Profile Formation and Sustainment of Autonomous Tokamak Plasma with Current Hole Configuration

Transcription

1 TH/- Pofile Fomation and Sustainment of Autonomous Tokamak Plasma with Cuent Hole Configuation N. Hayashi, T. Takizuka and T. Ozeki Naka JAERI, JAPAN

2 Intoduction [MA/m] [kev] Cuent hole (CH) with nealy zeo cuent in the cental egion has been obseved in tokamaks. In a CH plasma, high confinement is achieved due to the fomation of stong intenal tanspot baie (ITB) of box-type in the evesed-shea (RS) egion. In JT-U, the CH plasma has an autonomous popety because of the inteaction between pessue and cuent pofiles though lage bootstap cuent. It is necessay to claify the physical mechanism of pofile fomation and sustainment of the autonomous CH plasma. 8 E339, 5.s Te Ti q j cuent hole ITB T.Fujita, et al., PRL 5 Pupose of this pape We investigate the pofile fomation and sustainment of the autonomous CH plasma by.5d tanspot simulations fo JT-U paametes.

3 j eq [MA/m ] j [MA/m ] q eq, p [kpa].5d tanspot code with the cuent limit model inside Cuent-Hole (CH) based on the ATMI equilibium Z c Z x BS cuent R negative cuent positive cuent Cental zeo cuent equilibium is difficult to be teated by.5d tanspot code. Cuent inside CH is limited fo the stable ATMI equilibium. Z q ATMI >k c a Z c - Z x (T.Takizuka, JPFR.) Safety facto inside CH is limited by q limit =q A in the MHD equilibium calculation. ( ) q a q A. q limit CH p -. CH q D tanspot q, p [kpa] Negative cuent inside CH j q eq (),n(),t() Geomety p q eq < j eq > R [m] Z= j eq D MHD equilibium

4 Tanspot model fo stong ITB F(s-ka) Diffusivities in the tanspot eqs. : Anomalous tanspot : c ano = D ano = c F s - ka c k : abitay anomalous diffusivity : abitay constant ( ) c i = c e = c neo,i + c ano D i = C D D neo,i + D ano Negative magnetic shea is effective to stabilize the ballooning mode and mico-instabilities. F with k= was oiginally developed fo the ballooning type tubulence model. (A.Fukuyama, PPCF 995.) a > k< k= k> - - s Dependence on s and a (k >) is simila to that in the mico-instabilities evaluated by GLF3. (R.E.Waltz, PoP 997.) But, k~ is found to be eliable fom the compaison with JT-U expeiments.

5 Compaison with JT-U Expeiment

6 Shap eduction of anomalous tanspot in the RS egion can epoduce the JT-U expeiment. j [MA/m ] Tanspot becomes neoclassical-level in the RS egion, which esults in the autonomous fomation of pofiles with ITB and cuent hole. Paametes set to simulate the expeiment : k =, c =. m s, C D = Ip [MA] b N.5. B p /B t -. B t =3.7 T, R=3.3 m, a=.8 m Ip b N =.7 exp. sim..37 P NB j (MA/m ) P NB [MW] T [kev], ne [x 9 m -3 ]. CH Te ne j Ti t=s exp q q CH time (s) -. CH f ~ qmin

7 j BS [MA/m ] T i [kev] Autonomous fomation of CH plasma E [mv/m] c i [m /s] j [MA/m ] q Pessue pofile and cuent pofile stongly inteact with each othe though lage bootstap cuent and cuent hole is fomed..8. s CH () E () t = h E - h j BS m - t () () -. T i q q Neo. in RS Ano. in NS.

