Modeling of Plasmas and Neutrals Including Plasma-Wall Interaction for Long Term Tokamak Operation

Transcription

1 odelig of Plasmas ad Neutrals Icludig Plasma-Wall Iteractio for Log Term Tokamak Operatio Akiyoshi Hatayama 1, Kousuke Okamoto 1, Ryoko Tatsumi 1, Kazuhiro. Abe 1, ad Kazuaki Haada 2

2 1. Backgroud/otivatio (1) - Desity cotrol of the core/mai plasma i future fusio reactors like ITER/DEO is oe of the critical issues, especially for their log term operatio. - etal plasma facig materials (PFs) are expected to be oe of the promisig cadidates for such future fusio power plats. - Recetly, experimetal studies : the effects of the log time scale plasma PF wall iteractio o the mai plasma desity ad its cotrol have bee doe i the QUEST tokamak [1,2,3]. suggest that the wall H atom-ivetory play a key role! [1] K. Haada, et al., Nucl. Fusio 57(2017) [2] K. Haada, et al., Plasma Sciece ad Techology 18(2016) [3] T. Hoda, Departmet of Advaced Eergy Egieerig Sciece, Kyushu Uiversity, aster s thesis (2014).

3 1. Backgroud/otivatio (2) - The purpose of this study is to develop a simple plasma ad eutral model which icludes the log term plasma-wall iteractio, especially the iteractio betwee the plasma ad metal PFs - i order to uderstad basic characteristics of the log term behavior of particle balace i the overall system icludig : a) ai Plasma, b) SOL/Divertor/Limiter Plasma, c) Wall - Covetioal 2D/3D Edge plasma-eutral code (e.g. SOLPS(B2.5-Eiree), EDGE2D, UEDGE, SONIC) is too massive to simulate for such a log time dyamics of the system adopt zero-dimesioal (0D) approach takig ito accout the profile effect from the 2D/3D code results

4 2. odel (1) : Basic odel Cocept Particle Balace model for the overall system: (a) ai Plasma, (b)sol/divertor/limiter Plasma, (c)wall Particle Species i the System i),,, ii) Neutrals H 2, H iii) Wall aterial Fig.1 Schematic drawig of the model geometry (QEST limiter cofiguratio) Fig.2 Overall cocept of the preset model

5 t a 2. odel : Plasma odel (1) (1a) ai Plasma d dt =- + t t º 2a S a 2 D, (1a1) Plasma ioizatio Plasma trasport loss Source i the mai across the magetic field lie plasma 1 : Volume averaged plasma desity = dv V òv (1a2) 1 S : Volume averaged ioizatio source S = SdV V òv (1a3) : the particle cofiemet time of mai plasma (1a4) a : ior radius of tokamak D : Diffusio coefficiet across B : profile factor which relates the desity at the LCFS with the volume averaged desity = a LCFS LCFS (1a5)

6 2. odel : Plasma odel (2) (1b) SOL/Limiter Plasma d SOL dt = (1- f ) S - + S, SOL wall Diff SOL t // (1b1) S Diff = t (1b2) Plasma Source from the mai plasma SOL S Diff f S wall SOL t // a SOL 2a SOL C s : profile factor which relates the desity i frot of the limiter plate with the volume averaged desity : C s SOL Recyclig Source from the limiter plate Plasma loss alog the magetic field lie : Volume averaged plasma desity 1 = dv i the SOL/Limiter regio V ò (1b3) V : Diffusio source from the mai plasma across the LCFS : fractio of SDiff to the wall 1 SSOL = SSOLdV : Volume averaged ioizatio source V ò (1b4) VSOL SOL : the plasma cofiemet time i the SOL regio L// t = (1b5) L : SOL coectio legth alog B-field // // : Io soud speed alog B-field = a LI SOL SOL (1b6) LI

7 d 2. odel : Neutral odel (1) (2a) H2 olecules H dt = S + S + S -S -S - Gas-Puff Wall / Lim gai loss Pump H H H H H Gas-puffig source Recyclig source from the Wall ad Limiter Discuss later i the wall model Gas-pumpig sik H2 reactios i the gas phase Table 2.1 ai reactios take ito accout t H H t H 2 = 2 ( V / A ) V V A V a a H 2 v H 2 (2a1) V v V H2 H2 (2a2) : Volume of vacuum vessel : Surface area of vacuum vessel : Profile factor : average speed of H2 molecules

