Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

Abstract

In tokamak fusion plasmas, coherent fluctuations in the form of blobs or filaments are routinely observed in the scrape-off layer. Radio frequency (RF) electromagnetic waves, excited by antenna structures placed near the wall of a tokamak, have to propagate through the scrape-off layer before reaching the core of the plasma. While the effect of fluctuations on the properties of RF waves has not been quantified experimentally, it is of interest to carry out a theoretical study to determine if fluctuations can affect the propagation characteristics of RF waves. Usually, the difference between the plasma density inside the filament and the background plasma density is sizable; the ratio of the density difference to the background density being of order one. Generally, this precludes the use of geometrical optics in determining the effect of fluctuations since the relevant ratio has to be much less than one; typically, of the order of 10% or less. In this paper, a full-wave, analytical model is developed for the scattering of a RF plane wave by a cylindrical plasma filament. It is assumed that the plasma inside and outside the filament is cold and uniform, and that the major axis of the filament is aligned along the toroidal magnetic field. The ratio of the density inside the filament to the density of the background plasma is not restricted. The theoretical framework applies to the scattering of any cold plasma wave. In order to satisfy the boundary conditions at the interface between the filament and the background plasma, the electromagnetic fields inside and outside the filament need to have the same k ∥ , the wave vector parallel to the ambient magnetic field, as the incident plane wave. Consequently, in contrast to the scattering of a RF wave by a spherical blob [A. K. Ram, K. Hizanidis, and Y. Kominis, Phys. Plasmas 20, 056110-1-056110-10 (2013)], the scattering by a field-aligned filament does not broaden the k ∥ spectrum. However, the filament induces side-scattering leading to surface waves, and can also couple some power to the cold plasma wave different from the incident wave. The changes induced by a filament in the propagation of electron cyclotron waves and lower hybrid waves are illustrated by numerical results displaying the properties of the Poynting vector. The Poynting flux in the wake of the filament, and directed towards the core of the plasma, develops a spatial structure due to diffraction and shadowing. Thus, the fluctuations affect the uniformity of power flow into the plasma.

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.…”

Filament-assisted mode conversion in magnetized plasmas

“…In experimental magnetic confinement fusion devices, density filaments occur [1][2][3][4][5][6] , with which electromagnetic waves intended to heat the plasma interact. Such interactions are usually studied from the point of view of wave scattering 1,[7][8][9] : one wishes to ensure that not too much useful power will be scattered in unforeseen directions by the turbulent edge plasma. The possibility of mode conversion at density filaments in the edge plasma was briefly raised in 1 , and is the central topic of this paper.…”

“…We must impose, on every azimuthal mode m in the cylindrical coordinate system, four boundary conditions at r = r F : the tangential components of both the electric field and the magnetic field should be continuous 8…”

The deteriorating effect of plasma density fluctuations on microwave beam quality

“…In the 1980s high-power microwave sources became available and the interaction of injected microwaves and plasma edge density fluctuations in fusion-relevant scenarios was studied with geometrical-optics tools [14,15]. Due to the potentially negative consequences for NTM stabilization in ITER, this topic has gained significant traction since 2009 [16][17][18][19][20][21]. tion and the fluid equation of motion of the electrons on a 2D Cartesian grid.…”