Electron Bernstein Waves Research Articles

The Material Plasma Exposure eXperiment: Mission and conceptual design

• New linear plasma device MPEX will address plasma material interaction gaps for fusion. • MPEX will have increased capabilities over existing linear plasma devices and will be world-leading when completed. • MPEX will expose apriori neutron irradiated material samples for fusion reactor divertor relevant heat and particle fluxes. • The conceptual design of MPEX is finished. Mastering Plasma Material Interactions (PMI) is key for obtaining a high performance, high duty-cycle and safe operating fusion reactor. Numerous gaps exist in PMI which have to be addressed before a reactor can be built. In particular the lack of data at high ion fluence, fusion reactor divertor relevant plasma conditions and neutron displacement damage requires new experimental devices to be able to develop plasma facing materials and components. This has been recognized in the community and the U.S. fusion program is addressing this need with a new linear plasma device—the Material Plasma Exposure eXperiment (MPEX). MPEX will be a superconducting linear plasma device with magnetic fields of up to 2.5 T. The plasma source is a high-power helicon source (200 kW, 13.56 MHz). The electrons will be heated via Electron Bernstein Waves with microwaves using multiple 70 GHz gyrotrons (up to 600 kW in total). Ions will be heated via ion cyclotron heating in the so-called “magnetic beach heating” scheme in the frequency range of 6−9 MHz (up to 400 kW in total). An overview of the conceptual design and the project/design requirements is given.

Effect of magnetic field ripple on parallel electron transport during microwave plasma heating in the Proto-MPEX linear plasma device

The Prototype Material Plasma Exposure eXperiment (Proto-MPEX) is a linear plasma device located at Oak Ridge National Laboratory to develop the plasma source concept for the Materials Plasma Exposure eXperiment (MPEX). Recent experiments have demonstrated the heating of electrons in a high-density deuterium plasma () via electron Bernstein waves and source plasma production via helicon waves in this linear configuration. Moreover, experimental observations suggest that the magnetic ripple adversely affects the parallel transport of the heated electrons toward the target where material samples are to be exposed to the plasma. To understand the transport process during microwave application, a test-particle Monte-Carlo (MC) code has been developed that incorporates the effects of Coulomb collisions, magnetic mirror adiabatic trapping and electron cyclotron interaction via a quasilinear RF heating operator. MC calculations indicate that the absence of 2nd turning points along the trajectory of cyclotron heated electrons significantly reduces adiabatic trapping and maximizes power transport to the Target surface. Thermalization of cyclotron heating electrons is analyzed with the MC code and it is found that for conditions relevant to Proto-MPEX, a significant fraction of the absorbed heating power is coupled to the Target surface via ballistic fast electrons; however, under certain conditions, up to 60% of the absorbed RF power can be dissipated via thermalization of the fast electrons on the background plasma. Results are compared with experimental measurements. Finally, the implications of the results are discussed in the context of the upcoming MPEX device.

Electron Bernstein wave conversion of high-field side injected X-modes in QUEST

This paper presents a detailed design of the Q-shu University experimental steady state spherical tokamak’s (QUEST’s) high-field side (HFS) injection system for electron Bernstein wave (EBW) excitation and the results of an experimental comparison of the HFS eXtraordinary X-mode and low-field side (LFS) ordinary O-mode injection of 8.2 GHz radio frequency (RF) power. Waveguides, as an alternative to mirror polarizers for transmitting RF X-mode power from LFS to HFS for EBW conversion, were used instead of the installation of an RF mirror. Testing of LFS-to-HFS RF power transmission at 8.2 GHz, using an RG-50-type vacuum waveguide in a bench-scale device filled with SF6 gas at 0.03 Mpa, revealed that an RF power of 10.8 kW could traverse the fundamental electron cyclotron resonance layer for 60 s without breakdown. The short-length, open-ended waveguide antenna used in the HFS injection-induced wave diffraction reduced the efficiency of power delivery to the upper hybrid resonance (UHR) by approximately 7% at an electron temperature of 50 eV. The HFS injection was able to produce brighter camera images than the standard LFS injection. The location of the UHR, as estimated by measuring the density with an interferometer, agreed with its location as measured by plasma radiation low-field, side-edge positions shown by fast camera imaging. This indicates that the plasma was produced by mode-converted EBW. The HFS injection had an absorption efficiency of 96%, compared to 40% for LFS. A greater fluctuation of floating potential adjustable to the lower hybrid wave (LHW) was observed in the HFS case by installing a Langmuir probe, confirming that EBW conversion efficiency was higher in the HFS case. Moreover, after setting the poloidal field to BPF = 7.6 mT, plasma current (IP) in the HFS peaked at 1.3 kA, as opposed to 0.3 kA for LFS, despite LFS injection having a total power of 55 kW, compared to 40 kW for HFS. However, as the impurity level was comparatively high, it is believed that this IP is dominated by pressure-drive, which makes it difficult to analyze EBWCD. Finally, the line-integrated density in the HFS injection peaked at 1.6 × 1018 m−2, compared to 8 × 1017 m−2 in the LFS one.

