Harmonics Of Cyclotron Frequency Research Articles

Modeling the electron cyclotron emission radiation signature from suprathermal electrons in a tokamak.

An Electron Cyclotron Emission (ECE) modeling code has been developed to model ECE radiation with an arbitrary electron momentum distribution, a small oblique angle, both ordinary (O-mode) and extraordinary polarizations (X-mode), and multiple cyclotron frequency harmonics. The emission and absorption coefficients are calculated using the Poynting theorem from the cold plasma dispersion and the electron-microwave interaction from the full anti-Hermitian tensor. The modeling shows several ECE radiation signatures that can be used to diagnose the population of suprathermal electrons in a tokamak. First, in an n = 2 X-mode (X2) optically thick plasma and oblique ECE view, the modeling shows that only suprathermal electrons, which reside in a finite region of the velocity and space domains, can effectively generate cyclotron emissions to the ECE receiver. The code also finds that the O1 mode is sensitive to suprathermal electrons of both a high v⊥ and v‖, while the X2 mode is dominantly sensitive to suprathermal electrons of a high v⊥. The modeling shows that an oblique ECE system with both X/O polarization and a broad frequency coverage can be used to effectively yield information of the suprathermal electron population in a tokamak.

Efficient ECCD non-inductive plasma current start-up, ramp-up, and sustainment for an ST fusion reactor

The elimination of the need for an Ohmic heating solenoid may be the most impactful design driver for the realization of economical compact fusion tokamak reactor systems. However, this would require fully non-inductive start-up and current ramp-up from zero plasma current and low electron temperature of sub-keV to the full plasma current of ∼10–15 MA at 20–30 keV electron temperature. To address this challenge, an efficient solenoid-free start-up and ramp-up scenario utilizing a low-field-side-launched extraordinary mode at the fundamental electron cyclotron harmonic frequency (X–I) is proposed, which has more than two orders of magnitude higher electron cyclotron current drive (ECCD) efficiency than the conventional ECCD for the sub-keV start-up regime. A time dependent model was developed to simulate the start-up scenarios. For the Spherical Tokamak Advanced Reactor (STAR) (Menard et al 2023 Next-Step Low-Aspect-Ratio Tokamak Design Studies (IAEA)), it was found that to fully non-inductively ramp-up to 15 MA, it would take about 25 MW of EC power at 170 GHz. Because of the relatively large plasma volume of STAR, radiation losses must be considered. It is important to make sure that high Z impurities are kept sufficiently low during the early current start-up phase where the temperature is sub-keV range. Since the initial current ramp up takes place at a factor of ten lower density compared to the sustained regimes, it is important to transition into a higher bootstrap fraction discharge at lower density to minimize the ECCD power requirement during the densification. For the sustainment phase an array of eight gyrotron launchers with a total of about 60 MW of fundamental O-mode was found to be sufficient to provide the required axis-peaked external current drive. High efficiencies between 19–57 kA MW−1 were found with optimal aiming, and these were resilient to small changes in aiming angles and density and temperature profiles.

Origin of the zebra structure in the Jovian decameter radio emission

Context.We discuss the origin of quasi-harmonic emission bands that have been observed in the dynamic spectra of the Jovian decameter emission.Aims.We aim to show that the interpretation of the observed structure can be based on the effect of double plasma resonance (DPR) at ion cyclotron harmonics.Methods.According to the proposed model, in the extended source in the upper ionosphere of Jupiter, where the DPR condition is satisfied for one of the ion cyclotron frequency harmonics, the ion cyclotron waves are effectively excited at the frequency of the lower hybrid resonance. The observed electromagnetic radiation with a quasi-harmonic structure arises due to scattering of ion cyclotron waves by supra-thermal electrons.Results.Based on the VIP4 magnetic field model, we determine the longitudes at which the source of the considered radiation can be located. The obtained estimates of the plasma density and its height distribution in the source, as well as the energies of emitting ions and scattering electrons provide information about the plasma parameters in the upper ionosphere of Jupiter. Furthermore, these estimates are in good agreement with the observational data.

