue of respecting the known \ limitations of the CERN PS and ", "SPS ", StyleBox["synchrotrons, but ", FontVariations->{"CompatibilityType"->0}], StyleBox["falls short of delivering the requested annual rate of neutrinos", TextJustification->1, FontVariations->{"CompatibilityType"->0}], StyleBox[". We", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", FontSize->12, FontVariations->{"CompatibilityType"->0}], "report on a first analysis to increase the rate. A powerful method to \ understand the functional dependence of the many parameters that influence \ the figure of merit for a given facility is available with modern analytical \ calculation software. The method requires that a symbolic analytical \ description is produced of the full accelerator chain. Such a description has \ been made using Mathematica for the proposed beta beam facility at CERN. The \ direct access from Mathematica to an ORACLE database for reading basic design \ parameters and re-injecting derived parameters for completion of the \ parameter list is both convenient and efficient." }], "Abstract", TextJustification->1], Cell[CellGroupData[{ Cell["Introduction", "SectionFirst"], Cell[TextData[{ StyleBox["A powerful method to understand the functional dependence of the \ many parameters influencing the figure of merit for a certain facility is \ available with modern analytical calculation software. The method requires \ that a symbolic analytical description is produced of the full accelerator \ chain and such a description has been done for the proposed beta-beam \ facility at CERN using Mathematica", FontFamily->"Times New Roman"], StyleBox[" ", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["[3\[Dash]5]. Each process in each machine requires the solution \ of a set of differential equations to produce the resultant beam intensity \ given the intial one. The complete chain of accelerators is modelled simply \ by evaluating all such steps in the correct order. Care has been taken to \ express all inter-related parameters using delayed assignments. This permits \ dynamic scoping using the mechanism of Mathematica blocks. Thus, for example, \ results can be visualized as two-dimensional plots of the figure of merit as \ a function any of the machine parameters open to optimization. However, it is \ important to note that while such plots will help to identify the right \ parameter space for a requested machine design, they do not themselves \ guarantee that a realizable technical solution can be found. The work \ presented here has been done respecting the constraint of using the existing \ CERN accelerators, PS and SPS. In addition, the current decay ring design [6] \ is used even though it has been assumed that the Lorenz gamma of the stored \ ions can be changed without major changes to the lattice of the decay ring. \ For the stacking we have assumed that 15 6He bunches and 20 18Ne bunches can \ be merged in the decay ring without major losses. The situation is slightly \ better for 18Ne, which due to a more advantageous charge-to-mass ratio, will \ see an almost three times larger longitudinal acceptance of the decay ring. \ Theoretically this would permit up to 45 merges for 18Ne, but known limits in \ low level RF beam control precision restricts it to a maximum of 20 merges. \ All parameters for the EURISOL DS baseline of May 2005 are documented in the \ appendixes of [4,5].", FontFamily->"Times New Roman"], StyleBox["\n", FontFamily->"CMR10", FontSize->10] }], "Text", TextJustification->1], Cell[TextData[{ StyleBox["Below we can see the machines involved in the beta beam \ production from the proton driver (here a superconducting linear proton \ accelerator), accelerating protons for radiactive ion production on a target, \ to the final decay ring. 