Bernstein Wave Research Articles

High-Frequency Nongyrokinetic Turbulence at Tokamak Edge Parameters

First of a kind 6D-Vlasov computer simulations of high frequency ion Bernstein wave turbulence for parameters relevant to the tokamak edge show transport comparable to sub-Larmor-frequency gyrokinetic turbulence. The customary restriction of magnetized plasma turbulence studies to the gyrokinetic approximation may not be based on physics but only on a practical constraint due to computational cost. Deciphering turbulent transport is crucial since edge turbulence significantly influences the confinement properties of magnetically confined plasmas. Despite the high computational costs, performing 6D kinetic simulations is essential for understanding the limitations of our current models. Published by the American Physical Society 2024

Heating characteristic of electron Bernstein wave using high-field side X-mode injection in QUEST

Abstract A comparative investigation was conducted to assess the impact of high-field side (HFS) extraordinary (X) mode (HFS X) injection and low-field side (LFS) ordinary (O) mode (LFS O) injection of 8.2 GHz radio frequency (RF) power in the Q-shu University experimental steady-state spherical tokamak. In the case of the HFS X injection, the ratio of electron plasma frequency and RF frequency f pe / f RF was 1.3, indicating an overdense plasma, whereas in the LFS O injection, this ratio was 0.9. Distinctive features emerged in the electron temperature and density profiles between the two injection scenarios. In the HFS X injection, the profiles peaked between the fundamental electron cyclotron resonance (ECR) layer and the upper hybrid resonance layer. Conversely, in the LFS O injection, the peaks were situated near the 1st ECR layer. This implies effective excitation of the electron Bernstein wave (EBW) in the case of the HFS X injection, with the wave power being absorbed through the doppler-shifted ECR of the EBW. Density and temperature oscillations were observed only in the start-up phase of the HFS X injection, which may correlate with the presence of the left-hand cutoff of the X-mode. These findings will be contributed to understand the distinctive characteristics associated with plasma heating through EBW excitation in the HFS X injection.

Flat-top plasma operational space of the STEP power plant

Abstract STEP is a spherical tokamak prototype power plant that is being designed to demonstrate net electric power. The design phase involves the exploitation of plasma models to optimise fusion performance subject to satisfying various physics and engineering constraints. A modelling workflow, including integrated core plasma modelling, MHD stability analysis, SOL and pedestal modelling, coil set and free boundary equilibrium solvers, and whole plant design, has been developed to specify the design parameters and to develop viable scenarios. The integrated core plasma model JETTO is used to develop individual flat-top operating points that satisfy imposed criteria for fusion power performance within operational constraints. Key plasma parameters such as normalised beta, Greenwald density fraction, auxiliary power and radiated power have been scanned to scope the operational space and to derive a collection of candidate non-inductive flat-top points. The assumed auxiliary heating and current drive is either from electron cyclotron systems only or a combination of electron cyclotron and electron Bernstein waves. At present stages of transport modelling, there is a large uncertainty in overall confinement for relevant parameter regimes. For each of the two auxiliary heating and current drive systems scenarios, two candidate flat-top points have been developed based on different confinement assumptions, totalling to four operating points. A lower confinement assumption generally suggests operating points in high-density, high auxiliary power regimes, whereas higher confinement would allow access to a broader parameter regime in density and power while maintaining target fusion power performance.

Overview of recent results from the ST40 compact high-field spherical tokamak

Abstract ST40 is a compact, high-field (BT0 ≤ 2.1T) spherical tokamak (ST) with a mission to expand the physics and technology basis for the ST route to commercial fusion. The ST40 research programme covers confinement and stability; solenoid-free start-up; high-performance operating scenarios; and plasma exhaust. In 2022, ST40 obtained a central deuterium ion temperatures of 9.6 ± 0.4 keV, demonstrating for the first time that pilot plant relevant ion temperatures can be reached in a compact, high-field ST. Analysis of these high-ion temperature plasmas is presented, including a summary of confinement, transport and microstability characteristics and energetic particle instabilities. Recent scenario development activities have focused on establishing diverted H-mode plasma discharges across a range of toroidal fields and plasma currents, along with scenarios with high non-inductive current fractions. In future operations, beginning in 2025, a 1MW dual frequency (104/137 GHz) electron cyclotron (EC) system will be installed to enable the study of EC and electron Bernstein wave plasma start-up and current drive. Predictive modelling of the potential performance of these systems is presented.

