Computational studies on scattering of radio frequency waves by density filaments in fusion plasmas

Abstract

In modern magnetic fusion devices, such as tokamaks and stellarators, radio frequency (RF) waves are commonly used for plasma heating and current profile control, as well as for certain diagnostics. The frequencies of the RF waves range from ion cyclotron frequency to the electron cyclotron frequency. The RF waves are launched from structures, like waveguides and current straps, placed near the wall in a very low density, tenuous plasma region of a fusion device. The RF electromagnetic fields have to propagate through this scrape-off layer before coupling power into the core of the plasma. The scrape-off layer is characterized by turbulent plasmas fluctuations and by blobs and filaments. The variations in the edge density due to these fluctuations and filaments can affect the propagation characteristics of the RF waves-changes in density leading to regions with differing plasma permittivity. Analytical full-wave theories have shown that scattering by blobs and filaments can alter the RF power flow into the core of the plasma in a variety of ways, such as through reflection, refraction, diffraction, and shadowing [see, for example, A. K. Ram and K. Hizanidis, Phys. Plasmas 23, 022504-1-022504-17 (2016) and references therein]. There are changes in the wave vectors and the distribution of power-scattering leading to coupling of the incident RF wave to other plasma waves, side-scattering, surface waves, and fragmentation of the Poynting flux in the direction towards the core. However, these theoretical models are somewhat idealized. In particular, it is assumed that there is step-function discontinuity in the density between the plasma inside the filament and the background plasma. In this paper, results from numerical simulations of RF scattering by filaments using a commercial full-wave code are described. The filaments are taken to be cylindrical with the axis of the cylinder aligned along the direction of the ambient magnetic field. The plasma inside and outside the filament is assumed to be cold. There are three primary objectives of these studies. The first objective is to validate the numerical simulations by comparing with the analytical results for the same plasma descriptiona step-function discontinuity in density. A detailed comparison of the Poynting flux shows that the numerical simulations lead to the same results as those from the theoretical model. The second objective is to extend the simulations to take into account a smooth transition in density from the background plasma to the interior of the filament. The ensuing comparison shows that the deviations from the results of the theoretical model are quite small. The third objective is to consider the scattering process for situations well beyond a reasonable theoretical analysis. This includes scattering off multiple filaments with different densities and sizes. Simulations for these 2 complex arrangement of filaments show that, in spite of the obvious limitations, the essential physics of RF scattering is captured by the analytical theory for a sin...

Microwave beam broadening due to turbulent plasma density fluctuations within the limit of the Born approximation and beyond

“…The influence of edge plasma density fluctuations on injected microwaves has been studied with geometrical-optics tools in the 1980s in a fusion-relevant context when high-power microwave sources became available [11][12][13]. The topic has been brought back into focus by Tsironis in 2009 [14] which triggered a significant follow-up research looking into this problem using different techniques [15][16][17][18][19][20][21][22]. As a common agreement one can state that (a) substantial broadening of microwave beams due to edge plasma density perturbations is expected, (b) the situation in medium-sized tokamaks differs from large-scale tokamaks like ITER (due to differences in microwave frequency, size of turbulent structures, and propagation length), (c) further and more detailed studies with a minimum of simplifying assumptions are needed for the ITER scenarios which cannot be explored experimentally in today's tokamaks, and (d) the various numerical tools should be cross-benchmarked.…”

Millimeter-Wave Beam Scattering by Field-Aligned Blobs in Simple Magnetized Toroidal Plasmas

“…For blobs with a typical scale a such that λ/a ∼ 1 (as here), this approximation is no longer valid, and a more recent generalization of this approach [21] or a full-wave model is needed to capture the underlying physics [18]. We use 2D full-wave numerical simulations based on COMSOL MULTIPHYSICS [37,38]. Since the beam angular frequency ω satisfies ω ≫ j∂ t n e /n e j ≡ T −1 , one can show, by means of a two-scale expansion, that for t in a time interval ½τ; τ þ Δτ, Δτ ∼ T ≫ 2π/ω, the beam is well approximated by the solution of the cold plasma model with electron density frozen at a considered time τ.…”

Scattering of radio frequency waves by cylindrical filaments with general orientation relative to the magnetic field

“…For a cold plasma, the Faraday equation combined with the Ampere equation in the Fourier domain renders (see Ioannidis 2017): Note that Maxwell’s equations are expressed in cylindrical coordinates with respect to the flux tube, in order to maximally exploit the cylindrical geometry. It is assumed that the plasma equilibrium is time independent and the linearized perturbed electromagnetic fields have a time dependence of the form , with being the time.…”