corrent-snider mapdand

pravegak bhautikshastrat, courant-snider parameters (anekada twiss parameters kinwa see. ess. parameters mhanoon sandarbhit) haah bimmadhil kananchya sthitee aanee veganchya vitaranache varnan karnyasathi vaparla jaanara pramanancha sanch aahe. jevha eka bimmadhil pratyek kananchya tyaa parimanasah ekach pariman aanee veg (kinwa momenta) sobatchya sthitee fages space aakrutivar rekhatalelya asatat, tevha kananna vedhanara lambvartul samikaranadvare deela jaau shakatoh
jethe sootra _ 2 haah sthitee aksh aahe aanee sootra _ 3 haah veg aksh aahe. yaa sutramadhye, sootra 4, sootra 5 aanee sootra 6 heey dilelya akshasah bimsathi courant-snider parameters aahet aanee sootra 7 heey utsarjak aahe. bimsathi parametersche teen sanch mojale jaau shakatat, pratyek orthogonal dishene eka, x, y aanee z.
itihas.
kann kirananchya tappyatil avkash gunadharmanche varnan karnyasathi yaa mapdandancha vapar, accelerator bhautikshastra samudayamadhye ernest courant aanee hartland snider yanni tyanchya 1953 chya 'alternating-gradient syncrotroncha siddhant' yaa peparmadhye lokpriy keela. british khagolshastradnya richard kyu yanchyanantar pravegak bhautikshastra sahityat tyanna "twiss parameters" mhanoon dekhil mothya pramanavar sambodhale jaate. twiss, jaree tyache naav sutrashi kase sambandhit jhaale heey aspasht aahe.
tappyatil jaaga kshetrache varnan.
pravegak kinwa kiran vahtook reshedvare kananchya gatiche anukaran kartana, pratyek kananchya gaticha vaiyaktikaritya magova ghenyaivaji kananchya samoohachya ekoon gunadharmanche varnan karane bahudha isht asate. leovilchya prameyanusar heey darshavile jaau shakate qee jevha beemvar keval conservative forcecha parinam hoto tevha sthitee aanee momentum fages space plotwar vyapaleli ghanata sthir asate. yaa bhukhandavaril kiranane vyapalele kshetra kiran utsarjak mhanoon olakhale jaate, jaree yaa gunadharmachya achook ganiteey vyakhyesathi anek spardhatmak vyakhya aahet.
samanvay.
pravegak bhautikshastrat, samanvay sthitee samanyatah aadarshikrut "sandarbh kann" chya sandarbhat paribhashit kelee jaate, jee pravegkasathi aadarsh rachana prakshepavakra anusaran karate. yaa prakshepavkrasaha sanrekhit kelelya dishela 'zed' (kadhikadhi 'ess') asey sambodhale jaate aanee tyala 'rekhansh nirdeshank' asehi mhanatat. x aanee y yaa done anuprastha nirdeshank akshanchi vyakhya z akshala aanee ekmekanna lumb kelee jaate.
x, y aanee z akshanchya bajoone sandarbh kananchya sapeksh pratyek kananchya sthitiche varnan karnyavyatirikt, yaa pratyek mulyanchya badalachya daracha vichar karane dekhil aavashyak aahe. heey samanyatah velechya tulanet anudairdhya sthanachya (x '= dx/dz) sandarbhat badalacha darr mhanoon dile jaate. bahutek prakarananmadhye, x 'aanee y' heey donhi 1 peksha khoopach qamee asatat, kaaran kann beemchya margavar tyachya aadvya bajoone jaanyapeksha khoop vegane jaat asatat. hii dharana lakshat gheta, x 'aanee y' heey sadhya gunottaranaivaji coone mhanoon vyakt karnyasathi lahan konacha andaj vaparane shakya aahe. mhanoon, x 'aanee y' heey samanyatah milliredianmadhye vyakt kele jaatat.
lambvartul samikaran.
