Lower Hybrid Waves Research Articles

Lower-hybrid wave instability due to multiple fast heavy ion ring distributions in the SMART experiment

Development and stability of heavy ion ring beams created by high speed neutral atom injection in the Earth's ionosphere is analyzed in view of the upcoming space measurement of a rocket-released turbulence (SMART) mission. It is found that due to velocity dispersion of the injected neutral atoms, an ensemble of ion ring beams will be formed at a given location upon photoionization. Associated with the multiple-ion ring beams, various beam and lower-hybrid (LH) waves develop. Wave dispersion analysis indicates that the beam energy is extracted through double resonances with beam and LH modes (i.e., ω∼kvr∼ωlh, where ωlh is the LH frequency, k is the wavenumber, and vr is the ring mean speed). For the SMART experimental conditions, we find that, far from the release point, the velocity spacing between the ion ring beams Δv will be much less than the mean speed of the beams themselves, vr. Therefore, we show that the system will behave essentially as if represented by a single ring with an effective alpha (α) parameter (a ratio of ring to background plasma density), that is larger by a factor that is equal to N, the total number of rings. A major difference from the traditional single beam analysis is that for the more realistic multiple beam case, the effective instability is more intense because the wave growth rate now scales as ∼(Nα)2/5.

Influence of increased magnetic field on Alfvén eigenmodes on upgraded spherical tokamak Globus-M2

During modernization of the Globus-M tokamak, toroidal magnetic field and plasma current were increased, and a number of diagnostics were upgraded, which made it possible to study phenomena associated with the excitation of Alfvén waves in a spherical tokamak in a wider range of plasma parameters. In the experiments with neutral beam injection, the dependences of fast particle losses initiated by the toroidal Alfvén eigenmodes (TAE) on their magnitude in the magnetic field range of 0.4 – 0.7 T and currents of 180 – 330 kA were acquired. Resulting dependences confirm previously obtained results and indicate a decrease in losses with increasing magnetic field and plasma current. At the same time, a number of new phenomena, that have never been observed on Globus-M were detected. In experiments with neutral beam injection at the current ramp up stage, Alfvén cascades (AC) in the frequency range of 100 – 300 kHz were observed for the first time. By means of the Doppler backscattering diagnostics (DBS), it was shown that ACs are localized closer to magnetic axis unlike TAE. Also, during low hybrid wave current drive (LHCD) experiments, global Alfvén eigenmodes (GAE) were detected at a frequency close to 1 MHz, apparently driven in the resonance with runaway electron beam. Detected global eigenmodes are also able to arise in ohmic discharges, however, their magnitude is lower.

Scattering of Lower Hybrid Waves in a Magnetized Plasma

In this paper, the Maxwell equations for the electric field in a cold magnetized plasma in the half-space of x≥0 cm are solved. The boundary conditions for the electric field include a pointwise source at the plane x=0 cm, the derivatives of the electric field that are zero statV/cm2 at x=0 cm, and the field with all its derivatives that are zero at infinity. The solution is explored in terms of the Laplace transform in x and the Fourier transform in y-z directions. The expressions of the field components are obtained by the inverse Laplace transform and the inverse Fourier transform. The saddle-point technique and power expansion have been used for evaluating the inverse Fourier transform. The model represents the propagation of a lower hybrid wave generated by a pointwise antenna located at the boundary of the plasma. Here, the antenna is the boundary condition. The validation of the model is performed assuming that the electric field component Ey=0 statV/cm and by comparing it with the model of electromagnetic waves generated by a local small antenna located near the boundary of a tokamak, and an experiment is suggested.

Structure-preserving electromagnetic–kinetic simulations of lower hybrid-wave injection and current drive

In this article, we present a first-principles electromagnetic–kinetic simulation of the slow-wave branch of the lower hybrid waves (LHWs) in electron–deuterium plasmas with real ion–electron mass ratios. Several models of two-dimensional slab configuration containing a grill antenna are constructed using different plasma parameters. Based on our recently developed fully kinetic charge-conservative electromagnetic non-canonical symplectic particle-in-cell method, we studied the coupling, propagation, absorption and current driving effect of LHWs in hot plasmas. The results for the coupling coefficient of the grill antenna, accessibility condition, and electron Landau damping rate show good agreement with theory and previous simulation. The long-term non-linear energy and current deposition of propagating LHWs are also presented, which show a decrement of heating and current-driving efficiency compared with the linear theoretical prediction. The collision effect between electrons and ions is shown to be important for actually driving the current. The relation between the density of the current generated and the amplitude of the LHW is given, which shows a qualitative agreement with the 1D theoretical prediction.

