2D modeling of electromagnetic waves in cold plasmas

The consequences of sheath (rectified) electric fields, resulting from the different mobility of electrons and ions as a response to radio frequency (RF) fields, are a concern for RF antenna design as it can cause damage to antenna parts, limiters and other in-vessel components. As a first step to a more complete description, the usual cold plasma dielectric description has been adopted, and the density profile was assumed to be known as input. Ultimately, the relevant equations describing the wave-particle interaction both on the fast and slow timescale will need to be tackled but prior to doing so was felt as a necessity to get a feeling of the wave dynamics involved. Maxwell's equations are solved for a cold plasma in a 2D antenna box with strongly varying density profiles crossing also lower hybrid and ion-ion hybrid resonance layers. Numerical modelling quickly becomes demanding on computer power, since a fine grid spacing is required to capture the small wavelengths effects of strongly evanescent modes

A new approach to ICRF antennas modeling based on coupling the surface impedance matrix of the plasma to commercial antenna codes

Although modern commercial antenna codes can handle the complex 3D geometry of ion cyclotron resonance frequency (ICRF) antennas they still can not correctly describe hot fusion plasmas. In view of the impact the plasma has on the antenna-near fields and hence the need to use a sensible mock-up for the plasma behaviour, ICRF antenna modeling is currently mostly done by substituting the plasma with suitably chosen dielectric [1,2]. One of the limitations of this approach is the incorrect evaluation of the fields on the plasma surface. In this work a theoretical basis is given and a practical implementation is shown for coupling the spectral plasma surface impedance matrix [3] to modern commercial antenna codes for self-consistent correct calculation of the fields and scattering (‘S’) parameters of the ICRF antennas, hereby allowing to interface the antenna coupling code with a much more realistic model for capturing the subtleties of magnetized plasmas. The approach uses subsequent application of induction and uniqueness theorems of electromagnetism. In a first step the fields of the antenna in vacuum are computed. Once these incident fields are known one can use the surface impedance of the plasma to calculate the total electric and magnetic fields on the plasma surface and the power flow into the plasma. The evaluation of the S-parameters of the antenna requires a second step. We use the obtained tangential electric field on the plasma surface as a necessary boundary condition to solve the equivalent problem and find the Sparameters of the antenna and all the fields around it. This new approach is similar in physics potential to the TOPICA code [4] for its application to antenna design. Moreover, in the new approach it is possible to simulate the presence of cold low density plasma in the antenna box, which is needed for the correct evaluation of the fields and for addressing the sheath effect. The here presented, new approach is numerically more efficient and user-friendly than codes that attempt to directly incorporate the plasma response in the antenna computation. The paper also compares results obtained using the new approach with those obtained by other modeling methods. A new approach to the problem of the minimization of the toroidal electric field of the ICRH antennas is also proposed

Modelling RF sheath dynamics for fusion applications

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Modelling of sheath effects on radio-frequency antennas

The large voltages on radio frequency (RF) antennas that are used for heating of fusion plasmas, can create a thin sheath layer with largely negative potential and thus strong electric near-fields that attract and accelerate positively charged ions. The possible damage to antenna and in-vessel components due to local overheating and sputtering, is one of the main concerns for high power antennas in future fusion reactors. Good predictive simulation tools that take these sheath effects into account are still lacking. A practical implementation for modelling codes was proposed in [1], where sheath properties are introduced by means of a non-linear sheath boundary condition (SBC) on antenna surfaces. The sheath is represented by a scalar dielectric medium with relative permittivity sh = 1 + ish, i.e. a lossy vacuum layer. It is assumed that the electrons are inertia-free and therefore accelerated immediately into the metal surface, and that the power lost in the sheath is purely coming from ions accelerated in the rectified sheath potential. The sheath width (sh) is determined by the Child-Langmuir law, and the sheath potential depends on the electric field component normal to the surface. Continuity of the normal component of the displacement vector at the sheath plasma interface leads to the general description of the sheath as boundary condition Et = t ((sh/sh) n·pl·E) = t ((sh/sh) Dn), where Et is the tangential component of electric field and Dn the normal component of the displacement vector, all with respect to the sheath surface. For pl a cold plasma [2] description is used. Due to the Dn dependence of the sheath width the SBC is a non-linear equation, preventing a direct inversion of the underlying set of equations. A hybrid implementation of a SBC in the TOPICA code [3] was reported in [4], plasma properties were introduced for the calculation of the sheath parameters (sh, pl and sh), but the wave propagation was calculated using a vacuum Green's function. In the present paper a realistic finite density plasma is assumed to surround the antenna, and a cold plasma description assesses the impact of a magnetized dielectric medium on the antenna near-fields. The COMSOL Multiphysics [5] package was used for the RF modelling

