The propagation of electromagnetic waves in a linearly varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact solution is obtained for a given incoming wavefield specified on the boundary transverse to the direction of inhomogeneity by performing a spectral, rather than asymptotic, matching. Two case studies are then presented: a Gaussian beam at oblique incidence and a speckled wavefield at normal incidence. For the Gaussian beam, it is shown that when the waist $W$ is sufficiently large, oblique incidence manifests simply as rigid translation and focal shift of the corresponding diffraction pattern at normal incidence. The destruction of the hyperbolic umbilic caustic (corresponding to a critically focused beam) as $W$ is reduced is then demonstrated. The caustic disappears once $W \lesssim \delta _a \sqrt {L}$ ($L$ being the medium length scale normalized by the Airy skin depth $\delta _a$), at which point the wave behaviour is increasingly described by Airy functions, but experiences less focusing as a result. To maximize the intensity of a launched Gaussian beam at a turning point, one should therefore minimize the imaginary part of the launched complex beam parameter while having the real part satisfy critical focusing. For the speckled wavefield, it is shown that the transverse speckle pattern only couples to the Airy longitudinal pattern when the coupling parameter $\eta = \sqrt {L}/f_{\#}$ is large, with $f_{\#}$ being the f-number of the launching aperture. When $\eta \ll 1$, a reduced description of the total wavefield can be obtained by simply multiplying the incoming speckle pattern with the Airy swelling.

The response tensor is derived for a relativistically streaming, strongly magnetized, one-dimensional Jüttner distribution of electrons and positrons, referred to as a pulsar plasma. This is used to produce a general treatment of wave dispersion in a pulsar plasma. Specifically, relativistic streaming, the spread in Lorentz factors in a pulsar rest frame and cyclotron resonances are taken into account. Approximations to the response tensor are derived by making approximations to relativistic plasma dispersion functions appearing in the general form of the response tensor. The cold-plasma limit, the highly relativistic limit and limits related to cyclotron resonances are considered. The theory developed in this paper has applications to generalized Faraday rotation in pulsars and magnetars.

Quasilinear treatments are widely used for tokamaks to evaluate radio frequency (rf) heating and current drive. Even though the core of a tokamak plasma is weakly collisional, the solution of the linearized kinetic equation is evaluated using unperturbed collisionless trajectories while often treating successive poloidal circuits of the passing (and trapped) particles as uncorrelated or nearly so. In addition, the most important effect of tokamak geometry, the mirror force, is usually mistreated or ignored when obtaining the solution. These concerning aspects of rf treatments are clarified by considering lower hybrid heating and current drive to illustrate that the electrons in resonance with the applied rf are enclosed by narrow collisional boundary layers, and that tokamak geometry makes it necessary to retain poloidal variation when solving a weakly collisional linearized kinetic equation. Other aspects such as collisional boundary layers at the trapped–passing boundary, cyclotron resonances, and the limitations of quasilinear theory are also considered. The new insights lead to a fundamentally different formulation and interpretation of the solution of the linearized Fokker–Planck equation used for rf quasilinear theory in a tokamak, while retaining many of the features that have contributed to its successful application to rf heating and current drive.

This study presents observations of coherent modes (CMs) in a spherical tokamak using a microwave interferometer near the midplane. The CMs within the 30–60 kHz frequency range were observed during electron cyclotron resonance heating only, and the frequency of the CMs increased proportionally with the square root of the electron temperature near $R = 0.7m$. Generally, these modes displayed bursting and chirping signatures with strong density rise and fall. Their appearance indicated an increase in the intensity of hard x rays, suggesting a deterioration in energetic electron confinement. Furthermore, the effect of CMs on the intensity of energetic electron-driven whistler waves was observed. They decreased when CMs were present and gradually increased with the decrease in CM intensity. The CMs may influence the intensity of whistler waves by affecting the energetic electron confinement.

