A comprehensive description of methods, suitable for solving the kinetic equation for fast ions and impurity species in tokamak plasmas using 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. methods. In ASCOT4, we follow recent developments regarding these issues and treat the collisional and Hamiltonian parts consistently [7,8].

Abstract. Collective Thomson scattering (CTS) experiments were carried out at ASDEX Upgrade to measure the one-dimensional velocity distribution functions of fast ion populations. These measurements are compared with simulations using the codes TRANSP/NUBEAM and ASCOT for two different neutral beam injection (NBI) configurations: two NBI sources and only one NBI source. The measured CTS spectra as well as the inferred one-dimensional fast ion velocity distribution functions are clearly asymmetric as a consequence of the anisotropy of the beam ion populations and the selected geometry of the experiment. As expected, the one-beam configuration can clearly be distinguished from the two-beam configuration. The fast ion population is smaller and the asymmetry is less pronounced for the one-beam configuration. Salient features of the numerical simulation results agree with the CTS measurements while quantitative discrepancies in absolute values and gradients are found.

We present an ultrafast neural network (NN) model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 300 million flux calculations of the quasilinear gyrokinetic transport model QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modelling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order 1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study of density buildup following the L-H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modelling is a promising route towards enabling accurate and fast tokamak scenario optimization, Uncertainty Quantification, and control applications.

The wall loads due to fusion alphas as well as neutral beam injection- and ICRF-generated fast ions were simulated for ITER reference scenario-2 and scenario-4 including the effects of ferritic inserts (FIs), test blanket modules (TBMs), and 3D wall with two limiter structures. The simulations were carried out using the Monte Carlo guiding-centre orbit-following code ASCOT. The FIs were found very effective in ameliorating the detrimental effects of the toroidal ripple: the fast ion wall loads are reduced practically to their negligible axisymmetric level. The thermonuclear alpha particles overwhelmingly dominate the wall power flux. In scenario-4 practically all the power goes to the limiters, while in scenario-2 the load is fairly evenly divided between the divertor and the limiter, with hardly any power flux to other components in the first wall. This is opposite to earlier results, where hot spots were observed with 2D wall (Tobita et al 2003 Fusion Eng. Des. 65 561–8). In contrast, uncompensated ripple leads to unacceptable peak power fluxes of 0.5 MW m−2 in scenario-2 and 1 MW m−2 in scenario-4, with practically all power hitting the limiters and substantial flux arriving even at the unprotected first wall components. The local TBM structures were found to perturb the magnetic field structure globally and lead to increased wall loads. However, the TBM simulation results overestimate the TBM contribution due to an over-simplification in the vacuum field. Therefore the TBM results should be considered as an upper limit.

A strong toroidal rotation braking has been observed in plasmas with application of an n = 1 magnetic perturbation field on the JET tokamak. Calculation results from the momentum transport analysis show that the torque induced by the n = 1 perturbation field has a global profile. The maximal value of this torque is at the plasma core region (ρ < 0.4) and it is about half of the neutral beam injection torque. The calculation shows that the plasma is mainly in the ν √ ν regime in the plasma core, but it is close to the transition between the 1/ν and ν √ ν regimes. The neoclassical toroidal viscosity (NTV) torque in the 1/ν and ν √ ν regimes is calculated. The observed torque is of a magnitude in between that of the NTV torque in the 1/ν and ν √ ν regimes. The NTV torque in the ν √ ν regimes is enhanced using the Lagrangian variation of the magnetic field strength. However, it is still smaller than the observed torque by one order of magnitude.

A power-balance model, with radiation losses from impurities and neutrals, gives a unified description of the density limit (DL) of the stellarator, the L-mode tokamak, and the reversed field pinch (RFP). The model predicts a Sudo-like scaling for the stellarator, a Greenwald-like scaling, , for the RFP and the ohmic tokamak, a mixed scaling, , for the additionally heated L-mode tokamak. In a previous paper (Zanca et al 2017 Nucl. Fusion 57 056010) the model was compared with ohmic tokamak, RFP and stellarator experiments. Here, we address the issue of the DL dependence on heating power in the L-mode tokamak. Experimental data from high-density disrupted L-mode discharges performed at JET, as well as in other machines, are taken as a term of comparison. The model fits the observed maximum densities better than the pure Greenwald limit.

Tokamak Energy Ltd, UK, is developing spherical tokamaks using high temperature superconductor magnets as a possible route to fusion power using relatively small devices. We present an overview of the development programme including details of the enabling technologies, the key modelling methods and results, and the remaining challenges on the path to compact fusion.

Neutral beam injection (NBI) will be one of the main sources of heating and non-inductive current drive in ITER. Due to high level of injected power the beam induced heat loads present a potential threat to the integrity of the first wall of the device, particularly in the presence of non-axisymmetric perturbations of the magnetic field. Neutral beam injection can also destabilize Alfvén eigenmodes and energetic particle modes, and act as a source of plasma rotation. Therefore, reliable and accurate simulation of NBI is important for making predictions for ITER, as well as for any other current or future fusion device. This paper introduces a new beamlet-based neutral beam ionization model called BBNBI. It takes into account the fine structure of the injector, follows the injected neutrals until ionization, and generates a source ensemble of ionized NBI test particles for slowing down calculations. BBNBI can be used as a stand-alone model but together with the particle following code ASCOT it forms a complete and sophisticated tool for simulating neutral beam injection. The test particle ensembles from BBNBI are found to agree well with those produced by PENCIL for JET, and those produced by NUBEAM both for JET and ASDEX Upgrade plasmas. The first comprehensive comparisons of beam slowing down profiles of interest from BBNBI+ASCOT with results from PENCIL and NUBEAM/TRANSP, for both JET and AUG, are presented. It is shown that, for an axisymmetric plasma, BBNBI+ASCOT and NUBEAM agree remarkably well. Together with earlier 3D studies, these results further validate using BBNBI+ASCOT also for studying phenomena that require particle following in a truly three-dimensional geometry.