In spherical tokamaks, the electron plasma frequency is greater than the electron cyclotron frequency. Electromagnetic waves in the electron cyclotron range of frequencies are unsuitable for directly heating such plasmas due to their reduced accessibility. However, mode-conversion of the extraordinary wave to the electron Bernstein wave (X-B mode-conversion) at the upper hybrid resonance makes it possible to efficiently couple externally-launched electromagnetic wave energy into an overdense plasma core. Traditional mode-conversion models describe an X-mode wave propagating in a potential containing two cutoffs that bracket a single wave resonance. Often, however, the mode-conversion region is in the edge, where turbulent fluctuations and blobs can generate abrupt cutoffs and scattering of the incident X-mode wave. We present a new framework for studying the X-B mode-conversion which makes the inclusion of these fluctuations analytically tractable. In the new approach, the high-field cutoff is modelled as an infinite barrier, which manifests as a boundary condition applied to a wave equation involving only one cutoff adjacent to the resonance on the low-field side. The new model reproduces the main features of the previous approach, yet is more suitable for analyzing experimental observations and extrapolating to higher dimensions. We then develop an analytical estimate for the effect of small-amplitude, quasi-monochromatic density fluctuations on the X-B mode-conversion efficiency using perturbation theory. We find that Bragg backscattering of the launched X-mode wave reduces the mode-conversion efficiency significantly when the fluctuation wavenumber is resonant with the wavenumber of the incident X-mode wave. These analytical results are corroborated by numerically integrating the mode-conversion equations.
We study theoretically the mode conversion and the resonant absorption of high frequency electromagnetic waves into longitudinal modes in magnetized and stratified plasmas in the case where the external magnetic field is perpendicular to both the directions of inhomogeneity and wave propagation. Mode conversion is shown to occur only when the waves are extraordinary waves. We develop an efficient method for calculating the mode conversion coefficient for arbitrary spatial configurations of the plasma density and the external magnetic field in a numerically exact manner using the invariant imbe…
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify th…
The excitation of a slow extraordinary wave in a overdense plasma from an ordinary wave impinging on the critical layer in the plane spanned by the density gradient and magnetic field is solved analytically by formulating the problem in terms of a parabolic cylinder equation. A formula for the angular dependence of the transmission coefficient is derived.
The conversion of an ordinary wave to an extraordinary wave in a 2D inhomogeneous slab model of the plasma confined by a sheared magnetic field is studied analytically.
The separate spin evolution (SSE) of electrons causes the existence of the spin-electron acoustic wave. Extraordinary spin-electron acoustic waves (SEAWs) propagating perpendicular to the external magnetic field have large contribution of the transverse electric field. Its spectrum has been studied in the quasi-classical limit at the consideration of the separate spin evolution. The spin-spin interaction and the quantum Bohm potential give contribution in the spectrum extraordinary SEAW. This contribution is studied in this paper. Moreover, it is demonstrated that the spin-spin interaction lea…
The ordinary-extraordinary (O-X) mode conversion is modeled with the aid of a 2D full-wave code in the Pegasus Toroidal Experiment as a function of the launch angles. It is shown how the shape of the plasma density profile in front of the antenna can significantly influence the mode conversion efficiency and, thus, the generation of electron Bernstein waves (EBW). It is therefore desirable to control the density profile in front of the antenna for successful operation of an EBW heating and current drive system. On the other hand, the conversion efficiency is shown to be resilient to vertical d…
Multiple scattering from artificial random irregularities HF-induced in the ionosphere F region causes significant attenuation of both ordinary and extraordinary radio waves together with the conventional anomalous absorption of ordinary waves due to their conversion into the plasma waves. To study in detail features of this effect, purposeful measurements of the attenuation of weak probing waves of the extraordinary polarization have been performed at the Sura heating facility. Characteristic scale lengths of the involved irregularities are ~0.1-1 km across the geomagnetic field lines. To det…
The interaction of a high-frequency laser with plasma in the presence of an inhomogeneous external magnetic field has been studied here with the help of Particle-In-Cell simulation. It has been shown that laser enters inside the plasma as an extraordinary wave (X-wave), where the electric field of the wave oscillates perpendicular to both external magnetic field and propagation direction, and as it travels through the plasma, its dispersion property changes due to the inhomogeneity of the externally applied magnetic field. Our study shows that the X-wave's electromagnetic energy is converted t…
