ECRH power deposition from a quasi-optical point of view

Abstract

A quasi-optical description of the propagation and damping of the slowly varying wave amplitude across an arbitrary electron cyclotron wave beam is presented. This model goes well beyond those implemented in existing beam tracing codes, which typically require the spatial inhomogeneity across the wave beam to be small. The present model allows an accurate description of the wave beam evolution in the region of electron cyclotron power deposition, where the latter condition is quite generally broken. The additional physical effects from spatial inhomogeneity and dispersion included in the quasi-optical model are discussed in relation to their consequences for the power deposition profile. Quite generally, a broader power deposition profile is obtained in the quasi-optical calculations. The importance of these effects is analysed in a number of scans varying the injection geometry for typical conditions in both the ITER and the TEXTOR tokamak. Optimization of the power deposition profile towards a minimal width is found to require a focused wave beam with a waist of typically 2 cm width localized near the electron cyclotron resonance region. Calculations are also presented for beams injected from the ITER Upper Port electron cyclotron resonance heating (ECRH) launcher as it is currently being designed. These show that the additional power deposition profile broadening from quasi-optical effects may result in a drop in the predicted efficiency for neoclassical tearing mode or sawtooth control by up to a factor of 2.

Quasi-optical theory of microwave plasma heating in open magnetic trap

“…We use the Cartesian coordinates for the wave amplitudes and output of the results, and the internal cylindrical coordinates for the Hamiltonian taking advantage of the axial symmetry of the plasma configuration. As mentioned in the introduction, the development is based on our previous quasi-optical code LAQO, created for toroidal magnetic traps 16 . However, since conditions for the wave propagation in open mirror traps and toroidal traps are significantly different, we have eventually developed an entirely new code.…”

“…typical for radiation belts in Earth ionosphere or Solar flares, in a straightforward manner just by introducing new coordinates with a curvilinear axis z and taking into account the curvature when calculating a conjugated momenta operator. The similar approach was previously used for toroidal magnetic traps in which the axis z was chosen along the reference geometric optics ray representing the center of the quasi-optical wave beam [15][16][17] . However, using geometric optics rays as a reference for the quasi-optical equation in open traps is not optimal because such rays may be strongly curved and even divergent inside the plasma column in most interesting cases 9,11 .…”

“…In this paper, the quasi-optical approximation is adopted to describe the propagation of wave beams in a high-temperature plasma in an open magnetic trap. A similar approach was previously developed for toroidal magnetic traps 16,17 . However, description of the microwave heating in modern open traps needs substantial modification of the quasi-optical theory due to a requirement of more accurate accounting of the spatial dispersion inside the resonant absorption zone.…”

Paraxial WKB Method Applied to the Lower Hybrid Wave Propagation

“…In particular, this approach allows one to derive a set of ordinary differential equations as in geometrical optics, taking into account diffraction effects [11][12][13] (see Section II). Techniques other than the pWKB approximation, such as the parabolic wave equation [14][15][16][17][18] and the quasi-optics approximation [19][20][21][22][23] , which address asymptotic solutions of Maxwell's equations in the same regime (3), have also been considered in literature. With respect to the pWKB approximation, those other methods rely either on a set of partial differential equations (PDE) [14][15][16][17][18] or on constrained ordinary differential equations (ODE) [19][20][21][22][23] , the solution of which is, in general, computationally more demanding.…”

Quasi-optical approach for inhomogeneous dissipative media with high-order spatial dispersion

“…Such a description allows one to consistently take into account the media anisotropy, spatial inhomogeneity, dispersion, and resonance dissipation within the framework of a unified approach [2]. Its generalization to the case of anisotropic and gyrotropic media with spatial dispersion and dissipation [3] was used to simulate the propagation of quasi-optical wave beams in tokamaks and showed much higher accuracy for resonance absorption in comparison to the previously used approaches [4]. In this paper, we discuss the further generalization of the quasi-optical approach [5] and the features of its application in media of a special kind.…”