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 Alfvén 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. © 2014 Elsevier B.V. All rights reserved.

This paper explains how to obtain the distribution function of minority ions in tokamak plasmas using the Monte Carlo method. Since the emphasis is on energetic ions, the guiding-center transformation is outlined, including also the transformation of the collision operator. Even within the guiding-center formalism, the fast particle simulations can still be very CPU intensive and, therefore, we introduce the reader also to the world of high-performance computing. The paper is concluded with a few examples where the presented method has been applied.

The effect of ASDEX Upgrade (AUG) edge localized mode (ELM)-mitigation coils on fast ion wall loads was studied with the fast particle following Monte Carlo code ASCOT. Neutral beam injected particles were simulated in two AUG discharges both in the presence and in the absence of the magnetic field perturbation induced by the eight newly installed in-vessel coils. In one of the discharges (#26476) beams were applied individually, making it a useful basis for investigating the effect of the coils on different beams. However, no ELM mitigation was observed in #26476, probably due to the low plasma density. Therefore, another discharge (#26895) demonstrating clear ELM mitigation was also studied. The magnetic perturbation due to the in-vessel coils has a significant effect on the fast particle confinement, but only when total magnetic field, B tot, is low. When B tot was high, the perturbation did not increase the losses, but merely resulted in redistribution of the wall power loads. Hence, it seems to be possible to achieve ELM mitigation using in-vessel coils, while still avoiding increased fast ion losses, by simply using a strong B tot. Preliminary comparisons between simulated and experimental fast ion lost detector signals show a reasonable correspondence. © 2012 IAEA, Vienna.

A comprehensive suite of diagnostics has allowed detailed measurements of the Alfvén eigenmode (AE) spatial structure and subsequent fast-ion transport in the ASDEX Upgrade (AUG) tokamak [1]. Reversed shear Alfvén eigenmodes (RSAEs) and toroidal induced Alfvén eigenmodes (TAEs) have been driven unstable by fast ions from ICRH as well as NBI origin. In ICRF heated plasmas, diffusive and convective fast-ion losses induced by AEs have been characterized in fast-ion phase space. While single RSAEs and TAEs eject resonant fast ions in a convective process directly proportional to the fluctuation amplitude, δB/B, the overlapping of multiple RSAE and TAE spatial structures and wave-particle resonances leads to a large diffusive loss, scaling as (δB/B)2. In beam heated discharges, coherent fast-ion losses have been observed primarily due to TAEs. Core localized, low amplitude NBI driven RSAEs have not been observed to cause significant coherent fast-ion losses. The temporal evolution of the confined fast-ion profile in the presence of RSAEs and TAEs has been monitored with high spatial and temporal resolution. A large drop in the central fast-ion density due to many RSAEs has been observed as qmin passes through an integer. The AE radial and poloidal structures have been obtained with unprecedented details using a fast SXR as well as 1D and 2D ECE radiometers. GOURDON and HAGIS simulations have been performed to identify the orbit topology of the escaping ions and study the transport mechanisms. Both passing and trapped ions are strongly redistributed by AEs. © 2011 IAEA, Vienna.