Fusion Reactor Technology I ( , 3 Credits) Prof. Dr. Yong-Su Na (32-206, Tel )

Transcription

1 Fusion Recto Technology I (459.76, 3 Cedits) Pof. D. Yong-Su N (3-6, Tel )

2 Contents Week 1. Mgnetic Confineent/Fusion Recto Enegetics (Hs 8) Week. Tokk Oetion (I): sic Tokk Pls Petes (Wood 1.-3, Hs 9., Kdotsev 6) Week 4. Tokk Oetion (II): Sttu Week 5. Tokk Oetion (III): Tokk Oetion Mode Week 7-8. Tokk Oetion Liits (I): Pls Instbilities (Kdotsev 6, 7, Wood 6) Week 9-1. Tokk Oetion Liits (II): Pls Tnsot (Kdotsev 8, 9, Wood 3, 4) Week 11. Heting nd Cuent Dive (Kdotsev 1) Week 1. Diveto nd Pls-Wll Intection Week How to uild Tokk (Dendy 17 by T. N. Todd)

3 Objectives of the Tokk Oetion 1-3 nt E T ³ 3 1 kevs 5 b s High <n e >/n GW High b N High H 98 (y,) Pulse length 3

4 Pls Euilibiu, Stbility nd Tnsot Pls (Pls essue) 4

5 Objectives of the Tokk Oetion I (M) #1451 D P NI (MW) 4xl i H 98 (y,) b N fishbones (1) <n e >/n GW No swteeth, good confineent, nd b N ~ 3.5, T i ~ T e, <n e >/n GW ~.88, veged ove 3.6 seconds (~ 5 t E ). 5

6 Objectives of the Tokk Oetion P nbi (MW) I (M) #1451 D ~ 18 MW / 6 MW / Sll ELMs (tye II) oute diveto 4xl i b N fishbones (1) H 98 (y,) <n e >/n GW inne diveto 6

7 Pls s Colex Syste High-teetue ls, confined by gnetic field, is n excetionlly unusul hysicl object colex hysicl syste - Pesence of coscoic instbilities - Locl entoy oduction due to locl ls tnsot - Re Coulob collisions (nolous tnsot) - Non-line henoen (noise souce) in the edge ls ogting inside the ls coe leding to tnsot enhnceent - Heting esulting in dditionl noise genetion cf) OH heting: dift cuent velocity of electons ~ 1 5 /s sound velocity ( j ~ 1 M/, n e ~ 1-3 ) V lfven, Vdibtic sound g 7

8 Pls s Colex Syste tionl och to study colex systes consists of lge nube of exeients ied t undestnding eiicl lws suoted by develoent of theoeticl descition nd coute odels. ll this is ctively used in oden tokk studies. s exeience with othe colex systes shows, the genel ethod of scling nd diensionl och eesents oweful tool fo thei descition. 8

9 Diensionl nlysis of Tokks Diensionl och - ll the lws of hysics e bsed on echnics. - Mechnics uses conventionlly chosen units fo ss, length, nd tie. - The objective lws of ntue cnnot deend on those units. These lws e invint with esect to vitions of esueent units chosen by n. - This invince is seen oe ecisely when non-diensionl cobintions of diensionl vlues e used. - The non-diensionl etes define the intenl hysics of colex syste: indictos of the fundentl stte of the syste - Diensionl etes look like soe ojection of given syste on the extenl wold. 9

10 Diensionl nlysis of Tokks Diensionl och - Exle - Reynolds nube vs / L Re v / L s vsl vsl n Inetil foces Viscous foces ρ: density of the fluid v s : en velocity of the object eltive to the fluid L: tvelled length of the fluid μ: dynic viscosity ν: kinetic viscosity Vition in flow tten nd dg coefficients fo cylindes with incese in Reynolds nube (Hoene 1965) 1

