Electron Bernstein Waves Research Articles

Experimental Conditions for Electron Bernstein Wave Heating Using EC Waves Injected from High-Field Side in CHS

In the compact helical system (CHS), electron heating by electron Bernstein waves (EBWs) was experimentally investigated to study a technique for high-density plasma heating over cutoff density. The EBWs are excited through a mode conversion process by X-mode waves injected to plasmas from the high-field side. In the experiment, within the range of an oblique EC-wave beam injection angle, evident heating effect was observed. The dependences of the heating effect on the wave's toroidal injection direction and polarization show that the absorption of the mode-converted EBWs should be the cause of the plasma heating effect.

Recent Developments in the Theory of Electron Cyclotron Waves

Quantitative predictions of propagation, emission, and absorption of electron cyclotron (EC) waves rely on a solid theoretical background and are routinely employed in the analysis and preparation of present and future fusion experiments. Nonetheless, open problems still exist, and improvements are possible also within well-established models to make them faster, more accurate, or more general. This paper presents some of the recent advances in the theoretical investigation of EC waves. Particular emphasis is put on the “standard” approach based on the short-wavelength approximation and linear or quasi-linear computation of wave absorption, on the theory of electron Bernstein waves, and on the applications of cyclotron heating and current drive for ITER.

Flux averaged current drive efficiency of electron Bernstein waves

Electron Bernstein waves are of interest for heating and current drive in spherical tokamaks where the central region of the plasma is not accessible to the ordinary and extraordinary modes. In this paper we adapt an analytical theory of current drive in toroidal geometry developed by Lin-Liu et al (2003 Phys. Plasmas 10 4064) to this system. This involves taking account of the fact that the ratio of the Larmor radius to the perpendicular wavelength is not, in general, small for the Bernstein waves and also including the effects of a non-circular plasma cross section. By comparing the results with those of a full Fokker–Planck code, we demonstrate that the analytical method can yield a good approximation to the current drive efficiency in most regimes of practical interest. Since it is much less computationally demanding than using a Fokker–Planck code we suggest that it could be a useful tool for analysing experiments on Bernstein mode current drive in spherical tokamaks.

Wave excitation in inhomogeneous dielectric media

The equation describing the propagation of a mode driven by external currents in an inhomogeneous dielectric is derived from the principle of the conservation of wave energy density and wave momentum density. The wave amplitude in steady state is obtained in terms of a simple spatial integration of the driving current. The contribution from the spatial derivative of the dielectric response is found to be important. The analytical predictions are verified through comparison with deltaf particle-in-cell computations of electron Bernstein wave propagation, thus showing applicability to kinetic systems.

Relativistic ray-tracing of electron Bernstein waves in a spherical tokamak reactor

Electron Bernstein waves (EBW) can propagate between electron cyclotron harmonics in hot, dense plasmas with no high-density cutoff (unlike electron cyclotron waves). ARIES-ST is a spherical tokamak (ST) reactor study. A promising method of heating and driving current in such an ST reactor would be with electron Bernstein waves. These could be mode converted from microwave vacuum modes (X-mode and O-mode) launched from the edge. In this paper, fully relativistic ray-tracing calculations (both damping and propagation) of EBWs in ARIES-ST are presented, using the relativistic dispersion solver R2D2 and the ray-tracing code GENRAY. The ray paths, damping locations, and polarizations are compared with the more commonly used non-relativistic EBW ray-tracing. A range of frequencies are shown for EBWs with small n∥ that could be produced by the X-B mode conversion process, and EBWs with large n∥ ≈ 0.6, produced by the O-X-B mode conversion process. With the density and temperature profile chosen for this paper, the greatest depth into the core that could be reached with mode-converted EBWs is a radial location of approximately ρ = 0.4. Although the radial location of the damping in most cases was not significantly different between the relativistic and non-relativistic cases, there are differences in the poloidal locations, as well as in the polarizations of the wave along the ray path, especially in the damping region.