Demonstration of metaplectic geometrical optics for reduced modeling of plasma waves.

The Wentzel, Kramers, and Brillouin (WKB) approximation of geometrical optics is widely used in plasma physics, quantum mechanics, and reduced wave modeling, in general. However, it is well-known that the approximation breaks down at focal and turning points. In this paper, we present an unsupervised numerical implementation of the recently developed metaplectic geometrical optics framework, which extends the applicability of geometrical optics beyond the limitations of WKB, such that the wave field remains finite at caustics. The implementation is in 1D and uses a combination of Gauss-Freud quadrature and barycentric rational function inter- and extrapolation to perform an inverse metaplectic transform numerically. The capabilities of the numerical implementation are demonstrated on Airy's and Weber's equations, which both have exact solutions to compare with. Finally, the implementation is applied to the plasma physics problem of linear conversion of X mode to electron Bernstein waves at the upper hybrid layer and a comparison is made with results from fully kinetic particle-in-cell simulations. In all three applications, we find good agreement between the exact results and a reduced wave modeling paradigm of metaplectic geometrical optics.

On possibility of anomalous microwave power absorption and gyrotron frequency sub-harmonics emission in X2-mode ECRH experiments at the TCV tokamak

In this paper, we analyze theoretically the low-threshold parametric decay instability (PDI) that can be excited at the tokamak à configuration variable (TCV tokamak, Lausanne, Switzerland) during X2 electron cyclotron resonance heating experiments producing a two-dimensionally localized upper hybrid (UH) wave and a daughter extraordinary wave running from the decay layer outward to the plasma edge. The primary instability is then saturated due to the cascade of secondary decays into two-dimensionally localized UH and ion Bernstein waves. The level of plasma microwave emission in the frequency range substantially below half the pump wave frequency and of anomalous power losses of the pump are predicted.

Stability analysis of plasma waves driven by runaway electrons in tokamak hot plasmas

The local stability analysis of plasma waves driven by runaway electrons (REs) has been performed considering hot plasma Maxwellian background, with electron and ion temperatures of the order of 1 keV. It is shown that hot plasma waves, namely electron plasma waves (EPWs) and ion Bernstein waves (IBWs) can be driven unstable by RE at their coalescence frequency via Cherenkov resonance by RE with energy distribution peaked at about 8 MeV. A skew-normal distribution is used as a model of the RE energy distribution. The EPW and IBW couples of waves occur between any successive ion-cyclotron harmonics frequencies nf ci, above the lower hybrid resonance. At their confluence, the perpendicular group velocity vanishes and significant RF emissions are expected. The frequency gap between two successive confluences is ∼f ci. Groups of RF line emissions, separated by almost constant frequency gap ∼f ci/2 are detected during various quiescent runaway plasma discharges in the FTU tokamak. The analysis of a specific discharge suggests that the frequencies of the line emissions observed and the frequencies occurring at the EPW-IBW confluences are in reasonable agreement. A possible explanation of the line emissions with ∼f ci/2 gap in terms of nonlinear mode coupling is proposed.

Mass dependency of high-wavenumber turbulence in a linear partially magnetized plasma

We investigated the mass dependency of the high-wavenumber turbulence, which occurs at scales smaller than the ion effective Larmor radius, in a partially magnetized plasma column. In this system, two different types of fluctuations were observed: one exhibiting a coherent discrete spectrum, while the other displaying a broadband continuous spectrum. The phase velocities of both types showed a similar mass dependency, approximately matching the ion sound velocity or electron diamagnetic drift velocity. Additionally, we found that the discrete spectrum has a peak interval frequency comparable to the ion cyclotron frequency, which is consistent with ion cyclotron ranges of fluctuations, including ion Bernstein waves.

Cascades of Parametric Instabilities in the Tokamak Plasma Edge during Electron Cyclotron Resonance Heating.

