Upper-hybrid Layer Research Articles

Demonstration of metaplectic geometrical optics for reduced modeling of plasma waves.

The Wentzel, Kramers, and Brillouin (WKB) approximation of geometrical optics is widely used in plasma physics, quantum mechanics, and reduced wave modeling, in general. However, it is well-known that the approximation breaks down at focal and turning points. In this paper, we present an unsupervised numerical implementation of the recently developed metaplectic geometrical optics framework, which extends the applicability of geometrical optics beyond the limitations of WKB, such that the wave field remains finite at caustics. The implementation is in 1D and uses a combination of Gauss-Freud quadrature and barycentric rational function inter- and extrapolation to perform an inverse metaplectic transform numerically. The capabilities of the numerical implementation are demonstrated on Airy's and Weber's equations, which both have exact solutions to compare with. Finally, the implementation is applied to the plasma physics problem of linear conversion of X mode to electron Bernstein waves at the upper hybrid layer and a comparison is made with results from fully kinetic particle-in-cell simulations. In all three applications, we find good agreement between the exact results and a reduced wave modeling paradigm of metaplectic geometrical optics.

Nonlinear degradation of O-X-B mode conversion in MAST Upgrade

Spherical tokamaks like the MAST Upgrade device are often operated in an overdense regime. As a consequence, conventional electron cyclotron resonance heating (ECRH) and current drive (ECCD) are typically not possible. MAST Upgrade is planned to investigate a mode coupling scheme known as O-X-B at high power, which may allow gyrotrons to heat and drive current in overdense plasmas by coupling electromagnetic waves to electrostatic electron Bernstein waves (EBWs) at the upper hybrid (UH) layer. However at the gyrotron beam intensities planned for MAST Upgrade, several nonlinear effects may degrade the linear mode coupling into EBWs. Using particle-in-cell simulations, parametric decay instabilities (PDIs) and stochastic electron heating (SEH) are investigated in the region near the UH layer. It is found that nonlinear effect could have a substantial impact on the O-X-B scheme in MAST Upgrade at high gyrotron intensities.

A radiometer to diagnose parametric instabilities during linear excitation of electron Bernstein waves in the Mega Amp Spherical Tokamak (MAST) Upgrade.

Highly overdense magnetically confined fusion plasmas, such as the Mega Amp Spherical Tokamak (MAST) Upgrade, cannot easily be heated using conventional electron cyclotron resonance heating because high density cutoffs block microwave access to the plasma core. Instead, electromagnetic waves can be coupled to electron Bernstein waves (EBWs) through the O-X-B mode coupling scheme, and the EBWs can then be absorbed at higher densities. The excitation of EBWs occurs at the upper hybrid (UH) layer where nonlinear wave interactions, called parametric decay instabilities (PDIs), are known to occur at reduced power thresholds. We present a design for a radiometer to detect PDIs during O-X-B in MAST Upgrade. The radiometer will aid in determining at what power levels PDIs become important as well as inferring various parameters about both electrons and ions near the UH layer. We estimate a gyrotron power density threshold for PDI and expected frequency shifts to be produced in them. The design allows for shifts from several decays involving lower hybrid (LH) waves to be observed.

Pump Power Effects on Second Harmonic Stimulated Electromagnetic Emissions During Ionosphere Heating

