landau damping

bhautikshastrat, landau damping, jyala tyache shodhak, soviet bhautikshastradnya lev devidovic landau (1908-68) yanche naav denyat aale aahe, too plazma kinwa tatsam vatavaranatil anudairdhya avkash charge laharinchya dampingcha (veleche karya mhanoon ghatankiy ghat) parinam aahe. hii ghatana asthiratela vikasit honyapasoon rokhate aanee parameter spacemadhye sthiratecha pradesh tayar karate. nantar donald linden-belane assa yuktivad keela qee galactic dynamixmadhye ashich ghatana ghadat aahe, jithe sthiravidyut shaktindware parasparkriya paar electronchya vayuchi jaaga gurutvakarshan shaktindware parasparkriya paar karananya vayoo" neey ghetali jaate. landau damping heey kann-inn-seela simulationsarkhya sankhyatmak simulationmadhye tantotant hatalale jaau shakate. 1946 madhye landaune kelelya andajanantar jawaljawal done dashakannantar 1964 madhye malamberg aanee varton yanni prayogikdrushtya teey astitvat asalyache siddha kele.
tarang-kann parasparkriya.
fages velocity sootra _ 1 saha vidyutchumbakiy tarang aanee plazmamadhil kananmadhil urja devanghevanimule landau damping hote, jyacha veg andaje sootra _ 1 chya barobaricha asato, jeey laharishi jordarpane sanvad sadhu shakatat. sootra 1 peksha kinchit qamee veg asalele kann laharichya vidyut kshetradvare lahari tappyachya vegasah halanyasathi vegwan kele jaatil, tarr sootra 1 peksha kinchit jaast veg asalele kann laharishi urja gamavoon mandavale jaatilah kann laharishi samkramit honyacha cull asato. heey travelling-wave tubedware prayogikdrushtya siddha jhaale aahe.
aadarsh magnetohydrodianamic (emm. etch. dii.) plazmamadhye kananchya veganna bahudha andaje maxwellion vitaran karya manale jaate. jarr karyacha utaar nakaratmak asel tarr vegachya tappyatil vegapeksha kinchit qamee veg asalelya kananchi sankhya, veg asalelya kananchya sankhyepeksha kinchit jaast asate. tyamule, laharinna haravanyapeksha laharitoon urja midavanare adhik kann aahet, jyamule lahari olsar hotat.
tathapi, jarr karyacha utaar sakaratmak asel tarr wave fejchya vegapeksha kinchit qamee veg asalelya kananchi sankhya, veg thodya jaast asalelya kananchya sankhyepeksha qamee asate. tyamule, laharitoon laharitoon urjepeksha laharinkade urja gamavanare adhik kann aahet, jyamule laharichya urjet parinami vaadh hote. tyanantar landau dampingchya jaagi landau vaadh kelee jaate.
bhautik arth lavane.
landau dampingcha ganiteey siddhant kahisa samavisht aahe-khaleel vibhag pahaa. tathapi, eka sadha bhautik arth aahe [kalam 7.5 madhye eka chetavanisaha sadar keela aahe], joou jaree katekorpane yogya nasla taree yaa ghatanechi kalpana karnyas madat karato.
langmuir laata samudratil laata aanee surfers mhanoon tarang pakadanyacha prayatna karnare kann, serve ekach dishene jaat aahet, ashee kalpana karane shakya aahe. jarr surfer panyachya prushthbhagavar laharinpeksha kinchit qamee vegane jaat asel tarr too akheris pakadala jaeel aanee latansobat dhakalala jaeel (urja midvane), tarr laharinpeksha thoda vegane firnara surfer chadhati dishene jaat asatana latanvar dhakalala jaeel (laharila urja gamavane).
latanchya yaa urja parasparsanvadat keval surfersach mahattvachi bhoomika bajavat aahet heey lakshat ghenyasarkhe aahe; panyavar taranganara taranganara chendu (shoonya veg) laat jasjashi jaeel tasatasa varr aanee khalee jaeel, urja ajibat prapt karnar nahee. tasech, khoop vegane (latanpeksha vegwan) chalanari nauka latanshi jaast urjechi devanghevan karat nahee.
kananchya gatishilateche sadhe yantrik varnan, kananchya lahari [samikaran (1)] saha samkramanacha parimanatmak andaj pradan karate. adhik kathor drushtikon darshavito qee tarang chaukatitil veg damping retchya pramanat aanee tarang amplitudepasoon swatantra asalelya kanansathi sarvat majboot samkraman hote. aniyantritpane lahan amplitude asalelya laharinsathi landau damping hott asalyane, heey darshavite qee yaa dampingmadhil sarvat sakriy kann adakoon padane phaar door aahe. heey swabhavik aahe, kaaran trappingmadhe asha laharinsathi vel mojmap vegale karane samavisht asate (visheshtah wave amplitude sutrasathi sootra _ 5).
saiddhantik bhautikshastrah vlasovian chaukatitil vikshobh siddhant.
saiddhantik upchar sapekshata nasalelya shoonya-chumbakeey kshetra maryadet, vlasov-poison samikarananchya sanchatil vlasov samikaranapasun suru hoto. spasht upay eka chhotya sootra _ 7-kshetrachya maryadet prapt kele jaatat. vitaran karya sootra _ 8 aanee kshetra sootra _ 7 eka maliket vistarit kele jaatatah sootra _ 10, sootra _ 11 aanee samaan kramachya atty gola kelya jaatat.