A Hard X-Ray Pinhole Camera System for Fast Electron Bremsstrahlung Measurements in the HL-2A Tokamak

A hard X-ray pinhole camera system has been recently built at the HL-2A tokamak to measure the evolution of space-time distribution of fast electrons in the energy range of 20 to 200 keV. The camera is mainly composed of a fan-shaped detector array, an observation window, a pinhole mechanism, and a data processing system. The detector array consists of 21 CdTe detectors that are arranged in a poloidal section. The camera views the plasma perpendicularly through an observation window mounted in a horizontal port on the equatorial plane. The data processing is implemented by a fast spectrometry based on field-programmable gate array technology. The time and space resolution of the camera can reach 2 to 16 ms and 2 cm, respectively. During the HL-2A experiment campaign in 2018, measurements of fast electrons produced by lower hybrid waves using the camera were successfully performed. The performance of the camera and the first experimental results with some discussions are presented in this paper.

The factors determining the evolution of edge-localized modes in plasmas driven by lower hybrid currents

Modulated lower-hybrid waves (LHWs) are injected into the Experimental Advanced Superconducting Tokamak to determine the physical principles responsible for the suppression or mitigation of edge-localized modes (ELMs). There are two cases of modulated-ELM evolution (stable and unstable cases), because of two different modulated pedestal densities. They can be attributed to additional magnetic perturbations induced by the LHWs, similarly to the effect of resonant magnetic perturbations. As regards the case of unstable modulated ELM evolution, the plasma stored energy increases as the LHWs turn on. In contrast, the central line-averaged electron density decreases, which is different from the case of ELM suppression or from the stably modulated case. The effect of LHWs or density ‘pump-out’ effect can pass across the top of the pedestal region and enter the interior of the density pedestal, causing a decrease in the electron density gradient and its value at the top of the pedestal. Simultaneously, the pressure gradient and edge bootstrap current density increase. For ELM suppression (or for the stable) case, LHWs can couple only with the plasma outside the top region of pedestal, because of the higher top value of density pedestal. Thus, LHWs can pump out the electron density significantly only in the pedestal foot region, producing a larger gradient of electron density pedestal. Statistical analysis of the data indicates that there is a threshold value of the central line-averaged electron density for each of the two modulated ELM cases. Furthermore, the ELM amplitude is modulated by LHWs with a time delay of hundreds of microseconds, which may be further evidence that LHWs have a significant impact on the evolution of ELMs and pedestal structures. All these results imply that there is a significant correlation between the ELM behavior and the electron density profiles modulated by LHWs.

Lower Hybrid Waves at the Magnetosheath Separatrix Region

AbstractLower hybrid waves are investigated at the magnetosheath separatrix region in asymmetric guide field reconnection by using the Magnetospheric Multiscale (MMS) mission. Three of the four MMS spacecraft observe clear wave activities around the lower hybrid frequency across the magnetosheath separatrix, where a density gradient is present. The observed waves are consistent with generation by the lower hybrid drift instability. The characteristic properties of these waves include the following: (1) the waves propagate toward the x‐line in the spacecraft frame due to the large out‐of‐plane magnetic field, which is in the same direction of the diamagnetic drift of the x‐line; (2) the wave potential is about 20% of the electron temperature. These drift waves effectively produce cross‐field particle diffusion, enabling the transport of magnetosheath electrons into the exhaust region. At last, we suggest that the lower hybrid waves at the magnetosheath separatrix region represent some unique features of asymmetric guide field reconnection, which is different from that widely observed at the magnetospheric side of magnetopause reconnection.

