Parametric Effects of an Alternating Field on Inhomogeneous Plasmas

Amano, Tsuneo; Okamoto, Masayuki

doi:10.1143/jpsj.26.529

Cited by 47 publications

(23 citation statements)

References 16 publications

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“…This problem has previously been considered by a number of authors, e.g. in [4,5,10,11,18,35,40], and we shall point out when our results agree/disagree with some this earlier work. PDIs with electrostatic daughter waves are governed by the Boltzmann-Poisson system with external fields B = Be z and Re(E 0 e −iω 0 t ),…”

Section: Kinetic Theory Of Pdis In Homogeneous Plasmassupporting

confidence: 75%

Parametric decay instability near the upper hybrid resonance in magnetically confined fusion plasmas

Hansen

Nielsen

Salewski

et al. 2017

Plasma Phys. Control. Fusion

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In this paper we investigate parametric decay of an electromagnetic pump wave into two electrostatic daughter waves, particularly an X-mode pump wave decaying into a warm upper hybrid wave (a limit of an electron Bernstein wave) and a warm lower hybrid wave. We describe the general theory of the above parametric decay instability (PDI), unifying earlier treatments, and show that it may occur in underdense and weakly overdense plasmas. The PDI theory is used to explain the anomalous sidebands observed in collective Thomson scattering (CTS) spectra at the ASDEX Upgrade tokamak. The theory may also account for similar observations during CTS experiments in stellarators, as well as in some 1st harmonic electron cyclotron resonance and OX -B heating experiments.

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Section: Kinetic Theory Of Pdis In Homogeneous Plasmassupporting

confidence: 75%

Parametric decay instability near the upper hybrid resonance in magnetically confined fusion plasmas

Hansen

Nielsen

Salewski

et al. 2017

Plasma Phys. Control. Fusion

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“…A unified treatment of the problem of parametric coupling of waves in a magnetic field has been undertaken by Aliev et al (1966), Amano and Okamoto (1969), and Porkolab ( , 1974. These authors used the Vlasov equation, which can be solved after transformation to the oscillating frame of reference.…”

Section: Parametric Decay In a Magnetized Plasmamentioning

confidence: 99%

Nonlinear wave effects in laboratory plasmas: A comparison between theory and experiment

Porkoláb

Chang²

1978

Rev. Mod. Phys.

122

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The rich nonlinear phenomena that occur in plasmas are reviewed in a systematic way. The foundations of turbulence theory (both weak and strong) and-experiments performed in the past decade to verify such theories are presented. The aim is to emphasize those experiments that demonstrate clearly the validity (or failure) of' some of the theories. In particular, we discuss experiments that demonstrate the validity and/or limits of weak turbulence theory, strong turbulence theory, parametric instabilities, echoes, trapping of particles in large-amplitude waves, and electrostatic ion acoustic shocks. We present concluding remarks in each section regarding the present status of each of these phenomenon. CONTENTSimproving weak-turbulence theory by "renormalization, " namely, orbit diffusion and the concept of "clumps. " In Sec. VI we present results concerning large-amplitude waves and trapping, and in Sec. VII we discuss some experiments on ion acoustic shocks. We have deliberately avoided or discuss only briefly experiments that (in our opinion) are not yet well understood in terms of quantitative comparison with theories (e.g. , nonlinear drift waves, turbulent resistivity experiments, nonlinear tearing modes, magnetic reconnection, etc. ). II. WEAK-TURBULENCE THEORY AND EXP ER IMENTSA. Foundations of weak-turbulence theoryThe first comprehensive theory of plasma turbulence, what we today call "weak-turbulence theory, " was devel-Rev.