Electron Bernstein wave heating of over-dense H-mode plasmas in the TCV tokamak via O-X-B double mode conversion

This paper reports on the first demonstration of electron Bernstein wave heating (EBWH) by double mode conversion from ordinary (O-) to Bernstein (B-) via the extraordinary (X-) mode in an over-dense tokamak plasma, using low field side launch, achieved in the TCV tokamak H-mode, making use of its naturally generated steep density gradient. This technique offers the possibility of overcoming the upper density limit of conventional EC microwave heating. The sensitive dependence of the O-X mode conversion on the microwave launching direction has been verified experimentally. Localized power deposition, consistent with theoretical predictions, has been observed at densities well above the conventional cut-off. Central heating has been achieved, at powers up to two megawatts. This demonstrates the potential of EBW in tokamak H-modes, the intended mode of operation for a reactor such as ITER.

Overview of physics results from MAST

Substantial advances have been made on the Mega Ampère Spherical Tokamak (MAST). The parameter range of the MAST confinement database has been extended and it now also includes pellet-fuelled discharges. Good pellet retention has been observed in H-mode discharges without triggering an ELM or an H/L transition during peripheral ablation of low speed pellets. Co-ordinated studies on MAST and DIII-D demonstrate a strong link between the aspect ratio and the beta scaling of H-mode energy confinement, consistent with that obtained when MAST data were merged with a subset of the ITPA database. Electron and ion ITBs are readily formed and their evolution has been investigated. Electron and ion thermal diffusivities have been reduced to values close to the ion neoclassical level. Error field correction coils have been used to determine the locked mode threshold scaling which is comparable to that in conventional aspect ratio tokamaks. The impact of plasma rotation on sawteeth has been investigated and the results have been well-modelled using the MISHKA-F code. Alfvén cascades have been observed in discharges with reversed magnetic shear. Measurements during off-axis NBCD and heating are consistent with classical fast ion modelling and indicate efficient heating and significant driven current. Central electron Bernstein wave heating has been observed via the O–X–B mode conversion process in special magnetically compressed plasmas. Plasmas with low pedestal collisionality have been established and further insight has been gained into the characteristics of filamentary structures at the plasma edge. Complex behaviour of the divertor power loading during plasma disruptions has been revealed by high resolution infra-red measurements.

Progress towards steady state at low aspect ratio on the National Spherical Torus Experiment (NSTX)

Modifications to the plasma control capabilities and poloidal field coils of the National Spherical Torus Experiment (NSTX) have enabled a significant enhancement in shaping capability which has led to the transient achievement of a record shape factor (S ≡ q95 (Ip/a Bt)) of ∼41 (MA m−1 T−1) simultaneous with a record plasma elongation of κ ≡ b/a ∼ 3. This result was obtained using isoflux control and real-time equilibrium reconstruction. Achieving high shape factor together with tolerable divertor loading is an important result for future ST burning plasma experiments as exemplified by studies for future ST reactor concepts, as well as neutron producing devices, which rely on achieving high shape factors in order to achieve steady state operation while maintaining MHD stability. Statistical evidence is presented which demonstrates the expected correlation between increased shaping and improved plasma performance. Plasmas with high shape factor have been sustained for pulse lengths which correspond to τpulse = 1.6s ∼ 50 τE ∼ 5 τCR, where τCR is the current relaxation time and τE is the energy confinement time. Plasmas with higher βt ∼ 20% have been sustained for τpulse = 1.2s ∼ 25 τE ∼ 3 τCR with non-inductive current fractions fNI ∼ 50%, with ∼40% pressure driven current and ∼10% neutral beam driven current. An interesting feature of these discharges is the observation that the central value of the safety factor q(0) remains elevated and constant for several current diffusion times without sawteeth, similar to the ‘hybrid mode’. Calculations of the profiles of inductive and non-inductive current are compared with measurements of the total current profile and are shown to be in quantitative agreement. Results are shown from experiments which investigate the applicability of high harmonic fast waves (HHFWs) and electron Bernstein waves (EBWs) as current drive and heating sources, and the possibility of LHCD for future ST devices is raised. A calculated scenario which provides 100% non-inductive current drive is described. NSTX operates with peak divertor heat fluxes which are in the same range as those expected for the ITER device, i.e. with . High triangularity, high elongation plasmas on NSTX have been demonstrated to have reduced peak heat flux to the divertor plates to <3 MW m−2.