pratham kramane vlasov-poison samikarane vachali jaatat
landaune prarambhik vikshobh sootra _ 13 mule mule laharichi ganana kelee aanee laplas transform aanee samocch ektrikaranachya madatine, tarang sankhya sootra _ 15 aanee damping decrements form formula _ 14 chee damped travelling wave aadhalali.
yethe sootra _ 17 heey plazma ausilation frequency aahe aanee sootra _ 18 heey electron density aahe. nantar niko vanne campaignay heey siddha kele qee tech parinam forier transformdware prapt kele jaau shakatat. tyanni dakhavun dile qee rekheey vlasov-poison samikarananmadhye eksaman samanya paddhatinche satatche varnapat aahet, jyanna aata vanne campaign paddhati mhanoon olakhale jaate
jyaa sutramadhye _ 20 heey mukhya moolya darshavate, sootra _ 21 heey delta karya aahe (samanyikrut karya pahaa) aanee
plazma permitvity aahe. yaa paddhatinmadhil prarambhik vyatyay vighatit karoon tyane parinami parinami lahariche forier spectrum prapt kele. formula _ 17 jawal thodya vegalya frequencies yaa fourier modachya fages-mixingdware damping spashtikaran dile jaate.
takkar nasalelya plazmamadhye olava kassa houu shakato heey spasht navhteh lahari urja kuthe jaate? drav siddhantat, jyamadhye plasmache dispersive dialectric madhyam mhanoon pratirupan kele jaate, langmuir laharinchi urja dnyat aaheh kshetra urja gunile brilloin ghatak sootra _ 24.
parantu yaa modelmadhye damping midavata yet nahee. pratidhvanit electrons laharichya urja devanghevanichi ganana karnyasathi, vlasov plazma siddhant jaate kramane vistarava lagel aanee yogya prarambhik paristhiti aanee dharmnirpeksh sandnyambaddal samasya udbhavtat.
 refereemadhye. yaa samasyancha abhyas keela jaato. anant laharisathichya gananemadhye jaate kramane kamatarata asalyamule, laharichya sanchanche vishleshan kele jaate. jaate kramankachya prarambhik paristhiti aadhaltat jyaa dharmnirpeksh vartan dadapatat aanee laharichya sanchala uttejit karatat jyapaiki urja drav siddhantashi sahmat aahe. hii aakruti samooh vegane pravas paar lahari packetchi urja ghanata darshavate, tyachi urja tappyachya vegane pravas paar electrondware vahoon nellie jaate. ekoon urja, vakrankhalil kshetra sanrakshit kele jaate.
ganiteey siddhantah ashant upayansathichi kachee samasya.
utkrantichya samikaranasathi (yethe aanshik vibhedak vlasov-poison samikaran) aanee samadhanavaril andaj siddha karnyasathi, kathor ganiteey siddhant haah kachee samasyeche nirakaran karnyavar aadharit aahe.
pratham, landoupasoon eka sampoorn rekheey ganiteey siddhant vikasit keela gela aahe.
landau dampingchya ganiteey siddhantat rekheey samikaranachya palikade jaane aanee nonalinearity hatalane hii eka dirghakalin samasya aahe. 
purvi, naun-linier staravar eka ganiteey parinam mhanje eka vartulat vlasov-poison samikaranachya ghatankiy olsar upayanchya vargache astitva hote, jeey eka vikhurnyachya tantrachya madhyamatoon siddha jhaale hote (haah parinam alikadech vistaranyat aala aahe). tathapi, heey astitva parinam, "konatya" prarambhik mahitimule asha olsar upayanna chalana miloo shakate yabaddal kahihi sangat naheet.
french ganitshastradnya cedric vilani aanee clement mauhot yanni prakashit kelelya eka peparmadhye, prarambhik detacha muddah sodavala jaato aanee landau damping heey naun-linier vlasov samikaranasathi prathamach ganitiyadrushtya sthapit kele jaate. heey siddha jhaale aahe qee resheey sthir eksandh sthir dravanache kahee bhagat (vishleshanatmak kinwa gavery topologiesathi) suru honare upay sarvkalasathi (kakshiy) sthir asatat aanee jaagtik staravar velenusar olsar asatat. urja devanghevaniaivaji, anukrame sootra _ 26 aanee sootra _ 27 chey karya mhanoon sootra _ 8 chya niyamitatechya hastantaranachya drushtine damping ghatanecha punarvapar keela jaato. mothya pramanatil badal veg jaaget lahan aanee lahan pramanatil badalanmadhye jaatat, jeey sootra _ 27 chey karya mhanoon sootra _ 8 chya fourier spectrumchya shiftshee sambandhit asatat. resheey siddhantat suprasiddha asaleli hii shift, naun-resheey prakaranat tikoon asalyache siddha hote.
saiddhantik bhautikshastrah 'aine'-boddy framemadhe vikshobh siddhant.
siddhant kalapasoon ashakya manale jaat asatana, yantrik 'aine'-boddy varnan newtoncha gaticha dusra niyam aanee fourier malika jaanun asalelya vidyarthyansathi landau dampingchi kathor ganana karnyas saksham karate. yaa vyutpattisathi vlasov samikaran kinwa laplas transformchi aavashyakta nahee. electrons laharichya urjechya (adhik tantotant gatee) devanghevanichi ganana ashach prakare kelee jaate. 75 varshannantarhi landau damping anek aanee visangat arth ajunahi astitvat asale taree, hii ganana jawaljawal anunadit paar paar kananche samkraman mhanoon yaa dampingcha arth spasht aanee antardnyani banavate. aine-boddy gananechi german teey vanne campaignchi ganana dekhil tyach kagdavar upalabdh aahe.

