Scattering of ordinary-mode electromagnetic waves by density fluctuations in tokamaks

Abstract

Discussion and applications are presented for two approaches for estimating the effects of scattering of electromagnetic waves by turbulent density fluctuations in tokamaks. Ordinary-mode waves propagating nearly perpendicular to the equilibrium magnetic field are considered. The multiple-scattering approach provides analytic results for the angular and spatial spreading of a microwave beam by the turbulence. The single-scattering approach yields numerical results and is derived by a compact technique involving Wigner functions. Both approaches are applied to idealized tokamaks to clarify relationships between the approaches and to test limits of applicability of the multiple-scattering approach.

Millimeter-wave beam scattering and induced broadening by plasma turbulence in the TCV tokamak

“…This relation between the solution in free space and in a plasma slab is known [45]. The fact that the radiative transfer model (2) captures a diffractingbeam solution can be interesting on itself as it clearly shows that the wave kinetic equation properly accounts for diffraction effects, even though the underlying Hamiltonian structure is the same as in geometric optics [50][51][52].…”

The 3D study of X-mode reflectometry for density profile measurements on the JET tokamak

“…Ideally the propagation of an electromagnetic beam in a dielectric medium such as a plasma should be modelled through full-wave computations of the Maxwell equations [15]. To overcome the large computing times required by full-wave computations, ray-tracing techniques based on the WKB approximation have often been used in plasma physics [16][17][18]. Taking into account diffraction effects (which are neglected in ray-tracing calculations), alternative asymptotic methods have also been developed, such as the complex eikonal [19], beam-tracing [20,21] and quasi-optical Gaussian beam [22].…”

“…Although the exact expression (17) was used in the following, this shows that expression (20) (which avoids the use of the arctan function and therefore the need for phase jump corrections) could also be applied in our situation, where the phase variations across the antenna aperture are usually on the order of magnitude of a few radians. In the next section the multi-dimensional effects on reflectometry measurement of the density profile are studied comparing expression (17) with the 1D expression of the phase (which corresponds to the central ray):…”

“…This good agreement is validated by the phase shift distributions evaluated using both methods (depicted in figure 9). The phase versus frequency curves deduced from 1D and 3D expressions (17) and (21) in the case of the steep density profile are depicted in figure 10. In this work, it is assumed that the frequency of the first fringe and then the position of the n e = 0 layer are well determined so that only the phase shift in the plasma is represented in figure 10.…”

Analytical simulation of microwave reflectometry of a plasma cylinder

“…Most of the studies concentrated on the solution of the full-wave equation for microwave propagation in plasma, assuming either an analytical [8][9][10][11][12][13][14][15] or numerical approach. 16 -22 Besides the fullwave equation, a WKB approximation, 23 ray-tracing method, 24,25 and physical optics treatments 26,27 have proved to be useful for the understanding of particular problems of microwave reflectometry. The inherent advantage of a numerical approach is a complex accessible geometry, the potential capability to incorporate multidimensional effects, strong perturbation, magnetic shear, and temporal dependence of both the incident wave field and fluctuations.…”