Harmonic Electron Cyclotron Resonance Research Articles

Observation of second harmonic electron cyclotron resonance heating and current-drive transition during non-inductive plasma start-up experiment in QUEST

Noninductive plasma current start-up using 2nd harmonic electron cyclotron resonance heating (ECRH) with oblique radio frequency (RF) injection is demonstrated in a Q-shu University experiment with steady-state spherical tokamak. A strong transition was observed in the heating and plasma current ramp-up. The initial bulk electron heating regime exhibits T ebulk ∼ 140 eV and no hard x-ray (HXR) emission with a low I p of ∼15 kA; it abruptly transitions to a regime that exhibits a low T ebulk of ∼10 eV and a strong HXR emission with a high I p of ∼50 kA. This behavior is distinctly different from that observed in previous fundamental ECRH experiments. The mechanism of the heating and current drive transition are investigated considering wave power absorption and plasma power balance. The results indicate that the transition is caused by the favorable heating of tail electrons where the RF power absorption at the 2nd harmonic increases nearly linearly with T etail, while the power transfer from the tail electrons to the bulk electrons decreases with 1/T etail 0.5. This causes a rapid transition to a state with high T etail while reducing T ebulk towards colder ion temperature. The understanding of the transition mechanism helps to consider plasma current start-up using 2nd harmonic ECRH for tokamak reactors such as JT-60 SA and ITER.

Trapped upper hybrid waves as eigenmodes of non-monotonic background density profiles

Non-monotonic plasma density structures such as blobs and magnetic islands give rise to trapped upper hybrid (UH) waves. Trapped UH waves which satisfy Bohr–Sommerfeld quantization can be thought of as eigenmodes of a cavity. Using fully kinetic particle-in-cell simulations, we verify the existence of these UH eigenmodes and demonstrate their significance as only eigenfrequencies become unstable to three-wave interactions. The eigenmodes can be excited through parametric decay instabilities (PDIs) of an X-mode pump wave at approximately twice the UH frequency, as could be the case for a gyrotron beam traversing a blob in a magnetically confined fusion plasma. We derive a closed expression for the wavenumber of UH waves, which is accurate both close to the UH layer and to the electron cyclotron resonance. This allows for fast analysis of eigenmodes in a non-monotonic structure. An expression for the amplification of PDI daughter waves in an inhomogeneous plasma is extended to a decay region where the first several derivatives vanish. From the amplification in a convective PDI, we estimate the growth rate of the absolute PDI involving the trapped waves. We show that the excitation of eigenmodes through PDIs in our simulations are indeed absolute rather than convective due to the trapping of the daughter waves. Additionally, we show that only eigenmodes get excited through the PDIs, and that we are able to predict the growth rates of the daughter waves and how they scale with the pump wave intensity. This is evidence supporting a fundamental assumption of analytical theory describing low threshold strong scattering observed in magnetically confined fusion experiments during second harmonic electron cyclotron resonance heating (ECRH). Such low threshold instabilities can degrade ECRH performance but also offer novel uses for ion heating or as diagnostics.

Topology of the warm plasma dispersion relation at the second harmonic electron cyclotron resonance layer

The warm plasma dispersion relation, for waves in the electron cyclotron resonance range of frequencies, can be cast into the form of a bi-quadratic equation for N⊥, where the coefficients are a function of N⊥2 and an iterative procedure is required to obtain a solution. However, this iterative procedure is not well understood and fails to converge toward a solution at the second harmonic resonance layer, in particular at higher densities where the wave can couple to an electron Bernstein wave. This paper focuses on a solution to the poor convergence of the iterative method, enabling determination of the topology of the dispersion relation around the second harmonic using a fully relativistic code for oblique waves. A feed-forward controller is proposed with the ability to adjust the rotation of a step of N⊥2 within the complex plane, while also limiting the step-size. It is shown that implementation of the controller stabilizes unstable solutions, while improving overall robustness of the iteration. This allows the evaluation of the coupling between the fast extraordinary mode and electron Bernstein waves at the second harmonic electron cyclotron resonance layer, for non-perpendicularly propagating waves.

Reduction of anomalous absorption in the extraordinary mode second harmonic electron cyclotron resonance heating experiments

The possibility of suppressing low-power-threshold parametric decay instabilities excited at plasma auxiliary heating with an extraordinary wave at the second harmonic of the electron cyclotron resonance and reducing the anomalous absorption associated with this instability is considered. It is theoretically demonstrated that increasing the microwave pump beam width and its power allows reducing the related anomalous absorption rate.