Observations of enhanced Doppler frequency shift effect of the highly localized microwave backscattering in the upper hybrid resonance are reported. The experiment is performed at FT-2 tokamak, where a steerable focusing antenna set, allowing off equatorial plane plasma extraordinary wave probing from high magnetic field side, was installed. A separate line less than 1.5 MHz wide and shifted by up to 2 MHz is routinely observed in the backscattering spectrum under condition of accessible upper hybrid resonance. The enhanced frequency shift is explained by the growth of poloidal wave number of …
When a wave packet composed of short wavelength lower hybrid modes traveling in an homogeneous plasma region encounters an inhomogeneity, it can resonantly excite long wavelength whistler waves via a linear mechanism known as mode conversion. An enhancement of lower hybrid/whistler activity has been often observed by sounding rockets and satellites in the presence of density depletions (striations) in the upper ionosphere. We address here the process of linear mode conversion of lower hybrid to whistler waves, mediated by a density striation, using a scalar-field formalism (in the limit of col…
The ordinary-extraordinary-Bernstein (O-X-B) double conversion is considered and simulated with a kinetic particle model vs full wave model for parameters of the TJ-II stellarator. This simulation has been done with the particle-in-cell code, XOOPIC (X11-based object-oriented particle-incell). XOOPIC is able to model the non-monotonic density and magnetic profile of TJ-II. The first step of conversion, O-X conversion, is observed clearly. By applying some optimizations such as increasing the number of computational particles in the region of the X-B conversion, the simulation of the second ste…
Global particle simulations of the lower hybrid waves have been carried out using fully kinetic ions and drift kinetic electrons with a realistic electron-to-ion mass ratio. The lower hybrid wave frequency, mode structure, and electron Landau damping from the electrostatic simulations agree very well with the analytic theory. Linear simulation of the propagation of a lower hybrid wave-packet in the toroidal geometry shows that the wave propagates faster in the high field side than the low field side, in agreement with a ray tracing calculation. Electromagnetic benchmarks of lower hybrid wave d…
The propagation of plasma waves in a new non-linear, logarithmic electrodynamics model is performed. A cold, uniform, collisionless fluid plasma model is applied. Electrostatic waves in magnetized plasma are shown to correspond to modified Trivelpiece-Gould modes, together with changes of the plasma and upper-hybrid frequencies, driven by the logarithmic electrodynamics effects. Electromagnetic waves are described by a generalized Appleton-Hartree dispersion relation. The cases of propagation parallel or perpendicular to the equilibrium magnetic field are analyzed in detail. In particular, gen…
Kinetic simulations based on the Eulerian Hybrid Vlasov-Maxwell (HVM) formalism permit the examination of plasma turbulence with useful resolution of the proton velocity distribution function (VDF). The HVM model is employed here to study the balance of energy, focusing on channels of conversion that lead to proton kinetic effects, including growth of internal energy and temperature anisotropies. We show that this Eulerian simulation approach, which is almost noise-free, is able to provide an accurate energy balance for protons. The results demonstrate explicitly that the recovered temperature…
The dispersion properties of elliptically polarized electromagnetic (EM) waves in a magnetized electron-positron-pair (EP-pair) plasma are studied with the effects of particle dispersion associated with the Bohm potential, the Fermi degenerate pressure, and the exchange-correlation force. Two possible modes of the extraordinary or X wave, modified by these quantum effects, are identified and their propagation characteristics are investigated numerically. It is shown that the upper-hybrid frequency, and the cutoff and resonance frequencies are no longer constants but are dispersive due to these…
The non-solenoid start-up technique reported here relies on a double mode conversion for electron Bernstein wave (EBW) excitation. It consists of the mode conversion of the ordinary mode, entering the plasma from the low field side of the tokamak, into the extraordinary (X) mode at a mirror-polarizer located at the high field side. The X mode propagates back to the plasma, passes through electron cyclotron resonance and experiences a subsequent X to EBW mode conversion near the upper hybrid resonance. Finally the excited EBW mode is totally absorbed at the Doppler shifted electron cyclotron re…
LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学，巴黎西岱大学，塞吉-蓬图瓦兹大学，法国国家科学研究中心）；Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）；Institute of Atmospheric Physics of the Czech Academy of Sciences（捷克科学院大气物理研究所）；Institute for Humanity’s Unified Development（人类统一发展研究所）
The scattering and transformation of the waves propagating in magnetized plasma on a heavy stationary charged particle located at a plane plasma-vacuum boundary is considered. The scattering (transformation) occurs due to the nonlinear coupling of the incident wave with the polarization (shielding) cloud surrounding the particle. It is shown that the problem is reduced to the determination of the nonlinear (three index) dielectric tensor of magnetized plasma. The angular distribution and the cross section for scattering (transformation) of high-frequency ordinary and extraordinary waves and lo…
