Presentation on theme: "XGC gyrokinetic particle simulation of edge plasma"— Presentation transcript:
1XGC gyrokinetic particle simulation of edge plasma IEA Edge workshop, Sept. 2006, Krakow, PolandXGC gyrokinetic particle simulation of edge plasmaC.S. Changa and the CPESb teamaCourant Institute of Mathematical Sciences, NYUbSciDAC Fusion Simulation Prototype Center for Plasma Edge Simulation
2Contents XGC GK particle code development roadmap XGC-0 and XGC-1Unconventional and strong edge neoclassical physics to be coupled to edge turbulenceXGC-1 Full-f Gyrokinetic Edge Simulation (PIC)Potential profileRotation profileMovie of particle motion
3XGC Development Roadmap Full-f neoclassical ion root code (XGC-0)-Pedestal inside separatrixBuildup of pedestal along ion root by neutral ionization.Non-neoclassical electrons are assumed to follow ionsFull-f ion-electron electrostatic code (XGC-1)-Whole edgeNeoclassical solutionTurbulence solutionStudy L-H transitionMulti-scale simulation of pedestal growth in H-modeXGC-MHD Coupling for pedestal-ELM cycleFull-f electromagnetic code (XGC-2)Black: Achieved, Blue: in progress, Red: to be developed
4XGC-0 Code For pedestal physics inside separatrix Particle-in-cell, conserving MC collisions5D (3D real space + 2D v-space)Full-f ions and neutrals (wall recycling)Neoclassical root is followedMacroscopic electrons follow ion root (weak turbulence)Realistic magnetic and wall geometry containing X-pointHeat flux from coreParticle source from neutral ionizationBananadynamicsJr = r(Er-Er0)Jloss+Jreturn=0Electron contributionto macroscopic jr isassumed to be small= validation of NC equil.
5[164K particles on 1,024 processors] XGC-0 simulation of pedestal buildup by neutral ionization along ion root (B0= 2.1T, Ti=500 eV)[164K particles on 1,024 processors]Plasma densityVExB
6Unconventional and strong edge neoclassical physics b ~ Lp (Nonlinear neoclassical)f0 fM, P I p/rE-field and rotation can be easily generated from boundary effectsUnconventional and strong neoclassical physics is coupled together with unconventional turbulence (strong gradients, GAM, separatrix & X, neutrals, open field lines, wall effect, etc).
7Sources of co-rotation in pedestal Asymmetric excursionof hot passing ions frompedestal top due to X-ptLoss of counter travelingBanana ions
8Conventional knowledge of not only i, but also the Er & rotation physics do not apply to the edge.Ampere’s law in the plasma coreKNC~102>=-4nimic2KNC<||2/B2>/t + 4<Jext >Due to the sensitive radial return current (large dielectric response),net radial current (or dEr/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 dampthe toroidal rotation in the core plasma.In the scrape-off region, J|| return current can be large.Thus, Jr can easily spin the plasma up and down.In pedestal/scrape-off, Si (Neoclassical momentum transport) can be large. Highly unconventional and strong neoclassical physics.
9Neoclassical Polarization Drift. dEr/dt <0 case is shown
10analytic neoclassical flow eq in core Verification of XGC-1 againstanalytic neoclassical flow eq in coreui∥= (cTi/eBp)[kdlogTi/dr –dlog pi/dr-(e/Ti)d/dr]Analytict=30ibk=k(c)SimulationEr(V/m)’=0=0
11Conventional neoclassical vpol-v|| relation Breaks down in edge pedestalEr1
12Enhanced loss hole by fluctuating (from XGC) (50 eV, 100 kHz, m=360, n=20)At 10 cm above theX-point in D3DGreen: without Red: enhancedloss by Interplay between 5Dneoclassical and turbulenceafter 4.5x10-4 sec(several toroidaltransit times)Ku and Chang, PoP 11, 5626 (2004)
13fi0 is non-Maxwellian with a positive flow at the outside midplane K||lnfn()KperpKE (keV)Passing ionsfrom ped top()fV_parallelNormalized psi~[0.99,1.00]
14Experimental evidences of anisotropic non-Maxwellian edge ions (K. Burrell, APS 2003)
15Edge Er is usually inferred from ZiniEr = rp – VxB. Inaccuracy due to (p)r rp ???K. Burrell, 2003
16XGC-1 Code Particle-in-cell 5D (3D real space + 2D v-space) Conserving plasma collisionsFull-f ions, electrons, and neutrals (recycling)Neoclassical and turbulence integrated togetherRealistic magnetic geometry containing X-pointHeat flux from coreParticle source from neutral ionization
17Early time solutions of turbulence+neoclassical Correct electron masst = 10-4 ion bounce timeSeveral million particles is higher at high-B side Transient neoclassical behaviorFormation of a negativepotential layer just insidethe separatrix H-mode layerPositive potential aroundthe X-point (BP ~0) Transient accumulationof positive chargeDensitypedestalLn ~ 1cm
18XGC simulation results: The initial H-mode like density profile has notchanged much before stopping the simulation (<~10 bi),neutral recycling is kept low.n ~ 1cmGuiding centerdensities
19Turbulence-averaged edge solutions from XGC The first self-consistent kinetic solution of edge potential and flow structureWe 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” instabilitySimulation is for 1 to 30 ion bounce time ib =2R/vi (shorter for full-f and longer for delta-f): Long in a/vi time.