Numerical investigations of parametric decay into trapped waves in magnetized plasmas with a non-monotonic density background

Parametric decay instabilities (PDIs) exciting daughter waves trapped inside a magnetized plasma with a non-monotonic density profile are investigated numerically. The investigation is motivated in particular by observations of low threshold PDI signatures during second harmonic electron cyclotron resonance heating experiments in magnetically confined fusion experiments. We use the particle-in-cell code EPOCH to study conversion of a fast X-mode pump wave into a combination of half frequency X-mode and electron Bernstein waves and identify two regimes where PDIs can excite trapped electrostatic waves. Above the second harmonic upper hybrid (UH) density, a PDI known also as a two plasmon decay (TPD) instability excites a pair of UH waves that we locate in frequency and wavenumber space. At lower densities, a PDI known as stimulated Raman scattering may produce one trapped and one returning X-mode daughter wave with a much slower growth rate than the TPD instability. In both cases, we show that the frequency separation of the daughter waves depends on the density in a predictable manner. With little loss from the decay region, the trapped daughter waves become unstable with respect to secondary parametric instabilities (PIs), leading to distinctly different phases of the UH spectrum. Unlike the primary instability, the secondary PIs are shown to depend on ion dynamics. Furthermore, we observe escaping waves near the 3/2 pump frequency resulting from tertiary PIs in agreement with recently proposed backscattering during magnetically confined fusion experiments.

Turbulence measurements on the high and low magnetic field side of the DIII-D tokamak.

In this paper, we address the challenging question of measuring turbulence levels on the high magnetic field side (HFS) of tokamak plasmas. Although turbulence measurements on the HFS can provide a stringent constraint for the turbulence model validation, to date only low magnetic field side (LFS) measured turbulence has been used in validation studies. To address this issue, an eight channel Correlation Electron Cyclotron Emission (CECE) system at DIII-D was modified to probe both LFS and HFS. In contrast to the second harmonic extraordinary mode electron cyclotron resonance emission that is typically used in CECE, we show that it is possible to probe the HFS using fundamental O-mode electron cyclotron resonance emission. The required hardware modifications for the HFS measurements are presented here, and the potential issues in this measurement are discussed.

Parametric decay instability near the upper hybrid resonance in magnetically confined fusion plasmas

In this paper we investigate parametric decay of an electromagnetic pump wave into two electrostatic daughter waves, particularly an X-mode pump wave decaying into a warm upper hybrid wave (a limit of an electron Bernstein wave) and a warm lower hybrid wave. We describe the general theory of the above parametric decay instability (PDI), unifying earlier treatments, and show that it may occur in underdense and weakly overdense plasmas. The PDI theory is used to explain anomalous sidebands observed in collective Thomson scattering (CTS) spectra at the ASDEX Upgrade tokamak. The theory may also account for similar observations during CTS experiments in stellarators, as well as in some 1st harmonic electron cyclotron resonance and O-X-B heating experiments.

Theory of anomalous backscattering in second harmonic X-mode ECRH experiments

A quantitative model explaining generation of the anomalous backscattering signal in the second harmonic X-mode electron cyclotron resonance heating (ECRH) experiments at TEXTOR tokamak as a secondary nonlinear process which accompanies a primary low-threshold parametric decay instability (PDI) leading to excitation of two—upper hybrid (UH)—plasmons trapped in plasma is developed. The primary absolute PDI enhancing the UH wave fluctuations from the thermal noise level is supposed to be saturated due to a cascade of secondary low-threshold decays of the daughter UH wave leading to excitation of the secondary UH waves down-shifted in frequency and the ion Bernstein wave. A set of equations describing the cascade is derived and solved numerically. The results of numerical modelling are shown to be in agreement with the analytical estimations of the growth rate of the initial and secondary parametric decays and the saturation level. The generation of backscattering signal is explained by coupling of the daughter UH waves. The fine details of the frequency spectrum of the anomalously reflected extraordinary wave and the absolute value of the observed backscattering signal in the second harmonic X-mode ECRH experiments at TEXTOR are reproduced.

The upgraded Collective Thomson Scattering diagnostics of FTU

The 140GHz Collective Thomson Scattering (CTS) diagnostics installed on the Frascati Tokamak Upgrade (FTU) has been upgraded. The new system now is ready both to detect the thermal CTS radiation (for the first time with the probe frequency below the 1st harmonic electron cyclotron resonance) and to study the impact of possible parametric decay instability (PDI) processes on the received signals. The EC front-steering antenna and transmission system have been complemented with a receiving line that matches a quasi-optical line feeding the homodyne multi-channel radiometer. The scattering volume can be placed in a wide range of locations by means of fast poloidal and toroidal rotations of the two plasma-facing mirrors that have an up–down symmetry with respect to the equatorial plane of the torus. The data acquisition system has been improved adding a new digitizer, with a bandwidth of 5GHz and a maximum sampling rate of 12.5GS/s. The possibility of directly sampling and Fourier transforming the down-converted signals greatly improves the suitability of the new diagnostics to carry out thermal ion temperature measurements and to study the competing PDI processes whenever present.

