Observation of Electron Bernstein Wave Heating in a Reversed Field Pinch

Seltzman, Andrew; Anderson, J. K.; Diem, S. J.; Goetz, J. A.; Forest, C. B.

doi:10.1103/physrevlett.119.185001

Cited by 9 publications

(6 citation statements)

References 24 publications

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“…The slow X-mode will then reach the UHR and excite the EBW. Like the O-X-B mode-conversion, the X-B mode-conversion has been welldemonstrated experimentally [32,33,34]; unlike the O-X-B mode-conversion, however, the X-B mode-conversion is difficult to study analytically, and is typically studied computationally with particle-in-cell methods [35,36,37] or full-wave solvers [38,39]. This trend can probably be attributed in large part to the inherent non-locality of the X-B mode-conversion, which will be elucidated in the following section.…”

Section: Introductionmentioning

confidence: 94%

Mode-conversion of the extraordinary wave at the upper hybrid resonance in the presence of small-amplitude density fluctuations

Lopez

Ram

2018

Plasma Phys. Control. Fusion

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In spherical tokamaks, the electron plasma frequency is greater than the electron cyclotron frequency. Electromagnetic waves in the electron cyclotron range of frequencies are unsuitable for directly heating such plasmas due to their reduced accessibility. However, mode-conversion of the extraordinary wave to the electron Bernstein wave (X-B mode-conversion) at the upper hybrid resonance makes it possible to efficiently couple externally-launched electromagnetic wave energy into an overdense plasma core. Traditional mode-conversion models describe an X-mode wave propagating in a potential containing two cutoffs that bracket a single wave resonance. Often, however, the mode-conversion region is in the edge, where turbulent fluctuations and blobs can generate abrupt cutoffs and scattering of the incident X-mode wave. We present a new framework for studying the X-B mode-conversion which makes the inclusion of these fluctuations analytically tractable. In the new approach, the highfield cutoff is modelled as an infinite barrier, which manifests as a boundary condition applied to a wave equation involving only one cutoff adjacent to the resonance on the low-field side. The new model reproduces the main features of the previous approach, yet is more suitable for analyzing experimental observations and extrapolating to higher dimensions. We then develop an analytical estimate for the effect of small-amplitude, quasi-monochromatic density fluctuations on the X-B mode-conversion efficiency using perturbation theory. We find that Bragg backscattering of the launched X-mode wave reduces the mode-conversion efficiency significantly when the fluctuation wavenumber is resonant with the wavenumber of the incident X-mode wave. These analytical results are corroborated by numerically integrating the mode-conversion equations.to their compact size and attractive stability properties. However, since STs typically operate in an overdense regime, it is difficult to use traditional EC waves on STs for heating and current drive purposes.Fortunately, the electron Bernstein wave (EBW) provides a method to heat an overdense plasma in the EC frequency range. The EBW[10, 11] is a thermal mode which exists in the vicinity of the upper hybrid resonance (UHR) and the harmonics of the electron cyclotron resonance. It freely propagates within discrete frequency bands [12,13], which can be roughly mapped into discrete spatial bands for an inhomogeneous plasma. Importantly, the EBW which originates at the UHR propagates unimpeded towards larger magnetic field until it reaches the nearest cyclotron resonance, where it will damp strongly [14,15,16]. This feature makes the EBW ideal for heating overdense plasmas.Being a thermal mode of predominantly electrostatic polarization, the EBW does not propagate in vacuum; the excitation of the EBW via external means is non-trivial. Grills are not typically used due to the small grid spacing required to excite a wave whose wavelength is comparable to the electron gyroradius [11]. Instead, experiments often us...

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Section: Introductionmentioning

confidence: 94%

Mode-conversion of the extraordinary wave at the upper hybrid resonance in the presence of small-amplitude density fluctuations

Lopez

Ram

2018

Plasma Phys. Control. Fusion

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“…Recent studies [15] demonstrated RF heating in the RFP configuration using the EBW on Madison Symmetric Torus. A challenging heating environment exists in the RFP, where electromagnetic wave cutoffs occur within ~1cm of the edge and enclose the plasma volume due to an overdense plasma with no high field side.…”

Section: Ebw Heating Overviewmentioning

confidence: 99%

Construction of an EBW Heating System for the MST RFP

2019

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“…In the last few years, the study of electron Bernstein waves in plasma has been a particular field of interest due to its many applications in plasma heating [1], acceleration of charge particles [2], harmonic generation [3] and diagnostics [4]. The linear [5] and nonlinear [6] coupling of waves in plasmas is a promising nature for application in producing resonant heating of high β plasma and power excitation.…”

Section: Introductionmentioning

confidence: 99%

Excitation of electron Bernstein waves by beating of two cosh-Gaussian laser beams in a collisional plasma

Kumar

Varma

2021

Laser Phys.

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In this paper, a theoretical study has been proposed for excitation of electron Bernstein waves in collisional plasma with dc magnetic field by nonlinear interactions of two cosh-Gaussian laser beams. The beat wave with frequency ω = (ω 1 − ω 2 ) and wave vector ⃗ k = ⃗ k 1 + ⃗ k 2 , exerts a nonlinear ponderomotive force on electrons. This nonlinear force has the potential to drive the electron Bernstein wave in collisional plasma with dc magnetic field. The convective loss of waves in plasma is also discussed. An analytical formalism is developed for power going into the electron Bernstein wave with respect to total laser power. The variation of normalized potential and power distribution profile as a function of beam direction, normalized beat wave frequency, and normalized collisional frequency is demonstrated to excite Electron Bernstein waves (EBWs) under resonance conditions. The spatial shape of laser beam, optimum laser beam width parameter, decentred parameter, extreme value of electron thermal velocity and cyclotron frequency is proposed for much more excitation. This proposed theory of electron Bernstein wave excitation may be applicable for plasma heating.

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Observation of Electron Bernstein Wave Heating in a Reversed Field Pinch

Cited by 9 publications

References 24 publications

Mode-conversion of the extraordinary wave at the upper hybrid resonance in the presence of small-amplitude density fluctuations

Mode-conversion of the extraordinary wave at the upper hybrid resonance in the presence of small-amplitude density fluctuations

Construction of an EBW Heating System for the MST RFP

Excitation of electron Bernstein waves by beating of two cosh-Gaussian laser beams in a collisional plasma

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