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To improve the plasma performance and control the density and plasma quality during the flat top phase, wall conditioning techniques are used in large fusion devices like W7-X and in JT60-SA. To study the performance of electron cyclotron wall conditioning, numerous experiments were performed on the TOroidally MAgnetized System, which is operated by LPP-ERM/KMS at the FZ-Jülich. It is a facility designed to study plasma production, wall conditioning, and plasma–surface interactions. The produced electron cyclotron resonance heating plasmas are characterized in various conditions by density and temperature measurements using a movable triple Langmuir probe in the horizontal and the vertical direction, complemented by video and spectroscopic data, to obtain a 2D extrapolation of the plasma parameters in the machine. A way to calibrate the triple Langmuir probe measurements is also investigated. These data can be used to determine the direction of the plasma drift in the vessel and identify the power absorption mechanisms. This will give more insight in the plasma behavior and improve the efficiency of wall conditioning and sample exposure experiments. [ABSTRACT FROM AUTHOR]

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested. [ABSTRACT FROM AUTHOR]

Destabilization of ion cyclotron waves—waves with frequencies close to ion cyclotron harmonics—in inhomogeneous plasmas with Maxwell velocity distribution is considered. A new mechanism of destabilization of these waves is found, whereas the known interaction between cyclotron waves and drift waves is shown to be hardly able to lead to instabilities in realistic tokamak plasmas. Our finding is that the resonance wave–particle interaction in the presence of temperature gradient can change the diamagnetic drift frequency in such a way that the destabilizing influence of the diamagnetic drift exceeds Landau damping. This occurs when the energy of resonance particles is sufficiently high, which is always the case due to the infinite tail of the Maxwell distribution. Particles with higher energies provide a larger ratio of drive to damping, but the number of resonance particles and, thus, instability growth rates are exponentially small when particle energy is very high. Therefore, only moderately suprathermal particles can lead to observable instabilities. A condition for instabilities driven by these particles is obtained. Destabilization of electrostatic cyclotron waves and ordinary cyclotron waves is studied. [ABSTRACT FROM AUTHOR]

The saturated internal kink mode with m/n = 1/1 has been observed in the H-mode discharge of the experimental advanced superconducting tokamak, characterized by high β P and weak magnetic shear in the core. This observation was made using a combination of soft x-ray imaging and electron cyclotron emission diagnostics. It was noted that the repetitive bursting of m/n = 1/1 internal mode (large amplitude, short bursting duration) transitions into a long-lasting continuous one (small amplitude, constant frequency), when β p > 2.2 in H-mode, a much shorter bursting duration, transitioning into a long-lasting continuous one, with smaller amplitude and a constant frequency. Conversely, for typical β p < 1.5 in L/I discharge, the frequency of m/n = 1/1 mode decreases with time, associated with local poloidal electron diamagnetism drift velocity. The benign m/n = 1/1 mode in high β p has an amplitude much smaller than one in L-mode for high β P stabilization effect. By adjusting the power deposition of electron cyclotron resonance heating, it is found that the saturation level of m/n = 1/1 mode is independent of the local electron temperature gradient in H-mode discharge. It underscores that the flat current and, hence, weak magnetic shear are crucial factors influencing the saturation level of the m/n = 1/1 mode for both the off-axis electron cyclotron current driving current-dominant and off-axis bootstrap current-dominant cases. Furthermore, the outward movement with growth of the m/n = 1/1 mode in the process of L-H mode transition and the characteristic time of this process are close to the current diffusion time. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A nonlinear effect, RF (radio frequency) condensation, can be used to facilitate RF stabilization of magnetic islands. Previously studied semi-analytical models for RF condensation are suited mainly for broad deposition profiles and are unable to handle power depositions that are localized in the interior of a magnetic island. The power deposition profile of electron cyclotron waves, in particular, can be highly localized near a cyclotron resonance. Here, a model is developed that can handle both localized profiles and broad profiles. This allows a comparison of RF condensation for narrow vs broad deposition profiles, and it allows a study of the dependence of RF condensation of localized deposition profiles on key parameters. [ABSTRACT FROM AUTHOR]

Whistler waves are a type of low-frequency electromagnetic wave common in nature, which is usually associated with energetic electron phenomena. This study presents experimental observations of low-frequency whistler wave instabilities driven by energetic electrons through wave–particle interactions on EXL-50. The energetic electrons are generated by electron cyclotron waves (ECWs) through stochastic heating [Wang et al., J. Plasma Phys. 89, 905890603 (2023)] and do not match the characteristics of the runaway electrons [Shi et al., Nucl. Fusion 62, 086047 (2022)]. In the steady-state plasma of the Energy iNNovation XuanLong-50 (EXL-50), whistler waves within the 30–120 MHz frequency range were observed during electron cyclotron resonance heating. These waves displayed multiple frequency bands, and the frequencies of waves were directly proportional to the Alfvén velocity. Furthermore, it was interesting to find that superposition of lower hybrid wave into ECW resulted in the suppression of these whistler waves. The experimental results may indicate that the whistler waves are driven by energetic electrons (excluding runaway electrons). These discoveries carry significant implications for several areas of research, including the investigation of wave–particle interactions, the development of radio frequency wave current drivers, their potential impact on the electron dynamics in future fusion devices, and even the presence of unusually low-frequency whistler waves in Earth's radiation belts. [ABSTRACT FROM AUTHOR]

In this study, we observe avalanche-like electron thermal transport in Heliotron J under plasma conditions that exhibit power degradation to the central electron cyclotron heating (ECH). The newly installed GHz sampling electron cyclotron emission diagnostic allows for the observation of the long-distance radial propagation of electron temperature fluctuations. We find that the electron temperature fluctuations are associated with avalanches, because the Te fluctuations (i) propagate from the core to the edge with a speed comparable to the diamagnetic drift velocity, (ii) exhibit a 1/f power-law scaling in the frequency spectrum and a Hurst exponent close to 1, and (iii) dominate in the ECH deposition location and spread to the edge as the heating power increases. Furthermore, the electron heat avalanches can spread to the scrape off layer region when they are enhanced, i.e., the Te fluctuations correlate with the Dα emission, which also has a frequency spectrum that scales with a 1/f power law. [ABSTRACT FROM AUTHOR]

