High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
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Finallyafterabitofalgebraonecancomputetheuncertaintiesontheemittance,<strong>and</strong>theT<strong>and</strong> ()2= Tparameters:(~")2= +21221131111 1~"6212211(12)2+1112 12112211+1122 1~"2212(12)2+212 22122(11)2+411 2112212221112 4(11)2+211 4(22)2 4(22)2 (4.34)<br />
()2=1~"6222211(12)2+212211 12112121211+2121122 221222211+212211222312111112123111122 24(11)2+212222 11221221122 4(22)2 2 1112 (4.36) (4.35)<br />
ment,istakentobeequaltothemeasuredresolutionofthebeamprolemeasurementsystemi.e. computedelementsofthe-matrix<strong>and</strong>thenpropagatetheseuncertaintiesontheestimatedvalues fortheemittance<strong>and</strong>Twissparameters.Lastlythevalueof(i),theerroronbeamsizemeasure- Thereforebybuildingthecurvaturematrixwecangetanestimateoftheuncertaintiesonthe<br />
Onewayofvaryingthetransfermatrixbetweenareferencepoint<strong>and</strong>themeasurementistochange thestrengthofaquadrupole<strong>and</strong>observethevariationofbeamsizeonanOTRscreenupstream. 4.4.2Thequadrupolescanmethod (i)=60m:<br />
Althoughthismethodisgenerallyeasytoimplementspecialcaremustbetaken: theminimumbeamsizeshouldbechosentobelargewithrespecttotheresolutionofthe themaximumbeamspotsizeinbothdirectionmustbesmallerthatthedimensionofthe OTRscreen<br />
casewherethequadrupole<strong>and</strong>theprolemonitorareseparatedbyadrift(seereference[34]).In amoregeneralcasewherethetransfermatrixbetweenthequadrupoleexit<strong>and</strong>theprolemonitor Onequestionthatarisesishowtosettheopticsdownstreamthequadrupolethatisbeingvariedto getthewantedbeamsizevariationontheprolemonitor?Suchproblemhasbeenstudiedinthe beamsizemeasurement<strong>and</strong>largeenoughnottoproduceanysaturationontheCCDcamera<br />
isR,wec<strong>and</strong>eriveasimilarcriteriononthelatticefunctionsattheprolemonitorlocation:the thatisusedtomeasurethebeamsize.<br />
by: x;y<strong>and</strong>x;yTwissparametersattheentranceofthequadrupolebeingvariedshouldberelated x=R11 y=R33 R12x R34y<br />
(4.37)
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