Lagrangian particle model for 3D simulation of pellets and SPI fragments in tokamaks

Abstract

A 3D numerical model for the ablation of pellets and shattered pellet injection fragments in tokamaks in the plasma disruption mitigation and fueling parameter space has been developed based on the Lagrangian particle (LP) method Samulyak et al (2018 J. Comput. Phys. 362 1–19). The pellet code implements the low magnetic Reynolds number MHD equations, kinetic models for the electronic heating, a pellet surface ablation model, an equation of state that supports multiple ionization states, radiation, and a model for grad-B drift of the ablated material across the magnetic field. The LP algorithm is highly adaptive, capable of simulating a large number of fragments in 3D while eliminating numerical difficulties of dealing with the tokamak background plasma. The code has achieved good agreement with theory for spherically symmetric ablation flows. Axisymmetric simulations of neon and deuterium pellets in magnetic fields ranging from 1 to 6 Tesla have been compared with previous simulations using the FronTier code, and very good agreement has also been obtained. The main physics contribution of the paper is a detailed study of the influence of 3D effects, in particular grad-B drift, on pellet ablation rates and properties of ablation clouds. Smaller reductions of ablation rates in magnetic fields compared to axially symmetric simulations have been demonstrated because the ablated material is not confined to narrowing channels in the presence of grad-B drift. Contribution of various factors in the grad-B drift model has also been quantified.

Pellet Core Fueling in Tokamaks, Stellarators and Reversed Field Pinches

“…Despite the numerous approximations, this scaling was confirmed for Maxwellian plasmas by more sophisticated models taking into account the other shielding mechanisms and was validated over a large number of experiments in several machines ( [2,3] and references therein, [8,9]).…”

Massively-Parallel Lagrangian Particle Code and Applications

“…where d/dt is the Lagrangian time derivative, u, ρ and e are the velocity, density and specific internal energy, respectively, and P is the pressure. In addition, various extensions of the system (1 -4), including magnetohydrodynamic equations in the low Magnetic Reynolds number approximation [11] and granular flow equations [12], have been implemented. The LP method also implements various models for the equation of state (4) describing gases, plasmas, and liquids.…”

“…The Lagrangian Particle code has been extensively verified and validated using both classical hydrodynamic problems [9] and applied problems of plasma physics relevant to thermonuclear fusion [11,16]. Since the main novelty of the algorithmic part of this paper is the parallelization of the Lagrangian particle code for distributed memory supercomputers, it is sufficient to show that the parallel code gives the same accuracy as the original code for some typical hydrodynamic problems.…”

“…The fraction of electrons that reach the pellet surface is responsible for the pellet ablation rate. In our recent works, 2D axisymmetric [18] and full 3D simulations [11,16] of ablating pellets in tokamaks have been performed, and the influence of tokamak plasma conditions, magnetic field and 3D plasma drift effects on their ablation rates have been studied and compared with the available experimental data. The pellet ablation problem is intrinsically multiscale.…”

“…The LP method is second-order accurate in space and time and it is extendable to higher order accuracy. In addition to compressible hydrodynamics, the LP code implements equations of low magnetic Reynolds number magnetohydrodynamics [11] and granular flow equations [12].…”