Progress of HMGC Nonlinear Simulation

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1 Pogess of HMGC Nonlinea Simulation Andeas Biewage ENEA - Fascati Italy GSEP Wokshop 29 This wok is suppoted by SciDAC GSEP. Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 / 6

2 Outline Type and scope of simulations done with HMGC 2 HMGC status and plans 3 GSEP test case 4 Linea esults: n and β H scans 5 Nonlinea esults 6 Summay and outlook 7 Open issues 8 Appendix: Equations Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 2 / 6

3 Simulated Scenaio: Relaxation Concept: t < tstat : Fast ion density builds up ( amp phase ). t = tstat : Instability is let loose ( tigge phase ). tstat < t < t end : Relaxation phase. Linea gowth. Nonlinea satuation with unchanged instability dive. Nonlinea satuation with instability dive displaced o emoved. t > tend : Long-time tanspot pocesses (e.g., new amp phase). Applications: Pobe system fo MHD eigenmodes seen in expeiments. Study nonlinea satuation mechanisms. Test and compae physical models and numeical codes. Peliminay step towads multi-time-scale simulations. mode enegy δφ 2 amp elaxation amp 2 amp elaxation amp 2? t_stat t_end? fast ion density n H (=)?? t_stat t_end Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 3 / 6

4 HMGC Status and Plans EQUILIBRIUM FAST IONS β = n H ni ε 3, T H Ti ε 2 tooidal flux sufaces local f H (E, µ, ψ) with cicula x-section Maxw./SD/anisotopic ց MHD SOLVER evolves δψ and δφ given Π H β i =, β e = tooidicity O(ε 3 ) esistivity, viscosity shea Alfvén waves; teaing+intechange patially nonlinea = = δf PIC SOLVER evolves guiding centes given δψ, δφ computes Π H fully nonlinea LIMITATIONS (m, n) components δφ(, ), δψ(, ), Π H (, ) neglected EXTENSIONS load makes in tems of E, µ,p φ fo any f H (E, µ,p φ ) bulk ion FLR and kinetic compession fast ion FLR ealistic shaped flux sufaces Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 4 / 6

5 GSEP Test Case Paabolic safety facto pofile q(). Constant bulk density n i = n i. Easy-to-modify tanh-shaped fast ion density pofile n H (). Isotopic local Maxwellian distibution, f H (E, ) = n H ()F M (E) (T H = T H ). safety facto q() (a) continuum ω SAW / ω A (b) fast ion density n (,t=) / n H H (c) n H /n H n /n H H density gadient n H (,t=) / n H Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 5 / 6

6 Linea Results: n scan ω/ω A.6 n= n=2 n=3 n=4 n=6 n=8.6 ω /ω A m=2.2.4 m= m= m= m= m= gowth ate γ/ω A (a) n fuency ω /ω A (b) n β H =3% β H =4% β H =5% n H /n i vaied v H /v A const. v H /R const. Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 6 / 6

7 Linea Results: Mode Stuctue (n = 6, β H = 4%) φ m () (a) Fouie hamonics (8,6) (9,6) (,6) (,6) (2,6) m 2 (b) 5 Fouie spectum Z/a poloidal coss section (c) ρ 5.5 ρ (R R )/a.2 m = 9 m = 9 m = 9 (d) Re (e) Re (f) Im.2 Im.2 Re Im. (9,6). (,6). (,6) φ() φ() φ() Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 7 / 6

8 Linea Results: TAE/KTAE o EPM chaacte? (n = 6, vay β H aound β H = 4%).3 (a) (b).4 gowth ate γ/ω A.2. fuency ω /ω A.3 tooidicity induced gap (i) vay n /ni H, const. v H /v A (ii) vay v H /v A, const. v H /R (iii) vay v H /v A v H /R β H β H γ lin /ω lin.3 EPM chaacte: ω lin vaies with v H /R Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 8 / 6

9 Nonlinea Results: n = 6, β H = 4% movie E kin 5 (a) time histoy, t=245, γ=.22 φ(ρ) electostatic potential φ (b) (8,6) (9,6) (,6) (,6) (2,6) n E (ρ) / n E (c) enegetic ion density t= t=245 t= t ω A mode stuctue: poloidal coss section (d) Z/a (R R )/a m.5 ρ ω/ω A.5 ρ mode stuctue: Fouie spectum, n= powe spectum, ω =.29, ρ ω =.39.6 (e) (f) continuum 2 nq(ρ) ρ ρ Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 9 / 6

10 Nonlinea Results: n = 6, β H = 4%, obits Z a.2 Z.4 t=355 a.2 t= a.2 Z.4 b b b c c a b b 22 c pet. obit unpet. obit 2 t=25, [.5,.25] 2a 2 2 t=25, [.46,.56].4 3c 3c t=25, [.52,.62] (R R )/a (R R )/a (R R )/a 2 µ 4 v v v powe tansfe x Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 / 6