Plasma Waves near the Electron Cyclotron Frequency in the Near-Sun Solar Wind

Data from the first two orbits of the Sun by Parker Solar Probe reveal that the solar wind sunward of 50 solar radii is replete with plasma waves and instabilities. One of the most prominent plasma wave power enhancements in this region appears near the electron cyclotron frequency (f_ce). Most of this wave power is concentrated in electric field fluctuations near 0.7 f_ce and f_ce, with strong harmonics of both frequencies extending above f_ce. At least two distinct, often concurrent, wave modes are observed, preliminarily identified as electrostatic whistler-mode waves and electron Bernstein waves. Wave intervals range in duration from a few seconds to hours. Both the amplitudes and number of detections of these near-f_ce waves increase significantly with decreasing distance to the Sun, suggesting that they play an important role in the evolution of electron populations in the near-Sun solar wind. Correlations are found between the detection of these waves and properties of solar wind electron populations, including electron core drift, implying that these waves play a role in regulating the heat flux carried by solar wind electrons. Observation of these near-f_ce waves is found to be strongly correlated with near-radial solar wind magnetic field configurations with low levels of magnetic turbulence. A scenario for the growth of these waves is presented which implies that regions of low-turbulence near-radial magnetic field are a prominent feature of solar wind structure near the Sun.

Electron cyclotron modes of Bernstein waves in different plasma environments

Electron Bernstein waves are studied in plasma environment (relativistic, weakly relativistic and non- relativistic). The dispersion relation for electron Bernstein is derived by using the Maxwell-Juttner distribution function. As the integration in the relativistic dispersion relation cannot be solved analytically so the integration is approximated with the trapezoidal rule. It is observed that more than one mode exists for the Bernstein waves for a single harmonic number n due to relativistic effects defined by the value of (ratio of rest mass energy to thermal energy).

Electron Bernstein waves driven by electron crescents near the electron diffusion region

The Magnetospheric Multiscale (MMS) spacecraft encounter an electron diffusion region (EDR) of asymmetric magnetic reconnection at Earth’s magnetopause. The EDR is characterized by agyrotropic electron velocity distributions on both sides of the neutral line. Various types of plasma waves are produced by the magnetic reconnection in and near the EDR. Here we report large-amplitude electron Bernstein waves (EBWs) at the electron-scale boundary of the Hall current reversal. The finite gyroradius effect of the outflow electrons generates the crescent-shaped agyrotropic electron distributions, which drive the EBWs. The EBWs propagate toward the central EDR. The amplitude of the EBWs is sufficiently large to thermalize and diffuse electrons around the EDR. The EBWs contribute to the cross-field diffusion of the electron-scale boundary of the Hall current reversal near the EDR.