To expand on recent work, we introduce collisional terms in the analysis of the warm ion–electron, two-fluid equations for a homogeneous plasma at rest. Consequently, the plasma is now described by six variables: the magnetisation, the ratio of masses over charges, the electron and ion sound speeds, the angle between the wave vector and the magnetic field and a new parameter describing the electron–ion collision frequency. This additional parameter does not introduce new wave modes compared with the collisionless case, but does result in complex mode frequencies. Both for the backward and forward propagating modes the imaginary components are negative and thus quantify collisional damping. We provide convenient (polynomial) expressions to quantify frequencies and damping rates in all short- and long-wavelength limits, including the cutoff and resonance limits, whilst the one-fluid magnetohydrodynamic limit is retained with the familiar undamped slow, Alfvén and fast waves. As collisions only introduce a damping, the previously introduced labelling of the wave modes S, A, F, M, O and X can be kept and assigned based on their long- and short-wavelength behaviour. The obtained damping at cutoff and resonance limits is parametrised with the collision frequency, and can be tailored to match known kinetic damping expressions. It is demonstrated that varying the angle can introduce crossings between the wave modes, as was already present in the ideal ion–electron case, but also a collision frequency exceeding a critical collision frequency can lead to crossings at angles where previously only avoided crossings were found.

This study documents several correlations observed during the first run of the plasma wakefield acceleration experiment E300 conducted at FACET-II, using a single drive electron bunch. The established correlations include those between the measured maximum energy loss of the drive electron beam and the integrated betatron X-ray signal, the calculated total beam energy deposited in the plasma and the integrated X-ray signal, among three visible light emission measuring cameras and between the visible plasma light and X-ray signal. The integrated X-ray signal correlates almost linearly with both the maximum energy loss of the drive beam and the energy deposited into the plasma, demonstrating its usability as a measure of energy transfer from the drive beam to the plasma. Visible plasma light is found to be a useful indicator of the presence of a wake at three locations that overall are two metres apart. Despite the complex dynamics and vastly different time scales, the X-ray radiation from the drive bunch and visible light emission from the plasma may prove to be effective non-invasive diagnostics for monitoring the energy transfer from the beam to the plasma in future high-repetition-rate experiments.

We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation $\boldsymbol {A}{\boldsymbol{\psi} } = \boldsymbol {b}$ to be solved by using the quantum signal processing algorithm. The latter requires encoding of matrix $\boldsymbol {A}$ in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode $\boldsymbol {A}$ in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.

Linearized gravity around a rotating black hole or compact object introduces the concept of a gravitomagnetic field, which originates from the matter–current in the rotating object. Plasma in proximity to this object is subsequently subjected to motion guided by this gravitomagnetic term (where mass serves as the effective charge) in addition to the conventional magnetic field. Such an interplay of fields complicates the accessible plasma waves of the system and thus merits exploration to delineate this interplay, to identify any observable signatures of the gravitomagnetic field in weakly magnetized systems, and to motivate future numerical work in a fully relativistic setting where the effects may be stronger. In this work we analyse the dispersion of the upper and lower hybrid electrostatic waves in a plasma immersed in both magnetic and gravitomagnetic fields. In particular, we discuss the effective augmentation or cancellation of the two fields under the right conditions for the upper hybrid wave. In contrast, the lower hybrid wave experiences a frequency up-shift from the gravitomagnetic field regardless of whether it is parallel or antiparallel to the magnetic field for the studied field strengths.

In the limit of sufficiently fast rotation, rotating mirror traps are known to be stable against the loss-cone modes associated with conventional (non-rotating) mirrors. This paper calculates how quickly a mirror configuration must rotate in order for several of these modes to be stabilized (in particular, the high-frequency convective loss cone, drift cyclotron loss cone and Dory–Guest–Harris modes). Commonalities in the stabilization conditions for these modes then motivate a modified formulation of the Gardner free energy and diffusively accessible free energy to be used for systems in which the important modes have wavevectors that are orthogonal or nearly orthogonal to the magnetic field, as well as a modification to include the effects of a loss region in phase space.