20Comparison of o between mi/me = 100 and 1000 at t=1Ib 100 is reasonable (10 was no good)mi/me =100mi/me =1000(Similar solutions)<0 in pedestal and >0 in scrape-off
21Parallel plasma flow at t=1 and 4ib (mi/me = 100, shaved off at 1x104 m/s)Counter-current flownear separatrixCo-current flow inscrape-offCo-current flow at pedestal topt=1it=4iV|| 104 m/sSheared parallel flowin the inner divertor
22t=4i V|| <0 in front of the inner divertor does not mean a plasma flow out of the material wall becauseof the ExB flow to the pump.t=4iExBExB
23Strongly sheared V|| <0 around separatrix, but >0 in the (far) scrape-off.V||, DIII-DV||N1
24ExB profile without p flow roughly agrees with the flow direction in the edgeSign of strong off-diagonal P component?(stronger gyroviscous cancellation?)V||<0V||>0(eV)WallN
25Edge Er is usually inferred from ZiniEr = rp – VxB. Inaccuracy due to (p)r rp ???K. Burrell, 2003
26In neoclassical edge plasma, the poloidal rotaton from ExB can dominate over (BP/BT) V||.What is the real diamagnetic flow in the edge?(stronger gyroviscous cancellation?)How large is the off-diagonal pressure?
30Wider pedestal Stronger V||>0 in scrape-off, Weaker V|| <0 near separatrix.V||NWeak V|| (and ExB) shearingin H layerSharp V|| (and ExB) shearingin H layerV||, DIII-DV||N1Wider pedestalSteeper pedestal1
31V|| shows modified behavior with strong neutral collisions: V||>0 becomes throughout the whole edge (less shear)V||>0 source
32Phs-0: Simple coupling: with M3D or NIMROD XGC-MHD Coupling PlanPhs-0: Simple coupling:with M3D or NIMRODXGC-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 crashXGC supplies closure information to MHD during crashPhs-3: Advanced coupling:XGC performs the crashM3D supplies the B crash information to XGC during the crashBlack: developed, Red: to be developed
33Code coupling Initial state: DIIID g096333 XGC M3D No bootstrap current or pedestal of pressure, densityXGCread g eqdsk filecalculate bootstrap current and p/n pedestal profileM3DRead g eqdsk fileRead XGC bootstrap current andpedestal profilesObtain new MHD equilibriumTest for linear stability - found unstableCalculate nonlinear ELM evolution
34M3D equilibrium and linear simulations new equilibrium from eqdsk, XGC profiles Linear perturbed poloidal magnetic flux, n = 9Equilibriumpoloidal magnetic fluxLinear perturbed electrostatic potential
35At each check forlinear MHD stabilityAt each Update kineticinformation (, D, ,etc),In phase 2
36M3D nonlinear simulation pressure evolution ELM near maximumamplitudeT = 37Pressure relaxingInitial pressureWith pedestal
37Pressure profile evolution Pressure profile p(R) relaxes toward a statewith less pressure pedestal. P(R) is pressurealong major radius (not averaged).
38Density n(R) profile evolution T=0 – initial density pedestal at R = 0.5T=25 – ELM carries density across separatrixT=37 – density relaxes toward new profile
42Conclusions and Discussions In the edge, we need to abandon many of the conventional neoclassical rotation theoriesStrong 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 in near separatrix, >0 at pedestal shoulder.>0 in the scrape-off plasma, <0 in the pedestalGlobal convective poloidal flow structure in the scrape-offStrong sheared ExB flow in the H-mode layerGood correlation of ExB rotation with V||Flow pattern is different in an L-mode edgeWeaker sheared flow in H-layerHigh neutral density smoothens the V|| structure and further reduces the shear in the pedestal regionSources of V||>0 exist at the pedestal shoulder.Nonlinear ELM simulation is underway (M3D, NIMROD)XGC-MHD coupling started. Correct bootstrap current, Er, and rotation profiles are important.