Lower Hybrid Current Drive in High Aspect Ratio Tokamaks

A multi-machine study has been carried out to investigate the impact of a strongly bounded wave propagation domain on the Lower Hybrid current drive, a condition which occurs principally in high aspect ratio tokamaks. In this regime, the condition of kinetic resonance can be far above the upper boundary of the propagation domain, and may not be achieved by the usual toroidal upshift. Therefore no tail of fast electrons can be pulled out from the thermal bulk. Nevertheless, while tokamak plasmas are in principle almost transparent to the wave in this regime so-called “unbridgeable spectral gap”, full current drive is well achieved for the two tokamaks considered in this study, TRIAM-1M (Zushi et al. Nucl Fusion 43:1600, 2003) and WEST (Bourdelle et al. Nucl Fusion 55:063017, 2015), both characterized by a very large aspect ratio \(R/a>5.5\). The case of the high aspect ratio tokamak HL-2A (Liu et al. Nucl Fusion 45:S239, 2005) for which the wave propagation domain has also an upper boundary, but close to the resonance condition, is considered by comparison. First principles modeling of the rf-driven current and the fast electron bremsstrahlung using the ALOHA/C3PO/LUKE/R5-X2 chain of codes shows unambiguously that the spectral gap must be already filled at the separatrix in order to reproduce quantitatively observations and some important parametric dependencies. This result is an important milestone in the physics understanding of the Lower Hybrid current drive, highlighting the existence of a powerful and likely universal alternative mechanism to bridge the spectral gap, that is not related to toroidal magnetic refraction. With an initially broad power spectrum, lobes with low parallel refractive indexes that carry most of the plasma current can be absorbed in almost single pass, restoring the full validity of the ray-tracing approximation for describing the propagation of the Lower Hybrid wave in cold plasmas.

Study of turbulence-induced refraction of lower hybrid waves using synthetic scrape-off layer filaments

Turbulence-induced refraction effects to lower hybrid (LH) wave propagation and current drive are studied using synthetic scrape-off layer (SOL) blob/filament fields. A synthetic 3D, field-following, blob turbulence model is implemented in the ray-tracing/Fokker-Planck (RTFP) codes GENRAY/CQL3D. In Alcator C-Mod, the blob field is shown to significantly affect LH ray-trajectories, leading to increased on-axis damping and smoother current profiles. This effect depends on the average blob size and amplitude. In addition, the diffusion of ray-trajectories in phase-space caused by turbulence increases the robustness of the RTFP model. A modified launch spectrum, acting as a proxy for parametric decay instability (PDI) effects, is included in simulations with the blob model. A synergy between the modified launch spectrum and turbulence-induced refraction results in synthetic hard x-ray profiles that agree with experiment. Lastly, the blob model is used to predict the effect of SOL turbulence on DIII-D high-field side (HFS) LH launch. Assuming low turbulence amplitude in the HFS SOL (∼5%), turbulence-induced refraction is predicted to have little effect on current drive efficiency.

Toroidal field and q95 scalings on error field penetration in EAST

Toroidal field and q95 scalings of error field penetration are investigated with n = 1 resonant magnetic perturbation coil in EAST. The toroidal field scalings of error field penetration thresholds under fixed q95 are about in both ohmically and lower hybrid wave heated plasmas, where br21 is the vacuum error field at the q = 2/1 rational surface and BT is the toroidal field. These scalings indicate a favorable tolerance on error field in ITER. To make clear the underlying physics on toroidal field scaling, the theoretical analysis is given. By subtituting penetration related scaling parameters into the theory, the obtained theoretical scalings are consistent with the experimental observations using the vacuum penetration thresholds. To further investigate penetration threshold in larger operation region, the q95 scaling on penetration threshold with has also been observed. The rational surface radius rs and magnetic shear s, which are crucial to q95 scaling, are included in the theoretical analysis. The theoretical analysis is also consistent with the experimental scalings using the vacuum penetration thresholds. Moreover, the obtained theoretical scalings are easy to compare with experimental scalings. These theoretical analyses will stimulate the extrapolation of error field tolerance towards future reactors.