Explanation of core ion cyclotron emission from beam-ion heated plasmas in ASDEX Upgrade by the magnetoacoustic cyclotron instability

Bursts of ion cyclotron emission (ICE), with spectral peaks corresponding to the hydrogen cyclotron harmonic frequencies in the plasma core are detected from helium plasmas heated by sub-Alfvénic beam-injected hydrogen ions in the ASDEX Upgrade tokamak. Based on the fast ion distribution function obtained from TRANSP/NUBEAM code, together with a linear analytical theory of the magnetoacoustic cyclotron instability (MCI), the growth rates of MCI could be calculated. In our theoretical and experimental studies, we found that the excitation mechanism of core ICE driven by sub-Alfvénic beam ions in ASDEX Upgrade is MCI as the time evolution of MCI growth rates is broadly consistent with measured ICE amplitudes. The MCI growth rate is very sensitive to the energy and velocity distribution of beam-injected ions and is suppressed by the slowing down of the dominant beam-injected ion velocity and the spreading of the fast ion distribution profile. This may help to account for the experimental observation that ICE signals disappear within ∼3 ms after the NBI turn-off time, much faster than the slowing down times of the beam ions.

On possibility of strong anomalous damping of an ordinary pump wave in the electron cyclotron resonance heating experiments due to the low-power-threshold parametric decay instability

We analyze the low power-threshold parametric decay instability of an ordinary wave in the first electron cyclotron harmonic frequency range, which leads to the excitation of a localized upper hybrid (UH) wave and a lower hybrid wave. We investigate its transition into the saturation mode due to both the pump wave depletion and the cascade of successive secondary decays. A set of equations describing this nonlinear frequency down-conversion of the primary UH wave is derived and then solved both analytically and numerically under the conditions typical of the off-axis O1-mode electron cyclotron resonance heating experiments in the FTU tokamak. The possibility of a strong anomalous absorption of the pump power in the case of even-step cascade of secondary decays is discovered.

Origin of ion cyclotron emission at the proton cyclotron frequency from the core of deuterium plasmas in the ASDEX-Upgrade tokamak

Observations have recently been made of ion cyclotron emission (ICE) that originates from the core plasma in the DIII-D and ASDEX-Upgrade tokamaks. In some of these cases, the ICE spectral peaks correspond to the local cyclotron harmonic frequencies of fusion-born ions close to the magnetic axis. This is in contrast to the hitherto usual spatial localisation of the ICE source to the outer midplane edge in tokamak and stellarator plasmas. Here we show that a possible emission mechanism for core ICE in ASDEX-Upgrade deuterium plasmas can arise from the rapid onset and rise of local fusion reactivity. This would give rise to a transiently highly non-Maxwellian population of fusion-born protons near their birth energy, prior to collisional slowing-down on longer timescales. Such populations are often liable to fast radiative relaxation under the magnetoacoustic cyclotron instability which underpins ICE, depending also on bulk plasma parameter values. We, therefore, perform first principles computations of the self-consistent collective relaxation of such a population, using a particle-in-cell code, for plasma parameters appropriate to the ASDEX-Upgrade core. The resulting simulated ICE spectra include a strong peak at the proton cyclotron frequency that corresponds well to the observations.

On the Issue of Damping of a Transverse Ion Bernstein Wave in an Inhomogeneous Magnetic Field

With allowance for the centrifugal and gradient drifts of ions, a new approximate dispersion equation is obtained for the ion Bernstein (IB) wave propagating strictly transverse to the external inhomogeneous magnetic field. Using this equation, it is shown that if, in the high-temperature plasma, the drift of ions is taken into account, the resonance frequency ranges in the vicinities of the ion cyclotron frequency harmonics can strongly overlap. In this case, the ion Bernstein waves turn out to be strongly damped, despite the absence of the longitudinal component of the wave vector.

