edge two fluids and gyrokinetic continuum simulations
DESCRIPTION
Edge Two Fluids and Gyrokinetic Continuum Simulations. Xueqiao Xu Presented at ITER Fusion Simulation Workshop May 16, 2006, Peking University. Diverted tokamak magnetic fusion device and its poloidal Cross Section. The Edge Transport Barrier is Critical to ITER’s Performance. - PowerPoint PPT PresentationTRANSCRIPT
Edge Two Fluids and Gyrokinetic Continuum Simulations
Xueqiao Xu
Presented at ITER Fusion Simulation Workshop May 16, 2006, Peking University
Diverted tokamak magnetic fusion device and its poloidal Cross Section
After R. Waltz et al, 2002 SnowMass Mtg.
The Edge Transport Barrier isCritical to ITER’s Performance
• Transport barriers form spontaneously at plasma edge
• Studies of core turbulence show – Turbulent transport
constrains gradient scale lengths
Tcentral ~ proportional to Tped
• Tped is the largest source of uncertainty in projecting ITER’s performance – Fusion gain = Pfusion/Paux
Projection of ITER’s Fusion Gain
Edge codes (BOUT and TEMPEST… ) are aimed at reducing uncertainty in projections of ITER’s fusion gain
Edge simulation models/codes
• Two fluid model– Transport;
• UEDGE, B2– Turbulence
• BOUT• BDM• DALF3
• Gyrokinetic model– Continuum methods
• Tempest, FEFI– Particle-in-cell methods
• XGC, ASCOT, ELMFIRE
• Mont-Carlo Model– Degas, Eirene
BOUT is 3D EM Boundary Plasma Turbulence Code
• Braginskii --- collisional, two-fluids electromagnetic equations
• Realistic X-point geometry– open+closed flux surfaces
• BOUT is being applied to DIII-D, C-mod, NSTX, MAST, ITER (for Snowmass), ...
• LOTS of edge fluctuation data!– BES, GPI, PCI, Probe, and
Reflectometer– Provide excellent
opportunity for validating BOUT against experiments.
BOUT is a parallelized 3D nonlocal electromagnetic turbulence code using MPI
A suite of the codes work together to make BOUT simulation results similar to real experiments
A simple analytical neutral mode added
In BOUT simulations turbulence is found in divertor leg region
upperx-point
lowerx-point
ref=38
Cross-correlation plot shows that divertor turbulence is not correlated with upstream turbulence
Plot of spatial distribution of RMS fluctuations amplitude shows that fluctuations grow in regions of unfavorable curvature
BOUT simulations for C-Mod are consistent with experimental amplitude and spatial spectra of Ni
BOUT simulations yield filamentary structures as experiments for edge localized modes (ELMs)
• Ingredients of an ELM simulation– Nonlinear with “fast” explosive
nonlinearities– Produces fine scale fingers/blobs/ etc– Fast transport along the field line and
turbulent transport across the field line– Allow for magnetic reconnection
• BOUT simulations– Early structure & growth similar to linear
pressure-/current-gradient driven modes– Radially propagating filamentary
structures grow explosively (as seen in MAST, DIII-D)
– Filaments acting as conduits to pedestal, provide mechanisms for ELM losses
– Not able to simulate complete bursting event at present; mesh alignment is a problem
PRL 2004 A. Kirk et al.
BOUT simulations, Snyder et al, PoP 2005
Results show that strong spatial dependence of transport must be included
a) Typical previous model b) Our new coupled results
• Poloidal variation understood from curvature instability
Experiment (DIII-D, C-Mod)
0 2 4 Radial distance (cm)
0.1
Results consistent with expt.