Study Electron Cyclotron Double Mode Conversion in Overdense Plasma

Double mode conversion from ordinary mode O to extraordinary mode X is used to achieve electron Bernstein wave (EBWs) for the electron cyclotron resonance heating (ECRH). The efficiency of the mode conversion depends on many parameters including the density gradient Ln, magnetic field source B0 and optimum launching angle Nz. An analytical formalism together with a numerical computation have been employed, considering W7X stellarator main parameters, such as 140 GHz, k0 = 29 cm−1, 2.5 T and 2.4 ×1020 m−3, in order to investigate the efficiency of the mode conversion. The values of the density gradient Ln, obtained by numerical simulation, are from 1 to 10 cm. These values of Ln correspond to the power transmission window TOSX from 88 to 29%. Moreover, the dispersion relation of the EBW mode propagation up to 10 harmonics, ω = 10ωce, has been plotted to help a better visualization of the EBW mode heating. Finally, the power deposition profiles around the resonance layers were calculated and presented.

Induced scattering of a pump wave during electron Bernstein wave heating in the high poloidal beta regime

In the present paper we investigate induced scattering of the pump microwave during electron Bernstein wave heating in the regimes with the high poloidal beta. It occurs in the upper hybrid resonance vicinity and leads to the nonlinear excitation of electron Bernstein waves confined within a finite 3D region limited in the radial direction by a potential well at the LFS and in the poloidal and toroidal directions by the dimensions of the spot on the magnetic flux surface illuminated by the pump beam.

Electron heating of over-dense plasma with dual-frequency electron cyclotron waves in fully non-inductive plasma ramp-up on the QUEST spherical tokamak

A 28 GHz system with a high-power gyrotron tube has been used for the QUEST spherical tokamak to form an over-dense plasma for electron Bernstein wave (EBW) heating and current drive with an 8.2 GHz-wave. Non-inductive high-density plasma ramp-up experiments with dual-frequency (dual-f ) electron cyclotron (EC) (8.2 GHz and 28 GHz) waves were conducted. A spontaneous density jump (SDJ) to an over-dense state was first observed as a bifurcation phenomenon in the dual-f wave experiment. The over-dense plasma on the 8.2 GHz wave was non-inductively ramped up to 25 kA, and was maintained for 0.4 s under stable plasma equilibrium after two such jumps in one shot. Heating to mildly energetic electrons and bulk electrons was observed even in the over-dense region. The electrostatic EBW heating effect on the mildly energetic electrons in the over-dense region is assessed following a dispersion analysis of the 8.2 GHz wave. The bulk electron heating effect observed is explained as heat exchange from mildly energetic electrons heated by the electrostatic EBW. Remarkably, a high hard-x-ray-radiation temperature of ∼500 keV was also observed in tangential viewing for current-carrying electrons in the over-dense core region. Synergetic heating from the overlap of different 28 GHz EC harmonic resonances as well as higher harmonic heating is discussed for maintaining the highly energetic electrons in the over-dense core region. In addition, the SDJ process and mechanism are considered based on the discussion of the electron heating effects with the 8.2 GHz wave.

Particle-in-cell simulations of parametric decay instabilities at the upper hybrid layer of fusion plasmas to determine their primary threshold

Parametric decay instabilities (PDIs) are nonlinear processes by which energy from a strong pump wave may be directed into other waves at other frequencies, in particular natural modes of the medium, provided that energy and momentum are conserved. The particle-in-cell code EPOCH is used to simulate PDIs in a magnetically confined fusion plasma converting a 105 GHz microwave X-mode pump wave into electrostatic daughter waves at the upper hybrid layer. Modes associated with the PDIs as well as a linearly converted electron Bernstein wave are identified in f- and k-space. The PDI daughter modes are found to agree with experimental observations from ASDEX Upgrade as well as with analytical predictions, showing a nonlinear increase in power above a predicted threshold.

Mapping of power deposition zone of electron Bernstein waves externally excited in tokamak plasmas