Development of Electron Bernstein Wave Research in MAST

Burning plasma spherical tokamaks (STs) rely on off-axis current drive (CD) and nonsolenoid start-up techniques. Electron Bernstein waves (EBWs) may provide efficient off-axis heating and CD in high-density ST plasmas. EBWs may also be used in the plasma start-up phase because EBW absorption and CD efficiency remain high even in relatively cold plasmas. EBW studies on the Mega Ampere Spherical Tokamak (MAST) can be subdivided into four separate subjects: thermal electron cyclotron emission observations from overdense plasmas, EBW modeling, proof-of-principle EBW heating experiments with the existing 60-GHz gyrotrons, and EBW assisted plasma start-up at 28 GHz. These studies are also aimed at determining the potential for a high-power EBW system for heating and CD in MAST. The optimum choice of frequency and launch configuration is a key issue for future applications in MAST. This paper describes diagnostics, modeling tools, and high-power radio frequency systems developed specifically for EBW research in MAST. The experimental methodology employed in proof-of-principle EBW heating experiments along with experimental results is discussed in detail. EBW heating via the ordinary-extraordinary-Bernstein (O-X-B) mode conversion has clearly been observed for the first time in an ST.

Weakly Relativistic and Nonrelativistic Estimates of EBW Heating in the TJ-II Stellarator

The relativistic effects on electron Bernstein wave (EBW) heating of plasmas confined in the TJ-II stellarator are presented in this work. The Ordinary-eXtraordinary-Bernstein mode conversion at the fundamental electron cyclotron harmonic (f = 28 GHz for the TJ-II central magnetic field) is chosen as the scenario for these estimates. This heating scheme presents high absorbed power for central densities above 1.2 × 1019 m-3 and has no upper density limit. Relativistic and nonrelativistic calculations have been performed using the TRUBA beam/ray-tracing code. For this purpose, the weakly relativistic dispersion relation valid for any values of the parallel and perpendicular refractive indexes, thus suitable for EBW, has been obtained. This dispersion relation has been introduced in TRUBA to estimate the ray trajectories and the power absorption to all orders of Larmor radius in the weakly relativistic regime. The result of our comparison is that the relativistic effects are not negligible and must be taken into account both on the ray trajectories and in the power absorption estimations. We also show that the relativistic absorption coefficient is lower than the nonrelativistic one, for the values of parallel refractive index that happen in TJ-II, and the power deposition profile is more centered.

Electron Bernstein Wave Heating and Emission in the TCV Tokamak

Electron cyclotron resonance heating (ECRH) of high-density tokamak plasmas is limited because of reflections of the waves at so-called wave cutoffs. Electron Bernstein wave (EBW) heating (EBWH) via a double mode conversion process from ordinary (O)-mode, launched from the low field side, to extraordinary (X)-mode and finally to Bernstein (B)-mode offers the possibility of overcoming these density limits.In this paper, the O-X mode conversion dependence on the microwave injection angle is demonstrated experimentally. The dependence on the injection angle is studied in high-density plasmas in H-mode, in the presence of magnetohydrodynamic activity, edge-localized modes, and sawteeth. The results of localized heat deposition at an overdense location are presented, demonstrating EBWH for the first time via the O-X-B mode conversion process in a standard aspect-ratio tokamak. The results of global and local power deposition are compared with ray-tracing calculations. Moreover, a temperature increase due to EBWH is observed.Initial EBW emission measurements with a newly installed ECRH reception launcher are presented. The inverse double mode conversion process B-X-O is observed by measuring the emission for several frequencies at an optimum angle.