8 Compaison with JT-U Scalings fo ITB Stuctue Enegy Confinement inside ITB 3 simulation uns fo JT-U paametes

9 ITB widths detemined by the neoclassical-level tanspot agee with those measued in JT-U. D ITB [m] T i [kev] D ITB [m] D ITB [m] D ITB Stong ITB width was found to be popotional to the ion poloidal gyoadius at the ITB cente in JT-U. (Y. Sakamoto, NF.) ITB f ITB width in the simulation is clealy popotional to the ion poloidal gyoadius : D ITB ~.5 p,itb.5 exp..5 T i ~kev ~8 ~5.5 B p ~.T sim..5 pi,itb [m]µt i.5 /B p B p,itb - [T - ] 3 T i,itb.5 [kev.5 ]

10 Autonomous Limitation of Enegy Confinement in CH plasmas p Enegy confinement inside the ITB agees with the JT-U scaling. W scale = C e - f B p, f V coe e f B p, f V coe (T.Takizuka, PPCF.) : invese aspect atio at ITB foot : poloidal magnetic field at oute midplane ITB foot : coe volume inside ITB foot W coe ITB The above scaling is equivalently witten in the following fom. ( ) e f b p,coe = C ª.5 b p,coe : coe poloidal beta inside ITB W L f Wcoe [MJ] 5 I p ~.3MA f ~.7 ~.8 ~. Wscale [MJ] f ~.7.7MA MA.MA 5. e f b p,coe.5 3 P net =P NB -dw/dt [MW]

11 Sustainment and Contol of Autonomous Cuent-Hole Plasma by Extenal Cuent Dive

12 j [MA/m ] f CH Sustainment of CH plasmas by extenal CD C A D A C. B time [s] D(w CD) B Duing the CH fomation phase (t < s), CH adius ( CH ) and ITB foot adius ( f ) can be expanded by inceasing the heating powe. Afte the fomation phase, Plasmas with small CH and f BS < shinks due to the penetation of inductive cuent (case A, P NB = MW). Plasmas with lage CH is sustained with f BS ~ (case B, P NB =8 MW). Condition of f ~ qmin is impotant fo the sustainment. If > f qmin (k~), the ITB adius expands continuously (case C). This contadicts expeiments. Extenal CD (ex. EC) can pevent shinkage of case A by adding at the cuent peak with f BS +f CD ~ (case D). CH p j CD D -.5 CH f ~ qmin j q j BS p [xkpa], q

13 j [MA/m ] Contollability of CH plasmas by extenal CD j [MA/m ] CH adius and ITB position can be contolled by an appopiate CD. f E f CD ~ - f BS at CD stat CH CD. E time [s] CH adius and ITB foot adius can be expanded by adding CD outside the cuent peak (case E). Oute CD Outwad shift Inne CD Inwad shift. E F 5s s F CH adius and ITB foot adius can be educed by adding CD inside the cuent peak (case F)..5 F 5s s s -. j CD j CD -.

14 j [MA/m ] j [MA/m ] Autonomous esponse of CH plasmas to extenal CD f CH CD. D time [s] D G G Shinkage is pevented by adding CD with f CD ~ - f BS (case D). Lage amount of diven cuent with f CD >-f BS expands the CH adius (case G). Incease of q enhances the neoclassical tanspot. Enegy confinement and bootstap cuent faction ae educed and f BS +f CD ~ is ecoveed. CH p p [xkpa], q -.5 CH f ~ qmin j q j CD D Reduction of p & f BS Lage CD f BS +f CD > G -.5 Expansion of CH Incease of q & c neo p [xkpa], q Sustained with f BS +f CD ~

15 Conclusions Shap eduction of anomalous tanspot in RS egion can epoduce the JT-U expeiment. Tanspot becomes neoclassical-level in RS egion, which esults in the autonomous fomation of ITB and cuent hole though lage bootstap cuent. ITB widths detemined by the neoclassical-level tanspot agee with those measued in JT-U : D ITB ~.5 pi,itb. Enegy confinement inside the ITB agees with JT-U scaling : e f b p,coe ~.5. Plasmas with lage cuent hole ae sustained with full cuent dive by bootstap cuent. Plasmas with small cuent hole and small bootstap cuent faction shink due to the penetation of inductive cuent. This shink is pevented and CH size can be contolled by the appopiate extenal CD. CH plasmas ae found to espond autonomically to the extenal CD.