We report observations of nonlinear two-plasmon decay instabilities (TPDIs) of a high-power microwave beam, a process similar to half-harmonic generation in optics, during electron cyclotron resonance heating in a tokamak. TPDIs are found to occur regularly in the plasma edge due to wave trapping in density fluctuations for various confinement modes, and the frequencies of both observed daughter waves agree with modeling. Emissions from a cascade of subsequent decays, which indicate a generation of ion Bernstein waves, are correlated with fast-ion generation. This emphasizes the limitations of standard linear microwave propagation models and possibly paves the way for novel microwave applications in plasmas.

The ion cyclotron parametric instabilities and the anomalous heating of ions in the scrape-off layer of tokamak plasma in the high harmonic fast wave heating regime

The electrostatic parametric instabilities of a plasma, driven by the high harmonic fast wave (HHFW) with frequency at ion cyclotron (IC) harmonics of order 30–50 are investigated numerically. The derived numerical results are consistent with parametric decay of HHFW into the high harmonic IC (Bernstein) wave and an unobserved IC quasimode under conditions of the negligible small electron Landau damping. The detected instability develops in the finite interval of the HHFW wavelength along the toroidal magnetic field. The development of this ion kinetic quasimode decay instability is accompanied by the anomalous anisotropic heating of ions, resulted from the interaction of ions with IC parametric turbulence. It was found that the anomalous heating rate of ions across the magnetic field is much larger than the heating rate of ions along the magnetic field. The anisotropic heating of the scrape-off layer ions was observed on the National Spherical Torus Experiment experiments with HHFW heating and current drive at IC harmonics of order 10 [G. Taylor et al. Phys. Plasmas 17, 056114 (2010), and J. Hosea et al. Phys. Plasmas 15, 056104 (2008)]. The derived results predict that these experimental results will be reproduced qualitatively in the experiments with HHFW heating and current drive using HHFW at IC harmonics of order 30–50.

An alternative method to mimic mode conversion for ion cyclotron resonance heating

Ion cyclotron range of frequency waves in hot plasmas exhibit spatial dispersion effects and the wave equation takes the integro-differential form. Under the local plasma model assumption, the wave equation can be simplified to the differential form and adapts to the numerical scheme of the finite element method (FEM). Even though direct absorption of fast waves by ions and electrons can be described well by the local plasma model, linear mode conversion associated with non-local effects is absent. To deal with this issue, an alternative method is put forward in this paper where quasi-electrostatic fluid waves based on the multi-fluid warm plasma model are employed to take the place of ion Bernstein waves in mode conversion. On this basis, an interative fluid-kinetics (INTFLUK) code based on the FEM is developed for full-wave simulation in hot plasmas. Derivation of the wave equations as well as benchmarking of the INTFLUK code against other wave simulation codes are carried out. In both one- and two-dimensional cases, the validity of the INTFLUK code was verified by comparison of the wave field distributions and power deposition. As a useful illustration of the INTFLUK code including the scrape-off layer and a realistic antenna, the influence of the poloidal antenna phasing difference on ion cyclotron resonance heating is analyzed. Finally, it should be noted that the method in this paper has the potential to be extended to the three-dimensional case, which will be considered in the near future.

A performance portable implementation of the semi-Lagrangian algorithm in six dimensions

This paper describes our approach to developing a simulation software application for the fully kinetic 6D-Vlasov equation, which will be used to explore physics beyond the reduced gyrokinetic model. Simulating the fully kinetic Vlasov equation requires efficient utilization of compute and storage capabilities due to the high dimensionality of the problem. In addition, the implementation needs to be extensible regarding the physical model and flexible regarding the hardware for production runs. We start on the algorithmic background to simulate the 6-D Vlasov equation using a semi-Lagrangian algorithm. The performance portable software stack, which enables production runs on pure CPU as well as AMD or Nvidia GPU accelerated nodes, is presented. The extensibility of our implementation is guaranteed through the described software architecture of the main kernel, which achieves a memory bandwidth of almost 500 GB/s on a V100 Nvidia GPU and around 100 GB/s on an Intel Xeon Gold CPU using a single code base. We provide performance data on multiple node-level architectures discussing utilized and further available hardware capabilities. Finally, the network communication bottleneck of 6-D grid-based algorithms is quantified. A verification of physics beyond gyrokinetic theory, for the example of ion Bernstein waves, concludes the work.