Among various non-linear regimes of electron cyclotron instabilities that may be driven by a strong electron cyclotron resonance (ECR) heating in open magnetic traps, the continuous generation of a quasi-monochromatic wave, characterized by a smooth release of a free energy from a system, is especially important for applications, e.g., aimed at performance optimization of ECR ion sources. We study an universal model based on the quasilinear description of plasma–wave interactions that explains the condition of a continuous-wave regime of the cyclotron instability observed experimentally including, in particular, a strong dependence on a magnetic configuration. [ABSTRACT FROM AUTHOR]

We study the possibility of terahertz pulse generation based on cyclotron super-radiance (SR) of an extended (in the scale of the wavelength) bunch of rotating electrons, which moves in a cylindrical waveguide with a translational velocity close to the wave's group velocity. In the rest frame, this group synchronism regime corresponds to radiation of an unmoving bunch of excited cyclotron oscillators at a quasi-cutoff frequency of a waveguide mode. We develop the generalized self-consistent model of cyclotron SR in the group synchronism regime describing both the azimuthal self-bunching of rotating electrons and their longitudinal displacements under the action of Coulomb repulsive forces and recoil effects caused by high-frequency magnetic fields of the generated SR pulse. Within the framework of the developed analytical model and based on direct PIC simulations, we demonstrate the feasibility of generating picosecond SR pulses with a central frequency of 1 THz and a peak power of 90 MW by photoinjector-formed electron bunches guided in a strong magnetic field of 10.5 T. Simulations show that in the group synchronism regime, the SR pulse is less affected by longitudinal forces, as compared to the case of mismatched velocities. In addition, the Lorentz force can provide partial self-compression of the electron bunch with the formation of electron density filaments. [ABSTRACT FROM AUTHOR]

The Alfvén-ion cyclotron (AIC) mode is an instability that can be driven in magnetized plasmas with anisotropic pressure. Its chief deleterious effect is the driving of enhanced pitch-angle scattering of ions. Although the AIC mode has been observed in several mirror devices, it has not yet been observed in FRC devices developed by TAE Technologies [H. Gota et al., Nucl. Fusion 61, 106039 (2021)]. Previous theoretical work [T. Tajima et al., Phys. Rev. Lett. 39, 201 (1977)] has suggested that sufficient axial inhomogeneity, quantified by a critical axial plasma length, can stabilize this mode. This stabilization mechanism is examined in fully kinetic particle-in-cell simulations with one spatial dimension modeling a simplified magnetic mirror geometry for a plasma with β ∼ 1. A fast-ion population provides the driving anisotropy for the AIC mode, and the resulting effect on the fast-ion pitch angle distribution is examined. The severity of mode activity is recorded for a scan of plasma lengths for multiple fast-ion injection angles. This scan yields critical lengths that show good qualitative agreement with those from the past theoretical work. [ABSTRACT FROM AUTHOR]

This paper introduces a new model to find the velocity-space location of energetic ions generating ion cyclotron emission (ICE) in plasmas. ICE is thought to be generated due to inverted gradients in the v ⊥ direction of the velocity distribution function or due to anisotropies, i.e., strong gradients in the pitch direction. Here, we invert synthetic ICE spectra generated from first principles PIC-hybrid computations to find the locations of these ICE-generating ions in velocity space in terms of a probability distribution function. To this end, we compute 2D ICE weight functions based on the magnetoacoustic cyclotron instability, which reveals the velocity-space sensitivity of ICE measurements. As an example, we analyze the velocity-space sensitivity of synthetic ICE measurements near the first 15 harmonics for plasma parameters typical for the Large Helical Device. Furthermore, we investigate the applicability of a least-square subset search, Tikhonov regularization, and Lasso regularization to obtain the locations in velocity space of the ions generating the ICE. [ABSTRACT FROM AUTHOR]

In a recent paper [K. Min, Phys. Plasmas 30, 012904 (2023)], the formation of the banded chorus with a gap in intensity at half the electron cyclotron frequency ( Ω e / 2) is demonstrated by particle-in-cell simulations including an isotropic shell distribution at an intermediate energy. This follow-up study focuses on the phase space density (PSD) hill formation process and its role in the chorus wave damping at the gap. We first show that phase-trapped particles closely follow single wave characteristics in momentum space. This means that the formation of either PSD hole or hill is primarily determined by the temperature anisotropy, T ⊥ / T ‖ , of an initial distribution function. The critical value of T ⊥ / T ‖ increases (decreases) for a higher (lower) resonant frequency. We then revisit the recent banded chorus simulations to investigate how the presence of an isotropic shell distribution self-consistently affects chorus wave evolution at the gap. Initially, with an increasing wave frequency, more and more shell electrons get trapped and a PSD hill is formed. The enhanced PSD hill counteracts wave growth driven by phase-trapped anisotropic electrons and subsequently reduces wave amplitude. The weakened wave self-consistently feeds back to the particle trapping, ultimately suppressing both the PSD hole and hill. By the time the wave frequency reaches about 0.45 Ω e , the gyro-phase structure of the electron distribution becomes much less organized. In some cases, however, the wave growth at the upstream source region can be strong enough that waves still manage to go through the gap frequency, suggesting that additional process(es) should likely be accompanied. [ABSTRACT FROM AUTHOR]