16 Obsevation of CH plasmas in JT-U expeiments Nealy zeo poloidal magnetic field was obseved by a motional Stak effect (MSE) measuement. High plasma confinement was achieved by a stong box-type ITB in the RS egion. ITB was located just inside the minimum q suface. CH was also obseved without EC injection..5 Ip Ip PNB.5 [MA] PEC bn bn, bp.5 bp Bp Bt ~.7 cuent hole ~.37 E time [s] Simulation in this pape ~.7 ~.7 ~.8 PNB [MW] PEC [MW] contou plot of cuent density [MA/m ] [kev] 8 E339, 5.s cuent hole T i T e q ITB T.Fujita, et al., Phys. Rev. Lett. 87()5. j 5

17 Axisymmetic Ti-Magnetic-Islands (ATMI) equilibium T.Takizuka, et al., J. Plasma Fusion Res. 78()8. Idea of a new equilibium of a stongly-rs tokamak plasma with CH ATMI has thee islands along the R diection ( a cental-negative-cuent island and two side-positive-cuent islands ) and two x-points along the Z diection. ATMI equilibium is stable with the elongation coils when the cuent in the ATMI egion is limited to be small. Z c I + Z x BS cuent Stable condition : q ATMI Z >k c q a a Z c - Z x ( ) k = z q ATMI : Effective safety facto at the suface of ATMI q a : Engineeing safety facto at the suface of a whole plasma Z x, Z c : Position of x-points and elongation coils z JT-U paametes : q ATMI >3 fo Z c =, Z c -Z x =., a=.8, q a =, k = I - I + ª +k I - k I ATMI = I + -I - ~ I - > R negative cuent positive cuent (k ~)

18 D e eff /D NC JT-U expeimental analysis of paticle and heat diffusivities fo RS plasmas with box-type ITB Diffusivities at the box-type ITB laye wee quite small and educed to the level of neoclassical diffusivity. Diffusivities inside the ITB laye wee not always small. H.Shiai, et al., Nucl. Fusion 39(999)73.. E33, t=.5s c NC ITB laye c e c i.5 /a Paticle diffusivity is educed to below the ion neoclassical-level. H.Takenaga, et al., Nucl. Fusion 3(3)35.. high b p mode paabolic-type box-type ITB. c i /c NC

19 F Tanspot Model fo Cuent Diffusive Ballooning Mode (CDBM) Tubulent themal diffusivity c CDBM = F(s,a)a 3/ c Magnetic shea : Pessue gadient : Fitting fomula : F(s,a) = Ï Ô Ô Ì Ô Ô Ó - s w pe ( ) - s = q u A qr dq d a = -q R db d ( s + 3 s ) + 9 s 5/ - s + 3 s + ( s 3 ) ( s = s- a < ) ( s = s- a > ) A.Fukuyama, et al., Plasma Phys. Contol. Fusion 37(995) s-a Weak / negative magnetic shea and Shafanov shift educe themal diffusivity.

20 Dependence on s and a in GLF3 (R.E. Waltz, PoP 997. ) c ª 3 g net g d g k xm g + w g net = g - g E - g * Negative magnetic shea is effective to stabilize mico instabilities. g vs. s a= Incease of a shifts the s dependence to the s diection. (Invaiance with s-a) a=

21 Enegy confinement scaling fo RS plasmas with box-type ITB on JTU data T.Takizuka, et al., Plasma Phys. Contol. Fusion ()A3. p Stoed enegy is divided into two pats ; L-mode base pat W L and Coe pat inside ITB W coe ITB Analysis of the database gives the following scaling : W coe W scale = C e - f B p, f V coe e f : invese aspect atio at ITB foot B p, f : poloidal magnetic field at oute midplane ITB foot V coe : coe volume inside ITB foot The above scaling is equivalently witten in the following fom. e f b pc = C ª.5 b pc : coe poloidal beta inside ITB W coe (MJ) W L f.. W scale (MJ) Aveaged B p on a magnetic suface makes C lage than.5.

