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Meren´I Magnetických Pol´I Na Základe Deflexe Rychlých Iont˚U V Z

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Meren´I Magnetických Pol´I Na Základe Deflexe Rychlých Iont˚U V Z Cesk´evysok´euˇcen´ıtechnick´evˇ Praze Fakulta jadern´aa fyzik´alnˇeinˇzen´yrsk´a Katedra fyziky Obor: Fyzik´aln´ıinˇzen´yrstv´ı Zamˇeˇren´ı:Fyzika a technika termojadern´ef´uze Mˇeˇren´ımagnetick´ych pol´ına z´akladˇedeflexe rychl´ych iont˚uv z-pinˇc´ıch Measurement of magnetic fields on the basis of fast ion deflectometry in z-pinches V´yzkumn´y´ukol Vypracoval: Bc. Vojtˇech Munzar Vedouc´ıpr´ace: doc. Ing. Daniel Kl´ırPh.D. Rok: 2015 Pˇredsv´az´an´ımm´ıstot´ehlestr´anky vloˇz´ıtezad´an´ıpr´ace s podpisem dˇekana (bude to jedin´yoboustrann´ylist ve Vaˇs´ıpr´aci)!!!! Prohl´aˇsen´ı Prohlaˇsuji,ˇzejsem tuto pr´aci vypracoval samostatnˇea pouˇziljsem pouze podklady uveden´ev pˇriloˇzen´emseznamu. Nem´amz´avaˇzn´yd˚uvod proti uˇzit´ıtohoto d´ılave smyslu §60 z´akona ˇc.121/200Sb.o pr´avuautorsk´em,o pr´avech souvisej´ıc´ıch s pr´avem autorsk´yma o zmˇenˇenˇekter´ych z´akon˚u(autorsk´yz´akon). ........................................ V Praze dne .................... Bc. Vojtˇech Munzar Podˇekov´an´ı Pˇredevˇs´ımbych chtˇelpodˇekovat m´emu vedouc´ımu doc. Ing. Danielu Kl´ırovi, Ph.D. a Ing. Jakubu Urbanovi, Ph.D. a Ing. Karlu Rez´aˇcovi,Ph.D.ˇ za cenn´ekonzultace. Bc. Vojtˇech Munzar N´azevpr´ace: Mˇeˇren´ımagnetick´ych pol´ına z´akladˇedeflexe rychl´ych iont˚uv z-pinˇc´ıch Autor: Bc. Vojtˇech Munzar Obor: Fyzik´aln´ıinˇzen´yrstv´ı Druh pr´ace: V´yzkumn´y´ukol Vedouc´ıpr´ace: doc. Ing. Daniel Kl´ırPh.D. FEL CVUTˇ Abstrakt: T´ematemt´etopr´aceje protonov´adeflektometrie pro mˇeˇren´ırychle se mˇen´ıc´ıch elektrick´ych a magnetick´ych pol´ıv Z-pinˇc´ıch. Naˇs´ım ´ukolem bylo vyvi- nout numerick´ymodel, kter´yby prozkoumal moˇznostiprotonov´edeflektometrie. V teoretick´eˇc´astije kr´atcevysvˇetlenprincip Z-pinˇcea jeho nestabilit. Motivac´ı pro rozvoj protonov´edeflektometrie na Z-pinˇc´ıch je v´yzkummechanism˚ugenerace rychl´ych iont˚u,jejichˇzpodstata dosud nebyla vysvˇetlena.D´alese pr´acezab´yv´ame- chanismy vzniku a urychlov´an´ıproton˚uurˇcen´ych pro protonovou deflektometrii a generovan´ych pomoc´ıkr´atk´ych a velmi intenzivn´ıch laserov´ych pulz˚u.Pot´eje pops´an programovac´ıjazyk (Python) a numerick´esch´ema(Boris-Bunemanovo), pouˇzit´epro tvorbu simulac´ı.Nakonec jsou prezentov´any v´ysledkynaˇsich simulac´ıa srovn´an´ıs experiment´aln´ımi a