Recent Developments in Electron Cyclotron Emission Research on Magnetically Confined Plasmas

Electron cyclotron emission (ECE) has been an important diagnostic for measuring the temporal evolution of the electron temperature profile in magnetically confined plasma devices for more than 25 years. Recent advances in ECE measurements, such as two-dimensional ECE imaging and ECE intensity correlation techniques, have provided detailed information on sawtooth reconnection, neoclassical tearing mode behavior, electron heat transport, fast electron dynamics, and fast particle-driven Alfvén eigenmodes. ECE spectral analysis is benefiting from improved ECE modeling and significant increases in computational power that allow fast, real-time, temperature measurements. Mode-converted electron Bernstein wave emission (EBE) diagnostics are being developed to study overdense (ɷpe ≫ ɷce) plasmas, a regime where conventional ECE diagnostics cannot be applied and one commonly encountered in high-β devices, such as the spherical torus and reversed-field pinch. While ECE diagnostic techniques are now well established on many existing magnetically confined plasmas, significant challenges lie ahead for applying ECE techniques to reactor-grade plasmas such as ITER, where Te(0) is expected to reach 20 to 40 keV. This paper reviews the recent advances in ECE, electron cyclotron absorption, and EBE diagnostics and discusses the challenges for ECE measurements on ITER.

Experimental Observations of O-X-B Heating of Overdense Plasmas in CHS

Evident increases in the plasma stored energy by applying 54.5-GHz electron cyclotron (EC) waves have been observed in overdense plasmas sustained by neutral beam injection in the Compact Helical System. The heating effect was seen even for a high density of 8 × 1019 m-3, that is, more than twice the cutoff density of 3.8 × 1019 m-3 of the 54.5-GHz waves. The 54.5-GHz EC wave beams were obliquely injected into high-density plasmas. Dependences of the heating effect on the experimental conditions such as the polarization and the injection power of the EC waves, and the magnetic field were investigated. A higher left-hand circular polarization fraction and higher injection power resulted in a longer plasma duration time and a higher increment of the plasma stored energy. Variation of the electron temperature profile in the magnetic field scan experiment shows the power deposition in the plasma core region inside the plasma cutoff layer. These experimental results show that the main cause for this heating mechanism is electron Bernstein wave heating via an Ordinary-eXtraordinary-Bernstein (O-X-B) mode conversion process.

Recent Experimental Progress in Electron Cyclotron Resonance Heating and Electron Cyclotron Current Drive in Magnetically Confined Fusion Plasmas

A review of recent experimental results in electron cyclotron (EC) resonance heating and EC current drive (CD) (ECCD) is given. Special emphasis is put on the recent developments of new schemes in which EC waves can heat and drive current in magnetically confined fusion plasmas. These comprise scenarios to overcome the density cutoff experienced in application of the classical first-harmonic ordinary mode (O1) and second-harmonic extraordinary mode (X2) schemes as well as to increase the CD efficiency of EC waves while maintaining their good localization. In particular, we discuss recent experimental progress in tokamaks, stellarators, and spherical tori in the areas of the second-harmonic ordinary mode (O2), third-harmonic extraordinary mode (X3), and electron Bernstein wave schemes [mostly Ordinary-eXtraordinary-Bernstein (O-X-B) scheme] as well as experiments in which the combination of ECCD with lower hybrid CD leads to a synergetic increase of the ECCD efficiency. A particular application of ECCD that has recently received much attention and is therefore reviewed in this paper is the suppression of neoclassical tearing modes (NTMs) by ECCD. We show that the theoretically predicted requirements for ECCD in terms of deposition (maximizing the ECCD driven current density) and injection in phase with the O-point of the magnetic island associated with the NTM (which is needed when the island width falls below the deposition width) have been verified experimentally. Also, many of the elements needed for constructing a reliable, feedback-controlled NTM suppression system for ITER based on ECCD have now been demonstrated experimentally, and the next step, which is their integration into a reliable scheme, is well within reach.

A ‘multi-colour’ SXR diagnostic for time and space-resolved measurements of electron temperature, MHD activity and particle transport in MCF plasmas

A fast (⩽0.1 ms) and compact ‘multi-colour’ soft x-ray array has been developed for time and space-resolved electron temperature (Te) measurements in magnetically confined fusion (MCF) plasmas. The electron temperature is obtained by modelling the slope of the continuum radiation from ratios of the available 1D-Abel inverted radial emissivity profiles over different energy ranges, with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints or need of shot-to-shot reproducibility. This technique has been used to perform fast Te measurements in the National Spherical Torus Experiment (NSTX), avoiding the limitations imposed by the well-known multi-point Thompson scattering, electron cyclotron emission and electron Bernstein wave mode conversion diagnostics. The applicability of this ‘multi-colour’ technique for magnetohydrodynamic (MHD) mode recognition and a variety of perturbative electron and impurity transport studies in MCF plasmas is also discussed. Reconstructed ‘multi-colour’ emissivity profiles for a variety of NSTX scenarios are presented here for the first time.

