Simulazioni ibride (fluide/Particle-in-cell) - Enea
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Simulazioni ibride (fluide/Particle-in-cell)
per la fusione termonucleare
G. Vlad, S. Briguglio, G. Fogaccia, V. Fusco
ENEA for EUROfusion, via E. Fermi 45, 00044 Frascati (Roma), Italy
ICT E SUPERCALCOLO
AL SERVIZIO DI RICERCA E IMPRESE
RISULTATI E PROSPETTIVE
17 marzo 2015
ENEA – Via Giulio Romano n. 41, Roma
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 1 EUROfusion
Introduction
• Controlled thermonuclear fusion is one of the most promising energy sources
for the next near future.
• Reproducing in laboratory the nuclear processes which take place in the core of
stars is one of the major challenges of the present day research.
• Thermonuclear fusion occurs when light elements (like
Hydrogen or its isotopes) fuse together into new elements,
like Helium, releasing in that process a large amount of
energy.
• In order to fuse the light elements together, it is necessary to heat them to
energies of the order of several tens of KeV: in this condition, the gas is highly
ionized. If also high density and good thermal insulation is obtained, the ionized
gas (“plasma”) will undergo a large amount of fusion reactions and the process
will become energetically favourable.
• The most promising approach considered by the fusion community is the so-
called “Magnetically Confined Fusion”, and the most advanced experimental
devices are the “Tokamaks”.
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 2 EUROfusion
ITER
~ 40 m The plasma is confined in a Once the plasma, which
The next International toroidal chamber by a very curries a strong toroidal
Thermonuclear Fusion high (~6T) magnetic field current (~10 MA), is
experiment (ITER) produced, the topology
of the magnetic field
ITER is under construction in Saint Paul-lez-Durance becomes helicoidal
(France). First plasma: ~ 2020; D-T operation: ~ 2027
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 3 EUROfusion
Ignition device
• The plasma will be heated to the required temperature (~10 KeV) by joule
heating, strongly energetic neutral beams, radio frequency waves, …
• Several challenging issues are faced on the way of controlled thermonuclear
fusion:
- technology (high magnetic fields, superconductor coils, …)
- materials (heat exhaust, wall loading, blanket, tritium breeding, …)
- physics (plasma heating, energy confinement, MHD, turbulent transport, …)
• Once the thermonuclear reactions become dominant, the plasma temperature will
be sustained by the high energy α particles (Helium nuclei, 3.5 MeV)
• It is crucial to have well confined energetic particles (α’s, beams particles, radio
frequency accelerated particles, …) to allow them to slow down and release their
energy by collisions thus heating the bulk plasma
• Typical velocity of α particles in an ignited device is of the same order of the
Alfvén velocity (the velocity of propagation of a magnetic field perturbation)
• If an electromagnetic perturbation growths in time, because of the resonant
interaction with the energetic particles, the confinement of the energetic particles
themselves can be strongly reduced, before they are able to release their energy to
the bulk plasma, avoiding the “ignition” of the device. Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 4 EUROfusion
Theory and modelling
• The development of theoretical and computational models for the
study of the physical phenomena which determine the plasma
dynamics is of significant importance for the success of future
experiments (“ignition” regime not yet observed in present devices,
extrapolation from present “sub-ignited” regimes is required).
• We focus our activity in studying the interaction between Alfvén
waves and energetic particles (as, e.g., fusion α’s, beams particles,
radio frequency accelerated particles, …): linear dynamics,
turbulent transport, non linear saturation.
• The computational model considered is the so-called “hybrid
model”, where a thermal component of the plasma is treated as a
fluid, described by MagnetoHydroDynamics equations (MHD) and
the energetic particles are treated kinetically
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 5 EUROfusion
Single particle motion in torus
• The single particle motion in a tokamak can be very complicated: particles
rapidly gyrate perpendicularly to the equilibrium magnetic field (“gyro-motion”)
while transiting along the torus (“circulating particles”) or experiencing a almost
closed orbits bouncing back and forth (“trapped particles” and “banana orbits”)
because of the characteristic magnetic well of the tokamak configurations;
moreover, those trapped particles experience also a precession motion along the
torus.
• Thus several characteristic frequencies of energetic particles are present, which
can resonate with the frequencies of the Alfvénic waves, eventually driving them
unstable: kinetic treatment is important!