numerick´ymiv´ysledkylaboratoˇr´ına zaˇr´ızen´ıch OMEGA, Z a GIT-12. Kl´ıˇcov´aslova: Z-pinˇc,magnetick´epole, deflektometrie, svazky iont˚u,simulace Title: Measurement of magnetic fields on the basis of fast ion deflectometry in z-pinches Author: Bc. Vojtˇech Munzar Abstract: The subject of this thesis is proton deflectometry for measure fast chan- ging electric and magnetic fields in Z-pinches. Our goal was development of a nume- rical model that could explore possibilities of the proton deflectometry. The theore- tical part briefly explains principle of the Z-pinch and its instabilities. The motive for development of the proton deflectometry in Z-pinches is research of mechanisms of generation fast ions, whose origin wasn't yet explained. After that the thesis is concerned with mechanisms of creation and acceleration of protons which are used for proton deflectometry and which are produced by ultrashort and intensive laser pulses. Afterwards it is described a programming language (Python) and numerical method (Boris-Buneman) which were used for creation of our simulations. Finally the results of our simulations and comparisons with experimental and numerical results of the laboratories OMEGA, Z and GIT-12 are presented. Key words: Z-pinch, magnetic field, deflectometry, ion beams, simulation Obsah Uvod´ 8 1 Historie Z-pinˇc˚u 10 2 Teorie magnetick´ehopinˇce 13 2.1 Amp´er˚uvz´akon pro s´ılumezi dvˇemavodiˇci. 13 2.2 Pinˇcefekt . 14 2.3 Bennettova rovnov´aha . 15 2.4 Nestability . 16 2.4.1 m=0 nestabilita . 18 2.4.2 m=1 nestabilita . 18 2.4.3 Magnetick´aRayleigh-Taylorova nestabilita . 19 3 Mechanismy generace neutron˚ua rychl´ych iont˚uv Z-pinˇc´ıch 20 4 Generace proton˚upro protonovou deflektometrii 22 4.1 Target normal sheath acceleration (TNSA) . 23 4.2 Breakout afterburner (BOA) . 26 4.3 Radiation pressure acceleration (RPA) . 27 4.4 Zdroj proton˚uz f´uzn´ıch reakc´ı . 29 4.5 Detektory . 30 4.5.1 RCF . 30 4.5.2 Detektory CR-39 . 31 6 5 Simulace 33 5.1 Python pro vˇedeck´euˇzit´ı . 33 5.2 Boris-Bunemanovo sch´ema. 33 5.3 Porovn´an´ıBB a RK4 . 36 5.4 Fokusace a defokusace protonov´ehosvazku . 38 6 Porovn´an´ısimulac´ıs v´ysledkyjin´ych pracoviˇst' 42 6.1 Mapov´an´ıelektrick´ehoa magnetick´ehopole pomoc´ı3MeV proton˚u . 42 6.2 Experimenty v laboratoˇr´ıch SNL pomoc´ıZ-petawatt laseru . 45 6.3 Mˇeˇren´ıiontovou d´ırkovou kamerou na zaˇr´ızen´ıGIT-12 . 