Hybrid MHD-Gyrokinetic Simulations for Fusion ReseachG. Vlad, S. Briguglio, G. Fogaccia

Associazione EURATOM-ENEA, Frascati, (Rome) Italy

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”.

nuovo cluster HPC CRESCO4, ENEA Portici, 12/3/2014

~ 40 m The next International Thermonuclear Fusion

experiment (ITER)

The plasma is confined in a toroidal chamber by a very high (~6T) magnetic field

Once the plasma, which curries a strong toroidal current (~10 MA), is produced, the topology of the

magnetic field becomes helicoidal

• The plasma will be heated to the required temperature (~10 KeV) by joule heating, strongly energetic neutral beams, radio frequency waves, …

• 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 energy of the energetic particles in a fusion 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.

The hybrid MHD-gyrokinetic code HMGC to study the self-consistent nonlinear interaction of energetic particles with Alfvénic waves

• Thermal (core) plasma:- described by reduced O(0

3) visco-resistive MHD equations in the limit of zero pressure (0 ≡ a/R0 being the inverse aspect ratio of the torus; this model allows to investigate equilibria with shifted circular magnetic surfaces only).

- MHD fields, low-β limit: ψ (poloidal flux function), (scalar potential)• Energetic-particle population:

- described by the nonlinear gyrokinetic Vlasov equation,with equations of motion expanded up to order O()and O(B) (with ~H /Ln and B~H /LB<),

- guiding-center approximation k⊥ρH <<1(but magnetic drift orbit widths fully retained),

- energetic particle pressure: Π⊥, Π||,- solved by particle-in-cell (PIC) techniques.

•Coordinates system (r, θ, φ)

H the energetic ion Larmor radius,Ln the equilibrium density scale length,LB the equilibrium magnetic field scale length,k⊥ the component of the wave vector perpendicular to the magnetic field

HMGC

• The single particle motion in a tokamak can be very complicated: particles rapidly gyrate perpendicular 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.

Precession of a trapped particle(“bounce and precession frequencies”)

circulating particle (“transit frequency”)

projection of motion on the poloidal plane

PIC (Particle In Cell) approach:•electromagnetic fields (MHD model) are computed on a discretized spatial grid;•energetic particles are evolved in the continuum, interpolating the e.m. fields from the vertices of the cell the particle belongs to;•particle contribution to the MHD eqs. (pressure tensor) is computed collecting the contribution of each particle to the vertices of the cell it belongs to after each time step.

The PIC code is parallelized using a particle decomposition mode:•the spatial domain and e.m. solver is replicated on each node;•energetic particles are distributed among nodes.

………….node #1 node #2 node #n

………….

Application of HMGC: simulation of electron driven fishbone instability in tokamaks using CRESCO

• Deeply trapped energetic electrons, strongly anisotropic distribution function;• the code predicts that the mode is driven by trapped electrons (the power

exchange occurs within the trapped/circulating boundary)• the region of maximum power exchange (red region) is in good agreement

with the assumption that the mode resonates at the precession frequency of the energetic electrons (black solid curve, = - 0.095A0).

Wave-particle power exchange

• The mode frequency chirps down during saturation• Energetic electron spatial distribution is strongly modified during saturation

Wtot m,n

tA0

/A0|

r/a

tA0=300 /A0|

r/a

tA0=900 /A0|

r/a

tA0=1248 Wtot m,n

tA0

r/a

nEe(r)