11 Diensionl nlysis of Tokks Diensionl och - eing iesed in the extenl hysicl wold, ech colex syste cn ossess non-uniue set of diensionl etes. - Fo given set of diensionless etes the fily of systes cn exist with diffeent sets of diensionl etes. Self-siility - Theefoe, ll the objective lws of hysics y be esented s eltions between non-diensionl etes. - Diensionl nlysis should lwys be bsed on esonble hysicl etes which e secific fo ech ticul cse. Such n och cn llow us to ick out the ost elevnt etes nd to do the uniotnt ones. 11

12 Identity (Siility) Exeients Pls shes used in JET coed to SDEX Ugde δ ~. JET UG δ ~.44 1

13 Identity (Siility) Exeients UG 1787 (.1T) I (M) JET 5833 (1.7T) 95 P NI (MW) H 98 (y,) T i (kev) β N Sll MHD odes 13

14 Diensionless Petes ll the diensionl etes, R / R, T,, e, i Feuently used non-diensionl etes fo tokk lss, e, n, T / T R b / T 4nT / T i æ è * T i i ö ø 1/ i e * n æ n ii è T i i ö ø 1/ æ è R ö ø 3/ R 14

15 sic Tokk Vibles Cylindicl nd locl coodintes fo tokk - sect tio: R / ~ 3-5 ex) KSTR: 3.6, ITER: Invese sect tio: ε /R 15

16 sic Tokk Vibles Pls configution Stike oint If no liite nd diveto? Pls diffusing into the whole vessel long the gnetic field if touching the wll, iuities coing out dvntge of the diveto configution - Fist contct with teil sufce t distnce fo ls boundy - Reducing the influx of ionied iuities into the inteio of the ls by diveting the into n oute SOL 16

17 sic Tokk Vibles Pls euilibiu etes - Elongtion: κ - Tingulity: δ - Sueness: ζ 17

18 sic Tokk Vibles Pls euilibiu etes Elongtion Tingulity k b d c d c d R Z R cos k sin ( -d sin ) 18

19 sic Tokk Vibles Pls euilibiu etes - Oute nd inne sueness: ζ o,i R R Z k sin -1 cos( sin d sin ) ( sin ) o, i Hoewok: deive! 19

20 sic Tokk Vibles Pls euilibiu etes Petes KSTR ITER - Pls she Mjo Rdius, R Mino Rdius,.5. Pls Cuent, I P. M 15 M Elongtion, k x Tingulity, d x.8.5 Tooidl Field, 3.5 T 5.3 T Pulse Length 3 s 5 s Fuel H, D D, T

21 sic Tokk Vibles Pls Euilibiu Ñ J Ñ J Ñ Foce blnce ee s lw Closed gnetic field lines kinetic essue blnced by Jx (Loent) foce Ñ J Ñ induced by the essue gdient: cusing decese in dignetis Dignetic cuent Ñ vd, Ñ - n J n v n v i i D, i e e D, e Ñ - If Z is lied, ls euilibiu cn be built by itself due to induction of dignetic cuent. 1

22 sic Tokk Vibles Mgnetic Flux Sufces - In fusion configutions with confined lss the gnetic lines lie on set of nested tooidl sufces clled flux sufces. - Pessue is constnt long gnetic field line. - Mgnetic lines lie in sufces of constnt essue. - Flux sufces e sufces of constnt essue. - The cuent lines lie on sufces of constnt essue. - The cuent flows between flux sufces nd not coss the. - The ngle between J nd is bity. Mgnetic line Mgnetic xis J Ñ Ñ J Ñ If J J, Jx

23 3 Mgnetic Flux Sufces ò - Ñ d j 3 4 e e e - Ñ 1 þ ý ü î í ì ú û ù ê ë é ø ö è æ - e e v E v E dt dv 1 - Conside ticle otion in cylindiclly syetic configution, i.e. / θ j θ vecto otentil Eution of ticle otion sic Tokk Vibles

24 4 þ ý ü î í ì ú û ù ê ë é ø ö è æ - - þ ý ü î í ì ú û ù ê ë é ø ö è æ - e v e v v e v e e e v E dt dv 1 e t E t t E - - -Ñ - Ñ Eution of ticle otion v v v l v,, sic Tokk Vibles Mgnetic Flux Sufces