In toroidal plasmas, electron Bernstein (EB) waves mode-converted from X waves at the upper hybrid resonance (UHR) layer propagate toward the higher field side and are cyclotron-damped away at Doppler shifted frequency before arriving at the electron cyclotron resonance (ECR) layer. Resulting power deposition profile depends on local density, temperature and field profiles and is usually analyzed using the ray tracing technique for EB wave propagation and absorption in inhomogeneous magnetized plasmas. In axisymmetric tokamak plasmas, the ray tracing equation of EB waves can be cast into the form of equation of particle motion in a potential field. The particle trajectory and its momentum correspond to the wave trajectory and the refractive index, respectively. The potential field reflects the dispersion characteristics of EB waves, that is, the perpendicular refractive index strongly increases as the waves approach to the ECR layer from the lower field side, making a deep trench of potential along the ECR layer. Therefore the EB waves perpendicularly approach the ECR layer, which enable us to estimate the parallel refractive index and the parallel velocity of resonance electrons near the ECR layer. Thus, possible power deposition zone can be mapped and the associated current drive efficiency is roughly estimated directly from the information on wave frequency and plasma profiles without ray tracing calculations (direct mapping). The mapped zone, in the case of a moderately over dense plasma, is shown to be coincident with the ray tracing results for both XB and OXB schemes of mode conversion. In the cases of highly over dense, low safety factor and low aspect ratio plasmas, ω/Ωce is rather close to two at the UHR layer and the second harmonic cyclotron damping can take place along the ray trajectory just after OXB mode conversion, depending on the parameters. Here, ω is the wave frequency and Ωce is the local cyclotron frequency. It is shown that direct mapping also works in this case as well. The direct mapping technique is based on above picture of EB wave propagation and absorption, and is useful to guide the ray tracing analyses and cross-check the ray tracing results.

Development of the calibration method for a fast steering antenna for investigating the mode conversion window used in EBW heating in the LHD plasma

In this study, we developed a calibration method for a fast steering antenna for investigating the mode conversion window used in electron Bernstein wave heating in the large helical device. The calibration was carried out in under-dense plasma against a line-of-sight with an optical thickness which varied spatially. Although multi-reflected background radiation becomes dominant in optically thin lines-of-sight, we succeeded in calibrating the fast steering antenna by including the effect of multi-reflected background radiation in the solution of the radiation transfer equation as the constant by which the temperature of the center of the plasma is multiplied. In addition, we report the initial results of experiments investigating the mode conversion window in over-dense plasma using the calibrated antenna.

Construction of an EBW Heating System for the MST RFP

The first observation of rf heating in a reversed field pinch (RFP) using the electron Bernstein wave (EBW) has been demonstrated on Madison Symmetric Torus (MST). The design of the RF heating system used in this experiment is described. Klystron and antenna limitations are examined during launch into the plasma.

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

In spherical tokamaks, the electron plasma frequency is greater than the electron cyclotron (EC) frequency. Electromagnetic waves in the EC range of frequencies are unsuitable for directly heating such plasmas due to their reduced accessibility. However, mode-conversion of the extraordinary wave to the electron Bernstein wave (X–B mode-conversion) at the upper hybrid resonance makes it possible to efficiently couple externally-launched electromagnetic wave energy into an overdense plasma core. Traditional mode-conversion models describe an X-mode wave propagating in a potential containing two cutoffs that bracket a single wave resonance. Often, however, the mode-conversion region is in the edge, where turbulent fluctuations and blobs can generate abrupt cutoffs and scattering of the incident X-mode wave. We present a new framework for studying the X–B mode-conversion which makes the inclusion of these fluctuations analytically tractable. In the new approach, the high-field cutoff is modeled as an infinite barrier, which manifests as a boundary condition applied to a wave equation involving only one cutoff adjacent to the resonance on the low-field side. The new model reproduces the main features of the previous approach, yet is more suitable for analyzing experimental observations and extrapolating to higher dimensions. We then develop an analytical estimate for the effect of small-amplitude, quasi-monochromatic density fluctuations on the X–B mode-conversion efficiency using perturbation theory. We find that Bragg backscattering of the launched X-mode wave reduces the mode-conversion efficiency significantly when the fluctuation wavenumber is resonant with the wavenumber of the incident X-mode wave. These analytical results are corroborated by numerically integrating the mode-conversion equations.

