GTC Status: Physics Capabilities & Recent Applications

Y. Xiao for GTC team

UC Irvine

• Non-perturbative (full-f) & perturbative (f) simulation

• General geometry using EFIT & TRANSP data

• Kinetic electrons & electromagnetic simulation

• Neoclassical effects using Fokker-Planck collision operators conserving energy & momentum

• Equilibrium radial electric field, toroidal & poloidal rotations; Multiple ion species

• Parallelization >100,000 cores

• Global field-aligned mesh

• Parallel solver PETSc

• Advanced I/O ADIOS

• Applications: microturbulence & MHD modes

Global Gyrokinetic Toroidal Code (GTC)

[Lin et al, Science, 1998]Lin, Holod, Zhang, Xiao, UCIKlasky, ORNL; Ethier, PPPL;Decyk, UCLA; et al

General geometry and profiles• General global toroidal magnetic geometry from Grad-

Shafranov equilibrium• Realistic density and temperature profiles using spline fits

of EFIT and TRANSP data• No additional equilibrium model

is needed• Experimental validation

GTC poloidal meshRealistic temperature and density profiles from DIII-D shot #101391 [Candy and Waltz, PRL 2003]

Full-f capability

• Non-perturbative full-f and perturbative -f models are implemented in the same version

time

full-f ITG intensity

f ITG intensity

full-f zonal flows

f zonal flows

Kinetic electrons

• Hybrid fluid-kinetic electron model is used

• In the lowest order of electron-to-ion mass ratio expansion electrons are adiabatic: fluid equations

• Higher-order kinetic correction is calculated by solving drift-kinetic equation

Electromagnetic capabilities• Only perpendicular perturbation of magnetic field

considered

• Parallel electric field expressed in terms of effective potential, obtained from electron density

• Continuity equation for adiabatic electron density, corrected by drift kinetic equation.

• Inverse Ampere’s law for electron current

• Time evolution for parallel vector potential

• Gyrokinetic Poisson equation for electrostatic potential

Structure of GTC algorithm

ne A||

ue

fige

neniuiA|| ne1 ue

1

indesA|| ZF

Dynamics

Sources

Fields

Equilibrium flows and neoclassical effects

• Equilibrium toroidal rotation is implemented

• Radial electric field satisfies radial force balance

• Neoclassical poloidal rotation satisfies parallel force balance

• Fokker-Planck collision operator conserving energy and momentum

Multiple ion species

• Fast ions treated the same way as thermal ion specie

• Energetic ion density and current non-perturbatively enter Poisson equation an Ampere’s law

Numerical efficiency

• Effective parallelization >105 cores• Global field-aligned mesh• Parallel PETSc solver• Advanced I/O system ADIOS

Recent GTC applications

• Electrostatic, kinetic electron applications– CTEM turbulent transport [Xiao et al, PRL2009; PoP2010]– Momentum transport [Holod & Lin, PoP2008; PPCF2010]– Energetic particle transport by microturbulence [W. Zhang et al,

PRL2008; PoP2010]– Turbulent transport in reversed magnetic shear plasmas [Deng &

Lin, PoP2009]– GAM physics [[H. Zhang et al,NF2009; PoP2010]

• Electromagnetic applications– Electromagnetic turbulence with kinetic electrons [Nishimura et

al, CiCP2009] – TAE [Nishimura, PoP2009; W. Zhang et al, in preparation]– RSAE [Deng et al, PoP2010, submitted]– BAE [H. Zhang et al, in preparation]

The CTEM turbulent transport studies reveal

• Transport scaling---Bohm to gyroBohm with system size increasing

• Turbulence properties---microscopic eddies mixed with mesoscale eddies

• Zonal flow---Zonal flow is important for the parameter applied

• Transport mechanism

electrons: track global profile of turbulent intensity; but contain a nondiffusive, ballistic component on mesoscale. The electron transport in CTEM is a 1D fluid process (radial) due to lack of parallel decorrelation and toroidal precession decorrelation and weak toroidal precession detuning

ions: diffusive, proportional to local EXB intensity. The ions decorrelate with turbulence in the parallel direction within one flux surface

CTEM turbulent transport

Xiao and Lin PRL 2009

Xiao et al, POP 2010

Experimental validation• Real radial temperature and density

profiles are loaded• Zonal flow solver is redesigned for the

general geometry• Heat conductivity uses the ITER

convention• The measured heat conductivity

(preliminary) is close to Candy-Waltz 2003 value

Tq

2

Toroidal momentum transport

• Simulations of toroidal angular momentum transport in ITG and CTEM turbulence

• Separation of momentum flux components. Non-diffusive momentum flux

• Intrinsic Prandtl number

Pr 0.2 0.7 (ITG)

Pr 0.5(CTEM)

Holod & Lin, PoP 2008

Holod & Lin, PPCF 2010