Open - DIII-D Filled - C-Mod
A kinetic edge code is required to model
both today’s tokamaks and ITER
• Fluid approximation requires:
• Not satisfied on DIII-D todayWon’t be satisfied on ITER
• Need to move beyond fluid codes
DIII-D Edge Barrier
mfp T 2
n c ~ 2R
or
Describe each species with akinetic distribution function, F()(, , , E0, ,)
mfp
c
Orbit width orbit width plasma scale length
Tempest is a 5D Continuum Edge Gyrokinetic Plasma Code
• Gyrokinetic equations– Valid for edge ordering
• Nonlinear Fokker-Planck collision
• Realistic X-point geometry– open+closed flux
surfaces
Simulate neoclassical transport, turbulence and plasma-Surface interactions
Fully Nonlinear Ion gyrokinetic equations
We have designed and implemented a 4D edge simulation framework
pyMPI (parallel Python)pyMPI (parallel Python)
Gyrokineticmodule
Gyrokineticmodule
pyUEDGEmodule
pyUEDGEmodule
Visualization module (pyGist)
Visualization module (pyGist)
Co
llision
sC
ollisio
ns
Ad
vection
AccelerationS
treaming
Radial D
rift
Ad
vection
AccelerationS
treaming
Radial D
rift
Field
solve
Field
solve
SUNDIALSSUNDIALS
Distribution Function moduleDistribution Function module
Data ManagerData Manager
SAMRAISAMRAI
HypreHypre
We have implemented a gyrokinetic Poisson equation field solver
2
2
22
2
2
ln22
NDD
p
eZNnNZe
De
22
2 1
24
• Discretized in - coordinates using standard finite differencing• Uses Hypre library of parallel linear algebra solvers and
preconditioners– Solvers:
• Conjugate Gradient (CG)• Generalized Minimum Residual (GMRES)• Stabilized BiConjugate Gradient (BiCGSTAB)
– Preconditioners• Diagonal scaling• Block Gauss-Seidel with PFMG or SMG in each block• BoomerAMG
• Currently implemented with Boltzmann electron model
Ne=<Ni0 >ee/Te /< ee/Te>
Simulation results agree very well with neoclassical theory in Ring geometry
Radial Position R(m)
Ion distribution function F(R,Z,E0 in DIII-D geometrywith endloss at plates in the SOL looks as expected
V||
V||
V||
V||
Tempest recovers theoretical U|| inside separatrix and increases as expected in SOL
Tempest exhibits collisionless damping of GAMs and zonal Flow
• Axis-symmetric mode (no toroidal variation)– Parallel ion dynamics– Magnetic curvature TEMPEST should see GAMs
• Tempest model– Drift kinetic ions with radial drift, streaming,
and acceleration– Boltzmann electron– Gyrokinetic Poisson equation in limit small
s/Lx
– Dirichlet radial boundary conditions• GAMs provide opportunity to “verify” TEMPEST
physics– Rosenbluth-Hinton residual
– Frequency
2
( ) 1
( 0) 1 1.6
t
t q
7
8Ti
GAM Rv
Time(vti/R0)
Rosenbluth-Hinton Residual zonal flowCollisionless damping of zonal flow and GAM
(t)/t)
2
( ) 10.02, 2.23, 0.02
( 0) 1 1.6
tq
t q
GAMsim/GAM
th=1.06
Tempest exhibits collisionless damping of GAMs and zonal Flow
Time(vti/R0)
Rosenbluth-Hinton Residual zonal flowCollisionless damping of zonal flow and GAM
(t)/t)
2
( ) 10.02, 2.23, 0.02
( 0) 1 1.6
tq
t q
GAMsim/GAM
th=1.06
GAMs simulations converge with nv, n, and KEmax
KEmax=15rtol=10-7, atol=10-12
r/R=0.02q=2.23
n=30, n=50, nE=30, n=15
n=30, n=50, nE=60, n=30
n=30, n=50, nE=100, n=50
n=30, n=100, nE=60, n=30
n=30, n=50, nE=30, n=15, KEmax=10
Rosenbluth-Hinton Residual zonal flow
Maximum kinetic energy has to be 10x thermal energy
n=30, n=50, nE=30, n=15rtol=10-7, atol=10-12
r/R=0.02,q=2.2
KEmax=15
KEmax=10
KEmax=5
Contour plot of distribution function
Time=0 Time=75
resonance
Summary
• Edge simulation and modeling are critical to ITER’s Performance
• Two fluid turbulence code BOUT yields simulation results consistent with experiments for present day tokamaks
• Edge gyrokinetic continuum code TEMPEST is under development
• A lot of scientific phenomenon remain to be discovered via advanced computing!