Design and operation of future tokamak fusion reactors using a deuterium–tritium 50:50 mix requires a solid understanding of how energy confinement properties change with ion mass. This study looks at how turbulence and energy transport change in L-mode plasmas in the ASDEX Upgrade tokamak when changing ion species between hydrogen and deuterium. For this purpose, both experimental turbulence measurements and modeling are employed. Local measurements of ion-scale (with wavevector of fluctuations perpendicular to the B-field k ⊥ < 2 cm−1, k ⊥ ρ s < 0.2, where ρs is the ion sound Larmor radius using the deuterium ion mass) electron temperature fluctuations have been performed in the outer core (normalized toroidal flux ρ Tor = 0.65 − 0.8) using a multi-channel correlation electron cyclotron emission diagnostic. Lower root mean square perpendicular fluctuation amplitudes and radial correlation lengths have been measured in hydrogen vs deuterium. Measurements of the cross-phase angle between a normal-incidence reflectometer and an ECE signal were made to infer the cross-phase angle between density and temperature fluctuations. The magnitude of the cross-phase angle was found larger (more out-of-phase) in hydrogen than in deuterium. TRANSP power balance simulations show a larger ion heat flux in hydrogen where the electron-ion heat exchange term is found to play an important role. These experimental observations were used as the basis of a validation study of both quasilinear gyrofluid trapped gyro-Landau fluid-SAT2 and nonlinear gyrokinetic GENE codes. Linear solvers indicate that, at long wavelengths ( k ⊥ ρ s < 1), energy transport in the deuterium discharge is dominated by a mixed ion-temperature-gradient (ITG) and trapped-electron mode turbulence while in hydrogen transport is exclusively and more strongly driven by ITG turbulence. The Ricci validation metric has been used to quantify the agreement between experiments and simulations taking into account both experimental and simulation uncertainties as well as four different observables across different levels of the primacy hierarchy. [ABSTRACT FROM AUTHOR]

The propagation of nonlinear dust cyclotron (DC) cnoidal waves having superthermal distributed electrons and ions in the presence of external magnetic field and adiabatic dust charge variation is investigated. The effect of dust charge variation is profoundly modified due to the presence of the superthermal electrons and ions. The dust charge variation parameter decreases with an increase in the superthermality index of ions. Adopting the reductive perturbation approach, it is shown that the dynamics of the cnoidal structure is modeled by a Korteweg–de Vries equation. It is found that only negative potential DC cnoidal and solitary structures are observed in such a plasma. The results further reveal that the cnoidal structures strongly depend on the degree of superthermality, dust charge variation parameter, temperature and number density of fluid particles, angle of obliqueness, as well as on the magnetic field strength. The numerical results confirm that as the dust charge variation enters the picture, amplitude as well as the width of the cnoidal waves enhances. Furthermore, the analysis is performed through Sagdeev potential, plane phase plot and spatial variation of potential to elucidate various aspects of the cnoidal wave dynamics in the presence of the adiabatic dust charge variation. [ABSTRACT FROM AUTHOR]

A 2D-3V finite-element particle-in-cell model, which is applied to simulate the radial-azimuthal plane near the exit of Hall thrusters, has been presented to investigate the influence of axial oscillation on electron cyclotron drift instability (ECDI) and anomalous cross field electron transports. The simplified theoretical analysis about the ECDI and the anomalous electron transport has been introduced. The uniform and harmonic axial electric fields, which are based on the typical axial oscillations in Hall thrusters, have been considered in the simulations. It is concluded that different constant axial electric fields can influence the properties of instability but cannot significantly change the cross field electron mobility. However, the axial oscillation plays a significant role in the instability, and the electron transports provided that appropriate amplitudes and frequencies are achieved. The equilibrium of the instability is destroyed and reformed with the axial oscillation. The cross field electron transports are enhanced in the range of low amplitudes and frequencies and are suppressed when they are in a high value. In addition, it is observed that the variation of the electron mobility and electron–ion friction force show high consistency with the trend of electron temperature. It is further confirmed that the increase in electron temperature takes responsibility for the enhanced cross field electron transport due to the axial oscillation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Electron cyclotron drift instability (ECDI) and ion–ion two stream instability (IITSI) are both kinetic instabilities that can be present in low-temperature, partially magnetized plasmas. The coupling of instabilities in a three-dimensional configuration leads to the existence of more than one unstable roots to the kinetic dispersion relation. In this paper, a generalized method has been developed for numerically evaluating solutions to the three-dimensional dispersion relation for coupled ECDI and IITSI, assuming cold singly and doubly charged ions and a Maxwellian velocity distribution function for the electrons. The present study demonstrates the coupling between ECDI and IITSI that affects the most unstable mode as a function of the wavenumbers in three dimensions and various plasma properties, including the applied electric field, magnetic field, electron temperature, ion velocities, and plasma density. One of the most notable results is that, while the most unstable mode with the largest growth rate is in the direction of the E × B drift in the two-dimensional cases, the most unstable mode for the three-dimensional configuration occurs in the oblique direction between the applied electric field and the E × B drift. This agrees with experimental observations in cross field plasma sources using coherent Thomson scattering. [ABSTRACT FROM AUTHOR]

The physics of ion cyclotron heating (ICH) relevant to the steady-state linear machine MPEX (Material Plasma Exposure eXperiment) has been explored in its predecessor, short-pulse device: Proto-MPEX. MPEX will utilize fundamental ICH to increase heat flux at the target and produce ion temperatures and velocity distributions with improved fidelity to those found in a tokamak divertor region, in comparison to those produced by substrate biasing. In the experiments on Proto-MPEX described here, bulk ion temperatures up to ∼ 15 eV have been achieved with 20 kW net ICH power at 6.5 MHz, using ICH heating of a deuterium plasma produced by a helicon plasma source. The heat flux at the target has been observed to increase throughout the plasma cross section, including in the core region. Core Ti and target heat flux are observed to scale linearly with injected ICH power. Measurements of plasma loading and target heat flux as a function of the magnetic field strength at the antenna, together with modeling of the wave propagation from the antenna to the ion cyclotron resonance using the ANTENA and COMSOL codes with a warm plasma dielectric tensor, indicate that power is coupled to the core plasma via fast wave excitation of a kinetic Alfvén wave. [ABSTRACT FROM AUTHOR]