Experimental progress of hybrid operational scenario on EAST tokamak

Extensive experiments of advanced scenario development, which contribute to the ITER hybrid operational scenario have been carried out on experimental advanced superconducting tokamak (EAST) tokamak recently with the ITER-like tungsten divertor. The in this operational scenario is intermediate up to 2.1 (EAST#78987, ∼ 2.1, I p ∼ 0.45 MA, q 95 = 3.7, ∼ 1.5 T, 3 MW neutron beam injection and 1 MW 4.6 GHz lower hybrid wave). In these hybrid H-mode plasmas, the internal transport barrier (ITB) has been frequently observed with central flat q profile and it is found that the fishbone mode (m/n = 1/1) can be beneficial to sustain the central flat (q(0) ∼ 1) q profile, thus a stable ITB can be obtained. In this case, better plasma performance is achieved. The formation of the ITB of the electron density is related to the fishbone activities. Energy transport analysis shows that the fishbone instabilities have a suppression on electron turbulent energy transport, while the ITB of ion temperature is due to the suppression of high-k modes (electron temperature gradient). The mechanism of turbulence suppression from fishbone instabilities in the EAST tokamak is not clear and needs more investigation. It is also observed that the power threshold for ITB formation is 3.5 MW, which is consistent with the scaling law for other tokamaks. The dimensionless parameter () obtained in the EAST reaches 0.3, but is still lower than the ITER hybrid scenario design (G ≥ 0.4) and needs more extension. Further investigation of extending the operational regimes, such as expanding the ITB foot outwards, would be important for the development of the hybrid and steady-state scenarios for next-step fusion devices like ITER and CFETR.

Lower hybrid wave assisted laser third harmonic generation in magneto plasma

Electrostatic modes present in laser produced plasma are capable of generating strong harmonic radiation. Electrostatic waves provide phase matching and contribute to non-linear coupling. In this paper, lower hybrid waves assist in k-matching to produce the third harmonic of the laser. As the frequency of the lower hybrid wave is very small, the harmonic produced is close to exact. At normalized parameters (amplitude, density, and plasma length), the normalized amplitude of the third harmonic is quite high at a particular value of ω0/ωp and ωc/ωp. This occurs in the proximity of upper hybrid resonance as the process becomes resonant for this value. The magnitude of the normalized amplitude increases as ω02 is close to ωUH2.

Comparative Experiments on Lower Hybrid Wave Heating of Ions in High-Density Hydrogen and Deuterium Plasmas at the FT-2 Tokamak

In the framework of the isotope effect studies at the FT-2 tokamak, the efficiencies were compared of the lower hybrid wave heating of the ion components of the hydrogen and deuterium plasmas with high densities (close to the Greenwald limit, 〈ne〉 ≤ 1020 m–3). It was experimentally ascertained that, in accordance with the theoretical concepts, the efficient axial heating of the deuterium plasma ions occurs, as opposed to the peripheral heating of the hydrogen plasma ions. Such an isotope effect occurs due to the different localization of the plasma-RF wave interaction regions. The distinctive feature of these experiments is the fact that, in deuterium plasma, during the preliminary ohmic heating, the dependence of the energy lifetime on density τЕ(n) is linear (LOC dependence), and, with increasing density, the transition to the improved ohmic confinement mode occurs. In hydrogen plasma, on the contrary, the transition to the saturation mode is observed. In this study, the considerable decrease in τЕ was revealed, observed during the additional lower hybrid wave heating in both hydrogen and deuterium plasmas.

Characterization of disruption halo current between ‘W-Like’ graphite divertor and ‘ITER-Like’ divertor structure on EAST tokamak

The general characteristics of disruption halo currents, including current flowing paths between the components, are studied in the experiments of EAST tokamak with ‘W-Like’ graphite divertor and ‘ITER-like’ tungsten divertor. It is found that lower hybrid waves can efficiently reheat minor disruption plasma, this can drive plasma current for tens, or even hundreds, of milliseconds. The reheated plasma can lead to lower loop voltage and of course lower halo current. Additionally, it is confirmed that helium can not rapidly cool down plasmas with high thermal energy, but Argon can shut down plasma rapidly even with a little amount of gas. Until now no runaway electron plateau has been observed both in Argon and Helium mitigation experiments. The EAST disruption database shows that: (1) Larger loop voltage is driven in vertical displacement event disruptions than in major disruptions. (2) Halo currents decrease with the decrease of vertical displacement. (3) The boundary of is 0.72, less than the limit shown in IDDB. The experimental results described here can help to improve the design of the planned upgrade of the EAST lower divertor, and provide physics information for the ITER divertor.

