Transcript Document

Nonlinear Simulations of Energetic
Particle-driven Modes in Tokamaks
Guoyong Fu
Princeton Plasma Physics Laboratory
Princeton, NJ, USA
In collaboration with
J. Breslau, J. Chen, S. Jardin, W. Park (PPPL)
H.R. Strauss (NYU)
L.E. Sugiyama (MIT)
Outline
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Introduction
M3D code
Energetic particle-driven fishbone
Energetic particle-driven Alfven modes
Conclusions
Important issues for future
Introduction
• In a tokamak fusion reactor, fusion product alpha particles
have a birth speed comparable to Alfven phase velocity,
thus can destabilize Alfven waves via resonant interaction.
• The alpha-driven Alfven instability can cause alpha
particle loss which may lead to degradation in heating
efficiency and damage in the reactor’s first wall.
• In this work, we investigate nonlinear dynamics of
energetic particle-driven instabilities via Particle/MHD
hybrid simulations using M3D code.
M3D Code
• M3D is a 3D extended nonlinear MHD code
with multiple level of physics:
resistive MHD
two fluids
Particle/MHD hyrid
M3D XMHD Model
M3D code: numerical method
M3D uses finite elements in poloidal planes and finite difference in
toroidal direction.
M3D is implicit for resistive MHD model.
M3D runs on massively parallel super-computers.
3D numerical grids
Nonlinear kink (NSTX)
Sawteeth (NSTX)
RSAE (D3D)
Current hole (JET)
Internal kink (ITER)
TAE (NSTX)
ELM (ITER)
M3D hybrid simulations of fishbone:
Brief review of fishbone
• Fishbone instability was first discovered on the PDX tokamak. The
instability was named for its characteristic magnetic signal ( K.
MCGuire et al, Phys. Rev. Lett., 1983).
• The instability was later observed in others tokamaks and stellarators.
• The instability has characteristic bursting behavior with strong
chirping.
• The instability was explained as a n/m=1/1 kink mode resonantly
destabilized by trapped energetic ions:
precessional branch: w ~ wd (L. Chen et al , P.R.L., 1984)
w* branch:
w ~ w* (B. Coppi et al, P.R.L., 1985)
Experimental observation of fishbone instability in PDX
Excitation of Fishbone at high bh
Mode Structure: Ideal Kink v.s. Fishbone
Linear mode structure and dependence of mode frequency
and growth rate on energetic particle beta
Nonlinear evolution of mode structure and mode amplitude
Saturation amplitude scale as square of linear growth rate
Simulation of fishbone shows distribution fattening and
strong frequency chirping
distribution
Simulations of Beam-driven Alfven Modes in the National
Spherical Torus Experiment (NSTX).
• Recent NSTX experimental observations show rich
beam-driven instabilities: fishbone, TAEs etc and
associated fast particle losses.
• M3D simulations show beam-driven Alfven
instability with mode frequency consistent with
measurement.
• Nonlinear simulations show strong nonlinear
interaction among different modes.
E. Fredrickson
The bursting modes are in the TAE
frequency range (NSTX)
• Multiple modes burst at
the same time.
• Toroidal mode number, n,
ranges from 2 - 5 with the
dominant mode being
n=2 or 3.
• Mode frequencies in
reasonable agreement
with expected TAE
frequencies.
NSTX Parameters and Profiles
• NSTX shot #108530 at t=0.267sec:
• R=87cm, a=63cm, B=0.43T, ne(0)=2.5e13,
Ti=1.7kev, Te=1.4kev;
• q(0)=1.82, q(a)=12.9, weakly reversed;
b(0)=21%, bbeam(0)=13%;
• vbeam/vAlfven = 2.1, rbeam/a =0.17
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Nonlinear evolution of
single n=2 mode in NSTX
t=0.0
t=336
Conclusions
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Hybrid simulations of energetic particle-driven fishbone
instability in a circular tokamak show dynamic mode
saturation as the particle distribution is flattened and mode
frequency is reduced strongly. MHD nonlinearity reduces
the mode saturation level.
• Hybrid simulation of energetic particle-driven Alfven
modes in NSTX shows rich nonlinear dynamics: frequency
chirping, nonlinear interaction between multiple modes
and nonlinearly driven modes.
Important Energetic Particle Issues
• Linear Stability: basic mechanisms well
understood, but lack of a comprehensive code
which treats damping and drive non-perturbatively
• Nonlinear Physics: single mode saturation well
understood, but lack of study for multiple mode
dynamics
• Effects of energetic particles on thermal plasmas:
needs a lot of work