On the radiofrequency response of tokamak plasmas

Lamalle, P.

doi:10.1088/0741-3335/39/9/011

Cited by 54 publications

(88 citation statements)

References 31 publications

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“…This formulation is not valid near the axis because for the basis used in Ref. 12, the expansion over the drift parameter ⑀ D diverges as r→0 ͑see the remark in the following͒. Thus our result is not the limiting case of expressions obtained in the above-mentioned references.…”

mentioning

confidence: 75%

Dielectric response of plasma in reversed field pinches near the ion cyclotron frequency

Svidzinski

2002

Physics of Plasmas

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The dielectric tensor of reversed field pinch (RFP) plasma is calculated near the magnetic axis for cylindrical azimuthally symmetric equilibria in the limit k⊥ρL→0. Particle orbits are calculated to first order in the drift approximation near the axis such that geometrical corrections to gyrophase are included. It is demonstrated that these corrections are important for evaluation of the plasma heating rate near ion cyclotron resonance in RFPs while they can be neglected in tokamak modeling. Geometrical effects of this kind become important in RFPs because the ratio of poloidal and toroidal magnetic field components is substantially larger in RFPs relative to that in tokamaks.

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confidence: 75%

Dielectric response of plasma in reversed field pinches near the ion cyclotron frequency

Svidzinski

2002

Physics of Plasmas

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“…Many authors have contributed to finding practical expressions for the visionary yet formal expressions Kaufman proposed (see e.g. [9,10,11,12] and the references therein); but up to now no readily usable, sufficiently general expressions are available to guarantee a truly self consistent description of the wave-particle interaction underlying RF heating.…”

Section: Basic Formalismmentioning

confidence: 99%

Integro-differential modeling of ICRH wave propagation and damping at arbitrary cyclotron harmonics and wavelengths in tokamaks

Eester¹,

Lerche²

2014

AIP Conference Proceedings

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Both at low and higher cyclotron harmonics, properly accounting for finite Larmor radius effects is crucial in many ion cyclotron resonance frequency heating scenarios creating high energy tails. The present paper discusses ongoing work to extend the 1D TOMCAT wave equation solver [D. Van Eester & R. Koch, Plasma Phys. Contr. Fusion 40 (1998) 1949] to arbitrary harmonics and arbitrary wavelengths. Rather than adopting the particle position, the guiding center position is used as the independent variable when writing down an expression for the dielectric response. Adopting a philosophy originally due to Kaufman [A.N. Kaufman, Phys. Fluids 15 (1972) 1063], the relevant dielectric response in the Galerkin formalism is written in a form where the electric field and the test function vector appear symmetrically, which yields a power balance equation that guarantees non-negative absorption for any wave type for Maxwellian plasmas. Moreover, this choice of independent variable yields intuitive expressions that can directly be linked to the corresponding expressions in the RF diffusion operator. It also guarantees that a positive definite power transfer from waves to particles is ensured for any of the wave modes in a plasma in which all populations have a Maxwellian distribution, as is expected from first principles. Rather than relying on a truncated Taylor series expansion of the dielectric response, an integro-differential approach that retains all finite Larmor radius effects [D. Van Eester & E. Lerche, Plasma Phys. Control. Fusion 55 (2013) 055008] is proposed.

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“…There have been a number of studies on quasilinear diffusion due to plasma turbulence and plasma waves [11][12][13][14][15][16]. In a broad sense, there are essentially two approaches to the derivation of the diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

“…The time dependence of the diffusion operator is a consequence of the finite time interval used in calculating changes in the dynamical variables. Consequently, singular Dirac delta functions, which appear in the Kennel-Engelmann and Kaufman approaches and are commonly treated by including collisonal effects resulting to phase decorelation and resonance broadening [14], are not present in our diffusion operator.…”

Section: Introductionmentioning

confidence: 99%

Quasilinear theory of electron transport by radio frequency waves and nonaxisymmetric perturbations in toroidal plasmas

2008

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The use of radio frequency (RF) waves to generate plasma current and to modify the current profile in magnetically confined fusion devices is well documented. The current is generated by the interaction of electrons with an appropriately tailored spectrum of externally launched RF waves.In theoretical and computational studies, the interaction of RF waves with electrons is represented by a quasilinear diffusion operator. The balance, in steady state, between the quasilinear operator and the collision operator gives the modified electron distribution from which the generated current can be calculated. In this paper the relativistic operator for momentum and spatial diffusion of electrons due to RF waves and non-axisymmetric magnetic field perturbations is derived. Relativistic treatment is necessary for the interaction of electrons with waves in the electron cyclotron (EC) range of frequencies. The spatial profile of the RF waves is treated in general so that diffusion due to localized beams is included. The non-axisymmetry magnetic field perturbations can be due to magnetic islands as in neoclassical tearing modes. The plasma equilibrium is expressed in terms of the magnetic flux coordinates of an axisymmetric toroidal plasma. The electron motion is described by guiding center coordinates using the action-angle variables of motion in an axisymmetric toroidal equilibrium. The Lie perturbation technique is used to derive a diffusion operator which is non-singular and time dependent. The resulting action diffusion equation describes resonant and non-resonant momentum and spatial diffusion. Momentum space diffusion leads to current generation in the plasma and spatial diffusion describes the effect of RF waves and magnetic perturbations on spatial evolution of the current profile. Depending on the symmetry of the equilibrium and the corresponding relation of the action variables to the configuration space variables, additionally to diffusion along the radial direction, poloidal and toroidal electron diffusion is also described. In deriving the diffusion operator, no statistical assumption, such as the Markovian assumption, for the underlying electron dynamics, is imposed. Consequently, the operator is time dependent and valid for a dynamical phase space that is a mix of correlated regular orbits and decorrelated chaotic orbits. The diffusion operator is expressed in a form suitable for implementation in a numerical code.2

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On the radiofrequency response of tokamak plasmas

Cited by 54 publications

References 31 publications

Dielectric response of plasma in reversed field pinches near the ion cyclotron frequency

Dielectric response of plasma in reversed field pinches near the ion cyclotron frequency

Integro-differential modeling of ICRH wave propagation and damping at arbitrary cyclotron harmonics and wavelengths in tokamaks

Quasilinear theory of electron transport by radio frequency waves and nonaxisymmetric perturbations in toroidal plasmas

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