Comparing theory and simulation of ion cyclotron emission from energetic ion populations with spherical shell and ring-beam distributions in velocity-space

Observations have recently been made of ion cyclotron emission (ICE) that originates from the core plasma in the DIII-D (Thome et al 2018 Rev. Sci. Instrum. 89 10I102, Thome et al 2019 Nucl. Fusion http://iopscience.iop.org/10.1088/1741-4326/ab20e7) and ASDEX-Upgrade (Ochoukov et al 2018 Rev. Sci. Instrum. 89 10J101, Ochoukov et al 2019 Nucl. Fusion 59 014001) tokamaks. The ICE spectral peaks correspond to the local cyclotron harmonic frequencies of fusion-born ions close to the magnetic axis, in contrast to the hitherto usual spatial localisation of the ICE source to the outer midplane edge in tokamak and stellarator plasmas. Core ICE is temporally transient, and may sometimes be caused by the rapid onset and increase of local fusion reactivity. This would give rise to a highly non-Maxwellian population of fusion-born ions near their birth energy. In an idealised deuterium-tritium plasma, this distribution would initially be a thin spherical shell in velocity-space. For as long as it persists, as pointed out in (D’Inca 2014 Ion Cyclotron Emission on ASDEX Upgrade PhD Thesis Ludwig-Maximilians-Universitat), the shell might drive the magnetoacoustic cyclotron instability (MCI), which is the excitation process which underlies ICE. Here we present, under core plasma conditions, direct numerical simulations of ICE generation by a spherical shell distribution of fusion-born ions in velocity-space. These energetic minority ions are found to relax collectively in particle-in-cell (PIC) computations which follow their self-consistent gyro-orbit-resolved dynamics, together with that of the majority thermal ions and electrons, under the Maxwell–Lorentz system of equations. We relate the computational outputs, which extend into the nonlinearly saturated regime of the MCI, to the analytical theory of the linear MCI for shell-type energetic ion distributions, and to fully nonlinear simulations of related ring-beam energetic ion distributions relaxing under the MCI. We find that the MCI is excited in all cases, and that the linear growth phase of the shell simulations typically takes almost twice as long to reach saturation than in the ring-beam simulations. It is shown that for both types of velocity distribution, nonlinear wave-wave interactions play a vital role in the excitation of the ICE spectral peaks at lower cyclotron harmonics which are typically detected in experiments. We conclude that in future simulations for ICE interpretation, ring-beam distributions may provide an acceptable proxy for shell distributions, while using significantly fewer computational particles and still maintaining a satisfactory signal-to-noise ratio.

A 94 GHz continuous operation second harmonic gyroton with 1.8 T solenoid

The continuous operation of a W-band gyrotron without superconduct magnet was realized. The gyrotron operated at the second harmonic cyclotron frequency. Its operational frequency was 94.08 GHz and the operating mode was TE02. The required 1.8 T magnetic field was generated by a DC solenoid cooled by water. The power consumption of the solenoid was 28 kW and the driving current was 500 A. The inner bore diameter was 66 mm. The gyrating electron beam was generated by a triode magnetic injection gun. A high efficiency internal quasi-optical mode converter was used to separate the wave from the electron beam. In the test, 5 min stable operation was realized. The output power was 12 kW with an electron beam of 45 kV, 1.7 A. The output efficiency was 15.7%.

Electromagnetic Thermal Noise in Upper‐Hybrid Frequency Range

AbstractThe inner magnetosphere including the radiation belt and ring current environment is replete with high‐frequency fluctuations with peak intensity occurring near upper‐hybrid frequency and/or multiple harmonic electron cyclotron frequencies above and below the upper‐hybrid frequency. Past and contemporary spacecraft missions, including the Van Allen Probes, were designed to detect the electric field spectrum only for these high‐frequency fluctuations. Making use of the recently formulated generalized theory of electromagnetic spontaneous emission in thermal magnetized plasmas, it is shown that upper‐hybrid/multiple harmonic electron cyclotron emissions are characterized by a significant magnetic field component, even in the high‐frequency regime. Such a prediction may potentially be tested by upcoming spacecraft missions including the Solar Probe Orbiter and Parker Solar Probe. The present finding may also have a potentially significant ramification for the broader astrophysical contexts.

