A brief history of the concept of negative energy waves in fluid and plasma media is given. The theory of microwave tubes is highlighted, where the small signal power theorem was first derived, which led to the interpretation of these devices in terms of the interaction of positive and negative energy waves. Three examples are described to illustrate the use of negative waves in stability problems. The first is concerned with the Kelvin–Helmholtz instability in neutral fluids. The second comes from a kinetic theory of instability in a collisionless shock wave in a magnetized plasma, and the third is concerned with the effect of a resistive wall and plasma flow on the magnetohydrodynamic stability of a magnetically confined plasma. The paper ends with some general conclusions.

Several high velocity clouds (HVCs) are now known to be soft X-ray sources. In this paper we suggest that an interaction between the HVCs and the galactic halo is leading to plasma instabilities that generate energetic electrons which in turn generate X-ray emission. This process is essentially analogous to the interaction process between comets and non-magnetized planets with the solar wind which is also known to lead to the generation of X-rays. We show that for reasonable assumptions about the galactic halo magnetic field, the X-ray emission can be converted into an estimate of the mean galactic halo density at the position of the cloud. This provides a method for estimating the baryonic mass of the plasma halo provided that we can obtain a good estimate for the distance to the HVC.

The collective coupling of neutrinos and anti-neutrinos in a dense plasma is considered. Such a coupling is provided by the existence of electron plasma waves. These waves can parametrically excite neutrino–anti-neutrino pairs, and the parametric decay rate is established. This stimulated process for neutrino pair production can eventually become dominant over the single particle decay rates characteristic of the usual Urca process and provide an alternative mechanism for the neutrino cooling of collapsing neutron stars.

Electron acceleration by large amplitude electrostatic waves in astrophysical plasmas is studied using particle-in-cell (PIC) simulations. The waves are excited initially at the electron plasma frequency $\omega_{\rm pe}$ by a Buneman instability driven by ion beams: the parameters of the ion beams are appropriate for high Mach number astrophysical shocks, such as those associated with supernova remnants (SNRs). If $\omega_{\rm pe}$ is much higher than the electron cyclotron frequency $\Omega_{\rm e}$, the linear phase of the instability does not depend on the magnitude of the magnetic field. However, the subsequent time evolution of particles and waves depends on both $\omega_{\rm pe}/\Omega_{\rm e}$ and the size of the simulation box $L$. If $L$ is equal to one wavelength, $\lambda_0$, of the Buneman-unstable mode, electrons trapped by the waves undergo acceleration via the surfatron mechanism across the wave front. This occurs most efficiently when $\omega_{\rm pe}/\Omega_{\rm e} \simeq 100$: in this case electrons are accelerated to speeds of up $c/2$ where $c$ is the speed of light. In a simulation with $L=4\lambda_0$ and $\omega_{\rm pe}/\Omega_{\rm e} = 100$, it is found that sideband instabilities give rise to a broad spectrum of wavenumbers, with a power law tail. Some stochastic electron acceleration is observed in this case, but not the surfatron process. Direct integration of the electron equations of motion, using parameters approximating to those of the wave modes observed in the simulations, suggests that the surfatron is compatible with the presence of a broad wave spectrum if $\omega_{\rm pe}/\Omega_{\rm e}> 100$. It is concluded that a combination of stochastic and surfatron acceleration could provide an efficient generator of mildly relativistic electrons at SNR shocks.

Theories for the formation of plasma and dust voids (large-amplitude ion and dust holes) in a complex plasma with static and mobile negatively charged dust are presented. It is shown that a plasma (dust) void in a complex plasma with negatively charged static (mobile) dust can be formed due to the presence of negative (positive) plasma potential, which is built up owing to a non-isothermal ion (dust) distribution arising from ion (dust) trapping. The plasma voids shrink when the dust grains are added into the plasma, and they tend to disappear if the dust number density is sufficiently high. On the other hand, the dust voids shrink with an increase in the dust charge density, but enlarges with an increase in the dust temperature.

A novel integral representation suitable for the study of asymptotic ($L/L_{0}\,{\gg}\,1$, $L$ being the plasma length and $L_{0}$ the basic gain length) stability of the inhomogeneous three-wave interaction is formulated and applied to the special case of uniform gain and ramp wavenumber mismatch. The absolute instability condition is $\kappa L_{0} \,{<}\, \pi /8$ ($\kappa$ being the mismatch gradient), with the wave conversion performed in a zone of width $4/\kappa L_{0}$ located at the boundary of wave incidence.

The growth and damping of the low-frequency electrostatic dust-lower-hybrid (DLH) wave have been examined in the presence of dust charge fluctuations in a uniform magnetized dusty plasma. To obtain the dust charge fluctuation effects, the charging currents of electrons and ions to a spherical dust grain in a uniform magnetized dusty plasma have been calculated under the orbit-limited motion approximation. It is found that the external magnetic field reduces the charging currents, thereby reducing the dust charge fluctuation damping of a low-frequency electrostatic wave in a dusty plasma. However, for sufficiently low-frequency DLH wave having a finite parallel wave number, the thermal electrons may give rise to an instability of the DLH wave.