8 2. odel : Neutral odel (2) (2b) H atom i gas phase d dt H = S -S -S - gai loss CX H H H t H H (2b1) H reactios i the gas phase CX loss t H V V A V = ( V / A ) V a H v H V (2b2) Table 2.1 ai reactios take ito accout a H v H 2 : Volume of vacuum vessel : Surface area of vacuum vessel : Profile factor : average speed of H atoms

9 2. odel : Neutral odel (3) Table 2.1 ai reactios take ito accout i the model. H ioizatio H(p) + e H + + 2e H % dissociatio H % (v) + e 2 H + e H % ioizatio H % (v) + e H ( % + 2e H % dissociative ioizatio H % + e H + H ( + 2e H ( % dissociatio H ( % + e H + H ( + e H ( % dissociative recombiatio H ( % + e 2H H ( * dissociative recombiatio H ( * + e 3H (or H % + H) H ( * dissociative recombiatio H ( * + e 2 H + H ( + e H, H ( charge exchage H + H ( H ( + H H %, H ( charge exchage H % + H ( H ( % + H H ( * productio H % + H ( % H ( * + H H ioizatio by H ( H + H ( 2H ( + e H ( % dissociative ioizatio ( H % + e 2H ( + 2e

10 2. odel : Neutral odel (4) I additio to the groud-state atom modeled above, we solve a system of simultaeous rate equatios for the populatio desity of excited atoms with the quasisteady state collisioal-radiative model (QSS-CR) to compare the Ha itesity measured i the experimets have bee (QST 10A H - source, CERN Liac4 H - source, etc.)

11 2. odel : Wall & Limiter odel (1) (3a) Wall d G 2k = - dt d d Wall Wall Wall Wall Wall 2 Wall (3a1) Wall : H atom wall-ivetory (i the re-depositio layer) Plasma i-flux to the wall k Wall d Wall H2 out-flux from the wall : H atom recombiatio rate i the re-depositio layer : thickess of the re-depositio layer æ A ö LCFS AWall CX æ V ö G Wall = fwallg LCFS ç + SH ç è AWall ø AWall + ALim è ALCFS ø Io flux from the mai plasma Calculated by mai plasma model Eq.(1a1) ALCFS AWall A Lim (3a2) CX H atom flux Calculated by H atom model Eq.(2b1) : Surface area of LCFS, Wall ad Limiter, respectively

12 2. odel : Wall & Limiter odel (2) (3b) Limiter d G Lim 2k = - dt d d //, Lim Lim 2 Lim Lim Lim (3b1) Lim : H atom limiter-ivetory (i the re-depositio layer) Plasma i-flux to the limiter k Lim d Lim H2 out-flux from the limiter : H atom recombiatio rate i the re-depositio layer : thickess of the re-depositio layer V A æ V SOL SOL Lim CX G //, Lim = + SH ç t// asol ALim Awall ALim ALCFS Io flux from the SOL plasma Calculated by SOL plasma model Eq.(2a1) + è ø ö (3b2) CX H atom flux Calculated by H atom model Eq.(2b1)

13 3. Iitial odel Applicatio to QUEST(1) (1) ai Assumptios / Calculatio Coditios - Low desity sheath limited attached state i frot of the limiter has bee assumed - Wall ad Limiter aterial are the same for simplicity Table 3.1 Device ad Plasma Dimesios ajor radius : ior radius : Volume of mai plasma : Volume of vacuum vessel : Surface area of vacuum vessel : Table 3.2 Gas puffig ad pumpig parameters Gas puffig rate : 3.5x10 18 /puffig for 10ms Gas pumpig rate : 1.7x10 17 /s Fig.2 Schematic drawig of the model geometry (QEST limiter cofiguratio)

14 3. Iitial odel Applicatio to QUEST(1) Table 3.3 Iitial desity for each particle species Plasma D = 9 E = 1 10 GH m J*, : 9: = 1 10 GL m J*, 9 = 1 10 G m J* Plasma particle diffusio coeff. : D =0.3 Table 3.4 Profile factor of plasma & eutral desity Plasma profile factor : a =0.3 Neutral profile factor for H 2 : b =0.1 Table 3.5 Temperature for each particle species Electro : T e = 10 ev Io : T 5 = 1eV H2 olecule : T 9: = 0.01eV H atom : T 9 = 0.1eV Table 3.6 Wall parameters H recombiatio coefficiet for the wall : k wall =1x10-38 m 4 /s Thickess of the re-depositio layer : d wall =50 m

15 3. Iitial odel Applicatio to QUEST(2) (2) Time evolutio of mai plasma ad wall parameters e =10eV i =1eV =0.3 m 2 /s w =1.0x10-38 m 4 /s Fig. 3.1 (a) plasma desity ad Ha itesity Fig.3.1 (b) Wall H atom-ivetory 0 t 30 s - Durig early phase before the saturatio of the H atom wall-ivetory frequecy of gas puffig (correspodig to the rapid icrease i Ha sigal) is large - After the saturatio of wall H atom ivetory t ³ 60 s Ha sigal is almost costat ad the plasma desity is maily sustaied by the gas feed from the wall. - Saturatio level of H-atom wall ivetory agrees with that estimated i the experimets with a reasoable value of wall recombiatio coefficiet.