Spontaneous emission of electromagnetic fluctuations in Kappa magnetized plasmas

The present paper formulates the theory of spontaneously emitted electromagnetic (EM) fluctuations in magnetized plasmas containing particles with an anisotropic suprathermal (bi-Kappa) velocity distribution function. The formalism is general applying for an arbitrary wave vector orientation and wave polarization, and for any wave-frequency range. As a specific application, the high-frequency EM fluctuations emitted in the upper-hybrid and multiple harmonic electron cyclotron frequency range are evaluated. The model predictions are confirmed by a comparison with the particle-in-cell simulations. Theoretical analysis and numerical simulations are carried out for an isotropic Kappa but the formalism can be applied for any anisotropic distributions, as well as for lower frequencies ranges which involve the ion response.

Spontaneous emission of electromagnetic fluctuations in magnetized plasmas

This paper formulates a fully general expression for spontaneously emitted electromagnetic fluctuations in magnetized thermal plasmas. The formulation is based upon the Klimontovich plasma kinetic theory. Specific application is made for high-frequency electromagnetic fluctuations in the upper-hybrid and harmonic electron cyclotron frequency range. Potential application of the general formalism is discussed.

Use of Quasiregular Resonator Cavities with Short Phase Correctors in Gyrotrons Operated at Higher Cyclotron Harmonics

We discuss the possibilities of using quasiregular resonator cavities with short irregularities, which ensure correction of the wave phase, in low-power gyrotrons operated at higher cyclotronfrequency harmonics. The use of such phase correctors can help with solving two problems, namely, increasing the selectivity of excitation of a higher cyclotron harmonic and decreasing the diffraction Q-factor of the gyrotron wave excited in an extended cavity.

The Electron-Optical System of a Gyrotron with an Operating Frequency of 263 GHz for Spectroscopic Research

We describe specific features of modeling numerically the operation of magnetron-injection guns, which form high-quality helical electron beams in gyrotrons operated in the short-wave part of the millimeter-wave band (at a wavelength of 1 mm). As an example, we consider the gun of a gyrotron having an operating frequency of 263 GHz designed for spectroscopic research. It is shown that there are good reasons to perform calculations and optimization of the magnetroninjection un in two steps. At the first step, a simplest two-dimensional model can be used, which allows only for the influence of the field of the electrodes and the intrinsic space charge of the beam on the beam parameters. At the second, final stage one should allow for such factors as roughness of the emitting surface and thermal velocities of electrons. The electron distribution function in oscillatory velocities and the coefficient of electron reflection from the magnetic mirror should be calculated. It is demonstrated that the magnetron-injection gun, which is optimized by the method presented, is sufficiently universal and can be operated both at the first and second cyclotron-frequency harmonics. This opens up the possibility of developing gyrotrons for spectroscopy applications at frequencies of 263 and 526 GHz, respectively, which are required for biological and medical research.

Understanding the growth rate patterns of ion Bernstein instabilities driven by ring‐like proton velocity distributions

AbstractFast magnetosonic waves in Earth's inner magnetosphere, which have as their source ion Bernstein instabilities, are driven by hot proton velocity distributions (fp) with ∂fp(v⊥)/∂v⊥>0. Two typical types of distributions with such features are ring and shell velocity distributions. Both have been used in studies of ion Bernstein instabilities and fast magnetosonic waves, but the differences between instabilities driven by the two types of distributions have not been thoroughly addressed. The present study uses linear kinetic theory to examine and understand these differences. It is found that the growth rate pattern is primarily determined by the cyclotron resonance condition and the structure of the velocity distribution in gyroaveraged velocity space. For ring‐driven Bernstein instabilities, as the parallel wave number (k∥) increases, the discrete unstable modes approximately follow the corresponding proton cyclotron harmonic frequencies while they become broader in frequency space. At sufficiently large k∥, the neighboring discrete modes merge into a continuum. In contrast, for shell‐driven Bernstein instabilities, the curved geometry of the shell velocity distribution in gyroaveraged velocity space results in a complex alternating pattern of growth and damping rates in frequency and wave number space and confines the unstable Bernstein modes to relatively small k∥. In addition, when k∥ increases, the unstable modes are no longer limited to the proton cyclotron harmonic frequencies. The local growth rate peak near an exact harmonic at small k∥ bifurcates into two local peaks on both sides of the harmonic when k∥ becomes large.