In this paper an analysis is given for the conditions under which compressive and rarefactive ion-acoustic solitons may exist in a plasma containing two electron populations, one hot and the other cool. Compressive solitons exist in the collective Mach number range $1\,{<}\,M\,{<}\,M_{\rm c}$, which, for a given abundance ratio of the cool population, translates into an annular region in the ion-acoustic Mach numbers space. The upper limit $M_{\rm c}$ corresponds to a degenerate sonic point for the protons in which they tend to an infinite compression and are brought to rest at the wave centre. To form a charge neutral point in the rarefactive regime (a prerequisite to the existence of rarefactive solitons) it is necessary that the ‘scale height’ of the hot electrons be sufficiently large that their number density, which is nearly constant, approximately balances that of the protons, before the cool electrons experience their ‘atmospheric lid’. Furthermore, a sufficient condition for the existence of rarefactive solitons is found by requiring a solution to the wave structure equation at the ‘lid’. The case of very hot electrons (highly sub-ion-acoustic) is considered, and various parameter regimes in which compressive and rarefactive solitons exist are evaluated in this super-hot electron approximation, both for the polytropic case, $\gamma \neq 1$, and the isothermal case, $\gamma = 1$. This approximation is formally equivalent to the problem of a bi-ion plasma, including a super-massive negative species.

Non-thermal ion distributions are a characteristic feature of space plasmas, and in the current work the influence of such non-thermal ion distributions on the Jeans instability is examined. Following previous general models, the electrons are taken to be Boltzmann on the timescales involved, whilst the negative dust component is modelled by the continuity and momentum equations. The ion dynamics are described via a non-thermal Cairns distribution. The linear dispersion relation is derived and analysed for varying degrees of deviation from ordinary thermal behaviour, determined by the characteristic parameter of the Cairns distribution.

The Nonlinear self-modulation of dust acoustic waves is studied in the presence of non-thermal (non-Maxwellian) ion and electron populations. By employing a multiple scale technique, a nonlinear Schrödinger-type equation (NLSE) is derived for the wave amplitude. The influence of non-thermality, in addition to obliqueness (between the propagation and modulation directions), on the conditions for modulational instability to occur is discussed. Different types of localized solutions (envelope excitations) which may possibly occur are discussed, and the dependence of their characteristics on physical parameters is traced. The ion deviation from a Maxwellian distribution comes out to be more important than the electron analogous deviation alone. Both yield a de-stabilizing effect on (the amplitude of) DAWs propagating in a dusty plasma with negative dust grains, and thus favour the formation of bright- (rather than dark-) type envelope structures (solitons) in the plasma. A similar tendency towards amplitude de-stabilization is found for the case of the presence of positively charged dust in the plasma.

A theoretical explanation is given for tripolar electric field signals observed recently in the Earth's magnetosphere by the Cluster multi-spacecraft mission and in interplanetary space by the WIND mission, which feature an overall potential drop characteristic for weak double layers, with adjacent potential minima and maxima that trap both ions and electrons, respectively. A kinetic theory, based on Schamel's model for trapped particle distribution, is presented for electron and ion holes coupled with weak double layers, whose properties are studied analytically and numerically. In contrast to earlier models of double layers, which require external excitation in the form of asymptotically non-Maxwellian velocity distributions, tripoles only trap particles locally and the corresponding asymptotic particle distributions are Maxwellian. In the small amplitude limit, $e\phi\,{\ll}\, T_{\rm e}, T_{\rm i}$, such structures propagate with a speed that is in the ion thermal velocity range and they can only be excited if there is a relative drift between electrons and ions, whose speed is in the electron thermal velocity range. Conversely, non-propagating tripoles are found in the large amplitude regime and in the absence of particle streaming.

The effects of relativistic mass increase is considered in the context of intense laser–plasma interactions. It is found that the result of the relativistic effect is to enhance the self-compression and collapse of the intense laser pulse, making it possible to reach the Schwinger field limit, at which pair creation would need to be considered.

The effect of density and size of dust grains on the electron energy distribution function (EEDF) in low-temperature complex plasmas is studied. It is found that the EEDF depends strongly on the dust density and size. The behavior of the electron temperature can differ significantly from that of a pristine plasma. For low-pressure argon glow discharge, the Druyvesteyn-like EEDF often found in pristine plasmas can become nearly Maxwellian if the dust density and/or sizes are large. One can thus control the plasma parameters by the dust grains.

Two applications of the Noether method for fluids and plasmas are presented based on the Euler–Lagrange and Euler–Poincaré variational principles, which depend on whether the dynamical fields are to be varied independently or not, respectively. The relativistic cold laser–plasma equations, describing the interaction between an intense laser field with a cold relativistic electron plasma, provide a useful set of equations amenable to both variational formulations. The derivation of conservation laws by the Noether method proceeds from the Noether equation, whose form depends on the variational formulation used. As expected, the expressions for the energy–momentum conservation laws are identical in both variational formulations. The connection between the two Lagrangian densities is shown to involve the mass conservation and Lin constraints associated with the cold relativistic electron fluid.