11 Nonlinea esults: n = 6, highe β H = 5% enegy (δφ) 2 x 8 (B) (C) (D) (E) (8,6) (a) (9,6) (b) (A) (c) (,6) (B).5 (,6).8 (C) (D) (2,6).6 (E). (3,6) (A) t ω A t=82.2 (A a) t=53. (B) n f / n f t=2. (C a) n f / n f t=253.2 (A) (B) (C) (D) (E).5 (D) t= (E a).6 ω/ω A ω/ω A (A b) (A c) 2 (C b) (C c) 2 (E b) (E c) m 5 Z/a Z/a Z/a m (R R )/a.5 (R R )/a.5 (R R )/a Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 / 6 m 5

12 Nonlinea Results: Obsevations (n = 6, β H = 4%). SAW activity in tooidicity-induced gap (TAE/KTAE/EPM?). 2. Numbe of fast ions, d n H () dops by moe than % in the cental egion ρ.4 due to outwad tanspot. 3. Inteaction time < bounce time. Wok in pogess. Redistibution in v space...? Satuation mechanism...? Coss-code benchmak: hmgc, gtc, taefl, gyo. ω / ω A n H / n H enegetic ion density adius t= t= Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 2 / 6

13 Summay and outlook Septembe 28 Novembe 28: investigate poblems in simulations fo DIII-D shot #3277 case Spuious dynamics due to make loading in tems of (E,µ,ψ). Potential poblems due to coelation beween signal and noise. Decembe 28 Mach 29: simulations fo GSEP test case Linea and nonlinea esults obtained. Still peliminay and to be compaed with othe codes. Since May 29: code development Clean-up and modenization of code ( become fee to extend and modify) Add uied featues: Make loading in tems of constants of motion ( eliminate spuious dynamics) Restat function ( long uns with high esolution) Additional physics being added by colleagues at ENEA/Fascati and IFTS/Hangzhou (shaped flux sufaces, bulk ion FLR and kinetic compession, fast ion FLR). Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 3 / 6

14 Open Issues ω / ω A Poblems with multi-n uns: ΠH (,) component coupted because makes not loaded in tems of constants of motion. High-esolution uns teminate suddenly (bug in aay allocation?). Stalled simulations fo dedicated DIII-D shot #3277: Spuious dynamics due to make loading in tems of (E,µ,ψ). t=5 γ=.2, ω =.66, ρ ω = t=25 γ=.5, ω =.66, ρ ω =.484 (,6) (,6) enegy histoy (2,6) (3,6) (4,6) ω / ω A time t / ω A 25 Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 4 / 6

15 Open Issues (continued) Not yet established convegence w..t. esistivity: Satuation level and tanspot vay with esistivity; need fine adial gid and shote time steps; need HMGC with estat function enegy (δφ).5 x 9 (a) S= 5 (B) (C) (D) (E) (7,6) (8,6) (9,6) (,6) (,6) (2,6) enegy (δφ) 8 x 9 (b) (,6), S= 5 (,6), S= 6 n f / n f.2. (c) (A), S= 5 (E), S= 5 final, S= 6 ω/ω A (A) t ω A t= (A) t=244.2 (B a) t=28.2 (C a) t=3. (D).5 t=37.4 (E a) ω/ω A Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 5 / 6

16 Hybid-MHD-gyokinetic simulation model [Biguglio et al., PoP 95] Resistive educed MHD with zeo bulk pessue (β i = β e = ) and tooidal coections O(ε 3 ) (ε = a/r.3) Enegetic ions ente MHD momentum uation as component of divegence of pessue tenso computed fom gyocente distibution Fomal odeing: n H ni O(ε 3 ), T H Ti O(ε 2 ) β H βi O(ε). MHD module [Bondeson (986), Izzo et al. (983), Pak et al. (992)] R A R t = ψ t ( ˆρ D Dt 2 φ R B Z = R2 R B ( ψ ζ) φ φ R ζ + η µ ψ ) ( ) 2 φ + ( ˆρ) D Dt φ R B Z φ = B µ B ( ψ) B R [R 2 ( Π H ) ζ ] Kinetic module [Hahm et al. (988), Dimits et al. (992), Biguglio et al. (995)] [ ( )] Π H = F mh 2 H (t,r, µ,v ) µb m H Î + ˆbˆb v 2 µb d m H, dt F H = F H (t,z) (2) i δ(z z dµ i), dt =, dv dr dt = dyn., dt = dyn.+ difts ˆρ = R2 R 2 m i n i, D Dt = t + v, 2 = R R R R + 2 Z 2, ψ = R R R () ψ + 2 ψ R Z 2. Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation GSEP Wokshop 29 6 / 6

Search for a Critical Electron Temperature Gradient in DIII-D L-mode Discharges

Search for a Critical Electron Temperature Gradient in DIII-D L-mode Discharges Seach fo a Citical Electon Tempeatue Gadient in DIII-D L-mode Dischages.C. Deoo, S. Ciant 1, T.C. Luce, A. Manini, C.C. Petty, F. Ryte, M.E. Austin 3, D.R. ake, K.W. Gentle 3, C.M. Geenfield,.E. Kinsey