Simulazioni ibride (fluide/particle-in-cell) per la fusione termonucleare

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1 Simulazioni ibride (fluide/particle-in-cell) per la fusione termonucleare G. Vlad, S. Briguglio, G. Fogaccia, V. Fusco ENEA for, via E. Fermi 45, 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 G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 1

2 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 socalled Magnetically Confined Fusion, and the most advanced experimental devices are the Tokamaks. G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 2

3 ITER ~ 40 m The next International Thermonuclear Fusion experiment (ITER) The plasma is confined in a toroidal chamber by a very high (~6T) magnetic field ITER is under construction in Saint Paul-lez-Durance (France). First plasma: ~ 2020; D-T operation: ~ 2027 G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 3 Once the plasma, which curries a strong toroidal current (~10 MA), is produced, the topology of the magnetic field becomes helicoidal

4 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. G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 4

5 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 G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 5

6 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 ( bounce and precession frequencies ) G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 6 projection of motion on the poloidal plane

7 Particle orbit - 1 Trapped particle ( banana orbit) with precession motion G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 7

8 Particle orbit - 2 Trapped particle ( banana orbit) with zero precession G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 8

9 Particle orbit - 3 Circulating particle G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 9

10 Alfvén wave (TAE) frequency spectrum (ω,r): global mode (TAE) Alfvén continua poloidal cross section (R,Z) constant flux surface (φ,χ) G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 10

11 Hybrid model Hybrid model: extend MHD equations by adding a coupling term with energetic particles (EPs) The coupling term between bulk specie and EP specie is the divergence of the EP pressure + r (%v) = % dv = rp r P E + 1 dt c J B, d P = 0, dt % E + 1 c v B = 0, r E = ηj, r B = 4 c J, r B = 0. d + v r The EP term needs to keep the details of the wave-particles resonances: thus, we need a kinetic formalism f E is the EP distribution function described by Vlasov eq. (collisionless Boltzmann + v r r + q m (E + v B) r vf E =0 solved using the so-called gyrokinetic formalism Z P i,j;e v i v j f(r, v,t) dv E(t), B(t) are the solution of the MHD eqs. and provide the forces in the Vlasov eq. v i, v j are the EP velocity components G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 11

12 Computational models MHD models (field solver) Gyrokinetic model HMGC: Reduced MHD!two fields; simple geometry; finite difference in r, Fourier in θ!m pol, Fourier in φ! n tor ; fully non-linear. HMGC k ρ E << 1 (k is the component of the wave vector perpendicular to the magnetic field, ρ E is the energetic particle Larmor radius); magnetic drift orbit widths fully retained; energetic particle pressure: P, P ; solved by particle-in-cell (PIC) techniques; fully non-linear. HYMAGYC: HYMAGYC fully resistive MHD!14 fields; arbitrary geometry (curvilinear coordinate system); finite elements in s, Fourier in χ!m pol, Fourier in φ! n tor ; only linear MHD dynamics considered. G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 12 k ρ E = O(1); gyro-average fully retained; energetic particle pressure tensor: P ij ; solved by particle-in-cell (PIC) techniques; fully non-linear.

13 Computational requirements Goal: ITER relevant case, e.g., n = -30 TAE driven by energetic particles MHD (field solver) module of HYMAGYC axisymmetric (2D) equilibrium discretization scheme: FE in radius (s), Fourier in generalized poloidal (χ) and toroidal (φ) angles linear MHD:! single toroidal mode number: n tor = -30 # MHD eqs.:14 eqs. # radial mesh points: n s = 1000; # poloidal Fourier components: m pol = 100; linear system with # eqs.: n s m pol 14 = matrix elements (double complex): (# eqs.) 2 = maximum non-zero matrix (block tridiagonal) elements: 456 n s (m pol ) 2 = parallelization of the field solver done in collaboration with EFDA-HLST using MUMPS (MUltifrontal Massively Parallel sparse direct Solver), mainly to gain memory availability runs on CRESCO4 (also on HELIOS (IFERC), Japan) Memory cpu time (256 cores), MUMPS cpu time sequential solver Gb t inversion 200 s (inversion) t bs 1 s (backsolve per step) t inversion 3350 s (inversion) t bs 29 s (backsolve per step) Gyrokinetic module of HYMAGYC PIC model; # particles: n p =n s,χ,φ n ppc ; # particles per cell: n ppc =512 (v space); # poloidal mesh points: n χ 8 m pol,max =800; # toroidal mesh points: n φ 8 n tor =240; n s,χ,φ = n s n χ n φ = ; # particles: n p = n s,χ,φ n ppc 100 G! particles memory M p : 7 double real variables per particle, M p =5.5 Tb! Gyrokinetic module parallelized using Hierarchical MPI+OpenMP scheme (MPI inter-node, OpenMP intra-node) typical cpu time/particle/step: 3x10-6 s typical simulation: n steps =5x10 4 Memory cpu time (4576 cores) CRESCO4 (estimate) G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 13 cpu time (72000 cores) HELIOS(estimate) 5.5 Tb t simulation 40 gg t simulation 2.5 gg

14 ITER TAE example n = - 30 poloidal cross section (R,Z) constant flux surface (φ,χ) G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 14

15 JET model equilibrium n=4 non-linear simulation, soliton avalanches, energetic particles displaced toward the outer edge of the torus, critical phenomenology,! possibly preventing ignition! n4_soliton_avalanches.m4v Electrostatic potential ϕ Fourier components vs r movie caption: energetic particle pressure radial profile Electrostatic potential ϕ structure in (R,Z) frequency spectrum (ω,r): Energetic particle driven mode (EPM) + Alfvén continua G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 15

16 Non-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,P ϕ ), with Θ the wave phase seen by the energetic particles and P ϕ the toroidal angular momentum. peaked-off_eps0.1_pphi_phase_den_power_res_grande-desktop.m4v G. Vlad Workshop ICT e supercalcolo al servizio di ricerca e imprese risultati e prospettive" 17 marzo 2015 ENEA - Sede 16