Effect of ideal kink instabilities on particle redistribution H. E. Ferrari1,2,R. Farengo1, P. L. Garcia-Martinez2, M.-C. Firpo3, A. F. Lifschitz4 1 Comisión Nacional de Energía Atómica, Centro Atomico Bariloche, Bariloche, Argentina 2 CONICET, Centro Atómico Bariloche, Bariloche, Argentina 3 LPP, CNRS - Ecole Polytechnique, 91128 Palaiseau cedex, France 4 LOA, ENSTA, CNRS, Ecole Polytechnique, 91761 Palaiseau, France
Outline Motivation Model of the kink and code. Ni experiment. Integrable case with chaotic case. Results on Ni. W mitigation with a kink mode. Results on W. Future work.
Motivation Tokamaks with ITER like wall shows that W can migrate to the plasma core. Impurity accumulation in the plasma core can dilute the fuel and can degrade the performance due radiation losses. A method to mitigate this accumulation is necessary. The (1,1) kink instability appears as a dominant part in a sawtooth (q < 1) When q is slightly above 1 a marginally stable (1,1) kink can be sustained.
The model Equilibrium: analytical solution of Grad-Shafranov equation. Plus cylindrical kink perturbation (3 D fields). When it is possible experimental information is used. Displacement function, frequency of the modes. Electrical field from rotation ~ w and from the time dependence of growing part of the displacement function. Where B= B0 + δb E= - 1/c ξ/ t x B0, ideal Ohm's law. δb= rot (ξ x B0), ideal MHD.
The code We use the tracer approximation, means that the particles do not modify the fields. Full orbit code implemented in MPI to run in parallel CPU clusters and in CUDA C to run in GPU. The code is highly scalable since particles are independent. 2 d r d r m 2 =q B+ q E dt dt
The nickel experimet Experiment performed at JET, pulse number 21942, with a plasma current of 3 MA and a toroidal field of 2.8 T. The average electron density was 1.5 x 1019 m-3 6 MW of RF heating, central temperature 8 kev. The discharge was subjected to a sawtooth collapse, and the time crash was ~ 50 μs. A small amount of Ni was introduced into the plasma by evaporating a thin layer of Ni by laser ablation. Ni diffused and peaked at the surface q=1 before the sawtooth collapse. The sawtooth collapse moved the Ni to the central core (soft X ray measurement) The time scale for the Ni influx to the core was the same as for the flattening of the electron temperature ~50 μs
The nickel problem How does the Ni penetrates the core in a time scale of 50 μs? The same time scale the temperature collapses. Wesson argues that this fast Ni penetration can not be due to ergodization of the magnetic field. The reason being that thermal electrons will travel 2 km along the ergodized magnetic line in the crash time but a Ni ion only will travel a few meters. The time scales should be different. Transport in the Sawtooth Collapse, Wesson et al, Phys Rev. Lett. 79 5018-21
Poincaré plots: integrable and chaotic cases. Poincaré sections of B lines at the crash onset. (a) (1,1) displacement of 25 cm, and (b) (1,1) displacement of 25 cm and (2,1) displacement of 10 cm. Bt=2.8 T R= 3 m, a = 1 m
Ni ions trajectories during sawtooth collapse Trajectories between -50 μs and 150 μs. Typical orbits for the integrable case (a, b) and the stochastic case (c). Poloidal projection of the chaotic case is showed. As expected, if E=0 (a), the trajectories are not affected by the sawtooth collapse. If E is included (b) some particles are smoothly deflected towards the magnetic axis. In the chaotic case (c) the crash produces a large redistribution of particles. Some reach the magnetic axes and other are deflected towards the separatrix.
Ni migration during sawtooth collapse Ni ions initially in a ring around q=1 Only when the magnetic field lines displays chaos a significant fraction of Ni ions penetrates to the core in the crash time scale.
Can the electron temperature show a collective behaviour if the magnetic field lines are chaotic? Electrons are initially (t = -400μs) uniformly distributed inside the separatrix, T = 8 kev. The screenshots shows δt/t0 and start at the beginning of the crash(t = 0 μs).
Evolution of central electron temperature, central plasma ion density and central Ni density The electron temperature and the ion densities (Ni and H+) evolve in the same time scale
Summary: Ni ions numerical simulations When an integrable model is used for the magnetic field lines in the sawtooth collapse most of Ni ions remain close to q=1. Conversely, when modes of different helicities and suficiently large amplitudes are included to produce stochasticity close to q=1, Ni ions can reach the core. Simulations show that the electron temperature and the plasma density evolve in the same time scale. Do to their mass difference the electron motion is governed by the magnetic field while the ion motion is more affected by the electric force and the E x B drift. Due to Faraday's law both fields acts on the same time scale and are controlled by the electrons.
Mitigating W accumulation In an experiment performed at ASDEX U by Sertoli et al. Nuc. Fusion 55 (2015) 113029 the interplay between central ECRH and (1,1) MHD activity in mitigating W accumulations is investigated. Lower single null discharge with Ip= 1 MA, Bt= -2.5 T, externally heated with NBI and ECRH. H- mode. The heating set up allows for modification of the sawtooth period and allows MHD activity in between sawtooth crashes. We are interested in one part of the results of this paper. W profiles are measured just after the crash and just before the next crash. The application of ECRH for the mitigation of W accumulation at AUG is usually accompanied by long-lasting (m,n)=(1,1) MHD activity in between sawtooth crashed. Can our model reproduce this result?
Mitigating W accumulation The ECCD is applied at ρinv W density profiles. Black is after crash at t=4.884s. Red is before next crash at 4.965. There is a (1,1) kink with f = 10 khz. The kink is rotating with the plasma. Extracted from Interplay between central ECRH and saturated (m,n)= (1,1) MHD activity in mitigating tungsten accumulation at ASDEX Upgrade Sertoli et al, Nuc. Fusion 55 (2015) 113029
Modelling the experiment. Frequency of the (1,1) mode f = 10 khz. Maximum displacement? Particles uniformly distributed in a toroid of minor radius ~0.6. Initial velocity distribution: isotropic distribution? Or rotating with f? The thermal velocity of W ions (4.5 x 104 m/s ) < rotating velocity of the plasma (1.03 x 105 m/s). The thermal velocity of D is (4.37 x 105 m/s) >> rotating velocity of the plasma.
Modelling the experiment. When velocity is isotropically distributed the kink does not affect the radial particle distribution. Constructing an initial distribution rotating at a given frequency. Ex: pitch = 1. Particles poloidaly distributed in a radius r/a < 0.6 and all around the torus Distribution of frequencies, for E= 10.757 kev the W ions rotates on average with f~ 10 khz
Density W profile under the action of a saturated kink
W 2 D profile under the action of a saturated kink When the W rotates with a frequency close of the the frequency of the (1,1) mode the W is expelled from the plasma core. E = 10.757 kev ω = 8.81 khz
The depletion of W core ions depends on the mode frequency This depends on the energy of the particles (or the rotating frequency). Fixed frequency, ω = 8.81 khz Fixed Energy, E = 10.757 kev
Results Preliminary results show that W can be expelled from the plasma core if a saturated kink is present. The W ions should be rotating with a frequency close to the mode frequency. The initial distribution of W is partially recovered if the kink in shut off.
Future work Resistive kink. Realistic plasma cross section. Realistic initial W velocity distribution.
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