Ion cyclotron emission from fusion-born ions in large tokamak plasmas: a brief review from JET and TFTR to ITER

Ion cyclotron emission (ICE) was the first collective radiative instability, driven by confined fusion-born ions, observed from deuterium-tritium plasmas in JET and TFTR. ICE comprises strongly suprathermal emission, which has spectral peaks at multiple ion cyclotron harmonic frequencies as evaluated at the outer mid-plane edge of tokamak plasmas. The measured intensity of ICE spectral peaks scaled linearly with measured fusion reactivity in JET. In other large tokamak plasmas, ICE is currently used as an indicator of fast ions physics. The excitation mechanism for ICE is the magnetoacoustic cyclotron instability (MCI); in the case of JET and TFTR, the MCI is driven by a set of centrally born trapped fusion products, lying just inside the trapped-passing boundary in velocity space, whose drift orbits make large radial excursions to the outer mid-plane edge. Diagnostic exploitation of ICE in future experiments therefore rests in part on deep understanding of the MCI, and recent advances in computational plasma physics have led to substantial recent progress, reviewed here. Particle-in-cell simulations of the MCI, with fully kinetic ions and electrons, were reported in 2013, using plasma parameters for JET ICE observations. The hybrid approximation for plasma simulations, where ions are treated as particles and electrons as a neutralising massless fluid, was then applied and reported in 2014. These simulations extend previous studies deep into the nonlinear regime of the MCI, and corroborate predictions by linear analytical theory, thereby strengthening further the link to ICE measurements. ICE is a potential diagnostic for confined alpha-particles in ITER, where measurements of ICE could yield information on energetic ion behaviour supplementing that obtainable from other diagnostics. In addition, it may be possible to use ICE to study fast ion redistribution and loss due to MHD activity in ITER.

New Versions of Terahertz Radiation Sources for Dynamic Nuclear Polarization in Nuclear Magnetic Resonance Spectroscopy

Dynamic nuclear polarization in strong-field nuclear magnetic resonance (NMR) spectroscopy requires terahertz radiation with moderate power levels. Nowadays, conventional gyrotrons are used almost exclusively to generate such radiation. In this review paper, we consider alternative variants of electronic microwave oscillators which require much weaker magnetic fields for their operation, namely, large-orbit gyrotrons operated at high cyclotron-frequency harmonics and Cerenkov-type devices, such as a backward-wave oscillator and a klystron frequency multiplier with tubular electron beams. Additionally, we consider the possibility to use the magnetic field created directly by the solenoid of an NMR spectrometer for operation of both the gyrotron and the backward-wave oscillator. Location of the oscillator in the spectrometer magnet makes it superfluous to use an additional superconducting magnet creating a strong field, significantly reduces the length of the radiation transmission line, and, in the case of Cerenkov-type devices, allows one to increase considerably the output-signal power. According to our calculations, all the electronic devices considered are capable of ensuring the power required for dynamic nuclear polarization (10 W or more) at a frequency of 260 GHz, whereas the gyrotrons, including their versions proposed in this paper, remain a single option at higher frequencies.