MMS Observations of Electrostatic Waves in an Oblique Shock Crossing

AbstractHigh‐resolution particle and wave measurements taken during an oblique bow shock crossing by the Magnetospheric Multiscale (MMS) mission are analyzed. Two regions of differing magnetic behavior are identified within the shock, one with active magnetic fluctuations and one with laminar interplanetary magnetic field topology. A prominent reflected ion population is observed in both regions. The active magnetic region is characterized by large‐amplitude (>100 mV/m) electrostatic solitary waves, electron Bernstein waves, and ion acoustic waves, along with intermittent current activity and localized electron heating. In the region of laminar magnetic field, ion acoustic waves are prominently observed. Solar wind ion deceleration is observed in both regions of active and laminar magnetic field. All observations suggest that solar wind deceleration can occur as a result of multiple independent processes, in this case current and ion‐ion instabilities.

The spoke origin based on the coupling-induced wave model in high-power impulse magnetron sputtering plasma

Spokes, identified as the source of anomalous across-B field transport during the high-power impulse magnetron sputtering (HiPIMS) discharge, have been considered as a result of plasma instability. This paper investigates the evolution of the coupling between two azimuthal waves in HiPIMS plasma by revisiting the dispersion relation. A coupling-induced wave model is proposed for the origin of the spoke. The ion sound wave can be strongly coupled with a Doppler-shifted electron Bernstein wave, inducing a long-scale (cm size) electric field oscillation waving at the frequency difference. The spoke appears to be a collective behavior of ion rearrangement guided by the difference frequency wave along the azimuthal direction. The direct comparison of spoke characteristics, such as rotating velocity, frequency and dynamic features, given by this model with experimental and simulation results from the literature shows a good qualitative agreement. Moreover, the evolution of spoke behavior following on from the model are presented, including rotating velocity and mode number along the racetrack. Their variation tendency matches well with experimental findings, from the literature.

X-mode coupling to Bernstein wave in a plasma embedded with clusters

Parametric coupling between a large amplitude X-mode laser, propagating perpendicular to the ambient magnetic field Bszˆ, through a plasma embedded with clusters with short-wavelength electron Bernstein wave and a lower hybrid wave is investigated. The coupling arises through the ponderomotive force by the high frequency waves and the low frequency density perturbation beating with the oscillatory velocity due to laser. Finite Larmor radius effects on plasma electrons are included while those on free electrons inside the clusters are neglected. The clusters response to nonlinear coupling is enhanced due to the Plasmon resonance. The cluster Plasmon resonance strongly modifies the nonlinear coupling between modes. For typical parameters, k1⊥2vth2/(2ωc2)=1,nc(4π/3)rc3=0.001,eA0/(mω0c)=0.1, the growth rate turns out to be maximum when ω/ωLH=1.4 and decreases sharply with ω/ωLH.

High-Field-Side RF Injection for Excitation of Electron Bernstein Waves

High-Field-Side RF Injection for Excitation of Electron Bernstein Waves

Development of a triple probe array for mode conversion study of electron cyclotron wave.

A triple probe array has been designed with a modified triple probe technique and utilized on the Sino-UNIted Spherical Tokamak for mode conversion research from the electron cyclotron wave to the electron Bernstein wave. The probe array is designed to measure the radial profile of the electron density in the edge region. The probe array consists of 36 single molybdenum tips, constituting 12 sets of triple probes with an interval of 6 mm in the radial direction. The three tips in each triple probe are displaced slightly in the radial direction, and thus they are not at the same magnetic surface to avoid shadow effects in the toroidal direction. A modified triple probe technique is used. The radial profile of the electron density of ohmic heated plasmas has been measured by the triple probe array. The temporal evolution of the density profile is presented, and the mode conversion processes are discussed.

Overlapping of the harmonics of the cyclotron frequency in the Bernstein waves due to relativistic effects

By using the generalized expression for the plasma conductivity tensor, the general dispersion relation for the Bernstein waves is derived. To investigate the Bernstein waves for a weakly relativistic plasma, the Maxwell-Boltzmann-Juttner distribution function is employed. The propagation characteristics of the electron Bernstein waves (overlapping, propagation regions, and harmonic structures) are examined by using different values of η (ratio of rest mass energy to thermal energy) and ωpeωce (ratio of the plasma frequency to the cyclotron frequency). It is observed that the relativistic effects are the main cause of the harmonic overlapping which reduces the region of propagation.