Application of linear electron Bernstein current drive models in reactor-relevant spherical tokamaks

Electron Bernstein current drive (EBCD) systems in spherical tokamaks are sensitive to plasma and launch conditions, and therefore require large parametric scans to optimise their design. One particular bottleneck in the simulation workflow is quasilinear modelling of current drive efficiency. Linear adjoint models are an attractive alternative, offering a ∼103 × speed-up compared to quasilinear codes. While linear models are well-tested and commonly used for electron cyclotron current drive (ECCD), they have seen little use in EBCD modelling. In this work, variants of the linear model are applied to EBCD and compared to quasilinear results in a reactor-relevant plasma, i.e. Spherical Tokamak for Energy Production (STEP). This comparison reveals it is important to accurately model the collision operator and finite Larmor radius effects in the linear model. When done properly, good agreement is found with quasilinear calculations, at least for normalised minor radii ρ < 0.7 and at low power densities. The power density threshold for quasilinear effects during EBCD is found to be significantly lower than that of ECCD. This is attributed to the much lower group velocity of the electron Bernstein wave (EBW). Thus, the linear model is only valid for EBCD modelling at low power densities (e.g. ≲ 1 MW launched EBW power in STEP). This may be satisfied in present-day experimental devices, but certainly not in reactors targeting non-inductive operation.

Simulation study of the harmonic structure of lower hybrid waves driven by energetic ions.

By means of one-dimensional, electromagnetic, particle-in-cell simulations considering the effects of energetic-ion injection, we study the harmonic structure of lower hybrid waves (LHWs) driven by energetic ions under the condition where the electron plasma frequency (ω_{pe}) is smaller than the electron cyclotron frequency (Ω_{e}). It is found that after the LHWs are excited with the wave number and frequency of (k_{1},ω_{1}), many harmonic LHWs are generated at (mk_{1},nω_{1}) where m and n are integers, up to far beyond the lower hybrid resonance frequency, m and n∼10. We show that the harmonic LHWs are generated by nonlinear wave-wave coupling between the LHWs directly excited by the energetic ions and the energetic-ion cyclotron waves above the lower hybrid resonance frequency. We also find that the harmonic LHWs can exist even after the energetic ions are artificially removed because they can be coupled with ion Bernstein waves due to bulk ions. The effect of the energetic-ion injection and the dependence of ω_{pe}/Ω_{e} on the development of the harmonic LHWs are investigated to compare the simulation results with an observation in Earth's magnetosphere.

Oblique Bernstein wave propagation in electron‐ion plasma with electron quantization effects

AbstractWe have studied the role of electron quantization effects on the dispersion characteristics of the oblique electron Bernstein wave (EBW) in an electron‐ion plasma using Vlasov‐Poisson model. Our analysis shows that large thermal effects (as compared to quantization effects) give rise to the usual classical results while in the limit of strong magnetic field, the dispersion characteristics changes. The existence of a quantum Bernstein mode has been proposed which appears purely due to the electron quantization effects. The damping of the oblique EBW has also been analyzed in detail and we found that the magnitude of the damping of the wave decreases as we decrease the obliqueness parameter (parallel to perpendicular wavenumber ratio) which agrees with the earlier theoretical and experimental findings. Moreover, the strong quantization effects () also tend to suppress the damping of EBW which contributes to the stabilization of the waves. The present findings are relevant to the laboratory laser‐produced plasmas where strong external magnetic fields exist, and also to the dense astrophysical plasma environments.