An improved asymptotic matching technique to trace the wave amplitude of rays across singularities: Application to lower-hybrid wave propagation in tokamaks

A most persistent limitation of the geometrical-optics (GO) approximation is the difficulty in integrating the focusing/defocusing term in the equation for the wave amplitude when rays go through singularities (i.e., caustics and cutoffs), points where GO fails and wavelengths and other wave field-related quantities (e.g., the wave amplitude and energy density) become arbitrarily large. A new asymptotic matching (AM) technique is thus presented which allows one to recover the wave amplitude of rays crossing singularities and which improves on a previous approach [A. H. Glasser and A. Bravo-Ortega, Phys. Fluids 30, 797 (1987)]: it goes higher in the order of the asymptotic expansion about the singular point and eventually leads to a less critical violation of the GO ordering when a ray approaches and crosses a caustic or a cutoff. The implementation of this new AM technique is verified and validated against analytical solutions in slab geometry for the lower-hybrid (LH) cutoff and is illustrated with numerical examples of LH wave propagation in a tokamak plasma, using parameters characteristic of a LH current drive experiment. The new and previous approaches are compared regarding several computed ray quantities (e.g., the second derivatives of the eikonal phase, which contribute to the focusing/defocusing term, as well as the wave amplitude and energy density), the inclusion of more terms in the asymptotic expansion about the singularity making it possible to start, say, jumping the latter in a region where GO is less severely challenged. Practical criteria for AM implementation and for testing the validity of GO and of the asymptotic expansion are also provided and discussed.

The unstable ELM evolution modulated by lower hybrid waves on EAST

Modulated lower hybrid waves, are injected into the Experimental Advanced Superconducting Tokamak (EAST), to investigate the modulated evolutions of pedestal structure and unstable edge-localized modes (ELMs). The spectrum patterns of show that the ELM amplitude only slightly decreases while the ELM frequency becomes almost 3–5 times larger as the lower hybrid radio frequency (LHRF) jumps into the lower power level. Pedestal structure analysis indicates that higher LHRF power injection can increase the plasma stored energy and core plasma parameters, accompanying with the pedestal shift and gradient increase. Ion saturation contour current plots suggest that LHRF power can deposit in the plasma edge region to profoundly change the three-dimensional (3D) magnetic topology, similarly to the effect of resonant magnetic perturbations (RMPs), by inducing the helical current filaments (HCFs) following along the magnetic field lines in the scrape-off layer (SOL), which may cause the density pump-out effect by increasing the radial plasma transport. The modulated higher temperature and lower density of pedestal top-values can reduce the pedestal collisionality, which will strongly increase the bootstrap current density and gradually shift the Peeling-Ballooning mode (PBM) boundary. ELITE code stability analysis indicates that LHRF injection can lead to the relatively unstable ELMs with a higher pedestal gradient, simultaneously accompanying with the normalized pressure gradient and edge bootstrap current density increase. All of these results imply that there is a significant correlation between the ELM behavior and pedestal structure modulation because of LHRF dissipation at the plasma edge for the unstable ELM modulated case.

