A fast tool for ICRH + NBI modelling within the EU-IM framework

Abstract

Most if not all tokamak heating scenarios involve multiple ion populations being heated simultaneously. To allow the simulation of various aspects of physics dynamics determining the characteristics of operational scenarios in a flexible way, speedy yet sufficiently accurate models are needed, and they should be connected to each other via a ‘backbone’. Under the umbrella of EUROfusion's Integrated Modelling efforts, such a structure is provided. The present paper focuses on one physics aspect: auxiliary heating. After solving the wave equation or beam source equation, this requires solving a set of coupled Fokker–Planck equations for the various populations involved. The adopted modules – enabling accounting for the Coulomb collisional interaction of several non-Maxwellian (minority, majority and beam) populations – are discussed and a practical example of their use is provided: the JET ‘baseline’ scenario heating a minority of ${}^3\textrm {He}$ ions in a balanced D $+$ T mix heated by D and T neutral beams.

Simulation of heating and current drive sources for scenarios of the ITER research plan

“…For the specific example at hand, this is the case: the neutron rate associated with 9 Be-p reactions is reduced by an order of magnitude because the wave power is spread over a wider region, yielding lower tail energies and hence less reactions. This effect was already demonstrated in [6] and has recently been confirmed by simulations [30] using the FUSREAC code for calculating nuclear reactions [18,31].…”

“…All these steps are illustrated in figure 2. By default, the H & CD workflow first calculates all the sources [10] L I O N [ 14] NEMO [22] SPOT (α) GRAYSCALE [11] P I O N[ 15] TORBEAM [12] T OM CA T[16] Fokker-Planck calculation ASCOT [17] A S C O T A S C O T FOPLA [18] FOPLA FOPLA PION RISK [23] SPOT SPOT [19] SPOT STIXREDIST [20] (i.e. the wave, NBI and nuclear sources), then it solves the Fokker-Planck equations for each of these sources, and next merges them all together before filling the core sources and profiles for the solution of the transport equations.…”

“…which is the loss term introduced to achieve a steady-state solution of the Fokker-Planck equation-to compensate the source term-where τ E and τ P are the energy and particle loss times respectively. D vv,coll and F v,coll are coefficients of the collision operator for which the complete expressions can be found in Van Eester et al [18]. For a given ion species and given magnetic surface, K RF is adjusted to ensure that the RF power density corresponding to the distribution obtained solving the Fokker-Planck equation is equal to the externally imposed RF power density.…”

European transport simulator modeling of JET-ILW baseline plasmas: predictive code validation and DTE2 predictions

“…In the present paper, the emphasis is on auxiliary heating and more particularly on the impact of NBI/ICRH synergy on fusion performance. Two 1D Fokker-Planck solvers for arbitrary distribution functions have recently been implemented in ETS: StixRedist [16] and FoPla [17]. The former allows one to obtain distribution functions for non-beam populations heated at any cyclotron harmonic while interacting with multiple non-Maxwellian distributions via Coulomb collisions.…”

“…The neutron rate is given by a new EU-ITM module called 'FusReac', which for arbitrary 1D isotropic distribution functions of the various species computes the reactivities using DD, DT and TT cross-sections. The FusReac module is based on the cross-sections as provided for the relevant reactions by Bosch and Hale [30] accounting for the three components of the relative velocity but assuming isotropic distribution functions; some details can be found in [17]. Table 2 provides an example.…”