Echo-like nonlocal effect due to parallel magnetic inhomogeneity

The authors have written a code for the solution of the integro-differential equations describing coupling, propagation and absorption of high frequency waves in the ion cyclotron frequency range in tokamak plasmas, taking into account finite Larmor radius effects and parallel dispersion. The wave equations are discretized by a semi-spectral approach, using cubic Hermite finite elements in the radial direction and an expansion in Fourier modes in the poloidal direction. The latter permits analytic evaluation of the orbit integrals along magnetic field lines in the presence of a poloidal component of the static magnetic field. Thus, the code describes mode conversion to ion Bernstein waves, ion cyclotron damping at the fundamental and at the first harmonic, and electron transit time and Landau damping in full toroidal geometry. A few simulations of ion cyclotron heating of the ASDEX tokamak are presented. They show generally good agreement with the predictions of simpler models, namely plane layered models and ray tracing. Furthermore, the simulations can be used to identify a few interesting toroidal effects, particularly regarding the efficiency of mode conversion and the propagation of ion Bernstein waves.

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“…the power absorbed by ions at the first harmonic resonance, (41) and the power absorbed by electrons:…”

Section: Local Power Absorption In Tokamak Geometrymentioning

confidence: 99%

Numerical simulation of ion cyclotron heating of hot tokamak plasmas

1988

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“…We are thereby able to obtain a compact modified Fourier representation for with poloidally varying coefficients so geometric coupling of modes is treated in a natural manner in poloidally varying, axisymmetric tokamak magnetic fields. Our procedure provides a more general treatment of geometric effects than has been possible in the past (Faulconer 1987; Smithe et al. 1988; Catto, Lashmore-Davies & Martin 1993).…”

Section: Introductionmentioning

confidence: 99%

A quasilinear operator retaining magnetic drift effects in tokamak geometry

2017

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The interaction of radio frequency waves with charged particles in a magnetized plasma is usually described by the quasilinear operator that was originally formulated by Kennel & Engelmann (Phys. Fluids, vol. 9, 1966, pp. 2377–2388). In their formulation the plasma is assumed to be homogenous and embedded in a uniform magnetic field. In tokamak plasmas the Kennel–Engelmann operator does not capture the magnetic drifts of the particles that are inherent to the non-uniform magnetic field. To overcome this deficiency a combined drift and gyrokinetic derivation is employed to derive the quasilinear operator for radio frequency heating and current drive in a tokamak with magnetic drifts retained. The derivation requires retaining the magnetic moment to higher order in both the unperturbed and perturbed kinetic equations. The formal prescription for determining the perturbed distribution function then follows a novel procedure in which two non-resonant terms must be evaluated explicitly. The systematic analysis leads to a diffusion equation that is compact and completely expressed in terms of the drift kinetic variables. The equation is not transit averaged, and satisfies the entropy principle, while retaining the full poloidal angle variation without resorting to Fourier decomposition. As the diffusion equation is in physical variables, it can be implemented in any computational code. In the Kennel–Engelmann formalism, the wave–particle resonant delta function is either for the Landau resonance or the Doppler shifted cyclotron resonance. In the combined gyro and drift kinetic approach, a term related to the magnetic drift modifies the resonance condition.

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“…1988 for a brief but recent review and further references), usually implemented in I -D codes and which, sometimes. exhibit unexpected features like the echo-type phenomenon discussed by Faulconer (1987a), resulting from magnetic field gradients along the magnetic field lines.…”

Section: Introductionmentioning

confidence: 81%

A comparison between ICRF theory and experiment

Koch¹,

Descamps²,

Lebeau³

et al. 1988

Plasma Phys. Control. Fusion

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A review is made where the present status of, successively, RF modeling theory, experimental interpretation methods and comparison between theory and experiment is discussed. As far as the recent developments in theory are concerned, it is found that full wave models appear to be consistent with ray-tracing models and to yield comparable results when applied to selected cases where both are applicable. Methods for including consistent gradient terms in the wave equation have now been found; however, a unified understanding of the impact of such corrections is desirable. From the experimental point of view several procedures have been developed based on sawteeth analysis, modulation or simulation, to evaluate the fraction of the power coupled to the plasma bulk and the power deposition profiles. Comparison between experiments and theory on these subjects as well as for coupling indicates that the ICRF physics is well understood. Tall analysis has been done extensively only for PLT; further work is going on for JET and TEXTOR, which clearly reveals their presence and the importance of their role xe analysis in the presence of RF has also been done: however, several of the presently available thermal diffusion models seem to be able to fit the experimental data. It is concluded that, in the ICRF field, theory nowadays provides quite reliable tools and that extensive comparisons with experiments should be pursued in order to provide the basis for the understanding of the interplay between heating, velocity diffusion, confinement and edge effects.

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Echo-like nonlocal effect due to parallel magnetic inhomogeneity

Cited by 21 publications

References 6 publications

Numerical simulation of ion cyclotron heating of hot tokamak plasmas

Numerical simulation of ion cyclotron heating of hot tokamak plasmas

A quasilinear operator retaining magnetic drift effects in tokamak geometry

A comparison between ICRF theory and experiment

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