Although many theoretical models have been proposed over several decades, the origin of banded chorus with a gap in intensity at Ω e / 2 (Ωe being the angular electron cyclotron frequency) is still debated. In one of those models, the chorus gap formation is attributed to two anisotropic electron populations separated by an isotropized population (called the parallel plateau) at energy resonant with waves of frequency ∼ Ω e / 2. Here, we simplify the plateau population as an electron shell distribution in velocity space and investigate its role in the gap formation using a particle-in-cell code in a non-uniform magnetic field. The base plasma is configured to generate rising chorus elements spanning in frequency from below to above Ω e / 2. Then, multiple simulations are run with an additional shell distribution with different density values to investigate the gap formation. The simulation results show that even a relatively small fraction of shell is quite effective in arresting the frequency chirping of lower-band chorus at ∼ Ω e / 2 , resulting in a power gap there. Phase space analysis indicates that the resonant current contributed by the phase-trapped shell electrons (forming a phase space hill) can counteract nonlinear chorus growth driven by the phase space hole of energetic, anisotropic electrons. This process occurs in combination with the linear cyclotron damping suggested in earlier studies, and the resulting nonlinear damping may exceed the latter effect. [ABSTRACT FROM AUTHOR]

Numerical simulations have grown to play a central role in modern sciences over the years. The ever-improving technology of supercomputers has made large and precise models available. However, this accuracy is often limited by the cost of computational resources. Lowering the simulation's spatial resolution in order to conserve resources can lead to key processes being unresolved. We have shown in a previous study how insufficient spatial resolution of the proton cyclotron instability leads to a misrepresentation of ion dynamics in hybrid-Vlasov simulations. This leads to larger than expected temperature anisotropy and loss-cone shaped velocity distribution functions. In this study, we present a sub-grid numerical model to introduce pitch-angle diffusion in a 3D Cartesian velocity space, at a spatial resolution where the relevant wave–particle interactions were previously not correctly resolved. We show that the method is successfully able to isotropize loss-cone shaped velocity distribution functions, and that this method could be applied to simulations in order to save computational resources and still correctly model wave–particle interactions. [ABSTRACT FROM AUTHOR]

Lower hybrid (LH) wave is an effective tool for current drive (CD) on tokamak devices. Parametric instability (PI) has always been a troubling phenomenon decreasing the lower hybrid current drive efficiency. In this work, the PI behavior of the LH waves for plasma parameters on the Experimental Advanced Superconducting Tokamak is investigated via first-principle simulation with a two-dimensional full-particle-in-cell method. The PI processes where an LH pump wave decays into another LH sideband and a low-frequency mode [ion sound quasi-mode (ISQM) or ion cyclotron quasi-mode (ICQM)] are observed in simulations. The ICQM-type and ISQM-type decay channels dominate, respectively, in the high- and low-plasma regimes while appearing simultaneously in the intermediate regime, which agrees well with the theoretical prediction by solving the parametric dispersion relation. In addition, for both the decay channels, their LH sidebands are excited with a wide range of parallel refractive index N ∥ up to 30.0, which can resonantly interact with thermal electrons. The resulting electron heating can be enhanced due to overlap of resonances between the electrons and sidebands. Such electron heating not only dissipates the wave energy in the edge plasma but produces a significant portion of fast electrons, which may seriously affect tokamak discharges. The ion cyclotron heating due to the ICQMs is also observed in simulations. [ABSTRACT FROM AUTHOR]

Magnetized nonneutral plasma composed of electrons or positrons couples to the local microwave environment via cyclotron radiation. The equilibrium plasma temperature depends on the microwave energy density near the cyclotron frequency. Fine copper meshes and cryogenic microwave absorbing material were used to lower the effective temperature of the radiation environment in ASACUSA's Cusp trap, resulting in significantly reduced plasma temperature. [ABSTRACT FROM AUTHOR]

Relativistic electron scattering by electromagnetic ion cyclotron (EMIC) waves is one of the most effective mechanisms for >1 MeV electron flux depletion in the Earth's radiation belts. Resonant electron interaction with EMIC waves is traditionally described by quasi-linear diffusion equations, although spacecraft observations often report EMIC waves with intensities sufficiently large to trigger nonlinear resonant interaction with electrons. An important consequence of such nonlinear interaction is the resonance broadening effect due to high wave amplitudes. In this study, we quantify this resonance broadening effect in electron pitch-angle diffusion rates. We show that resonance broadening can significantly increase the pitch-angle range of EMIC-scattered electrons. This increase is especially important for ∼ 1 MeV electrons, where, without the resonance broadening, only those near the loss cone (with low fluxes) can resonate with EMIC waves. [ABSTRACT FROM AUTHOR]

In this paper, we develop the kinetic and hydrodynamic theories of the convective mesoscale flows driven by the spatially inhomogeneous electrostatic ion cyclotron parametric microturbulence in the pedestal plasma with a sheared poloidal flow. The developed kinetic theory predicts the generation of the sheared poloidal convective flow and of the radial compressed flow with radial flow velocity gradient. The developed hydrodynamic theory of the convective flows reveals the radial compressed convective flow as the dominant factor in the formation of the steep pedestal density profile with density gradient exponentially growing with time. This gradient density growth is limited by the formation of the radial oscillating with time ion outflow of pedestal plasma to the scrape-off layer. [ABSTRACT FROM AUTHOR]