Current generation by helicons and lower hybrid waves in modern tokamaks and reactors ITER and DEMO. Scenarios, modeling and antennae

The innovative concept and 3D full-wave code modeling the off-axis current drive by radio-frequency (RF) waves in large-scale tokamaks, ITER and DEMO, for steady-state operation with high efficiency is proposed. The scheme uses the helicon radiation (fast magnetosonic waves at high (20–40) ion cyclotron frequency harmonics) at frequencies of 500–700 MHz propagating in the outer regions of the plasmas with a rotational transform. It is expected that the current generated by helicons, in conjunction with the bootstrap current, ensure the maintenance of a given value of the total current in the stability margin q(0) ≥ 2 and q(a) ≥ 4, and will help to have regimes with a negative magnetic shear and internal transport barrier to ensure stability at high normalized plasma pressure β N > 3 (the so-called advanced scenarios) of interest for the commercial reactor. Modeling with full-wave three-dimensional codes PSTELION and STELEC showed flexible control of the current profile in the reactor plasmas of ITER and DEMO, using multiple frequencies, the positions of the antennae and toroidal wave slow down. Also presented are the results of simulations of current generation by helicons in the DIII-D, T-15MD, and JT-60AS tokamaks. Commercially available continuous-wave klystrons of the MW/tube range are promising for commercial stationary fusion reactors. The compact antennae of the waveguide type are proposed, and an example of a possible RF system for today’s tokamaks is given. The advantages of the scheme (partially tested at lower frequencies in tokamaks) are a significant decline in the role of parametric instabilities in the plasma periphery, the use of electrically strong resonator-waveguide type antennae, and substantially greater antenna-plasma coupling.

Observations of rotation in JET plasmas with electron heating by ion cyclotron resonance heating

The rotation of L-mode plasmas in the JET tokamak heated by waves in the ion cyclotron range of frequencies (ICRF) damped on electrons, is reported. The plasma in the core is found to rotate in the counter-current direction with a high shear and in the outer part of the plasma with an almost constant angular rotation. The core rotation is stronger in magnitude than observed for scenarios with dominating ion cyclotron absorption. Two scenarios are considered: the inverted mode conversion scenarios and heating at the second harmonic 3He cyclotron resonance in H plasmas. In the latter case, electron absorption of the fast magnetosonic wave by transit time magnetic pumping and electron Landau damping (TTMP/ELD) is the dominating absorption mechanism. Inverted mode conversion is done in (3He)-H plasmas where the mode converted waves are essentially absorbed by electron Landau damping. Similar rotation profiles are seen when heating at the second harmonic cyclotron frequency of 3He and with mode conversion at high concentrations of 3He. The magnitude of the counter-rotation is found to decrease with an increasing plasma current. The correlation of the rotation with the electron temperature is better than with coupled power, indicating that for these types of discharges the dominating mechanism for the rotation is related to indirect effects of electron heat transport, rather than to direct effects of ICRF heating. There is no conclusive evidence that mode conversion in itself affects rotation for these discharges.

MAGNETIZED NEUTRON STAR ATMOSPHERES: BEYOND THE COLD PLASMA APPROXIMATION

All the neutron star (NS) atmosphere models published so far have been calculated in the "cold plasma approximation", which neglects the relativistic effects in the radiative processes, such as cyclotron emission/absorption at harmonics of cyclotron frequency. Here we present new NS atmosphere models which include such effects. We calculate a set of models for effective temperatures T_eff =1-3 MK and magnetic fields B \sim 10^{10}-10^{11} G, typical for the so-called central compact objects (CCOs) in supernova remnants, for which the electron cyclotron energy E_{c,e} and its first harmonics are in the observable soft X-ray range. Although the relativistic parameters, such as kT_eff /(m_e c^2) and E_{c,e} /(m_e c^2), are very small for CCOs, the relativistic effects substantially change the emergent spectra at the cyclotron resonances, E \approx sE_{c,e} (s=1, 2,...). Although the cyclotron absorption features can form in a cold plasma due to the quantum oscillations of the free-free opacity, the shape and depth of these features change substantially if the relativistic effects are included. In particular, the features acquire deep Doppler cores, in which the angular distribution of the emergent intensity is quite different from that in the cold plasma approximation. The relative contributions of the Doppler cores to the equivalent widths of the features grow with increasing the quantization parameter b_eff = E_{c,e}/kT_eff and harmonic number s. The total equivalent widths of the features can reach \sim 150-250 eV; they increase with growing b_eff and are smaller for higher harmonics.