We present a theoretical analysis of electron pitch-angle scattering by ion-acoustic electrostatic fluctuations present in the Earth's bow shock and, presumably, collisionless shocks in general. We numerically simulate electron interaction with a single wave packet to demonstrate the scattering through phase bunching and phase trapping and quantify electron pitch-angle scattering in dependence on the wave amplitude and wave normal angle to the local magnetic field. The iterative mapping technique is used to model pitch-angle scattering of electrons by a large number of wave packets, which have been reported in the Earth's bow shock. Assuming that successive electron scatterings are not correlated, we revealed that the long-term dynamics of electrons is diffusive. The diffusion coefficient depends on the ratio $\varPhi _0/W$ between the wave packet amplitude and electron energy, $D\propto (\varPhi _0/W)^{\nu }$. A quasi-linear scaling ($\nu \approx 2$) is observed for sufficiently small wave amplitudes, $\varPhi _0\lesssim 10^{-3}W$, while the diffusion is nonlinear ($1<\nu <2$) above this threshold. We show that pitch-angle diffusion of ${\lesssim }1$ keV electrons in the Earth's bow shock can be nonlinear. The corresponding diffusion coefficient scales with the intensity $E_{w}^{2}$ of the electrostatic fluctuations in a nonlinear fashion, $D\propto E_{w}^{\nu }$ with $\nu <2$, while its expected values in the Earth's bow shock are $D\sim 0.1\unicode{x2013}100$ $(T_{e}/W)^{\nu -1/2}\,{\rm rad}^{2}\,{\rm s}^{-1}$. We speculate that in the Earth's quasi-perpendicular bow shock the stochastic shock drift acceleration mechanism with pitch-angle scattering provided by the electrostatic fluctuations can contribute to the acceleration of thermal electrons up to approximately 1 keV. The potential effects of a finite perpendicular coherence scale of the wave packets on the efficiency of electron scattering are discussed.

A modulational instability of nonlinearly interacting electron whistlers and magnetosonic perturbations is studied in the present paper. For typical parameters, there is no modulational instability. However, modulational instability appears in special cases. For example, when the whistler wavenumber is small enough, there is modulational instability. Its growth rate decreases as the angle between the external magnetic field and the perturbed wave's direction increases, while it increases as the whistler wavenumber increases. It is also found that there is no modulational instability when the whistler wavenumber is larger than a critical value ($k_0 > 0.05$), in which the perturbed wave frequency increases as the angle between the external magnetic field and the perturbed wave's direction increases when the angle between the external magnetic field and the perturbed wave's direction is large enough. Whereas, the perturbed wave frequency first increases as the whistler wavenumber increases, reaches a peak value and then decreases as whistler wavenumber increases.

It is known that a nonlinear Schrödinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron–positron plasmas in the weakly and strongly magnetized limits. Here, we show that such an equation can be written as a modified second Painlevé equation, producing accelerated propagating wave solutions for those nonlinear plasmas. This solution even allows the plasma wave to reverse its direction of propagation. The acceleration parameter depends on the plasma magnetization. This accelerating solution is different to the usual soliton solution propagating at constant speed.

The frequency spectra of the Trivelpiece–Gould modes of a waveguide partially filled with non-neutral plasma are determined numerically by solving the dispersion equation. The modes having azimuthal number $m = 1$ are considered. The results are presented for the entire acceptable range of electron densities, magnetic field strengths, for different values of the charge neutralization coefficient. The Cherenkov resonance condition of an ion with a diocotron mode having a finite value of the longitudinal wave vector was studied. The characteristics of resonant low-frequency electron–ion instability caused by relative azimuth motion of electrons and ions in crossed fields and by the anisotropy of the distribution function of ions are discussed. Ions are created by ionization of residual gas in the plasma volume. Due to the anisotropy, instability occurs not only in the vicinity of the resonance, but also outside it. For typical values of plasma parameters in experiments, estimations of the frequency growth rate are given. A conclusion is drawn that this instability can be the cause of the low-frequency oscillations observed in linear devices with non-neutral plasma produced in an electron beam channel.