The article titled "Response to 'Comment on 'ENN's roadmap for proton-boron fusion based on spherical torus'" addresses a comment made by Li regarding the study by Liu et al. The authors of the response acknowledge that Li's calculations and results are correct, as they are based on the formulas and findings presented in another study by Xie, who is one of the key authors of Liu et al.'s paper. However, the authors argue that Li's comment is based on a misunderstanding and does not provide any new insights. They emphasize that proton-boron fusion presents significant challenges that require more than basic calculations, and highlight the need for further research and validation of advanced concepts. The authors also mention that all fusion roadmaps face challenges and stress the importance of identifying and addressing these challenges systematically. [Extracted from the article]

It is found that the plasma waves driven by an electron beam rotating in a magnetized overdense plasma can be converted into terahertz electromagnetic radiation by new mechanisms. According to the particle-in-cell simulation results, the radiation modes include a dominant extraordinary (X) mode at twice the plasma frequency 2 f p and a subordinate X mode at f p . The 2 f p radiation can be generated by the coupling of a beam mode and a scattered upper-hybrid (UH) mode, or by the coupling of a beam mode and a right-handed X mode. Here, the beam mode can be a UH mode or a left-handed X mode driven by the beam under the Cherenkov condition, and the right-handed X mode can be induced by high-order electron cyclotron maser instability. The f p radiation is the right- or left-handed fundamental X mode escaping from the plasma boundary. This study also shows that the breakdown of beam modulation is responsible for the radiation attenuation. The scheme proposed in this paper can be applied in high-power THz radiation sources and diagnosis of magnetized plasmas. [ABSTRACT FROM AUTHOR]

Applying linear dispersion theory to a warm collisionless plasma, we investigate the effect of hot ion composition on electromagnetic ion cyclotron (EMIC) wave generation. The growth rate of oxygen band waves can divide into three components if hot anisotropic heavy ions are included. Their wave frequencies (0.05 ΩH+, 0.03 ΩH+, and 0.01 ΩH+) are sorted in relation to the cyclotron frequencies of H+, He+, and O+ ions (ΩH+, ΩH+/4, and ΩH+/16). The three sub-bands within the oxygen band form an unusual trifurcate structure of growth rate. A link between the three sub-bands and three hot species has been definitively established. That is to say, hot H+, He+, and O+ ions are responsible for the generation of sub-bands. The unstable frequencies of oxygen band waves are directly modulated by the actual composition of magnetospheric ions. The largest growth can arise between the extremely low frequency and the gyrofrequency of O+ (ΩO+). When O+ ions become the dominant hot component during the storm phase, oxygen waves can be generated at much lower frequencies than ΩO+. We perform a parametric study of oxygen sub-band generation in the magnetosphere by using a statistical survey of the plasma composition measured by the Van Allen Probes. The trifurcate structure of growth rate appears at wide L shells from the outer plasmasphere to the geostationary orbit. The new findings demonstrate that wave structures in the oxygen band are more complex than the hydrogen and helium bands. This may provide insight into the nature of the EMIC instability. [ABSTRACT FROM AUTHOR]

We develop a new self-consistent model for simulation of the electron–cyclotron maser interaction in cylindrical structures, where expansion of the fields in transverse eigenmodes cannot be directly applied. Instead of solving the nonhomogeneous equation for the fields as a differential equation, a different approach is followed. First, the Green's function for elementary azimuthal and radial RF current sources is analytically derived by expanding the fields in longitudinal modes. Then, the total generated field is calculated by representing the perturbed electron beam as a sum of elementary RF current sources along the axis with amplitude coefficients that are found from the kinematic quantities of the electrons. The self-consistent stationary solution is found by solving the equations of motion along with the field equation in an iterative procedure. The model is useful for the full-wave simulation of lossy structures, which are frequently found in gyro-devices, such as ceramic-loaded interaction circuits of gyro-traveling-wave tubes and beam tunnels of gyrotron oscillators. [ABSTRACT FROM AUTHOR]

We report on a novel investigation of the nonlinear regime of the electron cyclotron drift instability using a grid-based Vlasov simulation. It is shown that the instability occurs as a series of cyclotron resonances with the electron beam mode due to the E × B drift. In the nonlinear regime, we observe condensation of fluctuations energy toward the lowest resonance mode and below, i.e., an inverse energy cascade. It is shown that the characteristics of the nonlinear saturation state remain far from the ion-sound regime. [ABSTRACT FROM AUTHOR]

The effect of ion–neutral collisions on the propagation characteristics of electrostatic ion cyclotron (EIC) waves in a partially ionized plasma is investigated. The dispersion relation of EIC waves is derived using a fluid model taking neutral dynamics into account. The propagation properties of EIC modes, including the damping factor, are examined for various ionization degrees and collision frequencies, which determine the momentum transferred from ions to neutral particles. It is found that the motion of neutral particles driven by plasma–neutral coupling leads to an increase in the effective ion mass, and consequently, EIC waves can propagate even below the ion cyclotron frequency. In a hot neutral gas, the gas-thermal mode can also propagate as well as the EIC mode. The possibility of observing in the laboratory and the Earth's ionosphere is discussed. [ABSTRACT FROM AUTHOR]

Two different fluid models for collisionless plasmas are compared. One is based on the classical Chew–Goldberger–Low (CGL) model that includes a finite Larmor radius correction and the Landau closure for the longitudinal mode. Another one takes into account the effect of cyclotron resonance in addition to Landau resonance and is referred to as the cyclotron resonance closure (CRC) model [T. Jikei and T. Amano, Phys. Plasmas 28, 042105 (2021)]. While the linear property of the parallel firehose instability is better described by the CGL model, the electromagnetic ion cyclotron instability driven unstable by the cyclotron resonance is reproduced only by the CRC model. Nonlinear simulation results for the parallel firehose instability performed with the two models are also discussed. Although the linear and quasilinear isotropization phases are consistent with theory in both models, long-term behaviors may be substantially different. The final state obtained by the CRC model may be reasonably understood in terms of the marginal stability condition. In contrast, the lack of cyclotron damping in the CGL model makes it rather difficult to predict the long-term behavior with simple physical arguments. This suggests that incorporating collisionless damping both for longitudinal and transverse modes is crucial for a nonlinear fluid simulation model of collisionless plasmas. [ABSTRACT FROM AUTHOR]