jevha tappyatil jaaget kann vitaranbhovati lambvartul kadhale jaate, tevha lambvartulasathiche samikaran asey dile jaateh
"yethe 'kshetra' heey tappyatil jaageche kshetra aahe aanee tyat lambi * konache ekak aahet. kahee srot yaa kshetrachi vyakhya beam utsarjanache sootra 7 mhanoon karatat, tarr itar sootra 10 vapartat. 2 aayami gossian vitaranasah bimmadhil kanancha vishisht ansh mhanoon kshetrachi vyakhya karane dekhil shakya aahe.
itar teen gunank, sootra _ 4, sootra _ 5 aanee sootra _ 6, heey see. ess. mapdand aahet. heey lambvartul heey pravegkachya eka binduvaril kananchya sthitee aanee vegache tatkal aalekh asalyane, hii moolye kalanusar badaltil. x aanee x 'heey keval done swatantra chull asalyane aanee utsarjak sthir asalyane, fakt done see. ess. mapdand swatantra aahet. teen mapdandanmadhil sambandh khalilpramane deela aaheh
niyatkalik pranalinsathi vyutpann.
see. ess. mapdandanna tappyatil kananchya sankalanache anubhavjanya varnan mannyabarobarach, vidyutchumbakiy kshetrantil kananchya gatichya samikarananchya aadhare teey midvane shakya aahe.
gatiche samikaran.
majboot foaksing acceleratormadhye, anuprastha foaksing pramukhyane chaturbhuj chumbakadware pradan kele jaate. chumbak akshala samantar asalelya anuprastha gatisathi gatiche resheey samikaran asey aaheh
jethe sootra _ 16 haah "kendrit gunank" aahe, jyachi lambi-2 aahe aanee kwadrupol kshetrat keval shunyetar aahe. (lakshat ghya qee yaa sampoorn spashtikaranat x vaparla jaato, parantu k sathee chinh badalnyabarobarach y samaan pramanat vaparla jaau shakato. anudairdhya nirdeshank, zed, sathee kahise vegale vyutpann aavashyak aahe.)
sootra 16 niyatkalik aahe asey gruheet dharoon, udaharanarth, golakar pravegkapramane, heey dongral vibhedak samikaranasarkhech swaroop asalele vibhedak samikaran aahe. yaa samikaranacha upay mhanje eka chhadm harmonic ausilatorh
jethe a (z) heey dolananche amplitude aahe, sootra _ 19 haah "bitatron tappa" aahe joou sootra _ 16 chya mulyavar avalambun aahe aanee sootra _ 21 haah prarambhik tappa aahe. amplitudeche vighatan sthitivar avalambun asalelya bhag sutramadhye aanee prarambhik moolya sutramadhye kele jaate, jase keeh
kann vitaran.
gatichi hii samikarane dilee tarr, kiranatil kananchi sarasari moolye ghetalyane utpann milateh
khaleel vyakhyansah heey sope kele jaau shakateh
deneh
heey see. ess. mapdand aanee utsarjanachya utsarjanachya swarupat aahet. mapdandanmadhil sambandhasah ektrit, yamule aniyantrit (aavashyak nahee qee gossian) kann vitaranasathi utsarjanachi vyakhya dekhil milateh
malmatta.
see. ess. mapdandancha vapar karoon kann vitaranache parametrically varnan karnyacha fayda assa aahe qee pratyek kanavar laksh thevanyapeksha aanee nantar pravegak margavar anek bindunvar sthan ekatra karnyapeksha matricks optixcha vapar karoon ekoon vitaranachi utkranti adhik sahajpane mojali jaau shakate. udaharanarth, jarr sootra 4, sootra 5 aanee sootra 6 heey mapdand asalele kann vitaran l lambichya rikamya jagetoon jaat asel, tarr tyaa jagechya shevati sootra 39, sootra 40 aanee sootra 41 hii moolye dilee jaatatah
sootra _ 42