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“…The horizontal component of the propagation vector is then independent of the height, but the vertical component is a function of the height, both for the pump wave and for the 'standing wave.' The vertically incident pump wave is then a combination of upgoing and downcoming electromagnetic WKB solutions [Budden, 1961] and is described by the Airy function near the reflection level; the standing wave consists of two upgoing and two downcoming electrostatic WKB-like solutions with constant horizontal components of the propagation vector. In practice, the pump wave, which in a sense also resembles a standing wave, can again be replaced by a uniform oscillating field parallel to the planes of stratification in the present situation, because plasma oscillations excited near the reflection level are absorbed (by Landau damping) before they leave the relatively uniform part of the pump wave.…”

Section: Crude Estimate Of the Effects Of Inhomogeneitymentioning

confidence: 99%

“…The theory of parametric instabilities excited by an ac electric field of large amplitude in a laboratory plasma or in the ionosphere has recently been discussed by several authors. Previous theoretical work, with two exceptions [Amano and Okamoto, 1969;Perkins and Flick, 1971], deals with a homogeneous plasma, although the actual plasmas in the laboratory and in the ionosphere are inhomogeneous. Perkins and Flick [1971] assume the existence of WKB solutions that locally resemble the characteristic wave solutions (a pair of waves traveling in opposite directions rather than a single wave) in a uniform medium in the presence of the pump field.…”

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confidence: 99%

Purely growing parametric instability in an inhomogeneous plasma

Fejer¹,

Leer

1972

J. Geophys. Res.

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A simple method based on energy balance is used first to rederive the well-known threshold condition for the purely growing parametric instability in a homogeneous medium and later to estimate the effects of inhomogeneity in a semiquantitative manner. A method different from that of Perkins and Flick (1971) is then used to calculate the threshold in a more quantitative manner for the instance where the effects of inhomogeneity dominate over those of collisions. The result agrees with that of Perkins and Flick for k,1 >> 1 in their terminology. For k,l << 1, neither theory is directly applicable and the threshold is obtained by numerical methods. The present method of calculation has the advantages that its range of validity is easily checked, that it provides good physical insight, and that it is easily applicable to electromagnetic instabilities. The theory of parametric instabilities excitedby an ac electric field of large amplitude in a laboratory plasma or in the ionosphere has recently been discussed by several authors. Previous theoretical work, with two exceptions [Amano and Okamoto, 1969; Perkins and Flick, 1971], deals with a homogeneous plasma, although the actual plasmas in the laboratory and in the ionosphere are inhomogeneous. Perkins and Flick [1971] assume the existence of WKB solutions that locally resemble the characteristic wave solutions (a pair of waves traveling in opposite directions rather than a single wave) in a uniform medium in the presence of the pump field. They do not discuss the limits of validity of their treatment. The present paper has several aims. First, an extremely simple and yet rigorous derivation of the threshold criterion in a uniform medium is given, based on considerations of energy balance. Then, still using the same principle, a crude estimate of the importance of the inhomogeneity of the medium is obtained. A perturbation treatment is used to rederive the threshold criterion of Perkins and Flick [1971] for an inhomogeneous lossless plasma. The range of validity of the criterion is Copyright ¸ 1972 by the American Geophysical Union. 7OO then examined. Numerical methods are used to obtain a threshold criterion for the instance where both the present method and that of Perkins and Flick [1971] break down. I-IOMOGENEOUS M•mv• A spatially uniform oscillating electric pump field Eo sin •o• is assumed where Eo is parallel to the propagation vector k of the parametrically excited waves. It is convenient to consider the plasma from a reference frame oscillating with a hypothetical electron that in the absence of the oscillating field would have been stationary; the amplitude of oscillation of such an electron would be e = eEo/mO•o'. It has been shown [Dawson and Oberman, 1962] that in this reference frame, if the oscillating motion of the ions is neglected on account of their greater inertia and if a uniform ion density is assumed, the usual electrostatic plasma waves can propagate; they are only 'usual,' however, if their electric field is considered as a function of the coo...

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Parametric Effects of an Alternating Field on Inhomogeneous Plasmas

Cited by 47 publications

References 16 publications

Parametric decay instability near the upper hybrid resonance in magnetically confined fusion plasmas

Parametric decay instability near the upper hybrid resonance in magnetically confined fusion plasmas

Nonlinear wave effects in laboratory plasmas: A comparison between theory and experiment

Purely growing parametric instability in an inhomogeneous plasma

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