A. Snicker

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.

Simulations of fast ion wall loads in ASDEX Upgrade in the presence of magnetic perturbations due to ELM-mitigation coils

In this work the effect of the recently installed in-vessel coils (a.k.a. ELM mitigation coils) on the confinement and losses of fast particles in ASDEX Upgrade (AUG) is studied with the orbit-following Monte Carlo code ASCOT [1]. Since large Edge Localized Modes (ELMs) could be extremely detrimental to the first wall of ITER, a means to mitigate them is needed. Magnetic field perturbations have been suggested to reduce the size and increase the frequency of ELMs [2] and, to this end, ELM mitigation coils are also envisaged for ITER. In-vessel coils create a non-axisymmetric magnetic perturbation. While such a perturbation has been found to trigger weak and frequent ELMs, it could have a harmful effect on fast ion confinement. In fact, when the effect of a local magnetic perturbation due to test blanket modules (TBMs) was included in ASCOT simulations, fast ion losses were found to increase and become more localized [1]. To investigate the effect of ELM mitigation coils, eight coils were recently installed on ASDEX Upgrade. The preliminary results using the coils [3] have been encouraging; ELMs are succesfully mitigated. We have now simulated the fast ions produced by external heating, namely neutral beam injected (NBI) and radio wave heated (ICRH) particles, in AUG plasmas with the in-vessel coils turned on and off. ASCOT is able to take into account the full 3D structures of both the magnetic field and the first wall of the device. Thus it can give realistic estimates of the effect of the coils on fast particle power loads on the first wall elements and reveal possible changes in the fast ion population. According to the simulations in-vessel coils do not produce hotspots, but a slightly increased level of losses exhibiting an n = 2 structure. The simulations will be compared to FILD measurements during spring 2011.

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.

Orbit-following fusion alpha wall load simulation for ITER scenario 4 including full orbit effects

A large population of fusion-born alphas present in ITER scenario 4 is a potential risk to the first wall elements. In this study, the ITER scenario 4 alpha wall loads are estimated using the Monte Carlo orbit-following code ASCOT. To ensure realistic wall load profiles, we have adopted three different methods to record the wall collision points: (i) pure guiding centre tracking, (ii) guiding centre tracking away from the wall and gyro-orbit following close to it and (iii) pure gyro-orbit following. It is found that pure gyro-orbit simulation produces an averaged wall load roughly three times as large as the pure guiding centre wall load while the peak power loads differ roughly by a factor of five.

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.

Conceptual design of the ITER fast-ion loss detector

A conceptual design of a reciprocating fast-ion loss detector for ITER has been developed and is presented here. Fast-ion orbit simulations in a 3D magnetic equilibrium and up-to-date first wall have been carried out to revise the measurement requirements for the lost alpha monitor in ITER. In agreement with recent observations, the simulations presented here suggest that a pitch-angle resolution of ∼5° might be necessary to identify the loss mechanisms. Synthetic measurements including realistic lost alpha-particle as well as neutron and gamma fluxes predict scintillator signal-to-noise levels measurable with standard light acquisition systems with the detector aperture at ∼11 cm outside of the diagnostic first wall. At measurement position, heat load on detector head is comparable to that in present devices.

ITER fast ion confinement in the presence of the European test blanket module

This paper addresses the confinement of thermonuclear alpha particles and neutral beam injected deuterons in the 15 MA Q = 10 inductive scenario in the presence of the magnetic perturbation caused by the helium cooled pebble bed test blanket module using the vacuum approximation. Both the flat top phase and plasma ramp-up are studied. The transport of fast ions is calculated using the Monte Carlo guiding center orbit-following code ASCOT. A detailed three-dimensional wall, derived from the ITER blanket module CAD data, is used for evaluating the fast ion wall loads. The effect of the test blanket module is studied for both overall confinement and possible hot spots. The study indicates that the test blanket modules do not significantly deteriorate the fast ion confinement.

Effect of plasma response on the fast ion losses due to ELM control coils in ITER

Mitigating edge localized modes (ELMs) with resonant magnetic perturbations (RMPs) can increase energetic particle losses and resulting wall loads, which have previously been studied in the vacuum approximation. This paper presents recent results of fusion alpha and NBI ion losses in the ITER baseline scenario modelled with the Monte Carlo orbit following code ASCOT in a realistic magnetic field including the effect of the plasma response. The response was found to reduce alpha particle losses but increase NBI losses, with up to 4.2% of the injected power being lost. Additionally, some of the load in the divertor was found to be shifted away from the target plates toward the divertor dome.

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.