25 5 þ ý ü î í ì ú û ù ê ë é ø ö è æ - - e v e v v e v e dt dv [ ] t t dt d dt d t t t,, - ø ö è æ - ø ö è æ - ø ö è æ - Eution of ticle otion θ-coonent sic Tokk Vibles Mgnetic Flux Sufces

26 sic Tokk Vibles Mgnetic Flux Sufces d dt ( l) æ ö 1 è ø Multily by æ ö 1 è ø l Cnonicl oentu l due to the ottionl otion bout the -xis conseved æ è æ v è ^ d dt ö 1 ø ö 1 ø æ è L d dt d» ò ( Ñ ) e ö 1 ø l const. 6

27 sic Tokk Vibles Ñ Mgnetic Flux Sufces æ L ö l l è ø ( ) ( ) ( ) const. - L / << 1 The tjectoies of the ticles ust lie on sufces defined by const. Flux sufce lbel: The ticle s guiding centes ove on the in the bsence of othe foces (s conseuence of ngul oentu consevtion) - Mgnetic field lines lie within these sufces which cn be edily deonstted by oving tht the sufce s nol is othogonl to the field. e e ( Ñ ) - 1 ( Ñ ) ( ) 7

28 sic Tokk Vibles Pls Euilibiu Ñ J Ñ J Ñ Foce blnce ee s lw Ñ ( Ñ ) / Closed gnetic field lines [( Ñ) - Ñ( / )]/ Ñ( / ) ( Ñ) / ssuing the field lines e stight nd llel constnt kinetic essue blnced by Jx (Loent) foce * E g H Totl su of kinetic essue nd gnetic field enegy density will be constnt V 8

29 sic Tokk Vibles Concet of et b ls essue (ni ne ) kt gnetic / / Pessue (blloon tension) - The tio of the ls essue to the gnetic field essue - esue of the degee to which the gnetic field is holding non-unifo ls in euilibiu. - In ost gnetic configutions, fusion ls confineent euies n iosed gnetic essue significntly exceeding the ticle kinetic essue. 9

30 sic Tokk Vibles Concet of et Instbility (bd cuvtue egion) when with high ls essue gnetic essue b / the43sunsets.tistoy.co/tg/ 코카콜라 - b is elted with fusion ecto econoics nd technology. - Mxiu llowble vlue is set by MHD euilibiu euieents nd instbilities diven by the essue gdient. 3

31 31 sic Tokk Vibles ò ò ò d ds ds ) ( / - ssuing tht the gnetic sufces hve concentic, cicul CXs nd tht conditions e indeendent of φ. / ) (, ) ( 1 j j j d j I d j j j ò ò Ñ èe s lw 8, t I b b j Concet of et j b º b t b b The owe outut fo given gnetic field nd ls ssebly is ootionl to the sue of bet. - In ecto it should exceed.1: econoic constint

32 sic Tokk Vibles Nolied bet stbility liit b N bt I t - Fundentl eleents ffecting the b N -liit 1. Cuent ofile. Pessue ofile 3. Pls she 4. Stbilising wll 3

33 sic Tokk Vibles Nolied bet stbility liit b N bt I t - Fundentl eleents ffecting the b N -liit 1. Cuent ofile. Pessue ofile 3. Pls she 4. Stbilising wll 33

34 sic Tokk Vibles How to chieve high bet? - Poviding high heting owe nd educing loss by tnsot (seling, insultion) - If without educing tnsot loss, tnsient high bet chievble with high heting owe 34

35 sic Tokk Vibles Pls intenl inductnce 35 ò V d R I R L l i i 3 4 / / ò V d I L i Fo flt cuent density ofile, cicul cx b J J J < I b I I < b l i ln 1 - ò d J ò d R I L i 1

36 sic Tokk Vibles Pls intenl inductnce 36 - Fo ennett cuent density ofile, cicul cx b J I J < I 4 b I I < ø ö è æ 4 ø ö è æ ln 1 b l i

37 sic Tokk Vibles Pls intenl inductnce 37 - Fo oe genel cuent density ofile, cicul cx b J J J < ø ö è æ - 1 n 1 I J n b J J < ø ö è æ ø ö è - æ n n n? l i