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decay ring \ without major losses from the merging process itself, ", Cell[BoxData[ \(T\_rep\)]], " is the repetition period for the fills in the decay ring, ", Cell[BoxData[ \(\[Gamma]\_top\)]], " the gamma factor of the decay ring, ", Cell[BoxData[ \(t\_half\)], FontFamily->"Times New Roman", FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}], " the half life at rest for the ions, ", Cell[BoxData[ \(I\_in\)]], " the total number of ions injected into the decay ring for each fill, f \ the fraction of the decay ring length for the straight section generating the \ neutrino beam and ", Cell[BoxData[ \(T\_run\)]], " the length in seconds of the run. The first term gives the rate per \ chosen period for the ideal decay ring in which an endless number of merges \ can be accepted, the second term gives the limit set by the restriction on \ maximum number of merges that can be accepted due to longitudinal emittance \ limitations and the third term is by convention chosen as the length of a \ \[OpenCurlyDoubleQuote]snow mass year\[CloseCurlyDoubleQuote] [7] which is \ used as an international standard to calculate running time of high energy \ physics experiments and it is ", Cell[BoxData[ \(TraditionalForm\`10\^7\)]], " seconds long." }], "Text", TextJustification->1] }, Open ]], Cell[CellGroupData[{ Cell["Gamma Dependence of the CERN Baseline", "Section"], Cell[TextData[{ StyleBox["The gamma dependence of the rate is mainly due to the gamma \ dependence of the acceleration time in the SPS, the lifetime of the ions in \ the decay ring and of the available longitudinal acceptance in the decay \ ring. 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major issues of the accelerator chain of \ the beta-beam concept are beam losses caused by particle decay. The \ beta-decay of unstable isotopes changes the charge-to-mass ratio leading to \ beam loss due to the changed magnetic forces. Based on beta-beam cycle \ optimized for the neutrino rate [4,5] one can calculate the energy loss in \ the various machines of the accelerator chain. The parent particle population \ N(t) as a function of time during accumulation, acceleration and storage \ decreases like", FontFamily->"Times New Roman"]], "Text", TextJustification->1], Cell[BoxData[ \(\(d\/dt\) N \((t)\) = \(ln \((2)\)\)\/\(\(t\_\(1/2\)\) \[Gamma] \((t)\)\)\ \[Times]N \ \((t)\)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \((1)\)\)], \ "Text"], Cell[TextData[{ StyleBox["where ", FontFamily->"Times New Roman"], Cell[BoxData[ \(t\_\(1/2\)\)]], StyleBox[" is the half-live of the isotope at rest and ", FontFamily->"Times New Roman"], "\[Gamma](t", StyleBox[")", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" the usual relativistic parameter. The daugther particles with \ the changed charge-to-mass ratio are lost more or less equally distributed \ over the circumference of the machine. There is a certain dependence on the \ accelerator lattice, which is neglected here. The energy of the particles \ lost from the beam will be deposited in the vicinity of the beam line, mainly \ in magnetic elements and shielding. The lost energy is calculated as", FontFamily->"Times New Roman"] }], "Text", TextJustification->1], Cell[BoxData[ \(\(\(E\_\(loss/cycle\) = \[Integral]\_0\%\(t\_cycle\)dN\/dt\[Times] T \((t)\) dt\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \((2)\)\)\(\ \[IndentingNewLine]\) \)\)], "Text"], Cell[TextData[{ StyleBox["where T is the kinetic energy and ", FontFamily->"Times New Roman"], Cell[BoxData[ \(t\_cycle\)]], StyleBox[" ", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["is the cycle time of the Beta-beam complex. A \ representativenumber, which can be compared with other accelerator cases, is \ the time-averaged power loss per unit circumference of the machine:", FontFamily->"Times New Roman"] }], "Text", TextJustification->1], Cell[BoxData[ RowBox[{\(P\_\(loss/l\)\), "=", RowBox[{\(E\_\(loss/cycle\)\/\(t\_cycle\[Times] circumference\_machine\)\), " ", StyleBox[\((3)\), FontFamily->"Times New Roman"]}]}]], "Text"], Cell[TextData[StyleBox["\nThe acceleration cycle for the Beta-beam baseline \ accelerator complex [5] is shown below for 6He. For illustration purposes \ the single bunch intensities (green) are indicated for the 1st, 5th, 10th, \ 15th and 20th bunch. 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.17677 L .33021 .17566 L .34321 .17474 L .36815 .17341 L .39216 .17244 L .41768 .17162 L .44227 .17096 L .46592 .17041 L .49109 .1699 L .51532 .16947 L .53861 .16909 L .56342 .16872 L .58729 .1684 L .58767 .16839 L s 0 0 m .00073 0 L .00139 0 L .00215 0 L .00287 0 L .00353 0 L .00415 0 L .00482 0 L .00554 0 L .00626 0 L .00703 0 L .00776 0 L .00843 0 L .00921 0 L .00965 0 L .01006 0 L .01081 0 L .01161 0 L .01201 0 L .01243 0 L .01319 0 L .01362 0 L .01401 0 L .01444 0 L .01491 0 L .01531 0 L .01575 0 L .01654 0 L .01731 0 L .01802 0 L .01871 0 L .01936 0 L .02008 0 L .02084 0 L .0216 0 L .02241 0 L .02309 0 L .02384 0 L .02428 0 L .02468 0 L .02513 0 L .0256 0 L .02638 0 L .02683 0 L .02725 0 L .02803 0 L .02875 0 L .02914 0 L .02957 0 L .03035 0 L Mistroke .03082 0 L .03127 0 L .03167 0 L .0321 0 L .03257 0 L .03307 0 L .0335 0 L .03396 0 L .0344 0 L .0348 0 L .03526 0 L .03569 0 L .03647 0 L .03691 0 L .03731 0 L .03803 0 L .0388 0 L .03953 0 L .0402 0 L .04094 0 L .04176 0 L .04216 0 L .0426 0 L .04339 0 L .04382 0 L .04422 0 L .04466 0 L .04513 .61748 L .04591 .61413 L .04677 .61055 L .04984 .59979 L .07476 .52965 L .09875 .46992 L .12426 .41379 L .14882 .36607 L .17245 .32537 L .1976 .28702 L .21008 .26969 L .2162 .26159 L .22181 .25509 L .22726 .25027 L .233 .24619 L .24508 .23964 L .25725 .23472 L .26858 .23107 L .29265 .22508 L .30492 .22265 L .31824 .22059 L .33106 .21917 L .34289 .21814 L Mistroke .36718 .2165 L .39054 .21531 L .41541 .2143 L .43935 .21348 L .4648 .21274 L .48932 .21211 L .5129 .21158 L .53799 .21106 L .56215 .21062 L .58767 .21018 L Mfstroke 0 0 m .00073 0 L .00139 0 L .00215 0 L .00287 0 L .00353 0 L .00415 0 L .00482 0 L .00554 0 L .00626 0 L .00703 0 L .00776 0 L .00843 0 L .00921 0 L .00965 0 L .01006 0 L .01081 0 L .01161 0 L .01201 0 L .01243 0 L .01319 0 L .01362 0 L .01401 0 L .01444 0 L .01491 0 L .01531 0 L .01575 0 L .01654 0 L .01731 0 L .01802 0 L .01871 0 L .01936 0 L .02008 0 L .02084 0 L .0216 0 L .02241 0 L .02309 0 L .02384 0 L .02428 0 L .02468 0 L .02513 0 L .0256 0 L .02638 0 L .02683 0 L .02725 0 L .02803 0 L .02875 0 L .02914 0 L .02957 0 L .03035 0 L Mistroke .03082 0 L .03127 0 L .03167 0 L .0321 0 L .03257 0 L .03307 0 L .0335 0 L .03396 0 L .0344 0 L .0348 0 L .03526 0 L .03569 0 L .03647 0 L .03691 0 L .03731 0 L .03803 0 L .0388 0 L .03953 0 L .0402 0 L .04094 0 L .04176 0 L .04216 0 L .0426 0 L .04339 0 L .04382 0 L .04422 0 L .04466 0 L .04513 0 L .04591 0 L .04636 0 L .04677 0 L .04755 0 L .04825 0 L .04907 0 L .04984 0 L .05054 0 L .0513 0 L .05201 0 L .05267 0 L .05339 0 L .05419 0 L .05459 0 L .05501 0 L .05579 0 L .05621 0 L .0566 0 L .05703 0 L .05749 0 L .05826 0 L .05869 0 L Mistroke .0591 0 L .05986 0 L .06055 0 L .06135 0 L .06211 0 L .06283 0 L .06347 0 L .06422 0 L .06493 0 L .06558 0 L .06619 0 L .06685 0 L .06754 0 L .06825 0 L .06901 0 L .06972 0 L .07037 0 L .07113 0 L .07156 0 L .07196 0 L .07269 0 L .07347 0 L .07417 0 L .07494 0 L .07575 0 L .07649 0 L .07719 0 L .07783 0 L .07857 0 L .07926 0 L .08002 0 L .08082 0 L .0815 0 L .08225 0 L .08306 0 L .08351 0 L .08393 0 L .08473 0 L .0855 0 L .08621 0 L .08685 0 L .0876 0 L .0883 0 L .08895 0 L .08955 0 L .0902 0 L .0909 0 L .0916 0 L .09235 0 L .09306 0 L Mistroke .0937 0 L .09446 0 L .09489 0 L .09528 0 L .09601 0 L .09678 0 L .09752 0 L .09833 0 L .0991 0 L .09981 0 L .10051 0 L .10115 .61548 L .10189 .61236 L .10258 .60953 L .10883 .58959 L .12012 .55731 L .1439 .49497 L .16919 .4363 L .19355 .38639 L .2058 .36348 L .21697 .34378 L .22274 .33535 L .22901 .32842 L .23563 .32266 L .24191 .31816 L .25387 .31132 L .26707 .30544 L .29129 .29734 L .30422 .29391 L .31609 .2914 L .32771 .28959 L .33995 .2881 L .36346 .28592 L .38848 .28419 L .41257 .28286 L .43817 .28169 L .46283 .28073 L .48656 .27993 L .5118 .27916 L .53611 .27851 L .55948 .27793 L .58436 .27737 L .58767 .2773 L Mfstroke 0 0 m .00073 0 L .00139 0 L .00215 0 L .00287 0 L .00353 0 L .00415 0 L .00482 0 L .00554 0 L .00626 0 L .00703 0 L .00776 0 L .00843 0 L .00921 0 L .00965 0 L .01006 0 L .01081 0 L .01161 0 L .01201 0 L .01243 0 L .01319 0 L .01362 0 L .01401 0 L .01444 0 L .01491 0 L .01531 0 L .01575 0 L .01654 0 L .01731 0 L .01802 0 L .01871 0 L .01936 0 L .02008 0 L .02084 0 L .0216 0 L .02241 0 L .02309 0 L .02384 0 L .02428 0 L .02468 0 L .02513 0 L .0256 0 L .02638 0 L .02683 0 L .02725 0 L .02803 0 L .02875 0 L .02914 0 L .02957 0 L .03035 0 L Mistroke .03082 0 L .03127 0 L .03167 0 L .0321 0 L .03257 0 L .03307 0 L .0335 0 L .03396 0 L .0344 0 L .0348 0 L .03526 0 L .03569 0 L .03647 0 L .03691 0 L .03731 0 L .03803 0 L .0388 0 L .03953 0 L .0402 0 L .04094 0 L .04176 0 L .04216 0 L .0426 0 L .04339 0 L .04382 0 L .04422 0 L .04466 0 L .04513 0 L .04591 0 L .04636 0 L .04677 0 L .04755 0 L .04825 0 L .04907 0 L .04984 0 L .05054 0 L .0513 0 L .05201 0 L .05267 0 L .05339 0 L .05419 0 L .05459 0 L .05501 0 L .05579 0 L .05621 0 L .0566 0 L .05703 0 L .05749 0 L .05826 0 L .05869 0 L Mistroke .0591 0 L .05986 0 L .06055 0 L .06135 0 L .06211 0 L .06283 0 L .06347 0 L .06422 0 L .06493 0 L .06558 0 L .06619 0 L .06685 0 L .06754 0 L .06825 0 L .06901 0 L .06972 0 L .07037 0 L .07113 0 L .07156 0 L .07196 0 L .07269 0 L .07347 0 L .07417 0 L .07494 0 L .07575 0 L .07649 0 L .07719 0 L .07783 0 L .07857 0 L .07926 0 L .08002 0 L .08082 0 L .0815 0 L .08225 0 L .08306 0 L .08351 0 L .08393 0 L .08473 0 L .0855 0 L .08621 0 L .08685 0 L .0876 0 L .0883 0 L .08895 0 L .08955 0 L .0902 0 L .0909 0 L .0916 0 L .09235 0 L .09306 0 L Mistroke .0937 0 L .09446 0 L .09489 0 L .09528 0 L .09601 0 L .09678 0 L .09752 0 L .09833 0 L .0991 0 L .09981 0 L .10051 0 L .10115 0 L .10189 0 L .10258 0 L .10334 0 L .10414 0 L .10483 0 L .10558 0 L .10639 0 L .10685 0 L .10726 0 L .10806 0 L .10883 0 L .10947 0 L .11019 0 L .11093 0 L .11163 0 L .11229 0 L .11289 0 L .11354 0 L .11423 0 L .11494 0 L .11569 0 L .1164 0 L .11704 0 L .1178 0 L .11823 0 L .11862 0 L .11935 0 L .12012 0 L .12086 0 L .12168 0 L .12244 0 L .12316 0 L .12386 0 L .1245 0 L .12524 0 L .12594 0 L .1267 0 L .1275 0 L Mistroke .12819 0 L .12894 0 L .12975 0 L .13021 0 L .13062 0 L .13143 0 L .13219 0 L .13284 0 L .13355 0 L .1343 0 L .135 0 L .13566 0 L .13626 0 L .13691 0 L .1376 0 L .13831 0 L .13906 0 L .13977 0 L .14042 0 L .14117 0 L .1416 0 L .142 0 L .14272 0 L .14349 