AbstractDue to the potential for new diagnostic capabilities, there has been renewed interest in the generation of ionospheric stimulated electromagnetic emissions (SEEs) near the second harmonic of the pump frequency (ω0), a process known as second harmonic generation (SHG). Observations of SHG during experiments at the High Frequency Active Auroral Research Program facility in which ω0 was stepped near the third harmonic of the electron gyrofrequency, 3ωce, and the transmit power linearly increased over the heating cycle at each ω0, were reported recently. A key observation was the linkage between SEEs within ±30 Hz of ω0, due to stimulated Brillouin scatter, and within ±30 Hz of 2ω0. This current work reports further High Frequency Active Auroral Research Program observations that compare the time evolution of SEEs including SHG under the following two transmit power conditions (I) linear power ramp (II) maximum available power (2.8 MW). During these experiments, ω0 was stepped near 3ωce and also 2ωce. The results show that SEEs within ±100 Hz of ω0 and 2ω0 are both suppressed within a few seconds when the ionosphere is irradiated with the maximum available power. These SEEs appear to be suppressed before the onset of field‐aligned irregularities at the upper hybrid layer which is not in line with previous reports. Thus, other mechanisms, which are discussed, could possibly be responsible for the observed suppression of stimulated Brillouin scatter and SHG. Some preliminary diagnostics are derived from the SHG spectra temporal evolution by leveraging concepts from the field of laser plasma interactions.

Particle-in-cell simulations of parametric decay instabilities near the upper hybrid layer

The particle-in-cell (PIC) code EPOCH is used to simulate parametric decay instabilities (PDIs) converting a 105 GHz microwave X-mode pump wave into electrostatic daughter waves at the upper hybrid (UH) layer of a fusion plasma in 1D. The resulting fields are analyzed, identifying modes in f -and k-space, and estimating their spectral power as a function of pump wave intensity. Both linearly and nonlinearly converted modes are identified and their characteristics agree with literature. A dipole approximation employed in literature appears to be unjust.

Erratum: “Vlasov simulations of electron acceleration by radio frequency heating near the upper hybrid layer” [Phys. Plasmas 24, 102904 (2017)

Erratum: “Vlasov simulations of electron acceleration by radio frequency heating near the upper hybrid layer” [Phys. Plasmas <b>24</b>, 102904 (2017)

Vlasov simulations of electron acceleration by radio frequency heating near the upper hybrid layer

It is shown by using a combination of Vlasov and test particles simulations that the electron distribution function resulting from energization due to Upper Hybrid (UH) plasma turbulence depends critically on the closeness of the pump wave to the double resonance, defined as ω ≈ ωUH ≈ nωce, where n is an integer. For pump frequencies, away from the double resonance, the electron distribution function is very close to Maxwellian, while as the pump frequency approaches the double resonance, it develops a high energy tail. The simulations show turbulence involving coupling between Lower Hybrid (LH) and UH waves, followed by excitation of Electron Bernstein (EB) modes. For the particular case of a pump with frequency between n = 3 and n = 4, the EB modes cover the range from the first to the 5th mode. The simulations show that when the injected wave frequency is between the 3rd and 4th harmonics of the electron cyclotron frequency, bulk electron heating occurs due to the interaction between the electrons and large amplitude EB waves, primarily on the first EB branch leading to an essentially thermal distribution. On the other hand, when the frequency is slightly above the 4th electron cyclotron harmonic, the resonant interaction is predominantly due to the UH branch and leads to a further acceleration of high-velocity electrons and a distribution function with a suprathermal tail of energetic electrons. The results are consistent with ionospheric experiments and relevant to the production of Artificial Ionospheric Plasma Layers.

Generation of whistler waves by continuous HF heating of the upper ionosphere

AbstractBroadband VLF waves in the frequency range 7–10 kkHz and 15–19 kHz, generated by F region CW HF ionospheric heating in the absence of electrojet currents, were detected by the DEMETER satellite overflying the High Frequency Active Auroral Research Program (HAARP) transmitter during HAARP/BRIOCHE campaigns. The VLF waves are in a frequency range corresponding to the F region lower lybrid (LH) frequency and its harmonic. This paper aims to show that the VLF observations are whistler waves generated by mode conversion of LH waves that were parametrically excited by HF‐pump‐plasma interaction at the upper hybrid layer. The paper discusses the basic physics and presents a model that conjectures (1) the VLF waves observed at the LH frequency are due to the interaction of the LH waves with meter‐scale field‐aligned striations—generating whistler waves near the LH frequency; and (2) the VLF waves at twice the LH frequency are due to the interaction of two counterpropagating LH waves—generating whistler waves near the LH frequency harmonic. The model is supported by numerical simulations that show good agreement with the observations. The (Detection of Electromagnetic Emissions Transmitted from Earthquake Regions results and model discussions are complemented by the Kodiak radar, ionograms, and stimulated electromagnetic emission observations.

