Eero Hirvijoki

ASCOT: Solving the kinetic equation of minority particle species in tokamak plasmas

Abstract A comprehensive description of methods, suitable for solving the kinetic equation for fast ions and impurity species in tokamak plasmas using a Monte Carlo approach, is presented. The described methods include Hamiltonian orbit-following in particle and guiding center phase space, test particle or guiding center solution of the kinetic equation applying stochastic differential equations in the presence of Coulomb collisions, neoclassical tearing modes and Alfven eigenmodes as electromagnetic perturbations relevant to fast ions, together with plasma flow and atomic reactions relevant to impurity studies. Applying the methods, a complete reimplementation of the well-established minority species code ASCOT is carried out as a response both to the increase in computing power during the last twenty years and to the weakly structured growth of the code, which has made implementation of additional models impractical. Also, a benchmark between the previous code and the reimplementation is accomplished, showing good agreement between the codes.

Monte Carlo implementation of a guiding-center Fokker-Planck kinetic equation

A Monte Carlo method for the collisional guiding-center Fokker-Planck kinetic equation is derived in the five-dimensional guiding-center phase space, where the effects of magnetic drifts due to the background magnetic field nonuniformity are included. It is shown that, in the limit of a homogeneous magnetic field, our guiding-center Monte Carlo collision operator reduces to the guiding-center Monte Carlo Coulomb operator previously derived by Xu and Rosenbluth [Phys. Fluids B 3, 627 (1991)]. Applications of the present work will focus on the collisional transport of energetic ions in complex nonuniform magnetized plasmas in the large mean-free-path (collisionless) limit, where magnetic drifts must be retained.

The effect of non-axisymmetric wall geometry on 13C transport in ASDEX Upgrade

We present the first results of 3D simulations of global 13C transport in ASDEX Upgrade (AUG) indicating that the deposition profile of 13C exhibits toroidal asymmetry in the main chamber.In 2007, the migration of carbon in AUG was studied with a methane (13CH4) injection experiment (A. Hakola et al and the ASDEX Upgrade Team 2010 Plasma Phys. Control. Fusion 52 065006). The total amount of deposited 13C was estimated by assuming toroidally symmetric deposition. Remarkably, the total number of deposited atoms was observed to be less than 10% of the number of injected atoms.The experiment has been simulated with the 3D orbit-following Monte Carlo code ASCOT using both a realistic 3D wall geometry of AUG and a 3D magnetic field with toroidal ripple. The simulations indicate that the non-axisymmetric wall geometry causes notable toroidal asymmetry in the deposition profile in the outer (low-field side) midplane region which can provide a partial explanation for the missing carbon inferred from post-mortem analysis of 13C deposition.

Fast ion power loads on ITER first wall structures in the presence of NTMs and microturbulence

The level and distribution of the wall power flux of energetic ions in ITER have to be known accurately in order to ensure the integrity of the first wall. Until now, most quantitative estimates have been based on the assumption that fast ion transport is dictated by neoclassical effects only. However, in ITER, the fast ion distribution is likely to be affected by various MHD effects and probably also by microturbulence. We have now upgraded our orbit-following Monte Carlo code ASCOT so that it has simple, theory-based models for neoclassical tearing mode (NTM)-type islands as well as for turbulent diffusion. ASCOT also allows for full-orbit following, which is important close to the material surfaces and, possibly, also when strong toroidal inhomogeneities are present in the magnetic field. Here we introduce the new models, preliminary results obtained with them, and how these models could be made more realistic in the future. The simulations are carried out for thermonuclear alpha particles in ITER scenario 2 plasma, because we consider this combination to be most critical for the successful operation of ITER. Neither the turbulent transport nor NTM-type islands are found to introduce alarming changes in the wall loads. However, at this stage it was not possible to combine the island structures with the non-axisymmetric magnetic field of ITER, and it remains to be seen what the combined effect of drift islands together with the toroidal ripple and local field aberrations, such as those due to test blanket modules and resonant magnetic perturbations will be.

Power loads to ITER first wall structures due to fusion alphas in a non-axisymmetric magnetic field including the presence of MHD modes

We use the orbit-following Monte Carlo code ASCOT to calculate the wall power loads in ITER caused by fusion alphas. The simulations are carried out for a realistic 3D magnetic field that includes the effect of both ferritic inserts and the test blanket modules, both causing aberrations in the magnetic field structure, particularly at the edge. In addition to an magnetohydrodynamic (MHD)-quiescent plasma we now also address the power loads in the presence of relevant MHD events: both neoclassical tearing modes (NTMs) and toroidal Alfven eigenmodes (TAEs) are included in the simulation model. In the case of NTMs, the total power load to the wall is found to depend on the perturbation amplitude. Even with the strongest perturbation, however, the power load density stays within the design limit of the ITER wall materials. In the case of TAEs, while the wall power load density stays at the MHD-quiescent level, significant redistribution of alphas inside the plasma was observed. This was also found to affect the alpha heating profile.

ITER edge-localized modes control coils: the effect on fast ion losses and edge confinement properties

The magnetic perturbations due to in-vessel coils, foreseen to mitigate edge-localized modes (ELMs) in ITER, could also compromise the confinement of energetic ions. We simulate the losses of fusion alpha particles and neutral beam injection-generated fast ions in ITER under the influence of the 3D perturbations caused by toroidal field coils, ferritic inserts, test blanket modules and ELM control coils (ECCs) with the ASCOT code. The ECCs are found to stochastize the magnetic field deep inside the pedestal in the 15 MA inductive reference operating scenario. Such a field is found insufficient to confine not only the fast but also the thermal ion population, leading to a strongly reduced fast ion source in the edge. Therefore, even with a stochastic edge, no high fast ion power loads are expected. However, the plasma response has not yet been included in the calculation of ITER magnetic background data, and it is probable that the perturbation is currently overestimated.

Alfvén Eigenmodes and Neoclassical tearing modes for orbit-following implementations

Abstract Magnetohydrodynamical instabilities such as Alfven Eigenmodes and Neoclassical tearing modes redistribute energetic particles and, thus, potentially endanger the confinement of, e.g., fusion born alphas in Tokamaks. The orbit-following studies so far have been restricted either to time-independent approximation of the rotating modes, or to an axisymmetric magnetic field, which is an assumption severely compromised in ITER. In this paper we extend the previous work to accommodate time-dependent modes in non-axisymmetric magnetic fields.

Monte Carlo diffusion operator for anomalous radial transport in tokamaks

We have revised the numerical model for anomalous diffusion across the magnetic surfaces in tokamaks, originally derived in the cylindrical limit, i.e., at very large aspect ratio values, and assuming circular flux surfaces. The new model removes these restrictions and properly accounts for the toroidal geometry even in the limit of very tight aspect ratio, and is applicable with flux surfaces of arbitrary shape.