circulating particle (“transit frequency”)
Precession of a trapped particle projection of
(“bounce and precession frequencies”) motion on the
poloidal plane
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 6 EUROfusion
Particle orbit - 1
Trapped particle (“banana” orbit) with precession motion
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 7 EUROfusion
Particle orbit - 2
Trapped particle (“banana” orbit) with zero precession
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 8 EUROfusion
Particle orbit - 3
Circulating particle
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 9 EUROfusionAlfvén wave (TAE)
frequency spectrum (ω,r):
global mode (TAE)
Alfvén continua
poloidal cross section (R,Z) constant flux surface (φ,χ)
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 10 EUROfusionHybrid model
• Hybrid model: extend MHD equations by adding a coupling term
with energetic particles (EPs)
• The coupling term between bulk specie and EP • The EP term needs to keep the details of the
D+ divergenza
specie tensore pressione
is the divergence of the EPparticelle pressure tensor energetiche: wave-particles resonances: thus, we need a
@% kinetic formalism
+ r · (%v) = 0 , (9)
• fE is the EP distribution function described
@t
dv 1 by Vlasov eq. (collisionless Boltzmann eq.):
% = rP r · PE + J ⇥ B , (10)
✓ ◆ dt c
d P @fE q
= 0, + v · r +(11) (E + v ⇥ B) · rv fE = 0
dt % @t
r
m
1
E + v ⇥ B = ηJ, 0, • solved using the (12)so-called “gyrokinetic
c
formalism”
1 @B Z
r⇥E = , (13)
c @t Pi,j;E ⇠ vi vj f (r, v, t) dv
4⇡
r⇥B = J, (14)
c • E(t), B(t) are the solution of the MHD
r · B = 0. eqs. and provide (15) the forces in the Vlasov
d @ eq.
= +v·r • vi, vj are the(16) EP velocity components
dt @t Fusion Unit
law:
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 11 EUROfusionComputational models
MHD models (field solver) Gyrokinetic model
HMGC: HMGC
• Reduced MHD • k ρEComputational requirements
Goal: ITER relevant case, e.g., n = -30 TAE driven by energetic particles
MHD (field solver) module of HYMAGYC Gyrokinetic module of HYMAGYC
• axisymmetric (2D) equilibrium • PIC model;
• discretization scheme: FE in radius (s), Fourier in • # particles: np=ns,χ,φ ✕ nppc;
generalized poloidal (χ) and toroidal (φ) angles • # particles per cell: nppc=512 (v space);
• linear MHD: ! single toroidal mode number: ntor= -30 • # poloidal mesh points: nχ≈ 8 ✕mpol,max=800;
• # MHD eqs.:14 eqs. • # toroidal mesh points: nφ≈ 8 ✕ ntor=240;
• # radial mesh points: ns= 1000; • ns,χ,φ= ns✕nχ✕nφ= 192✕106;
• # poloidal Fourier components: mpol= 100; • # particles: np= ns,χ,φ ✕ nppc≈ 100 G
• linear system with # eqs.: ns✕mpol✕14 = 1.4✕106 • ! particles memory Mp: 7 double real
• matrix elements (double complex): (# eqs.)2 = 1.96✕1012 variables per particle, Mp=5.5 Tb
• maximum non-zero matrix (block tridiagonal) elements: • ! Gyrokinetic module parallelized using
456✕ns✕(mpol)2=4.56✕109 Hierarchical MPI+OpenMP scheme (MPI
• parallelization of the field solver done in collaboration inter-node, OpenMP intra-node)
with EFDA-HLST using MUMPS (MUltifrontal • typical cpu time/particle/step: 3x10-6 s
Massively Parallel sparse direct Solver), mainly to gain • typical simulation: nsteps=5x104
memory availability
• runs on CRESCO4 (also on HELIOS (IFERC), Japan) Memory cpu time (4576 cpu time (72000 cores)
Memory cpu time (256 cores), MUMPS cpu time sequential solver cores) CRESCO4 HELIOS(estimate)
(estimate)
72.96 Gb tinversion≈ 200 s (inversion) tinversion≈ 3350 s (inversion)
5.5 Tb tsimulation≈ 40 gg tsimulation≈ 2.5 gg
tbs ≈ 1 s (backsolve per step) tbs ≈ 29 s (backsolve per step)
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 13 EUROfusionITER TAE example n = - 30
poloidal cross section (R,Z) constant flux surface (φ,χ)
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 14 EUROfusionJET model equilibrium
• n=4 non-linear simulation,
• soliton avalanches,
n4_soliton_avalanches.m4v
• energetic particles displaced toward the
outer edge of the torus,
• critical phenomenology,
! possibly preventing ignition!
movie caption:
Electrostatic potential energetic particle
ϕ Fourier pressure radial profile
components vs r
Electrostatic potential frequency spectrum
ϕ structure in (R,Z) (ω,r):
Energetic particle
driven mode (EPM) +
Alfvén continua
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 15 EUROfusionNon-linear dynamics studies
Energetic electron driven internal kink instability: “e-fishbone”:
• MHD mode driven by energetic electrons (observed in present devices, similar dynamics of
certain energetic-ion instabilities driven in ignited plasmas)
• HMGC suited for detailed studies of non-linear saturation by Hamiltonian mapping techniques
• plots of energetic particles in the plane (Θ,Pϕ), with Θ the wave phase seen by the energetic
particles and Pϕ the toroidal angular momentum.
peaked-off_eps0.1_pphi_phase_den_power_res_grande-desktop.m4v
Fusion Unit
G. Vlad Workshop “ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 16 EUROfusionYou can also read