Simulations of ionospheric turbulence produced by HF heating near the upper hybrid layer

AbstractHeating of the ionosphere by high‐frequency (HF), ordinary (O) mode electromagnetic waves can excite magnetic field‐aligned density striations, associated with upper and lower hybrid turbulence and electron heating. We have used Vlasov simulations in one spatial and two velocity dimensions to study the induced turbulence in the presence of striations when the O‐mode pump is mode converted to large‐amplitude upper hybrid oscillations trapped in a striation. Parametric processes give rise to upper and lower hybrid turbulence, as well as to large amplitude, short wavelength electron Bernstein waves. The latter excite stochastic electron heating when their amplitudes exceed a threshold for stochasticity, leading to a rapid increase of the electron temperature by several thousands of kelvin. The results have relevance for high‐latitude heating experiments.

Artificial ionospheric layers driven by high‐frequency radiowaves: An assessment

AbstractHigh‐power ordinary mode radio waves produce artificial ionization in the F region ionosphere at the European Incoherent Scatter (Tromsø, Norway) and High Frequency Active Auroral Research Program (Gakona, Alaska, USA) facilities. We have summarized the features of the excited plasma turbulence and descending layers of freshly ionized (“artificial”) plasma. The concept of an ionizing wavefront created by accelerated suprathermal electrons appears to be in accordance with the data. The strong Langmuir turbulence (SLT) regime is revealed by the specific spectral features of incoherent radar backscatter and stimulated electromagnetic emissions. Theory predicts that the SLT acceleration is facilitated in the presence of photoelectrons. This agrees with the intensified artificial plasma production and the greater speeds of descent but weaker incoherent radar backscatter in the sunlit ionosphere. Numerical investigation of propagation of O‐mode waves and the development of SLT and descending layers have been performed. The greater extent of the SLT region at the magnetic zenith than that at vertical appears to make magnetic zenith injections more efficient for electron acceleration and descending layers. At high powers, anomalous absorption is suppressed, leading to the Langmuir and upper hybrid processes during the whole heater on period. The data suggest that parametric upper hybrid interactions mitigate anomalous absorption at heating frequencies far from electron gyroharmonics and also generate SLT in the upper hybrid layer. The persistence of artificial plasma at the terminal altitude depends on how close the heating frequency is to the local gyroharmonic.

Laser beam filamentation and stochastic electron heating at upper hybrid layer

This paper presents an investigation of the filamentation (single hot spot) of an ultrahigh-power laser beam in homogeneous plasma. Upper hybrid wave (UHW) coupling in these filaments has been studied. We have discussed two extreme scenarios: (1) The laser beam has ultrahigh power so that relativistic and ponderomotive nonlinearities are operative; and (2) the laser beam power is moderate, therefore only ponderomotive nonlinearity dominates. At ultrahigh laser powers, relativistic and ponderomotive nonlinearities lead to filamentation of the laser beam. In these filamentary regions, the UHW gets coupled to the laser beam, and a large fraction of the pump (laser beam) energy gets transferred to UHW and this excited UHW can accelerate the electrons. In the second case, nonlinear coupling between the laser beam and the upper hybrid wave leads to the localization of the UHW. Electrons interacting with the localized fields of the UHW demonstrate chaotic motion. The simulation result confirms the presence of chaotic fields, and interaction of these fields with electrons leads to velocity space diffusion, which is accompanied by particle heating. Using the Fokker–Planck equation, the heating of electrons has been estimated. The effect of the change of background magnetic field strength on heating has also been discussed.