Electron Bernstein wave aided Hermite cosh-Gaussian laser beam absorption in collisional plasma

In this paper, we theoretically study the electron Bernstein wave aided Hermite-Cosh-Gaussian laser beam absorption in collisional plasma with a static magnetic field. This laser beam may have the potential to couple the pre-existing electron Bernstein wave with the coupled wave frequency and wave number where and are the electron Bernstein wave and laser beam frequencies, respectively, and and are the electron Bernstein wave and laser beam wave numbers, respectively. The plasma electron oscillatory velocities associated with the coupled wave mode produce the linear and nonlinear current density. An expression for the nonlinear absorption coefficient of an electron Bernstein wave aided Hermite cosh-Gaussian laser beam is analytically derived and more concisely discussed via different relative graphs. The graphical results promise that the absorption coefficient is strongly dependent on Hermite mode index m, beam decentered parameter d associated with the cosh term, laser beam width, laser beam frequency, electron Bernstein wave frequency, electron cyclotron frequency, electron thermal velocity and collisional frequency. Nonlinear coupling, collision phenomena and laser beam decentered parameter (very sensitive parameter) play an important role in absorption processes. The association of a very small electron Bernstein wave frequency with the laser beam causes too much of an increase in the absorption coefficient compared to only the laser beam. This efficient nonlinear absorption process may be applicable to plasma electron heating and the harmonic generation process.

Excitation of electron Bernstein wave by nonlinear interaction of two copropagating Hermite–Gaussian laser beams in collisional plasma with static magnetic field

Excitation of electron Bernstein wave by nonlinear interaction of two copropagating Hermite–Gaussian laser beams in collisional plasma with static magnetic field

Wave Activities Throughout a Low‐Mach Number Quasi‐Parallel Shock: 2‐D Hybrid Simulations

AbstractIn this paper, two‐dimensional hybrid simulations are used to study wave excitation and evolution throughout a low‐Mach number quasi‐parallel shock. Simulation results show that quasi‐parallel fast magnetosonic waves, ion Bernstein waves with harmonics and possible Alfven/ion cyclotron waves can be excited in the upstream region, and their small phase velocities compared to injected flow velocity results in the convection to the shock front where they are mode converted into several groups of downstream waves, including Alfven waves along the directions parallel to downstream average magnetic fields and perpendicular to the shock normal, the quasi‐perpendicular kinetic slow waves and possible kinetic Alfven waves. We suggest that downstream Alfven waves originate from the mode conversion of upstream quasi‐parallel fast magnetosonic waves with left‐hand polarization in the downstream rest frame under helicity conservation, while the downstream left‐hand polarized kinetic slow waves and right‐hand polarized kinetic Alfven waves can be from the upstream quasi‐perpendicular ion Bernstein waves.

Simulations of energy deposition of electron cyclotron waves in a dipole-confined plasma based on ray trajectory

The energy deposition of electron cyclotron waves in a dipole-confined plasma is investigated for the RT-1 device, specifically including the effects of high-energy electrons and the electron Bernstein wave (EBW) excitation and absorption. Simulations of wave trajectories with various injection locations and angles indicate that the energy deposition of ordinary mode (O-mode) and extraordinary modes (X-mode) is small in low-temperature plasmas. The high-energy electrons in the plasma increase the energy deposition of the X-mode but have little effect on the O-mode. Meanwhile, the energy deposition of the slow X-EBW conversion and O-X-EBW conversion to excite EBW is also discussed. The results show that the converted EBW in an over-dense plasma is easily obtained, but it may not always have efficient energy deposition. Finally, the possible mechanism for the plasma production and heating by using electron cyclotron waves is proposed.

Obliquely propagating electron Bernstein wave in arbitrary degenerate plasma

Abstract On employing the linearized Vlasov–Maxwell model, the dispersion relation of obliquely propagating Bernstein wave in thermal electron gas including quantum effect of arbitrary/partial degeneracy in the presence of non-relativistic arbitrary magnetic field limits is derived. In particular, the results are obtained in the propagation range k z &gt; k x with k x ≠ 0 under high frequency (ω ≫ k.v) and weak propagation (Ω ≫ k.v or k → 0) limits. The propagation angle θ ′ $\left({\theta }^{\prime }\right)$ defines the obliqueness of wave such that for θ′ = 0° and 90° we obtain the perpendicular propagating pure Bernstein wave and parallel propagating Langmuir wave, respectively. The graphical analysis of newly reported results is made under the numerically evaluated values and the previously reported results are also retained. The possible applications of present results are found in partially/arbitrary dense astrophysical quantum plasma e.g., in brown dwarfs as well as they have wide ranging potential applications in modern technology e.g., in semi-conductors.