Parametric Instabilities of Waves in Magnetized Plasmas

Larsson, Jonas; Stenflo, L.

doi:10.1002/ctpp.19760160202

Cited by 23 publications

(5 citation statements)

References 32 publications

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“…In the review by Pustovalov & Silin (1975) there appears an algebraically tractable expression for e (2) (see (3.1) below). This result may also be obtained by two different and independent methods from more general results in Larsson & Stenflo (1976) and Larsson (1982). The result (3.1) is thus well validated.…”

Section: Introductionsupporting

confidence: 66%

“…A third formula for e (2) is obtained from equation (3.8) of Larsson (19796) (the result was essentially found in Larsson & Stenflo (1976), but was written in that paper as a coupling coefficient). From the relation where ky = kj/kp we obtain It is not difficult to check the agreement between the expressions (3.1) and (3.3) by direct calculation.…”

Section: Two Alternative Expressions For E (2)mentioning

confidence: 99%

“…The calculation of e <2> or associated three-wave coupling coefficients (see Appendix A) has been considered in several papers (e.g. Dum & Ott 1971;Stenflo 1971;Tataronis & Teichman 1971;Pustovalov & Silin 1975;Das & Banerjee 1976;Larsson & Stenflo 1976;Selim 1978;Bergmann 1986).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear interaction of electrostatic waves in a magnetized Vlasov plasma

Larsson

1988

J. Plasma Phys.

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A new expression for the second-order dielectric function є(2) (K1,ω1, K2,ω2) is derived from the Vlasov–Poisson equations. The formula is also suitable for the calculation of this quantity in general situations when it is essential to use kinetic theory and when the wave vectors K1 and K2 have arbitrary directions with respect to each other as well as to the external magnetic field. We also consider two earlier formulae for this response function and discuss advantages and disadvantages of the different expressions.

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Section: Introductionsupporting

confidence: 66%

Section: Two Alternative Expressions For E (2)mentioning

confidence: 99%

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Nonlinear interaction of electrostatic waves in a magnetized Vlasov plasma

Larsson

1988

J. Plasma Phys.

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“…In the problem presented in this paper and by including the damping terms one obtains directly the wave equations ( 12) and (13) from the system (Al) to (A3) for n e = n x = n 2 and n e H = n 3 . Accordingly, we obtain the coupling coefficients in Eqs( 14)and (15). where p satisfies the condition (applies for ions!…”

Section: = E M /Dv F(v)mentioning

confidence: 99%

Saturation of parametric instabilities in lower hybrid heating of tokamak plasmas

Heikkinen¹,

Karttunen²

1987

Nucl. Fusion

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A non-linear analysis of parametric instabilities in lower hybrid heating of tokamak plasmas is presented. Harmonic generation of the low frequency mode and its effect on the evolution of the parametric decay of a lower hybrid pump to another lower hybrid wave and a low frequency mode is investigated, and numerical calculations of the relevant wave system are carried out. It is found that the coupling of the low frequency wave to its harmonic may effectively suppress the spatial growth of the primary instability. This may be particularly true at the plasma edge of the tokamak, where electron and ion temperatures are low and the primary instability is strong at high pump intensity. The spectral dependence of the harmonic generation strength is compared with that of the primary instability, and the effect on pump depletion with relevant tokamak parameters is discussed.

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“…We assume that w2 s Q;, c2ka sin2 8 <w, and furthermore make the simplification sin2 4* = 1 , i.e. we put p =x/2 in (12). The dispersion relation (6) becomes after a lengthy calculation (cold plasma)…”

Section: Low-frequency Instabilitiesmentioning

confidence: 99%

Parametric Instabilities in Laser Heating of Magnetically Confined Plasmas

Karttunen¹,

Salomaa²

1977

Phys. Scr.

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This paper discusses the generation of parametric instabilities in laser heating of plasmas confined in a linear magnetic device. The nonlinearities are taken into account by the inclusion of a ponderomotive force. We derive a generalized dielectric tensor and the corresponding dispersion relation which enables us to determine the instability thresholds and linearized growth rates. The cases where the parametrically excited low frequency wave propagates either parallel or perpendicular to the magnetic field are analyzed in detail. Propagation in an oblique direction is briefly described. As regards the laser heating schemes, the low frequency filamentation and the stimulated Brillouin scattering seem to pose a possible difficulty. Fortunately, several of the potential instabilities cannot be excited in the configuration considered.

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Parametric Instabilities of Waves in Magnetized Plasmas

Abstract: Results from kinetic theory are reformulated in order t o generalize previous equations for wavewnve interactions in magnetized plasmas.

Cited by 23 publications

References 32 publications

Nonlinear interaction of electrostatic waves in a magnetized Vlasov plasma

Nonlinear interaction of electrostatic waves in a magnetized Vlasov plasma

Saturation of parametric instabilities in lower hybrid heating of tokamak plasmas

Parametric Instabilities in Laser Heating of Magnetically Confined Plasmas

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