0 L .14424 0 L .14505 0 L .14582 0 L .14654 0 L .14718 0 L .14789 0 L .14863 0 L .14932 0 L .15009 0 L .15089 0 L .15158 0 L .15233 0 L .15315 0 L .1536 0 L .15402 0 L .15482 0 L .15559 0 L .15624 .61749 L .15695 .61442 L .1584 .60848 L .16101 .59962 L .16689 .58226 L .19176 .51434 L .21569 .45648 L .22192 .4438 L .22873 .43365 L Mistroke .24113 .42044 L .25327 .41112 L .26621 .40342 L .29188 .39206 L .30476 .38759 L .3166 .38433 L .32818 .38198 L .3404 .38003 L .36383 .37718 L .38878 .37491 L .4128 .37317 L .43832 .37163 L .46291 .37037 L .48657 .36931 L .51174 .36831 L .53597 .36744 L .55927 .36668 L .58409 .36594 L .58767 .36584 L Mfstroke 0 0 m .00073 0 L .00139 0 L .00215 0 L .00287 0 L .00353 0 L .00415 0 L .00482 0 L .00554 0 L .00626 0 L .00703 0 L .00776 0 L .00843 0 L .00921 0 L .00965 0 L .01006 0 L .01081 0 L .01161 0 L .01201 0 L .01243 0 L .01319 0 L .01362 0 L .01401 0 L .01444 0 L .01491 0 L .01531 0 L .01575 0 L .01654 0 L .01731 0 L .01802 0 L .01871 0 L .01936 0 L .02008 0 L .02084 0 L .0216 0 L .02241 0 L .02309 0 L .02384 0 L .02428 0 L .02468 0 L .02513 0 L .0256 0 L .02638 0 L .02683 0 L .02725 0 L .02803 0 L .02875 0 L .02914 0 L .02957 0 L .03035 0 L Mistroke .03082 0 L .03127 0 L .03167 0 L .0321 0 L .03257 0 L .03307 0 L .0335 0 L .03396 0 L .0344 0 L .0348 0 L .03526 0 L .03569 0 L .03647 0 L .03691 0 L .03731 0 L .03803 0 L .0388 0 L .03953 0 L .0402 0 L .04094 0 L .04176 0 L .04216 0 L .0426 0 L .04339 0 L .04382 0 L .04422 0 L .04466 0 L .04513 0 L .04591 0 L .04636 0 L .04677 0 L .04755 0 L .04825 0 L .04907 0 L .04984 0 L .05054 0 L .0513 0 L .05201 0 L .05267 0 L .05339 0 L .05419 0 L .05459 0 L .05501 0 L .05579 0 L .05621 0 L .0566 0 L .05703 0 L .05749 0 L .05826 0 L .05869 0 L Mistroke .0591 0 L .05986 0 L .06055 0 L .06135 0 L .06211 0 L .06283 0 L .06347 0 L .06422 0 L .06493 0 L .06558 0 L .06619 0 L .06685 0 L .06754 0 L .06825 0 L .06901 0 L .06972 0 L .07037 0 L .07113 0 L .07156 0 L .07196 0 L .07269 0 L .07347 0 L .07417 0 L .07494 0 L .07575 0 L .07649 0 L .07719 0 L .07783 0 L .07857 0 L .07926 0 L .08002 0 L .08082 0 L .0815 0 L .08225 0 L .08306 0 L .08351 0 L .08393 0 L .08473 0 L .0855 0 L .08621 0 L .08685 0 L .0876 0 L .0883 0 L .08895 0 L .08955 0 L .0902 0 L .0909 0 L .0916 0 L .09235 0 L .09306 0 L Mistroke .0937 0 L .09446 0 L .09489 0 L .09528 0 L .09601 0 L .09678 0 L .09752 0 L .09833 0 L .0991 0 L .09981 0 L .10051 0 L .10115 0 L .10189 0 L .10258 0 L .10334 0 L .10414 0 L .10483 0 L .10558 0 L .10639 0 L .10685 0 L .10726 0 L .10806 0 L .10883 0 L .10947 0 L .11019 0 L .11093 0 L .11163 0 L .11229 0 L .11289 0 L .11354 0 L .11423 0 L .11494 0 L .11569 0 L .1164 0 L .11704 0 L .1178 0 L .11823 0 L .11862 0 L .11935 0 L .12012 0 L .12086 0 L .12168 0 L .12244 0 L .12316 0 L .12386 0 L .1245 0 L .12524 0 L .12594 0 L .1267 0 L .1275 0 L Mistroke .12819 0 L .12894 0 L .12975 0 L .13021 0 L .13062 0 L .13143 0 L .13219 0 L .13284 0 L .13355 0 L .1343 0 L .135 0 L .13566 0 L .13626 0 L .13691 0 L .1376 0 L .13831 0 L .13906 0 L .13977 0 L .14042 0 L .14117 0 L .1416 0 L .142 0 L .14272 0 L .14349 0 L .14424 0 L .14505 0 L .14582 0 L .14654 0 L .14718 0 L .14789 0 L .14863 0 L .14932 0 L .15009 0 L .15089 0 L .15158 0 L .15233 0 L .15315 0 L .1536 0 L .15402 0 L .15482 0 L .15559 0 L .15624 0 L .15695 0 L .1577 0 L .1584 0 L .15906 0 L .15966 0 L .16035 0 L .16101 0 L .16171 0 L Mistroke .16247 0 L .16318 0 L .16382 0 L .16458 0 L .16501 0 L .1654 0 L .16613 0 L .16689 0 L .16764 0 L .16807 0 L .16846 0 L .16919 0 L .16995 0 L .17064 0 L .17128 0 L .17198 0 L .17274 0 L .1735 0 L .17393 0 L .17434 0 L .17515 0 L .1756 0 L .17601 0 L .17675 0 L .17756 0 L .17831 0 L .17901 0 L .17966 0 L .18037 0 L .18103 0 L .18163 0 L .18234 0 L .18311 0 L .18383 0 L .18451 0 L .18527 0 L .18599 0 L .18663 0 L .18733 0 L .18809 0 L .18889 0 L .18958 0 L .19033 0 L .19114 0 L .19188 0 L .19227 0 L .1927 0 L .19315 0 L .19357 0 L .19434 0 L Mistroke .19505 0 L .19587 0 L .19664 0 L .19733 0 L .19807 0 L .19876 0 L .19939 0 L .20013 0 L .20094 0 L .20169 0 L .20239 0 L .20314 0 L .20394 0 L .2047 0 L .20538 0 L .20619 0 L .20665 0 L .20707 0 L .20785 0 L .20824 0 L .20867 0 L .20909 0 L .20953 0 L .21032 0 L .21076 0 L .21117 0 L .21161 0 L .21209 .6162 L .21251 .61443 L .21296 .61252 L .21378 .6092 L .21531 .60362 L .22114 .58733 L .22756 .57416 L .24054 .55538 L .25253 .54305 L .26542 .53279 L .29087 .51774 L .30359 .51185 L .31539 .50742 L .32681 .50427 L .33898 .50165 L .36465 .49751 L .38939 .49456 L .4132 .49229 L .43852 .49028 L .4629 .48863 L .48635 .48724 L .51131 .48593 L .53534 .48479 L Mistroke .56087 .4837 L .58548 .48274 L .58767 .48265 L Mfstroke 1 0 0 r 0 0 m .00578 .02993 L .00879 .02949 L .00961 .02936 L .01049 .02924 L .01092 .02917 L .01113 .02914 L .01133 .02911 L .0115 .02909 L .01169 .05996 L .01188 .05989 L .01208 .05982 L .018 .05793 L .02091 .05709 L .02174 .05686 L .02215 .05674 L .02235 .05668 L .02254 .05663 L .02271 .05658 L .02288 .08741 L .02306 .08733 L .02325 .08723 L .02403 .08685 L .02695 .08549 L .03016 .08413 L .03164 .08351 L .03245 .08317 L .03285 .08301 L .03322 .08286 L .03356 .08271 L .03374 .08264 L .03393 .11345 L .03412 .11333 L .03433 .1132 L .03471 .11297 L .03607 .11213 L .03901 .11044 L .04056 .10959 L .04222 .10869 L .04305 .10824 L .04383 .10782 L .04453 .10744 L .04473 .10734 L .04483 .10728 L .04493 .10723 L .0451 .13802 L .04529 .13787 L .04815 .13579 L .05093 .13389 L .05396 .13189 L Mistroke .05475 .13136 L .05519 .13108 L .0556 .13081 L .05579 .13069 L .05599 .13056 L .05609 .13049 L .0562 .1613 L .05631 .16121 L .0564 .16113 L .05713 .1605 L .06013 .158 L .06293 .15581 L .0644 .15467 L .06596 .15347 L .06675 .15287 L .06696 .1527 L .06708 .15262 L .0672 .15253 L .0673 .18333 L .06741 .18322 L .06762 .18303 L .06914 .18155 L .07216 .17878 L .07534 .17596 L .07685 .17464 L .07751 .17407 L .07788 .17374 L .07806 .17358 L .07823 .17344 L .07841 .20417 L .07857 .204 L .07893 .2036 L .07968 .20281 L .08124 .20116 L .08408 .1983 L .08552 .19688 L .08705 .19538 L .08836 .19411 L .08872 .19377 L .08891 .19358 L .08911 .19339 L .08928 .19322 L .08947 .22394 L .08965 .22373 L .08981 .22354 L .09564 .21698 L .09717 .21533 L .09883 .21355 L .0996 .21274 L .10001 .2123 L Mistroke .10022 .21208 L .1004 .21189 L .10057 .24261 L .10073 .2424 L .10109 .24195 L .10185 .24099 L .10756 .23412 L .10908 .23235 L .11051 .2307 L .11089 .23026 L .1113 .2298 L .11151 .22955 L .11163 .22941 L .11175 .26017 L .11194 .2599 L .11216 .25961 L .11365 .25761 L .11661 .25376 L .11818 .25179 L .11984 .24971 L .12131 .24788 L .12171 .24738 L .12215 .24685 L .12235 .2466 L .12256 .24634 L .12274 .24612 L .12294 .27675 L .12313 .27647 L .12331 .27621 L .12365 .27572 L .12442 .27462 L .1258 .27268 L .12854 .26895 L .1301 .26687 L .13156 .26493 L .13299 .26305 L .13341 .2625 L .13361 .26224 L .1338 .26199 L .13397 .29265 L .13415 .29238 L .13453 .2918 L .13768 .28712 L .14068 .28285 L .14225 .28064 L .14311 .27944 L .14391 .27832 L .14428 .27781 L .14463 .27732 L .14483 .27706 L Mistroke .14494 .2769 L .14504 .30766 L .14522 .30737 L .14541 .30707 L .14704 .30449 L .14992 .30009 L .15287 .2957 L .15416 .2938 L .15485 .2928 L .15558 .29174 L .15578 .29144 L .15598 .29115 L .15616 .32179 L .15635 .32147 L .15706 .32028 L .15848 .31796 L .1616 .31299 L .16458 .30837 L .16608 .30607 L .16649 .30544 L .16672 .3051 L .16694 .30477 L .16703 .30463 L .16713 .30447 L .16725 .3352 L .16735 .33501 L .16773 .33436 L .17338 .32493 L .17627 .32027 L .17706 .31901 L .17749 .31832 L .1779 .31769 L .17807 .3174 L .17824 .31714 L .17843 .34772 L .17861 .3474 L .17939 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they are injected in to the \ decay ring. The RCS is operated at 10 Hz. 20 RCS bunches are accumulated at \ injection energy in the PS over 1.9 seconds. The beam is then accelerated in \ PS and SPS to ", FontFamily->"Times New Roman"], StyleBox["\[Gamma] ", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["= 100. The magnet cycles of the RCS, PS and SPS are superimposed. \ The black, solid line indicates the repetition of post acceleration at 10 Hz, \ followed by the acceleration of the accumulated bunches through the PS and \ the SPS. 20 new bunches are sent from the SPS to the decay ring every 6 \ seconds in the 6He case. During the long accumulation in the PS at low gamma \ and the following acceleration at low gamma, the intensity of the bunches \ decreases remarkably. E.g., the first bunch injected into the PS has a \ remaining intensity at the end of the PS accumulation of about 35% for 6He. \ The bunches injected later remain with accordingly higher intensity at the \ end of PS accumulation. This is illustrated with green lines showing single \ bunch intensities. All intensities are normalized to the equivalent maximum \ intensity, which occurs at the individual injection from the RCS. The total \ intensity is indicated by the red line, normalized to the total number of \ ions injected into the RCS. The highest values of the time averaged power \ loss are estimated to 3 ", FontFamily->"Times New Roman"], StyleBox["W/m", FontFamily->"Times New Roman", FontVariations->{"CompatibilityType"->0}], StyleBox[", which occur in the PS machine and are comparable to the ones of \ existing high intensity operation scenarios like CNGS[8], which is to start \ in May 2006. \n", FontFamily->"Times New Roman"] }], "Text", TextJustification->1], Cell[TextData[{ StyleBox["\n", FontFamily->"CMR10"], StyleBox["Below is shown, as an example, the last step of the chain, the \ calculation of the intensity of accumulated 6He ions in the decay ring. \ Epern is the ion rest mass and topTpern is the ion top energy. ", FontFamily->"Times New Roman"] }], "Text", TextJustification->1], Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(decayringaccumulation := \((ClearAll[ n]; \[IndentingNewLine]gamma[t_] := 1 + topTpern/Epern; \[IndentingNewLine]decayrate[t_] := Log[2]\ n[t]/\((gamma[t]\ thalf)\); \[IndentingNewLine]eqns = {D[ n[t], t] \[Equal] \(-decayrate[t]\), n[0] \[Equal] nout6}; \[IndentingNewLine]nsinglebatch[t_] = n[t] /. DSolve[eqns, n[t], t] // First; \[IndentingNewLine]n[t_] = Sum[UnitStep[t - t0]\ UnitStep[ t0 + mergesratio*spsrepetitiontime - t]* nsinglebatch[t - t0], {t0, 0, t, spsrepetitiontime}]; \[IndentingNewLine]nout7 = n[\((mergesratio - 1)\) spsrepetitiontime])\)\n \(\(fullchain\)\(:=\)\((spsout; decayringaccumulation)\)\( (*\ spsout\ is\ the\ accumulated\ intensity\ from\ the\ preceding\ step, \ \ the\ SPS\ ring\ *) \)\)\)\)\)], "Input"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"fullchain", "\n", RowBox[{ RowBox[{"Plot", "[", RowBox[{\(n[t]\), ",", \({t, 0, \((mergesratio + 1)\) spsrepetitiontime + 10^\(-4\)}\), ",", \(PlotLabel \[Rule] name\), ",", RowBox[{ StyleBox[ RowBox[{"Frame", StyleBox["La", FontColor->GrayLevel[0]], "bel"}]], "\[Rule]", \({"\<[s]\>", None}\)}], ",", \(PlotRange \[Rule] All\)}], "]"}], ";"}]}]}]], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 %%ImageSize: 500 309.017 MathPictureStart /Mabs { Mgmatrix 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Basic design data is stored in a database and can be accessed \ after data base connection and reading in of baseline data from the data base \ and used in the calculations.