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XGC gyrokinetic particle simulation of edge plasma C.S. Chang a and the CPES b team a Courant Institute of Mathematical Sciences, NYU b SciDAC Fusion Simulation Prototype Center for Plasma Edge Simulation IEA Edge workshop, 11-13 Sept. 2006, Krakow, Poland

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Contents XGC GK particle code development roadmap –XGC-0 and XGC-1 Unconventional and strong edge neoclassical physics to be coupled to edge turbulence XGC-1 Full-f Gyrokinetic Edge Simulation (PIC) –Potential profile –Rotation profile –Movie of particle motion

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XGC Development Roadmap Full-f neoclassical ion root code (XGC-0) -Pedestal inside separatrix Buildup of pedestal along ion root by neutral ionization. Non-neoclassical electrons are assumed to follow ions Full-f ion-electron electrostatic code (XGC-1) -Whole edge Neoclassical solution Turbulence solution Study L-H transition Multi-scale simulation of pedestal growth in H-mode XGC-MHD Coupling for pedestal-ELM cycle Full-f electromagnetic code (XGC-2) Black: Achieved, Blue: in progress, Red: to be developed

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XGC-0 Code For pedestal physics inside separatrix Particle-in-cell, conserving MC collisions 5D (3D real space + 2D v-space) Full-f ions and neutrals (wall recycling) Neoclassical root is followed Macroscopic electrons follow ion root (weak turbulence) Realistic magnetic and wall geometry containing X-point Heat flux from core Particle source from neutral ionization Banana dynamics J r = r (E r -E r0 ) J loss +J return =0 Electron contribution to macroscopic j r is assumed to be small = validation of NC equil.

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XGC-0 simulation of pedestal buildup by neutral ionization along ion root (B 0 = 2.1T, T i =500 eV) [164K particles on 1,024 processors] Plasma densityV ExB

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Unconventional and strong edge neoclassical physics b ~ L p (Nonlinear neoclassical) f 0 f M, P I p/ r E-field and rotation can be easily generated from boundary effects Unconventional and strong neoclassical physics is coupled together with unconventional turbulence (strong gradients, GAM, separatrix & X, neutrals, open field lines, wall effect, etc).

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Sources of co-rotation in pedestal Asymmetric excursion of hot passing ions from pedestal top due to X-pt Loss of counter traveling Banana ions

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Conventional knowledge of not only i, but also the E r & rotation physics do not apply to the edge. Ampere’s law in the plasma core Due to the sensitive radial return current (large dielectric response), net radial current (or dE r /dt) in the core plasma is small. Consider the toroidal component of the force balance equation ( -sum) Since J is small, only the (small) off-diagonal stress tensor can raise or damp the toroidal rotation in the core plasma. In the scrape-off region, J || return current can be large. Thus, J r can easily spin the plasma up and down. In pedestal/scrape-off, S i (Neoclassical momentum transport) can be large. Highly unconventional and strong neoclassical physics. >=-4 n i m i c 2 K NC / t + 4 K NC ~10 2

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Neoclassical Polarization Drift. dE r /dt <0 case is shown

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Verification of XGC-1 against analytic neoclassical flow eq in core u i ∥ = (cT i /eB p )[kdlogT i /dr –dlog p i /dr-(e/T i )d /dr] Simulation Analytic E r (V/m) t=30 ib k=k( c ) =0 ’=0

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Conventional neoclassical v pol -v || relation Breaks down in edge pedestal ErEr 1

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At 10 cm above the X-point in D3D Green: without Red: enhanced loss by after 4.5x10 -4 sec (several toroidal transit times) Enhanced loss hole by fluctuating (from XGC) ( 50 eV, 100 kHz, m=360, n=20) Interplay between 5D neoclassical and turbulence Ku and Chang, PoP 11, 5626 (2004)

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Normalized psi~[0.99,1.00] n( ) ()() f i0 is non-Maxwellian with a positive flow at the outside midplane 0 V_parallel f KE (keV) lnf K || K perp Passing ions from ped top

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Experimental evidences of anisotropic non-Maxwellian edge ions (K. Burrell, APS 2003)

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Edge E r is usually inferred from Z i n i E r = r p – VxB. Inaccuracy due to ( p) r r p ??? K. Burrell, 2003

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XGC-1 Code Particle-in-cell 5D (3D real space + 2D v-space) Conserving plasma collisions Full-f ions, electrons, and neutrals (recycling) Neoclassical and turbulence integrated together Realistic magnetic geometry containing X-point Heat flux from core Particle source from neutral ionization

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Early time solutions of turbulence+neoclassical Correct electron mass t = 10 -4 ion bounce time Several million particles is higher at high-B side Transient neoclassical behavior Formation of a negative potential layer just inside the separatrix H-mode layer Positive potential around the X-point (B P ~0) Transient accumulation of positive charge L n ~ 1cm Density pedestal

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XGC simulation results: The initial H-mode like density profile has not changed much before stopping the simulation (<~10 bi ), neutral recycling is kept low. n ~ 1cm Guiding center densities

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Turbulence-averaged edge solutions from XGC The first self-consistent kinetic solution of edge potential and flow structure We average the fluctuating over toroidal angle and over a poloidal extent to obtain o. (1/2 flux-surface in closed and ~10 cm in the open field) Remove turbulence and avoid the “banging” instability Simulation is for 1 to 30 ion bounce time ib =2 R/v i (shorter for full-f and longer for delta-f): Long in a/v i time.