Optimization of the high harmonic ECRH scenario to extend a heating plasma parameter range in LHD

Effectiveness of high harmonic electron cyclotron resonance heating (ECRH) was investigated by both experiments and ray-trace analyses. The conditions of both the EC wave injection and the magnetic field configuration were optimized in the large helical device. In the case of the second harmonic ordinary mode injection with a frequency of 77 GHz and with the optimized injection angle, about 30–40% absorption could be kept beyond the cut-off density of the second harmonic extraordinary (X2) mode, which is 3.7 × 1019 m−3. In the third harmonic X (X3) mode heating experiment, the dependence of the absorption rate on plasma density and temperature of the target plasma was precisely investigated and compared with the ray-trace (TRAVIS code) calculation. The calculation results of the absorption rate show fairly good agreement with the experimentally obtained ones on the plasma-parameter dependences. The maximum absorption rate in the X3 heating experiment attained approximately 40% around the electron density of 1.5 × 1019 m−3 and the electron temperature of 1.2 keV. Superposed stepwise injection from three gyrotrons with a total of 3 MW increased the central electron temperature to about 3.5 times of the initial target plasma temperature of 0.6 keV. This shows that the temperature increase improves the absorption rate of the subsequent injection.

Observation of MHD Instabilities Driven by Energetic Electrons in the Large Helical Device**supported by the Grant-in-Aid for Encouragement of Scientists from the Japan Society for the Promotion of Science (No. 20656150). This work was also partly supported by the JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC: No. 11261140328 and NRF: No. 2012K2A2A6000443)

Coherent magnetic fluctuations in an acoustic range of frequency have been regularly observed in low-density (ne < 0.2×1019 m−3) plasmas with strong second harmonic electron cyclotron resonance heating (ECRH) on the Large Helical Device. Hard X-ray measurements indicated that energetic electrons are generated in these ECRH discharges. The magnetic fluctuations are suppressed in higher density discharges where energetic electrons are not present. The ECRH power modulation experiment indicated that the observed magnetohydrodynamic (MHD) mode has an acoustic nature rather than an Alfvénic nature.

Low-threshold absolute two-plasmon decay instability in the second harmonic electron cyclotron resonance heating experiments in toroidal devices

The effect of the X-mode parametric decay into two short wavelength upper hybrid (UH) plasmons propagating in opposite directions is analyzed. Due to the huge convective power loss of both the UH plasmons along the inhomogeneity direction, the power threshold of the convective parametric decay instability (PDI), which can be excited in the presence of a monotonous density profile is derived to exceed the gyrotron power range currently available. In the presence of the magnetic island possessing the local density maximum at its O-point the daughter UH plasmons can be trapped in the radial direction that suppresses their energy loss from the decay layer in full and makes the power threshold of the convective two-plasmon PDI drastically (three orders of magnitude) lower than in the previous case. The possibility of the absolute PDI being due to the finite size of the pump beam spot is demonstrated as well. The power threshold of the absolute instability is shown to be more than two orders of magnitude lower than the threshold of the convective instability at the monotonous density profile.

Energetic-particle modes driven by suprathermal electrons produced by off-axis second harmonic ECRH in compact helical system (CHS)

Recurrent bursting energetic-particle modes (EPMs) are observed in an l = 2 helical plasma heated by second harmonic electron cyclotron resonance heating (ECRH) without neutral beam injection. The observed instabilities are characterized by a rapid frequency downshift, propagating in the ion-diamagnetic drift direction. Such bursting MHD instabilities are seen only in fairly low-density plasmas with off-axis second harmonic ECRH. A soft x-ray detector operating in the counting mode indicates that there exist suprathermal electrons in low-density ECRH plasmas where EPMs are destabilized. The excitation of EPMs is supposed to be due to the helically trapped suprathermal electrons produced by the second harmonic ECRH.

Fast radiation dynamics during ELMs on TCV

Total radiative powers measured by AXUV diode based bolometer cameras have been measured in lower single null, third harmonic electron cyclotron resonance (X3 ECR) heated TCV ELMing H-mode discharges. Although, the non-flat spectral response of the diodes means that total radiated powers can be in error by as much as a factor 2, with time resolution on the order of several microseconds, the cameras can resolve plasma radiation dynamics on the ELM timescale. Observations show that: (i) most of the radiation comes from the divertor and outer midplane regions, (ii) about 70% of the ELM induced radiation occurs in the first third of the ELM cycle and (iii) only a maximum of ∼8% of the ELM energy is lost through radiation.

