kinetic approach to microscopic-macroscopic coupling in fusion plasmas koichi noguchi physics &...
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Kinetic Approach to microscopic-macroscopic coupling in fusion plasmas
Koichi NoguchiPhysics & Astronomy Dept., Rice Univ.
Giovanni LapentaPlasma Theory Group, Theoretical Division, LANL, USA
Collaborators: J.U Brackbill (Particle Solutions), W. Daughton (U Iowa), S. Markidis (UNM),
P. Ricci (Dartmouth), R. Nebel, E. Evstatiev, J. Park (LANL)
Outline
1. Multiscale processes in plasmas, the case of ITER
2. The implicit moment PIC method
3. Benchmarks
4. Applications:– 3D reconnection– Reconnection in low beta plasmas– Fusion applications
Scales involved in plasma physics
10-210-310510-3Pressure tensor
10-310-710-710-7Resistivity
10-810-110410-4Electron inertia
10-610110610-2Hall
Solar interiorSolar coronaEarth magnetotail
ITER (D @ 10keV)
Length scale
Scales where the various terms become important (SI UNITS)
• Eliminates the smaller scales
• Quasineutrality is imposed
• Reduces the velocity space to 2D
• Some high order non-linearity are neglected
Gyrokinetic PIC
ÏpLeq
<<1
Ï „Ï ‰cp
<<1
In ITER D=0.1 cm, He=10 cm and gyroaverage could have problems
Multiscale coupling in space plasmas
• High Collisionless
• Small scales, non gyromotion
• Macro/micro coupling
• Methods developed there could be used for ITER.
Gombosi et al., Univ. Michigan G. Lapenta, AGU Fall meeting, 2004
k Ïp>>1
Example of CELESTE3D
2 – Simulating micro-macro coupling
A possibility: implicit moment PIC
Description of implicit moment PIC
Fundamental Equations (Classical)
• We consider collisionless plasmas
• Vlasov-Poisson model - Vlasov equation
- Maxwell equations
(Newton equations)
Eulerian formulation
Lagrangian formulation
Time step and grid spacing limit:
– Explicit stability constraints
– Implicit accuracy conditions
ωpeÎ ”t 2
Δx λDe
vth ,e
Î ”t
Δxλ
Deω
pe
Î ”t
Δx1
cÎ ”t Δx
Summary of the Stability constraints
• Maxwell equations: implicit second order formulation for the field E
• Newton equations: implicit form
• Solver: Implicit moment method
Implicit formulation (Classical)
Particle mover
Field Solver
4 – V&V and applications
1. Reconnection physics in 3D
2. Parallelization & Relativity
3. Inertial Electrostatic Confinement
Explicit:Pritchett, JGR106, 3783 (2001) Implicit:
CELESTE3D
•Explicit [Pritchett, JGR, 106, 3783 (2001)] Grid 512 X 256 grid, 9,000,000 particles, Time step: massively parallel computer
•Celeste3D [Ricci et al., GRL, 29, 2088, (2002)]Grid: 64X64 200,000 particles, Time step: Workstation
TEST: GEM challenge
ωpeÎ ”t 0 .15
ωpeÎ ”t 1 . 5
Electron outflow Ion density
Ion outflow Bz
x x
x xImplicit:
CELESTE3D
x
T=0 T=8
T=16
T=32
T=24
T=48
z
Performance – See Poster
• New PRASEK project:– CELESTE– FLIP (MHD)– DEMOCRITUS (plasma-
material interaction, kinetic)– GLOW (plasma-material
interaction, fluid)– Relativity
• C++ object oriented
• Parallel
0
2
4
6
8
10
12
14
16
1 2 4 8 16
# processors
PARSEK speed-up
Ideal speed-up
PARSEK efficiency
Ideal efficiency
(logarithmic axis)
• Maxwell equations: New scheme for current prediction
• Newton equations: Implicit form, relativistic
• Solver: Implicit moment method,Newton-Krylov method,Energy conserving method
New Relativistic Formulation
Particle mover
Field Solver
xp
n 1xp
nup
n 1/2
γΠ”t , γ 1
vp
c
2-1
, upvpγ
up
n 1 up
nqsÎ ”t
ms
Ep
n θ xp
n 1/2up
n 1/2
γBp
n xp
n 1/2
Test: relativistic 1D two-stream instability
Growth Rate :
Im(p)
V0=0.9c, 100,000 particles, 128 mesh, Te=0.01eVtp=0.01 (Explicit), 0.2 (Implicit)
0E
2 )/2
t p
2 γ3ω
p
2 1
kv0ω
2
1
kv0ω
2
Can we use CELESTE in low beta, high toroidal field?
Electron acceleration
ExplicitImplicit
BT=0
BT=BP
BT=10BP
Vye
Mi/Me=180
Summary
Question: how can we study burning plasmas kinetically
Possibility: consider implicit moment PIC
Fully kinetic Able to capture micro-macro
modelingExtensive application to space
plasma physics
Conclusions:The method is matureRecent upgrades ParallelizationRelativitySuite of relevant applications
R&D100 prize in 2005
CartaBlanca: A High-Efficiency, Object-Oriented, General-Purpose Computer Simulation Environment
PARSEK
General tool for PIC simulations
Includes:•Implicit kinetic PIC (Celeste)•Implicit fluid PIC (Flip)•Plasma-material interface (Democritus)
Orbits -Gyromotion
• No averaging, accuracy determined by t, x
• Accurate gyroradius and drift motions at large t
• Valid at all beta
• Valid at all: ρk┴
• Short scales are not eliminated and the energy channel towards them remains open
Drifts and Gyroradius
Implicit corrected for
Method III
Implicit (described above)
Method II
Leap-Frog BorisMethod I
Vu, Brackbill, JCP, 116, 384 (1995)
μ B
3D reconnection: micro-macro coupling
Large scale processes
Small scale processes
Question: Is the small/large scale coupling captured?
Simulation of the small scale processes (LHDI)
• Free energy: diamagnetic drift
• Driving: density gradient
• Stabilization: high beta
• Frequency:
• Wavelength:
• Direction:
• Seen in space and experiments (e.g. MRX)
• Present only on the edges of the sheet
• Requires a kinetic treatment
e>> ω
i
k Ïe
1
k 0
Simulation with L=di
Daughton, Lapenta, Ricci, JCP, 116, 384 (1995)
Effect of microinstabilities captured correctly
.55
1.1
2.2
L/ρi
L
explicit implicit
•Current intensification•Temperature anisotropy
Reconnection isenhanced (Poster:FZ1.00008)
Can we use CELESTE in low beta, high toroidal field?
• We considered reconnection with different:
– B toroidal (guide field)– Using a Harris equilibrium
• We computed:– Reconnection rate– Onset– Ion/electron decoupling
mechanism– Break-up mechanism
• As BT increases we kept the same t, even while the gyrofrequency increased.
Reconnection rateExplicit
Implicit
mi
me
25
mi
me
180
mi
me
1836
BT=0 BT=BP BT=10BP