\n", FontFamily->"Times New Roman"] }], "Text", TextJustification->1] }, Open ]], Cell[CellGroupData[{ Cell["Baseline Parameters Database", "Section"], Cell[CellGroupData[{ Cell["Database Design", "Subsection"], Cell[TextData[{ "To develop a new project invloving many people and many institutes demands \ the use of similar standards and the same basic parameters and units \ troughout the community. Information accessible on the Web is not enough. The \ need is not only a common source but also versioning of the base-line \ parameter set and a possibility for users to read and make updates of the \ parameter lists from ", StyleBox["Mathematica", FontSlant->"Italic"], ". Our approach to these reqirements is to define a database for parameter \ storage. On top of this database is built a package in ", StyleBox["Mathematica", FontSlant->"Italic"], " that permits easy access to the parameters in the database. Users can \ develop their applications in ", StyleBox["Mathematica", FontSlant->"Italic"], " accessing directly the parameters, using their specific identifiers.\n\n\ We have designed a generic database able to store the description of any \ system with objects having a tree or a network structure. This design meets \ the requirements for the storage for the parameters of a system in evolution \ (storing the system metadata together with the parameters, extensibility, \ versioning, and logging the changes). To simplify the design the allowed type \ of the network was limited by the condition that each node may have only one \ or two parents. 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The transparent access to the parameter \ values is obtained through the stored database procedures, which encapsulate \ the optional parameter calculation and, if required, translate the parameter \ value into the number format, HTML or ", StyleBox["Mathematica", FontSlant->"Italic"], " strings." }], "Text", TextJustification->1] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Working with the Database in ", StyleBox["Mathematica", FontSlant->"Italic"], " " }], "Subsection"], Cell[TextData[{ "This loads the package ", StyleBox["DatabaseLink", FontSlant->"Italic"] }], "Text"], Cell[BoxData[ \(Needs["\"]\)], "Input"], Cell["\<\ Open the database connection (specific database access parameters \ may be added inside the square brackets or the user can select a named \ connection using the Connection Tool):\ \>", "Text"], Cell[BoxData[ StyleBox[\(conn = OpenSQLConnection[];\), FormatType->StandardForm]], "Input"], Cell["\<\ The following command uses an Oracle specific stored database \ package to add the application information to the current database session:\ \ \>", "Text"], Cell[BoxData[ \(\(SQLExecute[ conn, \ "\"];\)\)], "Input"], Cell[TextData[{ "This defines a function to retrieve a numeric parameter value from the \ database. BB.PVALUE is a custom PL/SQL package function stored in the \ database, which performs the work to search for the parameter named ", StyleBox["par", "InlineInputBold"], " for the component ", StyleBox["object", "InlineInputBold"], ":" }], "Text"], Cell[BoxData[ \(GetParameterValue[object_String, \ par_String]\ := First[First[\[IndentingNewLine]SQLExecute[ conn, \ "\