Millimeter-wave backscatter diagnostic for the study of short scale length plasma fluctuations (invited)

The development, laboratory tests, and experimental results relating to a new high-k diagnostic technique for the study of short scale length turbulence are reported. The system is based on backscattering of a millimeter-wave (94GHz) probe beam by density fluctuations within the plasma. This diagnostic has been fully integrated with an upgraded far-infrared forward scattering system on the DIII-D tokamak. The combined system monitors a broad turbulent spectral range from 0to40cm−1. Short-scale (e.g., electron temperature gradient scale) modes as well as longer wavelength (e.g., ion temperature gradient and trapped electron mode scale) instabilities are simultaneously monitored to accurately characterize plasma turbulence. The backscattering geometry and innovative use of the second harmonic electron cyclotron resonance as an internal “beam dump” allow detection of small level fluctuations at high k, while maximizing discrimination against the ubiquitous, larger level, low-k fluctuations.

Electron energy distribution function during second harmonic ECRH plasma breakdown

In this paper, the effect of electron–electron (e–e) collisions on second harmonic electron cyclotron resonance plasma breakdown is studied. A previously developed kinetic model for stellarators has been completed by means of a collision operator derived from the Fokker–Planck equation. It is shown that, although e–e collisions are not important for initial growth rate predictions and play a minor role in the breakdown time calculation, they must be considered if a realistic evolution of the electron energy distribution function is desired. Moreover, it is seen that the introduction of the e–e collision processes is needed in order to obtain a correct description of the power balance during breakdown.

High harmonic electron cyclotron resonance heating in the Large Helical Device

During the initial experimental phase, LHD, a stellarator of the heliotron/torsatron variety presently under construction, will operate at a magnetic field lower than the nominal one. In this scenario, the frequency of the available gyrotrons (chosen in view of second harmonic heating at full field operation) will be resonant with the third or the fourth harmonic of the electron gyrofrequency. The aim of this article is to analyse the electron cyclotron resonance heating (ECRH) at these high harmonics. By using linear absorption theory, together with transport predictions, good absorption is found over a wide density range for third harmonic heating. In the case of the fourth harmonic, the conditions for absorption are considerably more critical, but non-negligible heating (single pass absorption ≳ 10%) is expected in very low density, high temperature target plasmas. Owing to the strong temperature dependence of the absorption mechanism, heating at higher harmonics presents some peculiar characteristics. Quasi-linear effects are found to improve the absorption properties (as compared with those of linear theory), and bifurcation phenomena, as well as a critical power threshold, might appear. The physical origin and the consequences of these effects are discussed.

Excitation of the Alfvén Ion Cyclotron Mode Solely by the Ion Pressure Distribution

The Alfvén ion cyclotron (AIC) mode is spontaneously excited due to a temperature anisotropy in the ion cyclotron range of frequency (ICRF) heating experiments in the GAMMA10 tandem mirror. The behavior of the AIC mode is studied when the second harmonic electron cyclotron resonance heating is applied additionally. It is confirmed experimentally, that the excitation of the AIC mode is determined solely by the ion pressure and the ion pressure distribution.

Parametric instability producing broad symmetrical structure in the spectrum of ionospheric heating-induced radiation

A four-wave interaction process in which an O-mode electromagnetic pump decays parametrically into a lower hybrid decay mode and two-electron Bernstein sidebands is analyzed. It is shown that the instability can be excited in a spatial region near the electron Bernstein/upper hybrid double resonance and in a narrow pump frequency range slightly below the third harmonic electron cyclotron resonance. The two electron Bernstein sidebands have about the same intensity and thus, produce Broad Symmetrical Structure (BSS) in the emission spectrum after being converted into electromagnetic radiation by scattering off background field-aligned density irregularities. The results also show that the size of the instability zone becomes very small as the pump frequency operates near a cyclotron harmonic higher than the third. Thus, the converted emission will be too weak to be detected. This explains why the BSS feature in the spectrum of stimulated electromagnetic emissions (SEEs) has only been observed in the third harmonic case.

Non-relativistic response function for higher harmonic electron cyclotron resonance heating

A response function [Y. Kiwamoto et al., Phys. Plasmas 1, 834 (1994)] for higher harmonic cyclotron resonance heating is constructed through the analysis of electron trajectory under harmonic heating in an inhomogeneous magnetic field. General expressions of orbital displacement and energy gain for higher harmonic resonance are obtained. Phase-averaged energy gain of electrons by n-th harmonic electron cyclotron resonance heating (ECRH) is larger by a factor of n, if the effect of the orbital displacement from the unperturbed orbit is correctly included, than that evaluated based on an unperturbed orbit assuming small k⊥ρ. The energy gain for finite k⊥ρ is also obtained. These results are confirmed with a numerical calculation for second harmonics.