PROPAGATIVE AND EVANESCENT BEHAVIOUR OF ELECTROMAGNETIC WAVES IN COLD PLASMAS

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ANSYS HFSS as a new numerical tool to study wave propagation inside anisotropic magnetized plasmas in the Ion Cylotron Range of Frequencies

The paper demonstrates the possibility to use ANSYS HFSS as a versatile simulating tool for antennas facing inhomogeneous anisotropic magnetized plasmas in the Ion Cyclotron Range of Frequencies (ICRF). The methodology used throughout the paper is first illustrated with a uniform plasma case. We then extend this method to 1D plasma density profiles where we perform a first benchmark against the ANTITER II code. The possibility to include more complex phenomena relevant to the ICRF field in future works like the lower hybrid resonance, the edge propagation of slow waves, sheaths and ponderomotive forces is also discussed. We finally present a 3D case for WEST and compare the radiation resistance calculated by the code to the experimental data. The main result of this paper - the implementation of a cold plasma medium in HFSS - is general and we hope it will also benefit to research fields besides controlled fusion.Comment: 15 pages, 14 figure

Impact of minority concentration on fundamental (H)D ICRF heating performance in JET-ILW

ITER will start its operation with non-activated hydrogen and helium plasmas at a reduced magnetic field of B-0 = 2.65 T. In hydrogen plasmas, the two ion cyclotron resonance frequency (ICRF) heating schemes available for central plasma heating (fundamental H majority and 2nd harmonic He-3 minority ICRF heating) are likely to suffer from relatively low RF wave absorption, as suggested by numerical modelling and confirmed by previous JET experiments conducted in conditions similar to those expected in ITER's initial phase. With He-4 plasmas, the commonly adopted fundamental H minority heating scheme will be used and its performance is expected to be much better. However, one important question that remains to be answered is whether increased levels of hydrogen (due to e. g. H pellet injection) jeopardize the high performance usually observed with this heating scheme, in particular in a full-metal environment. Recent JET experiments performed with the ITER-likewall shed some light onto this question and the main results concerning ICRF heating performance in L-mode discharges are summarized here

Modelling of the ICRF induced E x B convection in the scrape-off-layer of ASDEX Upgrade

In magnetic controlled fusion devices, plasma heating with radio-frequency (RF) waves in the ion cyclotron (IC) range of frequency relies on the electric field of the fast wave to heat the plasma. However, the slow wave can be generated parasitically. The electric field of the slow wave can induce large biased plasma potential (DC potential) through sheath rectification. The rapid variation of the rectified potential across the equilibrium magnetic field can cause significant convective transport (E x B drifts) in the scrape-off layer (SOL). In order to understand this phenomenon and reproduce the experiments, 3D realistic simulations are carried out with the 3D edge plasma fluid and kinetic neutral code EMC3-Eirene in ASDEX Upgrade. For this, we have added the prescribed drift terms to the EMC3 equations and verified the 3D code results against the analytical ones in cylindrical geometry. The edge plasma potential derived from the experiments is used to calculate the drift velocities, which are then treated as input fields in the code to obtain the final density distributions. Our simulation results are in good agreement with the experiments

3D simulations of gas puff effects on edge plasma and ICRF coupling in JET

Recent JET (ITER-Like Wall) experiments have shown that the fueling gas puffed from different locations of the vessel can result in different scrape-off layer (SOL) density profiles and therefore different radio frequency (RF) coupling. To reproduce the experimental observations, to understand the associated physics and to optimize the gas puff methods, we have carried out three-dimensional (3D) simulations with the EMC3-EIRENE code in JET-ILW including a realistic description of the vessel geometry and the gas injection modules (GIMs) configuration. Various gas puffing methods have been investigated, in which the location of gas fueling is the only variable parameter. The simulation results are in quantitative agreement with the experimental measurements. They confirm that compared to divertor gas fueling, mid-plane gas puffing increases the SOL density most significantly but locally, while top gas puffing increases it uniformly in toroidal direction but to a lower degree. Moreover, the present analysis corroborates the experimental findings that combined gas puff scenarios-based on distributed main chamber gas puffing-can be effective in increasing the RF coupling for multiple antennas simultaneously. The results indicate that the spreading of the gas, the local ionization and the transport of the ionized gas along the magnetic field lines connecting the local gas cloud in front of the GIMs to the antennas are responsible for the enhanced SOL density and thus the larger RF coupling