Reflection of radiation from an output window may strongly affect operation of a gyrotron. In recent years, the control of gyrotron radiation by reflection has become a subject of active study. In this paper, we study the effect of reflection on mode competition in a multimode gyrotron. We consider the interaction of five modes with neighboring azimuthal indexes in a gyrotron with a fixed Gaussian axial field profile. We assume the mode spectrum to be nearly equidistant and set the spectral density parameter value as in high-power gyrotrons used for plasma heating. We analyze the domain of stability of the operating mode on the cyclotron frequency mismatch–normalized beam current parameter plane with and without the reflections. The possibility of suppressing spurious sideband modes and expanding the single-mode oscillation zone of the operating mode by injecting the reflected signal is demonstrated by numerical simulation. The most advantageous situation is when the designed mode is matched with the output window while the reflections of the parasitic modes are rather strong and the reflected waves return into the gyrotron resonator in the adverse phase reducing the Q-factors of the parasitic modes. [ABSTRACT FROM AUTHOR]

A typical problem of the development of high-harmonic short-wavelength gyrotrons, namely, the competition between the operating wave and a parasitic fundamental-harmonic wave, is studied. A specific case of the excitation of a far-from-cutoff parasitic wave in the backward-wave oscillator regime is considered. [ABSTRACT FROM AUTHOR]

A fully relativistic model of electron cyclotron current drive (ECCD) efficiency based on the adjoint function techniques is considered. Numerical calculations of the current drive efficiency in a tokamak by using the variational approach are performed. A fully relativistic extension of the variational principle with the modified test function for the Spitzer function with momentum conservation in the electron–electron collision is described in general tokamak geometry. The model developed has generalized that of Marushchenko et al., which is extended for arbitrary temperatures and covers exactly the asymptotic for u ≫ 1 when Z eff ≫ 1 , and is suited to ray-tracing and beam-tracing calculations. As a demonstration, the new model is applied in one of widely used ray-tracing codes, TORAY-GA, and yields distinct improvement on the fidelity for the calculation of ECCD in the hybrid operating scenario for the China fusion engineering test reactor. [ABSTRACT FROM AUTHOR]

The toroidal force related to electron cyclotron heating (ECH) is investigated in large helical device (LHD) plasmas. When we apply the ECH to the plasma kept by neutral beam injection (NBI) heating, the radial profile of the toroidal flow velocity changes drastically in LHD. ECH-generated supra-thermal electrons can apply forces on the plasma through radial electron current and collisions. We investigate the perturbed electron distribution due to ECH by using the GNET code, which can solve the 5D drift kinetic equation. We also evaluate the electromagnetic force due to radial current and the collisional force driven by ECH. As a result, we find a comparable force driven by ECH to that by NBI heating. The direction of the force is the counter (co) direction radially inside (outside) from the ECH heating location, and these directions correspond with that of experiment results. Finally, we evaluate toroidal flows in ECH and NBI heated plasma solving the radial diffusion equation and compare them with that of experimental observations. We reproduce the co-rotating toroidal flow quantitatively in the balanced-NBI+ECH heated case, but we see a difference in the toroidal flow profiles in the co-NBI+ECH heated case. [ABSTRACT FROM AUTHOR]

A theoretical study of high-frequency electron waves in the plasma of a Hall-type discharge with crossed electric and magnetic fields is presented. The analysis of dispersion relations for a homogeneous weakly collisional plasma with the electron velocity distribution function obtained in the relaxation approximation is performed. It is shown that the nonequilibrium character of the electron distribution function can lead to kinetic instability of cyclotron waves. This instability occurs when the thermal velocity of electrons is comparable with the drift velocity in crossed fields. In the quasilinear approximation, a compact form of the diffusion coefficient of the distribution function in the velocity space is obtained, describing unstable modes' evolution and saturation. The analytical solutions are compared with the results of numerical simulation by the particle-in-cell method. [ABSTRACT FROM AUTHOR]

Expansion of solar wind into the interplanetary space generates temperature anisotropy that cannot be justified by adiabatic fluid theory. Kinetic instabilities driven by the interplay between electrons and protons temperature anisotropy may be operative in order to explain the actual state of solar wind reported by satellite observations. Based on the temperature anisotropy, T ⊥ / T ∥ , and alternative different plasma beta, β, regimes of solar wind species, we investigate the unified wave spectrum where left-hand polarized electromagnetic proton cyclotron and electron firehose instabilities may co-exist or transit with each other. Linear stability analysis catches the co-existence/transition of these instabilities in the different propagation domain. A moment-based quasilinear approach is adopted to highlight the feedback effects of these instabilities on the initial distributions and also to validate the transition during the non-linear (or quasilinear) time-evolution of the instabilities. Looking at the solar wind observations, we assume a bi-Maxwellian dual core-halo electron and proton model that allows solar wind species temperatures to vary in time t in addition. By incorporating the radial expansion effects and inhomogeneities, our present findings may be applicable to the First Solar Parker Probe observations. [ABSTRACT FROM AUTHOR]