49 7 Z´avˇer 52 7 Uvod´ Princip magnetick´ehoz-pinˇceje jiˇzvelmi dlouho zn´am,ale rozloˇzen´ıhmoty, profil prot´ekaj´ıc´ıhoproudu a s n´ımsouvisej´ıc´ımagnetick´eho pole nen´ıdosud uspokojivˇe pops´an.V minul´ych letech bylo magnetick´epole z-pinˇcezkoum´anonˇekolika zp˚usoby. Jedn´ımzp˚usobem je jednoduch´amagnetick´asonda, coˇzje mal´asmyˇcka, kter´ase um´ıst´ıdo oblasti pobl´ıˇzproudov´ehovl´akna.Pouˇzit´ıt´etosondy m´avˇsaktu nev´yhodu, ˇzesonda ovlivˇnuje rozloˇzen´ı proudu ve v´yboji. Mus´ıme tedy pouˇz´ıvat jen mal´e mnoˇzstv´ısond v pomˇernˇevelk´evzd´alenostiod vlastn´ıhovl´aknaz-pinˇce. V d˚usledku vysok´ych proud˚u,prot´ekaj´ıc´ıch oblasti z-pinˇce,se magnetick´asonda velmi snadno nezvratnˇepoˇskod´ı. Dalˇs´ım zp˚usobem je vyuˇzit´ı Faradayovy rotace, neboli pouˇzit´ı line´arnˇepolarizo- van´eelektromagnetick´evlny v plazmatu, kter´ase pˇripohybu pod´elmagnetick´eho pole staˇc´ı.Tato metoda vˇsakvyˇzadujeznalost hustotn´ıhoprofilu pod´eltrajekto- rie elektromagnetick´evlny, kter´yse v pr˚ubˇehu pinˇce mˇen´ıa nen´ıpˇredempˇresnˇe zn´ama ˇcastoho nelze urˇcit.Znaˇcn´aˇc´astproudu prot´ek´aplazmatem s velmi ma- lou hustotou, kter´enelze kv˚ulinedostatku citlivosti diagnostikovat interferometrii. Dalˇs´ınev´yhodou t´etometody je, ˇzedoch´az´ıke ztr´atˇeprostorov´ehorozliˇsen´ımag- netick´ehopole. Vlna je ovlivˇnov´anamagnetick´ympolem v cel´empr˚ubˇehu ˇs´ıˇren´ı, zachycen´ysign´alje tak zpr˚umˇerovan´yv´ysledek´uˇcink˚umagnetick´ehopole. Vzhle- dem k vysok´ymhustot´amplazmatu z-pinˇcese elektromagnetick´avlna m˚uˇzeˇs´ıˇritjen plazmatem s hustotou menˇs´ıneˇzje jej´ımezn´ıhustota odpov´ıdaj´ıc´ımezn´ıfrekvenci. Naproti tomu vyuˇzit´ıˇc´asticov´edeflektometrie se v dneˇsn´ıdobˇejev´ıjako velmi efek- tivn´ızp˚usobzkoum´an´ımagnetick´ehopole z-pinˇce.Z dobˇredefinovan´ehozdroje vy- letuje svazek nabit´ych ˇc´astic,kter´yse v magnetick´empoli z-pinˇcedeformuje a kter´y nakonec dopad´ado detektoru. Vliv pol´ı se tedy integruje pˇrescelou trajektorii, stejnˇejako u Faradayovy rotace, ale vysokoenergetick´eˇc´astice,narozd´ılod elektro- magnetick´evlny, dok´aˇzouproletˇethust´ymplazmatem z-pinˇce.Bylo prok´az´ano,ˇze v´ysledkydeflektometrie r˚uzn´ych ˇc´asticjsou srovnateln´e.Generace proton˚uje vˇsak relativnˇesnadn´aa mechanismy jejich generace jsou pomˇernˇedobˇrepochopeny, a proto jsou pro deflektometrii nejuˇz´ıvanˇejˇs´ı.V kapitole 4 podrobnˇepop´ıˇsememecha- 8 nismy generace urychlen´ych iont˚upomoc´ıkr´atk´ych laserov´ych pulz˚u,kter´ese pro tento ´uˇcelpouˇz´ıvaj´ınejˇcastˇeji. Protonov´edeflektometrie se v posledn´ıdobˇehojnˇeuˇz´ıvalo a uˇz´ıv´apˇriv´yzkumu la- serov´ehoplazmatu. Viz.