Electron Landau damping in toroidal plasma with Solov’ev equilibrium

Grishanov, N. I.; Azarenkov, N. A.

doi:10.1134/s1063780x13120039

Cited by 3 publications

(5 citation statements)

References 25 publications

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“…Since the tokamak magnetic field H 0 is nonuniform and has a minimum, all plasma particles should be separated into two groups of, so-called, untrapped and trapped particles. Such a separation [8,12,13] can be done by the inequalities for and  :…”

Section: Discussionmentioning

confidence: 99%

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Drift-Kinetic Equations in Magnetized Current-Carrying Plasmas

Grishanov,

Azarenkov

2023

Problems of Atomic Science and Technology

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Kinetic models of magnetized current-carrying plasma have been developed to study the influence of magnetic drift effects on the wave-particle interactions in tokamaks and cylindrical plasma columns. The drift-kinetic equations are derived for the perturbed distribution functions of trapped and untrapped particles in a two-dimensional axisymmetric toroidal plasma, taking into account their bounce oscillations and the finite orbit-widths of their banana trajectories.

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Section: Discussionmentioning

confidence: 99%

“…The linearized Vlasov equation [7,8] for the perturbed plasma particle distribution functions || ( , , , , , , )…”

Section: Drift-kinetic Equationmentioning

confidence: 99%

Drift-Kinetic Equations in Magnetized Current-Carrying Plasmas

Grishanov,

Azarenkov

2023

Problems of Atomic Science and Technology

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“…Here (and hereafter), the subscript 'eq' denotes quantities evaluated at the outer equatorial plane, while quantities evaluated at the magnetic axis will have a subscript '0'. In (9), σ v is the sign of the parallel velocity on the outer midplane plane (v ∥ changes sign along the orbit only in the case of trapped electrons), and ϖ B is the highest angular transit frequency of electrons of energy m e ϵ v , namely those with…”

Section: Modelling the Effects Of Periodicity On Cerenkov-landau Reso...mentioning

confidence: 99%

“…These authors have pointed out that the poloidal modulation of the parallel velocity of charged particles modifies the longitudinal permeability of the plasma (whose imaginary part describes electron Landau damping of electrostatic waves). Grishanov et al [8,9] have specialized these calculations to two particular tokamak configurations. To the best of our knowledge, however, these effects have never yet been taken into account in a full-wave solver for toroidal geometry.…”

Section: Introductionmentioning

confidence: 99%

Toroidicity effects on the absorption of IC waves by electrons

Brambilla

Bilato

2020

Nucl. Fusion

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The poloidal modulation of the parallel velocity of charged particles in the tokamak magnetic field modifies the strength of electron absorption of the compressional wave in the Ion Cyclotron (IC) range of frequencies. We have developed a model of this effect which is sufficiently simple to be numerically tractable, and we have implemented it in the TORIC full-wave code, which solves the wave equation in toroidal axisymmetric geometry. We find that the effect is normally negligible in present-day devices, but its importance increases with the dimensions and the temperature of the plasma, and should be taken into account when estimating the competition between electron and ion heating and the efficiency of current drive in future reactor-grade plasmas.

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“…There are several interesting papers [33][34][35][36][37][38][39][40][41][42] on the existence and physical interpretation of linear electron Landau damping and experimentally this phenomenon was verified by Malmberg and Wharton [43]. Grishanova & Azarenkova [44] studied electron Landau damping in toroidal plasma with Solov'ev equilibrium. For the first time, Ott and Sudan [45] investigated the effect of linear electron Landau damping on IA solitary waves in a collisionless plasma.…”

Section: Introductionmentioning

confidence: 99%

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

Dalui

Bandyopadhyay

2020

Indian J Phys

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A Korteweg-de Vries (KdV) equation including the effect of Landau damping is derived to study the propagation of weakly nonlinear and weakly dispersive ion acoustic waves in a collisionless unmagnetized plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. The hotter energetic electron species follows the nonthermal velocity distribution of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] whereas the cooler electron species obeys the Boltzmann distribution. It is found that the coefficient of the nonlinear term of this KdV like evolution equation vanishes along different family of curves in different parameter planes. In this context, a modified KdV (MKdV) equation including the effect of Landau damping effectively describes the nonlinear behaviour of ion acoustic waves. It has also been observed that the coefficients of the nonlinear terms of the KdV and MKdV like evolution equations including the effect of Landau damping, are simultaneously equal to zero along a family of curves in the parameter plane. In this situation, we have derived a further modified KdV (FMKdV) equation including the effect of Landau damping to describe the nonlinear behaviour of ion acoustic waves. In fact, different modified KdV like evolution equations including the effect of Landau damping have been derived to describe the nonlinear behaviour of ion acoustic waves in different region of parameter space. The method of Ott & Sudan [Phys. Fluids 12, 2388Fluids 12, (1969] has been applied to obtain the solitary wave solution of the evolution equation having the nonlinear term (φ (1) ) r ∂φ (1) ∂ξ , where φ (1) is the first order perturbed electrostatic potential and r = 1, 2, 3. We have found that the amplitude of the solitary wave solution decreases with time for all r = 1, 2, 3.

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Electron Landau damping in toroidal plasma with Solov’ev equilibrium

Cited by 3 publications

References 25 publications

Drift-Kinetic Equations in Magnetized Current-Carrying Plasmas

Drift-Kinetic Equations in Magnetized Current-Carrying Plasmas

Toroidicity effects on the absorption of IC waves by electrons

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

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