Critical issues highlighted by collective Thomson scattering below electron cyclotron resonance in FTU

Strong anomalous spectra were systematically observed in collective Thomson scattering (CTS) at 140 GHz in the high-field tokamak FTU, a proof-of-principle experiment of CTS on thermal density fluctuations performed with propagation below electron cyclotron (EC) resonance with the final aim of demonstrating high-density CTS in the extraordinary mode. Following the results of two experimental campaigns expressly performed to investigate them, these spectra are ascribed to a gyrotron perturbation caused by a back-reflected signal originating in the beam injection port, where the electron cyclotron layer, the upper-hybrid layer and the right-handed cutoff layer unavoidably crossed by the probing beam are activated by a breakdown plasma sustained by the beam itself. The degree of generality ascribable to our results and the constraints they set on present and future CTS experiments with propagation below electron cyclotron resonance are discussed. A viable solution in terms of a transmit antenna robust against the risk of gyrotron perturbation is suggested.

Modification of the electron density profile near the upper hybrid layer during radio wave heating of the ionosphere

High frequency (HF) radio waves can modify the electron density profile of the ionosphere in the upper hybrid resonance region (UHR). The spatial and temporal development of this modification was investigated using a multi‐frequency Doppler diagnostic system at the TROMSØ facility [Lobachevsky et al., 1992]. We present the results of the simulations of the density profile modification near the upper hybrid resonance height for the parameters relevant to the experiment and show that the spatio‐temporal development of the density modification is quantitatively modelled by the mode conversion and the radio wave heating.

Modulation instability at the upper hybrid layer in high‐power radio wave ionospheric heating

A model of the evolution of finite amplitude upper hybrid waves generated at the upper hybrid resonance height during high‐power radio wave ionospheric heating is presented. We show that the threshold for modulation instability can be exceeded for upper hybrid wave amplitudes of the order of a few tens of millivolts per meter and will be excited for scale sizes, perpendicular to the geomagnetic field, of the order of a few tens of electron gyroradii.

Mode Conversion and Electron Heating by Oblique Injection of the Ordinary Mode into Over-Dense Plasma

An electromagnetic wave of the ordinary mode (O-mode) at a frequency near the second electron cyclotron harmonic was obliquely incident on an over-dense (ω p >ω) large-volume plasma. Two-dimensional measurements of the wave amplitude and phase suggest the occurrence of a cascade mode-conversion; the first conversion being from the O-mode to the X-mode at the critical density (ω=ω p ), and the second conversion being from the X-mode to the Bernstein mode at the upper hybrid resonance. For high-power incidence, electron heating took place locally around the upper hybrid layer where the intense Bernstein-mode signals were detected. The heating was observed only for \(\omega_{\text{p}}{\gtrsim}\omega\), supporting the theory of the cascade mode conversion.

Electron Heating by Oblique Injection of Ordinary Mode into Overdense Plasma

An electromagnetic wave of ordinary mode (O-mode) at a frequency near the second electron cyclotron harmorric is obliquely incident on an overdense (ω p >ω) large-volume plasma. Two-dimensional measurements of wave propagations suggest that this is a result of cascade modcc conversion, the first conversion being from the O-mode to the X-mode at the critical density (ω=ω p ), and the second conversion being from the X-mode to the Bernstein mode at the upper hybrid resonance. For high-power incidence, electron heating takes place locally around the upper hybrid layer where the intense Bernstein-mode signals are detected. The heating is observed only for ω p >ω, supporting the theory of cascade mode conversion.