The paper describes an implementation of a long mirror-based variant of cyclotron autoresonance which permits a local temporary change in the mirror's induction and provides a mode for filling the trap with primary plasma, and for the generation of plasma bunches with an energetic electron component and their accumulation within a single cavity. The approach does not require injection of external particles into the acceleration zone as particles can be generated directly within the mirror using specialized conditions of electron cyclotron resonance (ECR) as part of the operational mode. A detailed study of the spectral-angular distribution of Bremsstrahlung in various operational modes has been undertaken. The results of this study permit the optimal value of the time sequence between the leading edge of the pulsed magnetic field and the microwave pulse to be determined, which ensures the optimal mode of electron trapping in the cyclotron autoresonance mode. Bremsstrahlung radiation recorded in the transverse direction has a significantly higher intensity of photons and energy compared to the longitudinal direction during the acceleration and subsequent confinement mode of plasma bunches. The observed changes in the intensity and spectral distribution of the Bremsstrahlung, which depend on the values of the operating parameters for acceleration, afford the possibility to define the dependence of the number of initial plasma particles trapped by cyclotron autoresonance for the different operating modes. The results will improve our understanding of the processes taking place at various stages of the operational modes. In general, such studies are important for gaining an improved understanding of the mechanisms of generation and confinement of hot electron plasma bunches with an energetic electron component for autoresonant interaction in a long mirror. [ABSTRACT FROM AUTHOR]

Crossed-field space-charge limited current (CF-SCLC) represents the maximum stable current that can be produced in crossed-field devices (CFDs); prominent CFDs include magnetrons and cyclotrons, critical technologies in vacuum electronics. While planar crossed-field geometries have the most developed theoretical models, cylindrical geometries are far more common and useful in practical applications. CFDs are characterized by the strength of the externally applied magnetic field B , orthogonal (crossed) to the electric field; this is often normalized to the magnetic insulation condition, the Hull cutoff field B H . We apply variational calculus to derive a new theoretical model for CF-SCLC for planar and cylindrical devices below and above B H . The variational model offers a concise derivation for planar results without transforming to the time domain and gives the first analytic results from first principles for cylindrical CF-SCLC. We implement a fully three-dimensional simulation in CST Particle Studio which, in addition to additional derived simple theoretical models, explains the often overlooked experimental current scaling ∝ 1 − B / B H 2 1 / 2 which decreases to zero current as B → B H − . These additional simple models reduce the maximum mismatch magnitude between theory and experiments or simulations by up to 68% compared to the variational model, with the most improvement at the critical limit B → B H − . Justification for the variational model and future applications are discussed. [ABSTRACT FROM AUTHOR]

In saturated Ohmic confinement regime of the experimental advanced superconducting tokamak, significant changes in the relative electron temperature fluctuations T ̃ e / T ¯ e , measured by a correlation electron cyclotron emission system, have been observed. It was found that T ̃ e / T ¯ e is strongly dependent on the normalized electron temperature and density gradient, R / L T e = R ∇ T e / T e and R / L n e = R ∇ n e / n e . T ̃ e / T ¯ e stay at a high level when R / L T e is within the range of 17 − 25 and R / L n e is within the range of 4 − 6. It has been also observed that the energy confinement degradation is correlated with the increase in electron temperature fluctuations. The linear stability analysis results show that the electron temperature fluctuations are mainly attributed to the ion temperature gradient modes. [ABSTRACT FROM AUTHOR]

Electromagnetic ion cyclotron (EMIC) waves have been studied in this manuscript which are triggered by hot proton thermal anisotropy having energy ranging from 7 to 26 keV with a minimum resonant energy of 6.9 keV. However, an opposite effect can be observed for the hot protons for energy less than the minimum resonant energy. When the intensity of EMIC waves is large, the cold protons (ions) having low-energies can be energized by the EMIC waves. The possible reasons for this energization are the phase bunching of low energy ions with EMIC waves and the generation of electric fields at the relaxation time of substorm. As a consequence, these undetectable protons now become detectable, and the number density and temperature anisotropy of the protons also increase within the energy range from 1 to 100 eV. Accordingly, the helium ions are also energized by the EMIC waves. [ABSTRACT FROM AUTHOR]

The radial density profile of pre-thermal quench (pre-TQ) early-time non-thermal (hot) electrons is estimated by combining electron cyclotron emission and soft x-ray data during the rapid shutdown of low-density ( n e ≲ 10 19 m − 3) DIII-D target plasmas with cryogenic argon pellet injection. This technique is mostly limited in these experiments to the pre-TQ phase and quickly loses validity during the TQ. Two different cases are studied: a high (10 keV) temperature target and a low (4 keV) temperature target. The results indicate that early-time, low-energy (∼10 keV) hot electrons form ahead of the argon pellet as it enters the plasma, affecting the pellet ablation rate; it is hypothesized that this may be caused by rapid cross field transport of argon ions ahead of the pellet or by rapid cross field transport of hot electrons. Fokker–Planck modeling of the two shots suggests that the hot electron current is quite significant during the pre-TQ phase (up to 50% of the total current). Comparison between modeled pre-TQ hot electron current and post-TQ hot electron current inferred from avalanche theory suggests that hot electron current increases during the high-temperature target TQ but decreases during the low-temperature target TQ. The uncertainties in this estimate are large; however, if true, this suggests that TQ radial loss of hot electron current could be larger than previously estimated in DIII-D. [ABSTRACT FROM AUTHOR]

In low-power short-wavelength gyrotrons with weak intensity of the electron–wave interaction, determining of the optimal parameters of the system is a result of a trade-off between the enhancement of the electron efficiency and the increase in the Ohmic loss share with an increasing cavity length. In this paper, we investigate the question of whether it is more advantageous to use operating regimes with a higher current at a fixed electron beam power, or whether it is better to increase the accelerating voltage. The answer to the question is determined strictly by the number of the operating cyclotron harmonic of the gyrotron. [ABSTRACT FROM AUTHOR]