22 .5D tanspot code D tanspot equations : n i t t = Ê Á V V Ë n D i ˆ i + S Ê 3 n T ˆ j j Ë = Ê Á V V Ë T n j c j ˆ j + P j D cuent diffusion equation : t Ê Y ˆ Ë F = Ï D Ê E Y ˆ Ë F - S( j ) Ì BS Ó Nomalized mino adius defined by tooidal flux : = (F()/F()).5 ( < < ) ( j = e,i) V = dv d Paallel cuent density j = F m D R - D MHD equilibium : Gad-Shafanov equation ( Fixed bounday ) Model of cuent limit inside CH is applied. / Ê E Y ˆ Ë F Impuity : C +, T imp =T i, fixed pofile of Z eff NBI souce : Fixed pofile, Given deposition atio of ion to electon, R NB Neutal : Monte-Calo method, Given ecycling coefficient, R

23 F(s-ka) Reduction of anomalous tanspot in the RS egion (k~) can epoduce pofiles obseved in the JT-U expeiment. T i (kev) j (MA/m ) T i (kev) j (MA/m ) Dependence on nomalized pessue gadient in the F function k> : ITB foot position outside q min k< : ITB foot position inside q min Outwad moving Inwad moving k= k= - s a > s k< k= k> 5 s 5 s - - s

24 F(s) Shap eduction of anomalous tanspot in the RS egion can epoduce pofiles obseved in the JT-U expeiment. j (MA/m ) T i (kev) j (MA/m ) T i (kev) Dependence on magnetic shea in the F function ITB and cuent density peakedness become weak, when the magnetic-shea dependence of the function F becomes weak..5 s.5 s s

25 T i (kev) j (MA/m ) Dependence on NB souce pofile is weak. S NB s....8

26 Pofile fomation does not much depend on the initial q min position. q j (MA/m ) T i (kev) Dependence on initial q min position Pofiles at the end of CH fomation move slightly fo the diffeent position of initial q min..5 s 3 qmin.5 s

27 T (kev) T (kev) Reduction of paticle diffusivity is equied to simulate anothe shot (E395).5 Ip (MA) Ws (MJ) Pofiles with C D =.5 almost agee with those in E395 at t=.8s. Stoed enegy with C D =.5 is lage than that in the expeiment befoe t=.8s. E395 Paametes set to simulate the expeiment : k =, c = 3. m s sim. exp. exp. sim. sim time (s) PNB (MW) ne (x 9 m -3 ) 8 Te CD=.5 sim. Ti s exp. ne (x 9 m -3 ) 8 CD= sim. Te Ti s exp.

28 Impovement of tanspot model is necessay fo weakly-rs plasma. j [MA/m] j (MA/m ) T i (kev) CH and ITB wee fomed fom a weakly-rs plasma at shot E3933. Paametes set to simulate the expeiment : k =, c =. m s, C D = E Ip (MA) Ws (MJ) Pofile fomation qualitatively agees with that in the expeiment, but not quantitatively. exp. sim. sim. exp. 5 time (s) exp. sim. PNB (MW) Ti [kev] s 5.s 5.s 5.s 5.8s.s.s....8 Y.Miua, et al., 9th IAEA s 5s....8

29 Impovement of tanspot model is necessay fo a CH plasma fomed by low NB powe. j (MA/m ) j (MA/m ) T e (kev).5 Ip (MA) Ws (MJ) CH was fomed with low NB powe at shot E395. Paametes set to simulate the expeiment : k =, c = 3.9 m s, C D = E395 exp. exp. 3 5 time (s) sim. sim. T.Fujita, et al., Phys. Rev. Lett. 87() PNB (MW) Pofile fomation of cuent density (not ITB) qualitatively agees with that in the expeiment. exp s 3. s 3. s 3.8 s 3.98 s.. 8 sim. 5s t=3.s....8