Direct Observation of Electron-Bernstein Wave Heating byO−X−B-Mode Conversion at Low Magnetic Field in the WEGA Stellarator

The ordinary-extraordinary-Bernstein-mode conversion process for overdense plasma heating with electron-Bernstein waves is demonstrated in the WEGA stellarator at low magnetic field (approximately 50 mT) at 2.45 GHz. For the first time the conversion from an O wave to an X wave is clearly demonstrated by probe measurements of amplitude and phase of the wave field in the conversion region and supported by two-dimensional full-wave calculations. The propagation and resonant absorption of the Bernstein wave is measured in fast power modulation experiments.

Simple and accurate approximate relativistic dispersion relation for electron Bernstein waves

A new simple and accurate approximate electrostatic relativistic dispersion relation for electron Bernstein waves in a Maxwellian plasma has been obtained. The relativistic relation is valid for an arbitrary value of parallel refractive index. Comparisons with corresponding exact formulae are given.

Emission of electromagnetic waves by proton beams propagating in nonuniform solar plasmas

Aims. We investigate the dynamics of proton beams propagating along a uniform magnetic field, as well as across the magnetic field in nonuniform solar plasmas, paying attention to the emission process of electromagnetic waves. The aim is to understand a new solar-burst component emitting only in the terahertz range during the solar flare observed by Kaufmann et al. (2004, ApJ, 603, L121). Methods. We used a 2D3V, fully relativistic, electromagnetic particle-in-cell (PIC) simulation. Results. From the simulation where the proton beams propagate along a uniform magnetic field into the high-density region, we found that strong electromagnetic waves are generated behind the proton beams. When the proton beams propagate perpendicular to the magnetic field, we found that the extra-ordinary mode can be excited from two electron Bernstein waves through three-wave interactions. These simulation results could be applied to the electromagnetic wave emission from the solar photosphere during the solar flares.

Parametric excitation of electron Bernstein waves by radio waves in the ionosphere and its possible consequence for airglow

A high power radio wave, launched into the polar ionosphere at angle θ with the earth's magnetic field from a ground-based transmitter in the vicinity of twice the electron cyclotron frequency (2.75 MHz), is reported to create an airglow at an effective radiated power (ERP) = 10 MW. We interpret this result as a consequence of parametric decay of the radio wave into an electron Bernstein wave (EBW) and an ion acoustic wave (IAW). The oscillatory velocity of electrons due to the pump couples with the density perturbation due to the IAW to produce a current, driving the Bernstein mode. The latter, in connection with the pump, exerts a ponderomotive force on electrons, driving the IAW. The growth rate of the parametric instability is maximum for θ = 0. At the same time, for any given value of θ, the growth rate increases with and attains a maximum around b ∼ 2, then falls gradually. The EBW produces energetic electrons via cyclotron damping. These electrons collide with the neutral atoms of the plasma to excite them to higher energy states. As the excited atoms return to lower energy states, they radiate in the visible.

Parametric up-conversion of an electron Bernstein mode by a relativistic electron beam in a plasma

A relativistic electron beam, propagating with velocity v0b‖ẑ in a magnetized plasma, parametrically up-converts a pre-existing electron Bernstein wave (ω0,k0) into electromagnetic radiation when k0∙v0b&amp;lt;0. The Bernstein wave couples with a negative energy space-charge mode (ω,k) to produce a frequency up-converted sideband electromagnetic wave. The sideband and the Bernstein wave exert a ponderomotive force, driving space-charge mode. In the Compton regime, the growth rate of the parametric instability scales as two-third power of the pump amplitude, whereas in the Raman regime, it goes linearly.