16 Fi.g.3.2(a) 3. Iitial odel Applicatio to QUEST(3) (3) Compariso with the experimets - Effect of the wall temperature o the H atom wall-ivetory Experimetal results [3] odelig results Low Low Wall Temp. : Room Temp High Wall Temp. : 373K Fi.g.3.2(b) Wall Temp. kw= 0.2x10-38 m 4 /s High Wall Temp. kw= 1.0x10-38 m 4 /s odelig results reproduces basic tred of the effect of the wall temperature o the H atom wall ivetory with varyig k w i a reasoable rage at the reasoable saturated values! - Quatitatively, however, time to reach the saturatio i the modelig is relatively short (~ s) compared with those ( > 100s) i the modelig [3] T. Hoda, Departmet of Advaced Eergy Egieerig Sciece, Kyushu Uiversity, aster s thesis (2014).

17 3. Iitial odel Applicatio to QUEST(4) (3) Compariso with experimets : Time evolutio of Ha sigal Experimetal results [3] Low Wall Temp. : Room Temp. High Wall Temp. : 373K odelig results Low Wall Temp. kw= 0.2x10-38 m 4 /s High Wall Temp. kw= 1.0x10-38 m 4 /s Fi.g.3.3 (a) Fi.g.3.3 (b) odelig results reproduces basic tred of Ha sigal - I High Wall Temp. Case, Ha sigal becomes almost costat more earlier tha i Low Temp. Case mai plasma desity is maily sustaied/cotrolled ot by the exteral gas puffig, but by the wall out-flux after the saturatio [3] T. Hoda, Departmet of Advaced Eergy Egieerig Sciece, Kyushu Uiversity, aster s thesis (2014).

18 3. Iitial odel Applicatio to QUEST(6) (4) Our model really robust? - Sesitivity aalysis of the results o key assumptios/parameters T e Fig.3.4 (a)t e =10eV plasma desity ad Ha itesity Wall H atom-ivetory (b)t e =30eV (c)t e =50eV

19 3. Iitial odel Applicatio to QUEST(7) (4) Our model really robust? - Sesitivity aalysis of the results o key assumptios/parameters D Fig.3.6 (a) D=0.3 m 2 /s * typical value i most of 2D Edge Plasma simulatios plasma desity ad Ha itesity Wall H atom-ivetory (b) D=0.6 m 2 /s (c) D=1.2 m 2 /s * estimated by Bohm diffusio D~(1/16)(Te/B)

20 4. Summary & Future Problem (1) - we have developed a simple zero dimesioal (0D) model which cosists of the particle balace equatios for the followig three differet particle species: i) hydroge plasma (elec., H +, H 2+, H 3+ ), ii) eutral hydroge atoms (H) ad molecules(h 2 ) i the gas phase iii) wall-stored H atoms. - The model has bee applied to a log term operatio (up to ~ s) with the limiter cofiguratio i the QUEST tokamak.

21 4. Summary & Future Problem (2) - odelig results of the log time evolutio ( ~ s) reasoably reproduce experimetal tedecies: - Desity feedback cotrol by Ha sigal ad exteral gas puffig is efficiet i the early phase ( <100s) - For more log time scale (>100s), the particle balace of the system is maily sustaied ot by the exteral particle source/pumpig, but by the wall recyclig source. - odelig results of the H-atom wall ivetory reasoably agree well with those i the experimets with a reasoable value of wall recombiatio coeff.

22 4. Summary & Future Problem (3) - However, further model validatio ad improvemet will be eeded: - ore Systematic sesitivity aalysis of the results o the mai assumptios ad iput parameters: e.g. T e, T i, D, profile factor from 2D/3D Edge simulatio, As for the T e, D, the basic tedecies are ot so sesitive o these parameters, if we chage these parameters i the reasoable rage: T e ~10~50eV, D~ m 2 /s - For more log term pheomea (~ several s,) further model improvemet will be ecessary : e.g. takig ito accout effects of the H trappig site i depositio layer [1] [1] K. Haada, et al., Nucl. Fusio 57(2017) & this Cof.