Generalising the Elsässer variables, we introduce the $Q$-variables. These are more flexible than the Elsässer variables, because they also allow us to track waves with phase speeds different than the Alfvén speed. We rewrite the magnetohydrodynamics (MHD) equations with these $Q$-variables. We consider also the linearised version of the resulting MHD equations in a uniform plasma, and recover the classical Alfvén waves, but also separate the fast and slow magnetosonic waves into upward- and downward-propagating waves. Moreover, we show that the $Q$-variables may also track the upward- and downward-propagating surface Alfvén waves in a non-uniform plasma, displaying the power of our generalisation. In the end, we lay the mathematical framework for driving solar wind models with a multitude of wave drivers.

The paper presents an investigation of the plasma fluctuation in the SMOLA helical mirror, which is suspected to be responsible for anomalous scattering. The helical mirror confinement is effective when the ion mean free path is equal to the helix pitch length. This condition can be satisfied in hot collisionless plasma only by anomalous scattering. The wave, which scatters the passing ions, is considered to receive energy from the trapped ions. The oscillations of the electric field in the helically symmetric plasma were observed in experiment. The oscillations have both regular highly correlated and chaotic components. The dependency of the regular component frequency on the Alfvén velocity is linear for $V_{\rm A} < 2.8 \times 10^6\ \text {m}\ \text {s}^{-1}$ and constant for higher values. It is shown experimentally that the condition for the wave to be in phase resonance with the trapped ions is satisfied in a specific region of the plasma column for the highly correlated component. The amplitude of the chaotic component (up to $3\ \text {V}\ \text {cm}^{-1}$) is higher than the estimated electric field required for the ion scattering.

The self-consistent propagation of electrical impulses and of the accompanying distortions of the electron surface in the framework of a cold plasma model with a sharp boundary has been described with help of a derived system of two equations. The method of ‘shallow water theory’ has been applied for the case of bounded plasma and deriving an equation with which to link the spatial and temporal structures and evolution of the boundary curvature and the surface charge. Under certain conditions, such perturbations can propagate along the boundary without changing their shape for a long distance. An approximate analytical solution has been found, and numerical calculations have been performed. Mutual connections between basic parameters of the considered perturbations (velocity components, electrostatic field, etc.) have been presented.

We investigate the linear and nonlinear evolution of the current-driven ion-acoustic instability in a collisionless plasma via two-dimensional (2-D) Vlasov–Poisson numerical simulations. We initialise the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding physically unrealisable super-critical initial conditions. A comprehensive analysis of the nonlinear evolution of ion-acoustic turbulence (IAT) is presented, including the detailed characteristics of the evolution of the particles’ distribution functions, (2-D) wave spectrum and the resulting anomalous resistivity. Our findings reveal the dominance of 2-D quasi-linear effects around saturation, with nonlinear effects, such as particle trapping and nonlinear frequency shifts, becoming pronounced during the later stages of the system's nonlinear evolution. Remarkably, the Kadomtsev–Petviashvili (KP) spectrum is observed immediately after the saturation of the instability. Another crucial and noteworthy result is that no steady saturated nonlinear state is ever reached: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived, challenging earlier theoretical results. Towards the conclusion of the simulation, electron-acoustic waves are triggered by the formation of a double layer and strong modifications to the particle distribution induced by IAT.

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$, describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$, and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$. The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

We analysed the excitation of a surface magnetoplasmon wave by the mode conversion of a p-polarized laser beam over a rippled semiconductor (n-type)-free space interface. The pump surface magnetoplasmon wave exerts a ponderomotive force on the free electrons in the semiconductor, imparting a linear oscillatory velocity at the laser modulation frequency to them. This linear oscillatory velocity couples with the modulated electron density to produce a current density, which develops a resonant surface magnetoplasmon wave in the terahertz region. The amplitude of the terahertz surface magnetoplasmon wave can be tuneable with an external magnetic field and the semiconductor's temperature.