Controlling and mitigating plasma disruptions are a matter of serious concern for tokamak operation since they can cause serious damage to the machine. Dedicated experiments on disruption mitigation have been carried out in ADITYA (R = 75 cm, a = 25 cm), an Ohmically heated circular limiter tokamak. A rapid growth of magneto hydrodynamic (MHD) modes is found to be the major cause of disruptions in ADITYA tokamak. Stimulated disruptions induced by hydrogen gas puffing are successfully mitigated through stabilization of these MHD modes by applying a biased-electrode placed inside the last-closed flux surface prior to the gas injection. However, as biased electrodes cannot be placed inside the plasma in bigger tokamaks, the application of ion-cyclotron waves (ICWs) prior to disruption has been successfully attempted to mitigate disruptions through stabilization of MHD modes in ADITYA tokamak. The amplitude of MHD modes (m/n = 3/1, 2/1) is significantly reduced upon the application of ICW prior to disruption, and the stimulated disruptions are successfully mitigated by preventing the growth and overlapping of these MHD modes. These experimental results demonstrate that MHD driven disruptions may be mitigated due to stabilization of m = 2 modes by ponderomotive force of the IC waves. [ABSTRACT FROM AUTHOR]

The large differential drift motion between electrons and ions that is created by the E × B current can produce different instabilities, such as the electron cyclotron drift instability, perpendicular to the magnetic field, and the Modified Two-Stream Instability (MTSI), with a component along the magnetic field. In this paper, we derive and validate a stability condition for the apparition of the MTSI modes in 2D particle-in-cell simulations of E × B discharges in the radial-azimuthal plane of a Hall thruster. We verify that, by choosing properly the domain dimensions, it is possible to capture correctly the MTSI growth and its corresponding number of azimuthal periods. In particular, we show that an azimuthal length that is smaller than a certain threshold prevents the MTSI from growing. Moreover, we show that the MTSI growth does not depend on the plasma density, but is affected by the axial electric field (perpendicular to the simulation domain). Additionally, we show that during its linear growth in the early times of the simulations, the MTSI produces an enhanced heating of the electrons in the magnetic field direction as well as an increased cross field mobility. For longer times, in the nonlinear regime, the system evolves toward a more chaotic state with the presence of structures that mostly exhibit large azimuthal wavelengths. [ABSTRACT FROM AUTHOR]

Interest in gyrotron operation at cyclotron harmonics is motivated by the users' desire to reduce the magnetic fields required for operation at a given frequency. However, operation at harmonics is more complicated than at the fundamental resonance because in harmonic gyrotrons there are many parasitic modes at the fundamental, which can be prone to excitation. The present study is devoted to the analysis of automodulation instability in harmonic gyrotrons. Such instability may occur, for example, when in the vicinity of the desired second harmonic mode there is a pair of parasitic modes at the fundamental, for the frequencies and azimuthal indices of which some specific conditions are met. In this paper, the equations describing this instability are derived in the cold-cavity approximation. The study is then focused on a second harmonic gyrotron with the parameters optimal for efficient operation. For such a gyrotron, the region of instability is determined in the plane of frequency mismatches between the operating and parasitic modes. This treatment performed within the framework of the general theory is complemented by consideration of some gyrotrons operating in specific modes, which are surrounded by specific sideband modes at the fundamental. [ABSTRACT FROM AUTHOR]

Experimental and modeling investigations of high βp scenarios on DIII-D and EAST tokamaks show advantages in high energy confinement, avoidance of n = 1 MHD, and core-edge integration with reduced heat flux, making this scenario an attractive option for China Fusion Engineering Test Reactor steady-state operation. Experiments show that plasmas with high confinement and high density can be achieved with neutral beam injection on DIII-D (βp ∼ 2.2, βN ∼ 3.5, fBS ∼ 50%, fGw ∼ 1.0, and H98y2 ∼ 1.5) and pure RF power on EAST (βP ∼ 2.0, βN ∼ 1.6, fBS ∼ 50%, fGw ∼ 0.8, and H98y2 > 1.3). By tailoring the current density profile, a q-profile with local (off-axis) negative shear is achieved, which yields improved confinement and MHD stability. Transport analysis and simulation suggest that the combination of a high density gradient and high Shafranov shift allows turbulence stabilization and higher confinement. Using on-axis Electron Cyclotron Heating injection, tungsten accumulation is avoided on EAST, and this is reproduced in modeling. Reduced heat flux (by > 40%) and maintenance of high core confinement is achieved with active feedback control of the radiated divertor, an important result for long pulse operation in tokamaks. The improved physics understanding and validated modeling tools are used to design a 1 GW steady-state scenario for CFETR. [ABSTRACT FROM AUTHOR]

The theory of the ion cyclotron (IC) electrostatic parametric instabilities of the inhomogeneous plasma that are driven by the inhomogeneous electric field of the fast wave (FW) in front of FW antenna is developed. It is found that the spatial inhomogeneity of the parametric IC turbulence and of the drift turbulence is at the origin of the flows that transport a large part of FW power, deposited to the pedestal plasma, to the scrape-off layer and later to the divertor mostly along field lines. [ABSTRACT FROM AUTHOR]

In strong electromagnetic fields, unique plasma phenomena and applications emerge whose description requires recently developed theories and simulations [Y. Shi, Ph.D. thesis, Princeton University (2018)]. In the classical regime, to quantify effects of strong magnetic fields on three-wave interactions, a convenient formula is derived by solving the fluid model to the second order in general geometry. As an application, magnetic resonances are exploited to mediate laser pulse compression, whereby higher intensity pulses can be produced in wider frequency ranges, as confirmed by particle-in-cell simulations. In even stronger fields, relativistic-quantum effects become important, and a plasma model based on scalar quantum electrodynamics (QED) is developed which unveils observable corrections to Faraday rotation and cyclotron absorption in strongly magnetized plasmas. Beyond the perturbative regime, lattice QED is extended as a numerical tool for plasma physics, using which the transition from wakefield acceleration to electron-positron pair production is captured when laser intensity exceeds the Schwinger threshold. [ABSTRACT FROM AUTHOR]