30 T i (kev) Validity of the neoclassical theoy in the simulation In the conventional neoclassical theoy, the scale length of plasma paamete vaiation is assumed to much lage than the ion poloidal gyoadius. Scale length of T i vaiation, L T, is slightly lage than the ion poloidal gyoadius at the ITB and is lage than it except fo the ITB position. 8 Cuent hole T i q 3 q Scale length of q vaiation, L q, is smalle than the ion poloidal gyoadius inside the ITB. Extended neoclassical theoy may be necessay inside the ITB. bi, pi, L T, L q. L T L q pi bi.....8

31 MHD Equilibium Limit (V.S. Mukhovatov, NF 97.) Cylindical model Z Pessue balance : B q + B jv m m ª p + B ji m X point R min R p q R Equilibium limit condition : B q,in = m p max - È Î Í B jv = R R B jv ( B ) jv - B ji ( ) Ê Ë Á B ji = R R B ji R R min ˆ = Unifom pessue j Poloidal magnetic field at oute midplane : B a q,out = 8m p max R Suface cuent a Condition of poloidal beta value : eb q,out =.5

32 Lage ITB position can poduce highe nomalized beta value and highe bootstap cuent faction. Nomalized beta value and bootstap cuent faction by the plasma inside ITB can be evaluated by the analytical model. P W c W b j BS e f b p,coe = C ITB DP c f j BS ª C BS e f / B pf f q a b N,coe = : ITB foot adius : engineeing safety facto at plasma suface q f : safety facto at ITB foot (almost equal q min ) DP c L P b N,coe /b N m C q a p q f b N f f f BS,ITB = C -/ q a BSCe a.5.5 q f f BS f f f BS,ITB /f BS L P 3 f ITB position contol is impotant..5 f

33 j [MA/m ] j [MA/m ] Condition of ~ f qmin necessay fo the sustainment can be obtained even fo k by adding an appopiate CD. k=- : Condition of f ~ qmin can be obtained as the same way as in the case of k~. qmin CH f H H. time [s] I (w CD) f ~ qmin I p Inwad shift with local t R BS inconsistent pofiles qmin k= : Sustainment needs a cuent extenally diven in the opposite diection. f qmin CH J f ~ qmin K J. time [s] K(w CD) p q BS q qmin f f Outwad shift with local t R.5 CH p j CD -.5 f ~ qmin. -. q j j CD I K f ~ qmin p [xkpa], q p [xkpa], q

34 j [MA/m ] j [MA/m ] j [MA/m ] Contollability of CH plasmas with f BS ~ f B The plasma with lage CH is sustained with f BS ~. (case B) M B L (w CD) ITB adius can be educed by adding an extenal CD inside the cuent peak (case L). CH M. time [s] Afte CD off, the plasma becomes the same one as that fomed with small CH size (case M). The plasma in the case M is sustained by lage bootstap cuent outside ITB. q p CH B j -.5 p [xkpa], q -.5 j CD L p [xkpa], q -.5 M p [xkpa], q

35 E (mv/m) j (MA/m ) Cuent hole shinks due to the penetation of inductive cuent. Pofiles of the paallel cuent density and bootstap cuent density move inwad togethe keeping those shapes. Positive electic field diffuses into the cental egion and educes the cuent hole egion. 3s j case j BS s

36 T i (kev) T i (kev) j (MA/m ) CDBM model : c ano = c CDBM Lage anomalous diffusivity Weak ITB The cuent hole is fomed, but its adius is small. Oiginal model does not epoduce featues of E T i c i q c CDBM....8.s 8 q, c (m /s) s

37 T i (kev) T i (kev) j (MA/m ) CDBM model : c ano =.c CDBM Smalle anomalous diffusivity ITB is weake than that in E339. ITB foot position is located outside the q min position. 8 T i c i q.c CDBM....8 s 8 q, c (m /s) s