Dielectric Tensor in Vlasov Plasmas near Cyclotron Harmonics

Shkarofsky, I. P.

doi:10.1063/1.1761710

Cited by 195 publications

(66 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Previous studies of the X and O modes have also noted the need to include relativistic effects in the resonance condition [21]. From (A20) we obtain…”

Section: F Weakly Relativistic Approximation For Obliquely Propagatimentioning

confidence: 66%

See 1 more Smart Citation

Relativistic description of electron Bernstein waves

Decker

Ram

2006

Physics of Plasmas

View full text Add to dashboard Cite

The application of the extraordinary and ordinary electron cyclotron waves for heating and current drive in overdense, magnetized plasmas is restricted. For frequencies near low harmonics of the electron cyclotron frequency these waves are cutoff near the edge of the plasma. For higher frequencies the interaction of the waves with electrons is weak leading to very low absorption of wave power. However, electron Bernstein waves provide means for heating and current drive in overdense plasmas since they have no density cutoffs and are strongly damped near harmonics of the electron cyclotron resonance. This paper discusses properties of electron Bernstein waves that make them an attractive means for delivering energy and momentum to electrons. An approximate analytical model for electrostatic waves in the weakly relativistic and weak damping limits is developed. From this model the propagation and damping characteristics of electron Bernstein waves and their dependence on plasma parameters are derived. It is found that relativistic effects are necessary to properly describe the resonant interaction of electron Bernstein waves with electrons. The characteristics of electron Bernstein wave propagation and damping are very different depending on whether the electron cyclotron harmonic resonance is approached from the low-or the high-field side. The results from the analytical model and the associated analysis agree well with the results from the exact numerical calculations. This validates the physics of the simplifying assumptions on which the model is based. The electron Bernstein waves are completely damped well before the electron cyclotron resonance due to the Doppler shift. Within the damping region the waves interact with suprathermal electrons thereby having the potential for efficient current drive.

show abstract

“…Previous studies of the X and O modes have also noted the need to include relativistic effects in the resonance condition [21]. From (A20) we obtain…”

Section: F Weakly Relativistic Approximation For Obliquely Propagatimentioning

confidence: 66%

“…The resonant interaction between electrons and the plasma waves is given by the resonance condition (21). The resonance curves defined in (p ⊥ , p ) momentum space are ellipses for n < 1, parabolas for n = 1, and hyperbolas for n > 1.…”

Section: Electrostatic Dispersion Relationmentioning

confidence: 99%

Relativistic description of electron Bernstein waves

Decker

Ram

2006

Physics of Plasmas

View full text Add to dashboard Cite

show abstract

“…Godfrey et al 1975). Thus the results derived here are a necessary preliminary for the derivation of properties of a weakly magnetized thermal plasma for temperatures between the known mildly relativistic limit ρ 1 (Shkarofsky 1966) and the known extremely relativistic limit ρ → 0 (Melrose 1997c).…”

Section: Discussionmentioning

confidence: 98%

“…Trubnikov's tensor is used (see e.g. Shkarofsky 1966;Bornatici et al 1983;Robinson 1986;Melrose 1997a) to treat the mildly relativistic (ρ 1), small-gyroradius (k 2 ⊥ Ω 2 e ρ) limit in which r(ξ) is assumed large so that the Macdonald functions may be approximated by their asymptotic forms. The weakly magnetized limit is obtained by expanding in powers of Ω e , both in (4.1) and elsewhere in the relevant integrands.…”

Section: Discussionmentioning

confidence: 99%

“…Secondly, the Trubnikov functions are particularly important for a magnetized, relativistic, thermal electron gas, where they provide a starting point for detailed calculations, specifically in the mildly relativistic limit (see e.g. Shkarofsky 1966). Trubnikov's result may also be used to treat the weakly magnetized case (for arbitrarily temperature) by expanding in powers of the magnetic field.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Trubnikov functions for unmagnetized plasmas

Melrose

1999

J. Plasma Phys.

View full text Add to dashboard Cite

Abstract.A class of relativistic dispersion functions for unmagnetized thermal plasmas is defined by generalizing functions first defined by Trubnikov in 1958. Recursion relations are derived that allow one to generate explicit expressions for the class of functions in terms of the relativistic plasma dispersion function T (z, ρ) introduced by Godfrey et al. in 1975. These functions are relevant to the description of the response of a weakly mangetized, highly relativistic, thermal plasma.

show abstract

Propagation and Absorption of ECR Waves in a Low Temperature Toroidal Plasma of Small Size and Magnetic Field

Someșan

1985

Contrib Plasma Phys

View full text Add to dashboard Cite

The propngntion nnd nbsorption of ECR wnves in n toknmnk plasma with sm;ill size and low values of the elertron temperature and the toroidal mngnetic field is studied numerically. The cold plasma dispersion equation is solved and my tracing calculations are prformcd to find thc nccessibility conditions nnd the optimal tingle of wnve launching for maximal ECR absorption.Absorption coefficients nre computed in the high density approximation. In troduc t,ionAs it has been shown by analizing the power balance of a tokamak type plasriia it is not possible to obtain t hernionuclenr ignition by mere ohniic heating. Therefore various scheiires have been developed in the last years in view of auxiliary heating of hot plasmns. Among them the methods based on launching of high power microwaves in the tokamak plasma showed to be very efficient. Progress in this field is related on one hand to the development of high power techniqurs of generation, transmission and launching of niicrowaves and on the other hand to a n extensive theoretical work elucidating the niechanimis of the energy transfer from the electromagnetic field to t,he plasma.Wave injection near the electron cyclot.ron resonance (ECR) frequency has been theoreticly stidied [ 1-81 and successfully applied to heat the plasiila in varioris toroiclal devices as TM-3, T-10, ISX-B, TFR, PLT, WT-1, ,JIPPT-11, JFT-2, Tosca etc. [9-191. The heating efficiences are of 5-7 eV/kW by using the extraordinarl\. oscillation nrode (with elliptical polarization perpendicrilar to the toroitlnl inagnct ic field) and of 2-4 eV/kW for the ordinary oscillation mode (with linenr polarization parnllcl t o the 1i1ag-nntic field). The ternperatlire growth is of 40--609/, (from 1,5 keV to 2,3 kc\-in T-10, 0,fi to 1 krV in JFT-2, 0,7 to 0,9 keV in Tosca, 0,8 to 1,3 keV in ISX-I3 etc.). The prtwnee of nn ECR wave in the plasma seems to be harmleas from the point of vien Wlierens in tokaniaks of sufficiently great tliniensions, a high teriiperntrire plasiirii itlap absorb conipletely the incident energy arid 1000/, cfficiencies of energy transfer are obtained without iiiajor difficulties, the heating rates have less encorrraging values for plasmas of modest sizes and temperatures; Good efficiencies niay be obtained in

show abstract

Dielectric Tensor in Vlasov Plasmas near Cyclotron Harmonics

Cited by 195 publications

References 12 publications

Relativistic description of electron Bernstein waves

Relativistic description of electron Bernstein waves

Generalized Trubnikov functions for unmagnetized plasmas

Propagation and Absorption of ECR Waves in a Low Temperature Toroidal Plasma of Small Size and Magnetic Field

Contact Info

Product

Resources

About