Upper hybrid emission from a magnetized gas discharge plasma

Measurements are presented of electromagnetic radiation emitted perpendicular to a strong magnetic field in a gas discharge. The discharge plasma is characterized by electron densities in the range 1010-3*1012 cm-3, an electron temperature of approximately 2 eV, and a dilute energetic electron tail extending out to the discharge voltage (<or approximately=200 V). Emission measurements are made in the frequency range 12-18 GHz. It is shown that the emission is predominantly in the extraordinary mode, originates at the upper hybrid layer in the radially inhomogeneous plasma, and is generated by the energetic electron tail. Combined with earlier detailed measurements of the energetic electron properties it is shown that the emitted power varies linearly with the hot electron density in the vicinity of the upper hybrid radius and varies as the 3/2 power of the tail temperature. Absolute power estimates are provided to link the authors measurements to the fundamental emission parameters. There are indications that tunneling of radiation is not playing a role in these experiments, but this conclusion requires a lot of further study.

Electron cyclotron resonance heating and confinement in the W VII-A stellarator

Plasma generation and heating of OH-current free plasmas by strong ECR-wave irradiation were studied on the Garching W VII-A stellarator for three kinds of wave launching: direct irradiation of the gyrotron modes (mainly TE02 mode corresponding to a 50% O-mode and 50% X-mode mixture) from the low field side, and advanced wave launching (linearly polarized TE11 and HE11 mode) in O-mode orientation (E//Bo, Bo, k perpendicular to Bo). The nonabsorbed fraction was reflected into the plasma in the X-mode (E perpendicular to Bo) by a focusing polarization twist reflector mounted to the inner torus wall. The experiments were performed at 28 GHz (1 Tesla resonance B-field) with 200 kW RF power and a pulse duration of <or approximately=40 ms. In all modes of operation clean stellarator plasmas could be generated from a neutral gas background (d2, H2) and could be heated to reasonable parameters. In the first case electron temperatures around 700 eV were achieved, whereas the central temperature could nearly be doubled (Te approximately 1200 eV) with the small aperture polarized waves. However, in both cases the heating efficiency was almost the same (<or approximately= 40% and 50%, respectively). The reflected X-mode fraction does not contribute to bulk plasma heating via Bernstein wave conversion and absorption as expected. The reason seems to be local absorption of the arising Bernstein waves due to a macroscopically turbulent structure around the conversion zone (upper hybrid layer). Correlated with X-mode irradiation direct ion heating was observed (500 eV ion tail), possibly due to wave decay into lower hybrid waves. Studies of the transport and confinement properties of the l=2 stellarator in the plateau and LMFP regime were performed by variation of the characteristic parameters (rotational transform t, plasma density, RF power, power deposition profile, etc.).

Nonlinear mode conversion of intense ordinary waves into electrostatic upper-hybrid waves

A high-power ordinary wave launched from the low field side is observed to undergo nonlinear mode conversion process and is partially transformed into a short-wavelength electrostatic upper-hybrid wave at the upper-hybrid layer. The nonlinear conversion process can be explained as due to a periodic modulation of upper-hybrid frequency at twice its value, while the frequency modulation comes from the combination of electron mass oscillation and oscillating density modulation induced by the ordinary wave.

Computer simulations of upper-hybrid and electron cyclotron resonance heating

A 2 1/2 -dimensional relativistic electromagnetic particle code is used to investigate the dynamic behavior of electron heating around the electron cyclotron and upper-hybrid layers when an extraordinary wave is obliquely launched from the high-field side into a magnetized plasma. With a large angle of incidence most of the radiation wave energy converts into electrostatic electron Bernstein waves at the upper-hybrid layer. These mode-converted waves propagate back to the cyclotron layer and deposit their energy in the electrons through resonant interactions dominated first by the Doppler broadening and later by the relativistic mass correction. The line shape for both mechanisms has been observed in the simulations. At a later stage, the relativistic resonance effects shift the peak of the temperature profile to the high-field side. The heating ultimately causes the extraordinary wave to be substantially absorbed by the high-energy electrons. The steep temperature gradient created by the electron cyclotron heating eventually reflects a substantial part of the incident wave energy. The diamagnetic effects due to the gradient of the mode-converted Bernstein wave pressure enhance the spreading of the electron heating from the original electron cyclotron layer.