Parametric decay of plasma waves near the upper-hybrid resonance

Dodin, I. Y.; Arefiev, Alexey

doi:10.1063/1.4979168

Cited by 12 publications

(26 citation statements)

References 31 publications

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“…A detailed analytical study of the instability discussed here is somewhat lengthy, so we report it in a separate paper 15 . Here we present the final answer only.…”

Section: Theoretical Interpretationmentioning

confidence: 96%

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

et al. 2017

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Spherical tokamak plasmas are typically overdense and thus inaccessible to externally-injected microwaves in the electron cyclotron range. The electrostatic electron Bernstein wave (EBW), however, provides a method to access the plasma core for heating and diagnostic purposes. Understanding the details of the coupling process to electromagnetic waves is thus important both for the interpretation of microwave diagnostic data and for assessing the feasibility of EBW heating and current drive. While the coupling is reasonably wellunderstood in the linear regime, nonlinear physics arising from high input power has not been previously quantified. To tackle this problem, we have performed one-and two-dimensional fully kinetic particle-in-cell simulations of the two possible coupling mechanisms, namely X-B and O-X-B mode conversion. We find that the ion dynamics has a profound effect on the field structure in the nonlinear regime, as high amplitude shortscale oscillations of the longitudinal electric field are excited in the region below the high-density cut-off prior to the arrival of the EBW. We identify this effect as the instability of the X wave with respect to resonant scattering into an EBW and a lower-hybrid wave. We calculate the instability rate analytically and find this basic theory to be in reasonable agreement with our simulation results.

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“…A detailed analytical study of the instability discussed here is somewhat lengthy, so we report it in a separate paper 15 . Here we present the final answer only.…”

Section: Theoretical Interpretationmentioning

confidence: 96%

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

et al. 2017

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“…(27), which relates the forcing operator to the susceptibility. When evaluating B 2 1 , we have used expression (23) for B 1 , followed by simplification using the momentum space electric field equation (33). This term is then combined with v 2 s1 , calculated using Eq.…”

Section: A First Order Equationsmentioning

confidence: 99%

“…The final result is simplified using identity (30) for the forcing operator F s,k . Now that we have introduced the wave energy operator H k , the momentum space electric field equation (33) can be converted into a form that is closely related to the wave energy…”

Section: A First Order Equationsmentioning

confidence: 99%

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Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

2017

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Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.

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“…Strong enhancement of the electric field of the X-mode pump wave near the UHR 26,34 allows the thresholds of various PDIs to be exceeded. PDIs for X-mode radiation near the UHR are relevant for fundamental ECR heating both with X-mode [19][20][21]30,35 and O-mode 21,27 (O-mode can be converted to X-mode by reflections 21,26,27 ), for O-X-B heating, 22,28,29,[36][37][38] for collective Thomson scattering, [24][25][26]31 and for ionospheric modification experiments; 39 similar PDIs also enter as secondary instabilities in the saturation phase of two-plasmon decay instabilities occurring for harmonic X-mode ECR heating 23,33 and direct-drive inertial confinement fusion. 4,40 Particular cases where such PDIs may occur in future experiments include ECR start-up at ITER, MAST-U, NSTX-U, and future fusion reactors, [41][42][43] O-X-B heating at W7-X, and ionospheric modification experiments with significant O-X-conversion at the O-mode cutoff.…”

Section: Introductionmentioning

confidence: 99%

Power threshold and saturation of parametric decay instabilities near the upper hybrid resonance in plasmas

et al. 2019

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Parametric decay instabilities (PDIs) occur for large-amplitude waves in quadratically nonlinear media, where they provide a limit of validity of linear theories and allow efficient coupling between different, well-defined wave modes. We investigate PDIs near the upper hybrid resonance in plasmas by injection of high-power electron cyclotron (EC) waves at the ASDEX Upgrade tokamak. Our measurements of PDIs have an unprecedented frequency resolution, far below the ion cyclotron frequency, allowing the first observations of secondary and tertiary PDIs during the saturation phase in a controlled laboratory setting. Furthermore, we are for the first time able to systematically compare theoretical predictions of the EC wave power thresholds, which must be exceeded to excite such PDIs, to experimental observations, validating the theory. Our findings are relevant for EC wave heating and current drive in tokamaks and stellarators, including future fusion power plants, as well as in low-temperature laboratory and industrial plasmas, inertial confinement fusion, and ionospheric modification experiments.

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Parametric decay of plasma waves near the upper-hybrid resonance

Cited by 12 publications

References 31 publications

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

Power threshold and saturation of parametric decay instabilities near the upper hybrid resonance in plasmas

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