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Comparison of o between m i /m e = 100 and 1000 at t=1 Ib 100 is reasonable (10 was no good) (Similar solutions) 0 in scrape-off m i /m e =100m i /m e =1000

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Parallel plasma flow at t=1 and 4 ib (m i /m e = 100, shaved off at 1x10 4 m/s) t=1 i t=4 i V || 10 4 m/s Sheared parallel flow in the inner divertor Counter-current flow near separatrix Co-current flow in scrape-off Co-current flow at pedestal top

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t=4 i V || <0 in front of the inner divertor does not mean a plasma flow out of the material wall because of the ExB flow to the pump. ExB

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Strongly sheared V || <0 around separatrix, but >0 in the (far) scrape-off. V ||, DIII-D V || NN 1

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Wall (eV) NN V || >0V || <0 ExB profile without p flow roughly agrees with the flow direction in the edge Sign of strong off-diagonal P component? (stronger gyroviscous cancellation?)

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Edge E r is usually inferred from Z i n i E r = r p – VxB. Inaccuracy due to ( p) r r p ??? K. Burrell, 2003

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In neoclassical edge plasma, the poloidal rotaton from ExB can dominate over (B P /B T ) V ||. What is the real diamagnetic flow in the edge? (stronger gyroviscous cancellation?) How large is the off-diagonal pressure?

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Strongly sheared ExB rotation in the pedestal t=4 i ExB

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Cartoon poloidal flow diagram in the edge

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Wider pedestal Stronger V || >0 in scrape-off, Weaker V || <0 near separatrix. V || NN V ||, DIII-D V || NN 1 Wider pedestal Steeper pedestal Sharp V || (and ExB) shearing in H layer Weak V || (and ExB) shearing in H layer 0 1

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V || shows modified behavior with strong neutral collisions: V || >0 becomes throughout the whole edge (less shear) V || >0 source

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XGC-MHD Coupling Plan Phs-0: Simple coupling: with M3D or NIMROD XGC-0 grows pedestal along neoclassical root. MHD checks instability and crashes the pedestal. The same with XGC-1 and 2. Phs-2: Kinetic coupling: MHD performs the crash XGC supplies closure information to MHD during crash Phs-3: Advanced coupling: XGC performs the crash M3D supplies the B crash information to XGC during the crash Black: developed, Red: to be developed

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Code coupling Initial state: DIIID g096333 –No bootstrap current or pedestal of pressure, density XGC –read g096333 eqdsk file –calculate bootstrap current and p/n pedestal profile M3D –Read g096333 eqdsk file –Read XGC bootstrap current and pedestal profiles –Obtain new MHD equilibrium –Test for linear stability - found unstable –Calculate nonlinear ELM evolution

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M3D equilibrium and linear simulations new equilibrium from eqdsk, XGC profiles Equilibrium poloidal magnetic flux Linear perturbed poloidal magnetic flux, n = 9 Linear perturbed electrostatic potential

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At each Update kinetic information ( , D, ,etc), In phase 2 At each check for linear MHD stability

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M3D nonlinear simulation pressure evolution T = 37 Pressure relaxing T = 25 ELM near maximum amplitude Initial pressure With pedestal

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Pressure profile evolution T=0 T=25 T=37 Pressure profile p(R) relaxes toward a state with less pressure pedestal. P(R) is pressure along major radius (not averaged).

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Density n(R) profile evolution T=0 T=25 T=37 T=0 – initial density pedestal at R = 0.5 T=25 – ELM carries density across separatrix T=37 – density relaxes toward new profile

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Temperature T(R) profiles T=0 T=25 T=37

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Toroidal current density J(R) evolution T=0 T=37 T=25 T=0 – bootstrap current peak is evident at R = 0.5 T=25 – ELM causes current on open field lines T=37 – current relaxes toward new profile

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XGC-ET Mesh/Interpolation M3D-L (Linear stability) P ,P || Stable? XGC-ET Mesh/Interpolation M3D (x i, v i ), E E,B tt Stable? B healed? Mesh/Interpolation P ,P ||, , N,T,V,E, ,D Blue: Pedestal buildup stage Orange : ELM crash stage V,E, , XGC-M3D workflow (x i, v i ) Yes No E,B E (x i, v i ) Start (L-H) Mesh/Interpolation services evaluate macroscopic quantities, too.

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Conclusions and Discussions In the edge, we need to abandon many of the conventional neoclassical rotation theories –Strong off-diagonal pressure (non-CGL) –Turbulence and Neoclassical physics need to be self-consistent. In an H-mode pedestal condition, –V || >0 in the scrape-off, 0 at pedestal shoulder. – >0 in the scrape-off plasma, <0 in the pedestal –Global convective poloidal flow structure in the scrape-off –Strong sheared ExB flow in the H-mode layer –Good correlation of ExB rotation with V || Flow pattern is different in an L-mode edge –Weaker sheared flow in H-layer –High neutral density smoothens the V || structure and further reduces the shear in the pedestal region Sources of V || >0 exist at the pedestal shoulder. Nonlinear ELM simulation is underway (M3D, NIMROD) XGC-MHD coupling started. Correct bootstrap current, E r, and rotation profiles are important.

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