Semi-analytical derivation of the 2D all-FLR ICRH wave equation as a high-order partial differential equation

For 1-dimensional applications, Bude's method [Bude et al, Plasma Phys. Control. Fusion, 63 (2021) 035014] has been shown to be capable of accurately solving the all-FLR (Finite Larmor Radius) integro-differential wave equation as a high-order differential equation allowing to represent all physically relevant (fast, slow and Bernstein) modes upon making a polynomial fit that is accurate in the relevant part of k-space. The adopted fit is superior to the Taylor series expansion traditionally adopted to truncate the series of finite Larmor radius corrections, while the differential rather than integro-differential approach allows for significant gain in required computational time when solving the wave equation. The method was originally proposed and successfully tested in 1D for radio frequency (RF) waves and in absence of the poloidal field [D. Van Eester & E. Lerche, Nucl. Fusion, 61 (2021) 016024]. In the present paper, the derivation of the extension of that procedure to 2D and for finite poloidal field - semi-analytically yielding the coefficients of the relevant high-order partial differential equation - is discussed in preparation of future numerical application

A crude model to study radio frequency induced density modification close to launchers

The interplay between radio frequency (RF) waves and the density is discussed by adopting the general framework of a 2-time-scale multi-fluid treatment, allowing to separate the dynamics on the RF time scale from that on the time scale on which macroscopic density and flows vary as a result of the presence of electromagnetic and/or electrostatic fields. The focus is on regions close to launchers where charge neutrality is incomplete and waves are commonly evanescent. The fast time scale dynamics influences the slow time scale behavior via quasilinear terms (the Ponderomotive force for the case of the equation of motion). Electrons and ions are treated on the same footing. Also, both fast and slow waves are retained in the wave description. Although this work is meant as a subtopic of a large study-the wave induced "convective cell" physics at hand is of a 2- or 3-dimensional nature while this paper limits itself to a single dimension-a few tentative examples are presented

Simulation of RF-fields in a fusion device

In this paper the problem of scattering off a fusion plasma is approached from the point of view of integral equations. Using the volume equivalence principle an integral equation is derived which describes the electromagnetic fields in a plasma. The equation is discretized with MoM using conforming basis functions. This reduces the problem to solving a dense matrix equation. This can be done iteratively. Each iteration can be sped up using FFTs

3-D discrete dispersion relation, numerical stability, and accuracy of the hybrid FDTD model for cold magnetized toroidal plasma

The Finite-Difference Time-Domain (FDTD) method in cylindrical coordinates is used to describe electromagnetic wave propagation in a cold magnetized plasma. This enables us to study curvature effects in toroidal plasma. We derive the discrete dispersion relation of this FDTD scheme and compare it with the exact solution. The accuracy analysis of the proposed method is presented. We also provide a stability proof for nonmagnetized uniform plasma, in which case the stability condition is the vacuum Courant condition. For magnetized cold plasma we investigate the stability condition numerically using the von Neumann method. We present some numerical examples which reproduce the dispersion relation, wave field structure and steady state condition for typical plasma modes

Simulations of combined ICRF and NBI heating for high fusion performance in JET

We report on simulations aimed at optimizing external heating using neutral beam injection (NBI) and radiofrequency waves in the ion cyclotron range of frequencies (ICRF) for high fusion yield in the JET tokamak. In this paper, D and DT plasmas are analyzed taking into account the NBI+RF synergy focusing on two different minority ICRF schemes, He and H, respectively. Our results show that by increasing external heating power to the maximum power available, the fusion neutron rate can be enhanced in D plasma by a factor of 2-3 with respect to our reference record D discharge. Regarding the DT plasma we present the external heating performance under the variation of key plasma parameters. We also study the impact of the effects of ICRH to the fusion yield and show that the ICRH power results in an enhanced fusion yield in the whole parameter space studied.This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Dani Gallart would like to express his gratitude to “La Caixa” for support of his PhD studies.Postprint (author's final draft

SOL RF physics modelling in Europe, in support of ICRF experiments

A European project was undertaken to improve the available SOL ICRF physics simulation tools and confront them with measurements. This paper first reviews code upgrades within the project. Using the multi-physics finite element solver COMSOL, the SSWICH code couples RF full-wave propagation with DC plasma biasing over “antenna-scale” 2D (toroidal/radial) domains, via non-linear RF and DC sheath boundary conditions (SBCs) applied at shaped plasma-facing boundaries. For the different modules and associated SBCs, more elaborate basic research in RF-sheath physics, SOL turbulent transport and applied mathematics, generally over smaller spatial scales, guides code improvement. The available simulation tools were applied to interpret experimental observations on various tokamaks. We focus on robust qualitative results common to several devices: the spatial distribution of RF-induced DC bias; left-right asymmetries over strap power unbalance; parametric dependence and antenna electrical tuning; DC SOL biasing far from the antennas, and RF-induced density modifications. From these results we try to identify the relevant physical ingredients necessary to reproduce the measurements, e.g. accurate radiated field maps from 3D antenna codes, spatial proximity effects from wave evanescence in the near RF field, or DC current transport. Pending issues towards quantitative predictions are also outlined