Simulation of divertor heat flux width on EAST by BOUT++ transport code

The BOUT++ edge plasma transport code is applied to study the effects of neutral recycling, drifts and heating scheme on edge plasma profiles and the divertor heat flux width of two discharges of the experimental advanced superconducting tokamak (EAST) steady-state H-mode plasmas heated by low hybrid wave (LHW) and neutral beam (NB), respectively. Neutral recycling seems to have played an important role in the plasma density profile. The edge plasma density drops dramatically for the case w/o neutral recycling, while it can be sustained for the case w/ neutral recycling. Drifts are found to have significant influences on edge plasma profiles. Both the amplitude and width of the divertor heat flux are found to have increased a lot due to drifts. The simulated heat flux width w/ drifts for the two discharges shows reasonable agreement with the experiments. However, the width from the simulation and experiment for the LHW heated discharge is much larger than that of the NB heated discharge. Comparison with Goldston’s drift-based model and more detailed analysis on the heat flux contributions from drifts versus turbulence show that drifts are the dominant factor in edge plasma transport for both LHW and NB heated discharges, while turbulence may have played a more important role in determining the heat flux width in LHW heated discharges than that in NB heated discharges. This may account for the larger heat flux width in the LHW heated discharge. The magnetic topology and the equilibrium change by the LHW power may also be a potential reason for the larger heat flux width in the LHW heated discharges, which still needs more evidence and studies to support it. Additional SOLPS simulation w/o drifts for the two discharges show reasonable agreement with the counterpart from the BOUT++ simulation, suggesting the two are both suitable codes for EAST edge plasma simulation.

Power threshold and confinement of the I-mode in the EAST tokamak

Sixty-five discharges have been confirmed as I-mode discharges after searching the EAST database from 2016 to 2018, and some additional I-mode discharges were obtained in 2019. The I-mode regime features no edge localized modes (ELMs), high energy confinement, and a steep temperature pedestal, while particle confinement remains at L-mode levels. The I-mode regime has been obtained over a small parameter space (BT = 2.4 – 2.7 T, Ip = 0.4 – 0.6 MA, q95 = 4 – 6) using a configuration with drift away from the active X-point. Most of the discharges in EAST are dominated by lower hybrid wave (LHW) heating. In addition, some are heated with both LHW and neutral beam injection (NBI) heating, and a few discharges are heated by NBI and electron cyclotron resonance heating (ECRH). Turbulence suppression in density perturbation has been defined as signaling the onset of the L-I transition. The power threshold of the I-mode is slightly larger than that of the 2008 ITPA scaling law of H-mode. The minimum L-I power threshold varies only weakly with BT, and the power range for the I-mode increases with increasing BT. The I-mode is superior to the L-mode in terms of energy confinement but is still slightly inferior to the H-mode under similar conditions, although the energy confinement time decreases more slowly with increasing heating power than it does in the typical H-mode case. NBI has some benefit for achieving higher confinement. The I-mode is very sensitive to the density near the edge. Under a constant high heating power, a small enhancement in the density will terminate the I-mode, sometimes leading to the I-H transition.

Excitation of lower hybrid wave by an ion beam in magnetized plasma – Reinvestigated

Study of various kinds of waves propagating through partially or fully ionized plasma has been of great interest for scientists. In this direction, theoretical and experimental studies have been carried out and results have been published in series of papers from time to time. Excitation of lower hybrid wave by an ion beam in magnetized plasma has been considered by Prakash et al. [11]. We have looked into that work and have found several major discrepancies. Therefore, the results of that paper may not be reliable.

Core tungsten transport in WEST long pulse L-mode plasmas

Tungsten transport is investigated in WEST long pulse L-mode plasmas operated with the strike point on the actively cooled upper tungsten divertor. The pulses are mostly heated by lower hybrid waves. It is experimentally found that tungsten does not centrally accumulate throughout these ∼ 30 s reproducible discharges despite large normalised electron density gradients . To explain these observations, turbulent and neoclassical transport of electrons and tungsten ions are computed with GKW Peeters A.G. et al (2009 Computer Phys. Commnun. 180 2650) and NEO Belli E. and Candy J. (2008 Plasma Phys. Control. Fusion 50 095010), Belli E. and Candy J. (2012 Plasma Phys. Control. Fusion 54 015015) respectively. Additionally, interpretative integrated modelling simulations are also performed to keep data coherency despite the lack of measurements of some quantities such as the Ti profiles. Modelled are found consistent with interferometry inversions and the tungsten peaking factor remains comparable to due to dominant turbulent diffusivities inside . In the central region neoclassical W transport dominates but the convective velocities are several order of magnitudes lower compared to plasmas with toroidal rotation velocities induced by a neutral beam injection (NBI) torque. Finally, nitrogen is seeded in these pulses leading to an enhanced energy content which is consistent with stabilised ion temperature gradient modes from dilution.