[6, 30, 45] Protony vˇsaklze zkoumat nejen magnetick´e,ale i elektrick´epole. Nab´ız´ıse tak apli- kace protonov´edeflektometrie pro studium mechanism˚uurychluj´ıc´ıionty v z-pinˇc´ıch, kter´ejsou pravdˇepodobnˇeurychlov´any siln´ymindukovan´ymelektrick´ympolem. C´ılemt´etopr´aceje vytvoˇritprogram, kter´yby byl schopen simulovat deflektuj´ıc´ıse svazek proton˚upˇripr˚uchodu elektrick´yma magnetick´ympolem Z-pinˇce.Je tak´e nutn´e ovˇeˇrit spr´avnost simulac´ı porovn´an´ım s experiment´aln´ımi a numerick´ymi v´ysledkyz jin´ych pracoviˇst'. 9 Kapitola 1 Historie Z-pinˇc˚u Prvn´ıexperimenty s koncentrovanou elektrickou energi´ıprovedl v roce 1790 Mar- tinus van Marum v Holandsku. Pouˇzilpˇritom Leydensk´elahve, coˇzbyly sklenˇen´e lahve pokryt´ezvenku a zevnitˇrkovem. Jednalo se tedy o primitivn´ıkondenz´atory s kapacitou ∼ 5 nF. Triboelektrick´ym jevem pomoc´ısklenˇen´ych kotouˇc˚unabil 100 Leydensk´ych lahv´ıs celkovou kapacitou 500 nF na energi´ı1 kJ, kter´evybil do 1 m dlouh´ehodr´atu,kter´yexplodoval a vypaˇrilse. Byl to asi prvn´ıexperiment s explo- duj´ıc´ımdr´atkem. Pinˇcov´yefekt, neboli imploduj´ıc´ı proudov´evl´akno,byl poprv´epozorov´anv roce 1904. [4]. Tento jev objasnili v roce 1905 Pollock a Barraclough v Austr´alii.Vysvˇetlili, ˇzedeformaci mˇedˇen´etrubice bleskosvodu, kterou zas´ahlblesk 1.1, zp˚usobilprot´ekaj´ıc´ı proud blesku pomoc´ıLorentzovy s´ıly. B2 Vztah pro rovnov´ahu mezi magnetick´ymtlakem pm = 2µ , kter´epinˇcstlaˇcuje,a ki- netick´ymtlakem pk = NkT , kter´ynut´ıobjem plazmatick´evl´aknak expanzi, odvodil v roce 1934 Bennett [3]. Viz kapitola 2. 2 8πNkBT (1 + Z) = µ0I V roce 1937 pˇriˇselTonks s pojmem ,,pinch"(ˇceskypinˇc)z anglick´ehov´yrazupro stisk ˇcistlaˇcen´ı. Pozdˇejiv 50. letech se pˇridalprefix z a θ a zaˇcalose pouˇz´ıvat oznaˇcen´ı z-pinˇc a θ-pinˇc podle smˇeru,kter´ymteˇceproud vl´aknem(z { osov´ysmˇer, θ { azimut´aln´ısmˇer). 10 Nejvˇetˇs´ı pozornost z´ıskaly z-pinˇce v 50. letech 20. sto- let´ı ve spojitosti s termojadernou f´uz´ı. Sir Thompson a Blackman z Imperial College si nechali v roce 1946 patentovat pinˇc stoˇcen´y do prstence (toroid´aln´ı pinˇc) jako termojadern´y reaktor [14], kter´ym pˇri 500 kA mˇeli z´ıskat z deuteriov´e n´aplnˇe 9 MW f´uzn´ıho v´ykonu. Tato idea se uk´azala b´yt myln´a, ale motivovala dalˇs´ı v´yzkum na toroid´aln´ıch pinˇc´ıch. V roce 1957 na toroid´aln´ım pinˇci ZETA v Harwellu, na kter´em pˇredt´ım byla po- prv´e pozorov´ana kor´alkov´a nestabilita, slavili Sir Coc- kroft a Dr.
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