Effects of Magnetic Ripple on Lower-Hybrid Wave Propagation

Bizarro, João P. S.; Ferreira, J.; Rodrigues, Paulo Canas; Arslanbekov, Robert; Peysson, Y.

doi:10.1103/physrevlett.75.1308

Cited by 13 publications

(13 citation statements)

References 12 publications

(28 reference statements)

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“…Indeed, its characteristics are crucial in determining accurately the wave dynamics. In this section, an infinite column of plasma of circular section is considered, surrounded by a discrete set of magnetic field coils equally spaced by a distance L. 19 In this model, it is assumed that a plasma equilibrium consistent with the plasma current I p is achieved, which corresponds to nested circular flux surfaces whose radii are periodically modulated in the axial direction Oz. Neglecting finite ␤ effects, 22 the total magnetic field B is the sum of two terms, BϭB t ϩB p , where B t is the vacuum magnetic field created by the magnetic coils, and B p results from the current flow in the plasma.…”

Section: A Model Equilibriummentioning

confidence: 99%

“…18,19 It was focused on wave refraction effects, which are of primary importance in such inhomogeneous media, and have been neglected in previous investigations. 9,10 As a first step, it was shown that for parameters of practical interest in present-day tokamak experiments, the discreteness of the toroidal field system may significantly alter the picture of LH wave propagation obtained from a straight cylindrical geometry.…”

Section: Introductionmentioning

confidence: 99%

“…9,10 As a first step, it was shown that for parameters of practical interest in present-day tokamak experiments, the discreteness of the toroidal field system may significantly alter the picture of LH wave propagation obtained from a straight cylindrical geometry. 19 Hence, the well known cylindrical accessibility condition for the LH wave to penetrate to the plasma center is no longer valid, so the predicted power deposition profiles are expected to be greatly modified.…”

Section: Introductionmentioning

confidence: 99%

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Magnetic ripple and the modeling of lower-hybrid current drive in tokamaks

et al. 1996

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Using ray tracing, a detailed investigation of the lower-hybrid ͑LH͒ wave propagation in presence of toroidal magnetic field ripple is presented. The local ray behavior is first depicted for a cylindrical equilibrium periodically modulated along the axial direction. Variations along ray trajectories in the component of the wave vector parallel to the equilibrium magnetic field are observed, with a maximum relative amplitude that is locally of the order of the ripple level. For the full rippled toroidal equilibrium, a similar local behavior is found when the ray trajectory crosses a high ripple region. Despite the modest amplitude of the local ray perturbation, its global influence on ray trajectories may be strong, as a consequence of the combined effects of toroidal and poloidal inhomogeneities. By coupling ray tracing with a one-dimensional relativistic Fokker-Planck code, simulations of LH experiments have been performed for the TORE SUPRA tokamak ͓Equipe TORE SUPRA, in . It is shown that magnetic ripple may induce significant modifications in the LH power deposition profiles, mainly in the ''few passes'' regime when the wave makes some, but not many, passes inside the plasma before being absorbed. The effect of magnetic ripple leads then to a broadening of the power deposition profile and a shift towards the center of the plasma, and a better coupling with high energy electrons. This behavior may be explained by an increase in the overall ray stochasticity. Taking into account magnetic ripple in LH simulations, a better agreement is found between numerical predictions and experimental observations.

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Section: A Model Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Magnetic ripple and the modeling of lower-hybrid current drive in tokamaks

et al. 1996

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“…However, when applying the rigorous Hamiltonian formalism as developed in [31], taking as Hamiltonian the electrostatic dispersion relation and trying to give some analytical insight of the nonlinear LH ray dynamics, the conclusion is that the LH propagation in cylindrical plasmas with magnetic ripple is generally regular. In [30], instead, the filling of the spectral gap was reached by chaotic diffusion due to the presence, in the electromagnetic case, of a separatrix.…”

Section: Introductionmentioning

confidence: 99%

“…If the LHW is launched by an antenna, located at the plasma edge, and the condition of Landau absorption is not fulfilled inside the plasma, the wave remains trapped without absorption in the confined plasma. As an example, when the parallel (to the confining magnetic field) wave Further applications of this stochastic approach to the LHW propagation can be found in [29][30][31] in which various mechanisms breaking the cylindrical symmetry, like toroidicity and magnetic ripple, can induce chaotic evolution of the trajectories and can help with bridging the spectral gap. However, when applying the rigorous Hamiltonian formalism as developed in [31], taking as Hamiltonian the electrostatic dispersion relation and trying to give some analytical insight of the nonlinear LH ray dynamics, the conclusion is that the LH propagation in cylindrical plasmas with magnetic ripple is generally regular.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Chaotic Behavior of the Lower Hybrid Wave Propagation in Magnetised Plasma by Hamiltonian Theory

Casolari

Cardinali

2016

Entropy

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Abstract:The Hamiltonian character of the ray tracing equations describing the propagation of the Lower Hybrid Wave (LHW) in a magnetic confined plasma device (tokamak) is investigated in order to study the evolution of the parallel wave number along the propagation path. The chaotic diffusion of the "time-averaged" parallel wave number at higher values (with respect to that launched by the antenna at the plasma edge) has been evaluated, in order to find an explanation of the filling of the spectral gap (Fisch, 1987) by "Hamiltonian chaos" in the Lower Hybrid Current Drive (LHCD) experiments (Fisch, 1978). The present work shows that the increase of the parallel wave number n due to toroidal effects, in the case of the typical plasma parameters of the Frascati Tokamak Upgrade (FTU) experiment, is insufficient to explain the filling of the spectral gap, and the consequent current drive and another mechanism must come into play to justify the wave absorption by Landau damping. Analytical calculations have been supplemented by a numerical algorithm based on the symplectic integration of the ray equations implemented in a ray tracing code, in order to preserve exactly the symplectic character of a Hamiltonian flow.

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The geometrical-optics law of reflection for electromagnetic waves in magnetically confined plasmas: Specular reflection of rays at the last closed flux surface

Bizarro¹

2010

Physics of Plasmas

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Within the geometrical-optics approximation, it is shown that the reflection of rays describing the propagation of electromagnetic waves in fusion-grade, magnetically confined plasmas and impinging on the last closed flux surface, or plasma surface, is necessarily specular or mirror-like. More precisely, the component of the wave vector tangential to that surface does not change, whereas the component normal to it reverses its sign while keeping its magnitude. The well-known law of reflection, stating that the angle of incidence equals that of reflection, is thus generalized to anisotropic media.

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Effects of Magnetic Ripple on Lower-Hybrid Wave Propagation

Cited by 13 publications

References 12 publications

Magnetic ripple and the modeling of lower-hybrid current drive in tokamaks

Magnetic ripple and the modeling of lower-hybrid current drive in tokamaks

Analysis of the Chaotic Behavior of the Lower Hybrid Wave Propagation in Magnetised Plasma by Hamiltonian Theory

The geometrical-optics law of reflection for electromagnetic waves in magnetically confined plasmas: Specular reflection of rays at the last closed flux surface

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